help-42

[tame spoke]

Idk what to do at all

[calm coral]

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[gaunt violet]

How would u express e^(2ia) - ½e^(-2b) as a hyperbolic function lmao

[grand glacier]

Do you mean hyperbolic trigonometric function?

Then you can use the fact that $e^x = \cosh(x) + \sinh(x)$

[potent lotus]

τγρθ

[gaunt violet]

I need to simplify:
$$\frac{sinh(4b)}{2}(e^{2ia} - \frac{e^{-2b}}{2})$$

[potent lotus]

KnightOnF1 ♘

[gaunt violet]

@grand glacier where from here lmao

I know that it will expand to sin²(z)+cos²(z) for z = a+bi

But I need to simplify

[grand glacier]

keep transforming the exponentials into trig functions

[gaunt violet]

Oh okay

[grand glacier]

then use trigonometric identities

[gaunt violet]

So e^(2ia) = sinh(2ia) + cosh(2ia) helps here?

[grand glacier]

maybe. Also, are you sure you need hyperbolic trig functions? Because $e^{ix} = \cos(x) + i\sin(x)$

[potent lotus]

τγρθ

[gaunt violet]

Yes I've already used that formula

But getting from trig to hyp

But yes I used it to reach this stage @grand glacier

I'd be going backwards doing that

I'm going trig to non trig

[grand glacier]

what's the original problem?

[gaunt violet]

I'm trying to verify if sin²(x) + cos²(x) = 1 for x being complex where x = a+bi

I can show how I got to that stage if you want?

[grand glacier]

yeah sure

[gaunt violet]

@grand glacier so how would I simplify from here if not euler's formula

Wait I have an idea

I'm so mf close

@grand glacier surely this helps

[grand glacier]

give me a second

[gaunt violet]

$$=e^{2ia}(sinh^{2}(2b)-\frac{e^{4b}}{4})$$

[potent lotus]

KnightOnF1 ♘

[gaunt violet]

Wait I think i got it

2 min

[grand glacier]

couldn't you replace sin(a+bi) and cos(a+bi) with their exponential representation? Maybe that'd be simpler

[gaunt violet]

Wait a moment

$$sinh^{2}(x) = cosh^{2}(x) - (e^{-x})^{2}$$

[potent lotus]

KnightOnF1 ♘

[gaunt violet]

@grand glacier is that true?

[grand glacier]

,w sinh^2(x) == cosh^2(x) - e^(-2x)

[potent lotus]

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[grand glacier]

doesn't look like it

[gaunt violet]

Yeah I got it wrong

Hang on

[gaunt violet]

This is $$\frac{e^{-2ia-4b}-2}{4}$$

[potent lotus]

KnightOnF1 ♘

[gaunt violet]

@grand glacier can you check that pls?

FUCK I made a mistake earlier

I'm gonna do it alone brb

[grand glacier]

what do you want me to check sorry?

[gaunt violet]

This is wrong @grand glacier

I'm now trying to simplify

NEVERMIND I FUCKED IT UP

[grand glacier]

what exactly are you trying to do? I'm getting confused 😅

[gaunt violet]

Simplify it

I fucked up here

@grand glacier is what I've circled true or not

My brain is fried

[grand glacier]

you can always use wolframalpha.com to verify

or ,w in this server

[gaunt violet]

fixed it

But where now

[grand glacier]

I won't lie, I don't understand your method. I would have just transformed sin^2 and cos^2 into their exponential form

[gaunt violet]

Fair enough

However that's only proven for x being real @grand glacier

I'm working with complex

[grand glacier]

doesn't matter

,w sinx in exponential

[potent lotus]

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[gaunt violet]

Ah yes, much nicer

[grand glacier]

replace x in the first one with a+bi

[gaunt violet]

I'm gonna shower and come back to it

[grand glacier]

Sure. Always helps to take a break

[gaunt violet]

Also

@grand glacier that exponential form is only true when X is real

Substituting a+bi breaks it

I think

[grand glacier]

,w (e^(a+bi) - e^(-a-bi))/2i = sin(a+bi)

it won't show? Cringe

[potent lotus]

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[gaunt violet]

Oh

See it doesn't work

Right?

Check the wiki for the sine function lol

[grand glacier]

I'm not sure it breaks anything. There's even a relationship between sin and sinh when subbing ix instead of x

@gaunt violet take a look at this :) https://www.wolframalpha.com/input?i=sin(a%2Bbi)

(going away for now but feel free to @ helpers later if you still need help)

[calm coral]

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[distant hinge]

so im trying to do this and end up getting 3x(x - 7) + 2(x + 7)

and ik the answer is supposed to end up being like x = -2/3 and x = 7

[dull wagon]

show work

[distant hinge]

oh wait

yah

3x^2 + 19x - 14

-42

-21 + 2

3x^2 - 21x + 2x + 14

3x(x - 7) + 2(x + 7)

i thought so too so maybe like

[dull wagon]

-21 +2 = -19
not 19

[distant hinge]

its the problem

this is the problem im solving it just ends up lioke 3x^2 + 19x - 14

[distant hinge]

shoot

so i get
3x(x - 7) - 2(x - 7)

is that right

and then like
(x - 7)(3x - 2)?

[dull wagon]

no

[distant hinge]

oof

what am i doin wrong there?

[dull wagon]

algebraic mistakes

also 1sec

[distant hinge]

oh

3x(x + 7)

[dull wagon]

in your original question you do want -19

[distant hinge]

no positive

[dull wagon]

recall how to get determinants

[distant hinge]

i just

plug it into the calculator

[dull wagon]

what calculator

[distant hinge]

TI-84 Plus CE

[dull wagon]

show what you're putting into the calc

[distant hinge]

det(A), A being the matrix of whatever matrix i wish to find the det for

[dull wagon]

show exactly what you're putting in and what's coming out

[distant hinge]

for this specific equation nothin cause i cant put x into it

for whatever reason or another

[dull wagon]

2by2 matrix isn't complicated enough to warrant the use of a calc for its determinant

do you know how to calculate it without a calculator

[distant hinge]

absolutely not lol

i have to learn too much within a week every week to remember something like that

[dull wagon]

ideally you should look that up first

det of 2by2 is pretty simple / easy to remember

[distant hinge]

.close

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[earnest spade]

How would you solve this for N

[earnest spade]

can you give me a detailed step by step method

[slim meteor]

emmm

[steep mountain]

First identify where the variable you want is

In this case it's in the exponent there

[slim meteor]

yes

[steep mountain]

Now look at all the things that are happening to it

What is the outside most thing?

I.e. the last thing that occurs

It would be multiply by 800 right

Start by undoing the outside thinh

[earnest spade]

what do you mean

so should I first divide both sides by 800?

[steep mountain]

Yes

Keep unpacking the expression like this

[earnest spade]

Can I show you my work and tell me where I went wrong?

So now do I multiply both sides by 0.04/12

?

[calm coral]

@earnest spade Has your question been resolved?

[manic oriole]

Yeah

You should do that

[calm coral]

@earnest spade Has your question been resolved?

[earnest spade]

Okay then I get 0.04167 = 1-(1+0.04/12)

Then what do I do here

[manic oriole]

Subtract 1

Just try to isolate n

[earnest spade]

Okay so I get -0.95833 = -(1+0.04/12)^-n

then what do I do?

Should I distribute the - into the brackets?

[calm coral]

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[vast timber]

i need some help with part 2 of this problem

[vast timber]

This is what I have, but the answer is -0.003

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<@&286206848099549185>

[vast timber]

.close

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[remote crown]

can i reduce this to echelon from without knowing what it is equal to?

[calm coral]

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<@&286206848099549185>

[weary wyvern]

you can reduce any matrix. it depends on what you are trying to find out about the matrix.

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[subtle osprey]

Using the identity that $\frac{3}{2x^2-7x+5}=\frac{2}{2x-5}-\frac{1}{x-1}$, evaluate $\int_5^\infty \frac{3}{2x^2-7x+5}dx$ or show that the integral diverges.

[potent lotus]

Jash

[subtle osprey]

does it diverge

[leaden thunder]

can you do the integral?

[subtle osprey]

ye

[leaden thunder]

show work

[subtle osprey]

i got $\lim_{t\to\infty} \left(\ln{\abs{2x-5}}-\ln{\abs{x-1}}\right)\big|_5^t$

[potent lotus]

Jash

[leaden thunder]

and what is that limit equal to?

[subtle osprey]

isnt it infinity - infinity

[leaden thunder]

use log rules

,tex .log rules

[potent lotus]

riemann

[subtle osprey]

so $\lim_{t\to\infty} \ln{\abs{\frac{2x-5}{x-1}}}\biggr|_5^t$

[potent lotus]

Jash

[leaden thunder]

yea do that

[calm coral]

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[remote mural]

Prove that if A is a matrix such that $A^T = -A$ then tr(A) = 0.

[potent lotus]

Derivative

[remote mural]

How do i prove this?

[visual nimbus]

do you know the formula of the trace of the transpose of A ?

🤔

[remote mural]

no

i forgot it

maybe my textbook has it

[visual nimbus]

if I'm not wrong tr(A^T) = tr(A)

need someone to confirm

yea I verfied on google, im right

A^T + A = 0

tr is a linear application

tr(A^T) + tr(A) = 0

[remote mural]

ah ok I am trying to find it in my textbook haha

[visual nimbus]

tr(A^T) = tr(A)

therefore 2tr(A)=0

tr(A) = 0

[remote mural]

ok got it thanks

good day!

.close

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[rapid seal]

for f

we assume some t in the preimage of f(U)

where f(t) is in the basis for the product topology

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[calm coral]

@blissful osprey Has your question been resolved?

[blissful osprey]

<@&286206848099549185>

[manic oriole]

how would it be 8! ways to arrange them

you still count different rotations of the same setup to be different ways right

isnt it just 9!

[blissful osprey]

but since its a circle so wherever the first person sits doesn't matter cuz it would just be a rotation in the same direction which is the same way i believe

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[empty pumice]

I used the sign chart method and got + + + for all the sign values

[empty pumice]

this would indicate no local extreme points?

[median rampart]

correct

[empty pumice]

?

[pure kayak]

to say it has no extreme points is to imply f'(x) cant be 0

[empty pumice]

but if there was no sign change, i thought that would indicate no minima or maxima

what would the answer be?

[pure kayak]

nvm that

[pure kayak]

what values of x will f'(x)=0 for

[empty pumice]

-4 and 4 but i thought vertical asymptotes cannot be critical points

[pure kayak]

btw there is definitely a sign change, take x=5 and x=3.5 for example

[pure kayak]

its not 0 at those points, its undefined

[empty pumice]

plug in 5 top and bottom you get a positive output

and plug in 2

you get a positive output

-/-

= +

[pure kayak]

yeah i was being a melon

try 3.5

any number between 3 and 4

[pure kayak]

for something like this, you only really need to be looking at when the numerator is 0

[severe dawn]

what points did you use for the sign chart method?

[empty pumice]

i dont remember the exact points but i picked simple whole numbers, to test the left side of -3 i picked -5 for example and to test the right side I could of picked +1 and so on

i wouldnt think to use a decimal

but thats strange to me bc we cant use 4

and anythig between 3 and 4 is a - but anything more than 4 is a positive

so its tripping me up

its literally just that specific range

[severe dawn]

Yeah, you can't use absolutely any point

[empty pumice]

yeah less than for the left side and greater than for the right

but its weird that i need to account for a decimal, when using a whole number is positive

like 3.5

gives me a negative output

[severe dawn]

It's because of the asymptote

[empty pumice]

but 5 is good for a positive output

[severe dawn]

This is the actual function

If you go past 4, you get to positive slopes, for example

[empty pumice]

😂 bro wtffffff, ive gotten this question multiple times and its never jumped like that

would the answer be D?

[severe dawn]

You can check with the sign chart. Just choose 2.9, 3.1, etc

[empty pumice]

hold on let me try another attempt

and lets see what it looks like

@severe dawn ig this one gave me less trouble

unless i did something wrong idk

C i think

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[alpine skiff]

A 20m pole at one corner of a rectangular field is anchored by a wire stretched from the top of the pole to the opposite corner of the field as shown above. What is the length of the wire?

[alpine skiff]

Could anyone help me solve this problem? I have no clue on how to find the base of the triangle formed by the wire

[neon shadow]

diagonal of the rectangle is the base of the triangle

[alpine skiff]

you mean like this?

but how I find this

[clear delta]

like this

remember the field is rectangular, the reason it's not drawn that way is because of the viewpoint

the line marked 30m is perpendicular to the line marked 18m

[alpine skiff]

Oh, I see, tysm

.close

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[static pumice]

a

[static pumice]

if the aspect ratio of a normal computer screen is 16:9, whats the aspect ratio of a normal math grid

just like the one on desmos

[leaden thunder]

What

What are you actually trying to do

[clear delta]

grids are usually made of squares

[static pumice]

perspective projection matrix

[leaden thunder]

Well that's a lot of context you're leaving out

[static pumice]

fair enough

[amber wedge]

Lmao

I dont think it works like that

[static pumice]

.close

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[vital reef]

help

i don’t know how to finish it

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[remote mural]

Andrea reads a 500-page book in 20 days and reads 1 hour a day. How many minutes should she read daily so that under equal conditions she can read an 800-page book in 15 days?

[white briar]

If she reads 1 hour a day for 20 days that means it took her 20 hours or 1200 minutes to read 500 pages. So you would need to find how many pages she reads a minute and find out how many minutes it would take to read 800 pages, and then divide that by 15 to figure out how long she has to read per day

[remote mural]

m yes, I did that, I got 22,2... minutes

But it's wrong
Idk if it's because of my calculations or is something else, what did you get

?

[white briar]

I got 128 minutes, could you show me what you did?

[remote mural]

That's the answer, I should have made a mistake

I will take a photo

I will try to explain

I think I know why

I did 1200/500

not 500/1200

idk if that's why

I'll see

[white briar]

Yeah since you want pages per minutes you would need to divide the total pages by the total minutes so 500/1200

[remote mural]

mm yes, I did minutes per page right?

[white briar]

Yes

[remote mural]

thanks for the help

.close

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[stray mountain]

How to do it ?

Using a calculator

Or something

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@stray mountain Has your question been resolved?

[carmine spoke]

Maybe it'll help if you visualise it :)

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[calm coral]

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[desert panther]

Is this valid?

[calm coral]

@desert panther Has your question been resolved?

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@desert panther Has your question been resolved?

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@desert panther Has your question been resolved?

[desert panther]

bro?

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[umbral copper]

Is that a logical equivalence on line 2?

[calm coral]

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[solemn geyser]

Is it correct to say: Char(R) = Char(Q(R))

[solemn geyser]

Since we have a monomorphism from R into Q. r mapped to r/1

Or atleast what I could follow is that Char(Q(R)) is smaller or equal to R

But is it correct to say its equal?

[rigid kettle]

try #groups-rings-fields

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[bronze adder]

$\int_0^1 \arctan \left ( \frac{x - 1}{x} \right ) \dd{x}$

[potent lotus]

jan Nejon

[bronze adder]

Sub x --> 1 - x and add it to the original integral

[eager acorn]

1/1+ (1-x)^2

[bronze adder]

w h a t

[zealous spear]

h u h

[eager acorn]

1 to 0 Integration arctan(-x/1-x) dx

[bronze adder]

yess

Now add that to the original integral, what do you get

[eager acorn]

You meant arctanx dx =1/(1+x^2)

[bronze adder]

no what I do not mean that

[eager acorn]

Ohh it's derivative

[bronze adder]

wat

[bronze adder]

yes but

We aren't going to be using that

Also that absolute value is redundant

[eager acorn]

What will we do then?

Should I not replace it?

[calm coral]

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@eager acorn Has your question been resolved?

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[frank sundial]

Anna got from her grandma in testament 300.000$.
She decided deposit it to bank for fifteen years without taking any money.

The interest rate is 3% per year. And the days are 360.

How would you do this? Am I correct

300.000 * 3% * 360
———————————
100 * 360

??? And then you get 9.000 per year right? And then multiply by 15?

[calm coral]

Please don't occupy multiple help channels.

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[fresh goblet]

find the graddient of the straight line with the equation 5x + 2y = 7

[fresh goblet]

can someone please explain

[remote mural]

gradiant is the slope

y=mx+b

slope is the m

[stuck rivet]

So 5 is m

[fresh goblet]

yes

[fringe reef]

not quite

you have 2y instead of y

[stuck rivet]

So we should simplify them all

Dividing by 2

To all of them

Right?

[fringe reef]

yes

but also, is it 5 or -5?

[stuck rivet]

It’s 5

[fringe reef]

rearrange and see cuz it matters

[fringe reef]

try making it into the y=mx+b form

[stuck rivet]

It will be

Y = -2.5x + 3.5

[fresh goblet]

whered u getthe .5 from

and why -2

god this isso confusing

[broken crater]

5x + 2y = 7 if you minus 5x from both sides what do you get

[fresh goblet]

ohh

alr alr

tysmm

.close

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[boreal night]

Can someone help with this? I was able to solve it in my head, but I have no idea how to solve it doing a statement and reasoning chart. I wrote down the givens in the chart, but I do not know what to write after that.

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[cunning veldt]

@stone grotto in english, a predicate has variables, like

[cunning veldt]

P => Q, is true or false depending on P and Q

and when you take specific P and Q

either it's true or false, and it's a statement

[stone grotto]

so a predicate is generalized

[cunning veldt]

the same subtlety exists in french, but french can put the word proposition almost everywhere, except when you'll want to write predicate

where you can use prédicat

[stone grotto]

so it's the same in french

but

if in french prédicat= proposition

[cunning veldt]

you would use the french word assertion for a statement

if you really want to make the difference

[stone grotto]

in english predicate=/= proposition, proposition is a statement

[cunning veldt]

yes

but I've never seen french lessons being picky about these words, except predicate which is usually translated as prédicat

assertion is for the proposition

so most of the time you see proposition written everywhere

bc proposition exists in french too

[stone grotto]

but that complicate things

[cunning veldt]

it's just bc the difference is very slim, if they give you a predicate they will say it's a prédicat, and if they tell you to evaluate the truth of some statement, they'll write "montrer que la proposition/assertion suivante est vraie"

[stone grotto]

for example if i want to talk about a prédicat and i use the word proposition, then my friend who studied in english would understand that's im mere talking about statements not about predicates

[cunning veldt]

bc of the different meanings, you won't be able to be confused between the 2

in all languages, context matters a lot, and in french it's quite to an extreme degree, esp. when the difference is slim/not important without more context

[stone grotto]

okay, so if we want to conclude what we talked about

[cunning veldt]

I think that in all my french math exams, predicate was translated as proposition and statement was randomly translated as proposition or assertion, and I've seen the word prédicat in one course in 5 years

no french question will be ambiguous don't worry

[stone grotto]

i will pass my exams in english

[cunning veldt]

oh

[stone grotto]

but the exercices i have are in french

we used to study in french and now the president changed and said from now on ull study in english

[cunning veldt]

didn't know about that, are you taking a specific degree for that or is it just the usual licence/master now ?

[stone grotto]

its just the usual licence/master

[cunning veldt]

what a pain lmao, so yeah to conclude, the distinction existing mainly in english, you can remember that predicate = there are variables
statement = it's a mathematical affirmation as it is, and is true or false

[stone grotto]

what about assertion?

[cunning veldt]

assertion says in an implicit way that it's true

it's a true statement

you'll see questions like "prove the following assertion"

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[stone grotto]

really?

[cunning veldt]

yeah

?

[stone grotto]

u know the boob schaums's outline to logic?

book

[cunning veldt]

never read it

[calm coral]

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[lapis blade]

Would someone mind double checking my work here?

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[remote mural]

How do i start this?

[remote mural]

Prove or disprove: $\exists n \in \mathbb{N}$ S.T : $n^2 +n + 41$ is not prime

[potent lotus]

<:F_button:1095679234497843251>

[remote mural]

I started with $(n+\frac{1}{2})^2 +40.75 = p$

[potent lotus]

<:F_button:1095679234497843251>

[dull wagon]

that seems to make it more complicated,

note that there's a trivial case here

[still marlin]

I guess completing square can be used to better show that the polynomial can't be factored - since it shows poly is always positive so there's no root

[dull wagon]

that doesn't do much in relation to what the question is asking

[cunning veldt]

Idk how to give a useful hint without spoiling, but note that you can look at n²+n+41 mod some primes until you find 0 so that n²+n+41 is not prime

and there is an obvious one

also, don't factor, 1/2 and 40.75 are not integers it really doesn't help you to do arithmetic here

[remote mural]

okay

I shall try

[dull wagon]

try to identify the

trivial case
an obvious one
it'll hit you in the face once you realise

[remote mural]

oh

41*41 +41 + 41 is not prime?

[cunning veldt]

indeed, it can be divided by 41

[remote mural]

Thank you everyone

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[lavish prairie]

is this correct

cuz limit is where both sides approach at a point

so would it be DNE

or would I just plugin the value at 9 for that specific equation

[calm coral]

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[lavish prairie]

<@&286206848099549185>

[severe dawn]

What conditions do you need for the two sided limit to exist?

[lavish prairie]

continous

?

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[unkempt apex]

Can someone tell me the steps to do these type of q? And also what is the topic of it?

[zenith ginkgo]

By integrating the acceleration once, you find the velocity, and then by integrating another time, you find the displacement. So you have to integrate twice. But when you integrate, you find constants, which can be found with the initial conditions given at the beginning

[unkempt apex]

Kinda stopped here

Idk how to keep going

[barren nymph]

ooo, this is intergration so you forgot the C

[unkempt apex]

Like this?

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[grim whale]

do i multiply both sides by sqrt x or sqrt x-3 or sqrt x+3...

and why

[severe dawn]

The last

Difference of squares makes it work out

Or you can factor the numerator

[grim whale]

i did it and the numerator turned wonky...

3x + x sqrt x - 9 sqrt x -27

[sweet briar]

dont multiply the numerator out

[grim whale]

o

[sweet briar]

you'll see some nice cancellation

[grim whale]

isnt the rule that we have to multiply both top n bottom tho

[sweet briar]

yes

but dont expand that multiplication

[grim whale]

oooooo

thanks :DD

[sweet briar]

👍

[grim whale]

.close

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[heady kestrel]

@manic oriole sorry the channel closed

Yeah the 5th line

Can someone please explain it

Where did the modulus come from?

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[autumn pollen]

interesting question

[autumn pollen]

appart from the initial factorization, im kinda stuck

any ideas ...

[marsh bronze]

i'm thinking of doing u sub, but what should i sub... hmmm

[hot temple]

integration by parts

[autumn pollen]

oh hell no lol

Im pretty sure this was done by u-sub

[hot temple]

@autumn pollen did it through integration by parts

well at least i tried lemme check with a website

[autumn pollen]

If you did, you're built different

wait, I have the solutions

do you want me to send them through

[hot temple]

sure

it involves some thinking that i didn't exactly write down

[fringe reef]

i got it too

[fringe reef]

yeah i did the same thing

[hot temple]

every coefficient just cancels out to 0

[fringe reef]

except that i just guessed it lol

[hot temple]

gotta love integration by parts

[fringe reef]

hold on, why 2021?

[hot temple]

2021 where

[fringe reef]

oh it's 2022 nvm

i misread your handwriting

[hot temple]

ah, my writing

a classic

[fringe reef]

why are the last 3 steps valid?

i don't get it

[autumn pollen]

this was the suggested answer

[fringe reef]

bruh

[autumn pollen]

in hindsight, it wasn't too bad

[fringe reef]

yeah

[autumn pollen]

but hindsight is alwasy 20/20 lol

[calm coral]

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[distant hinge]

I'm a little confused by this question

i get the "coding matrix" but not sure what to do with it

i try doing the coding matrix times the numerical information but it obviously ends up in an error

[stray tundra]

you cannot multiply a 3x3 matrix by a 1x3 matrix;
You either multiply the 1x3 by the 3x3, or transpose the 1x3

[distant hinge]

ohhh i didnt know i could do BA instead of AB

ty

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[stray tundra]

heh, it's a funny exercise

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[stray tundra]

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[sweet jolt]

can someone pleae explain what does it mean when a sequence majorizes another sequence?

[calm coral]

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[sweet jolt]

<@&286206848099549185>

[oblique carbon]

hey

@sweet jolt

[sweet jolt]

hi

[oblique carbon]

hi

[oblique carbon]

ok

[sweet jolt]

Yeah.

[leaden thunder]

Show the usage of this word from context where you read it from. Screenshot or picture is best

[sweet jolt]

I dont understand the part with k, is it saying that x_1≥y_1, and then x_1+x_2≥y_1+y_2 up to n-1?

[leaden thunder]

Yes your interpretation is correct

[sweet jolt]

so 5,0,0 would majorize say (4,1,0)?

[spice obsidian]

guys

can u help me in my help stream

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[cedar ether]

How do you go about solving the inequality $$x\leq e^{ax},$$ where $a\in\mathbb R$? Appreciate any hints.

[potent lotus]

sunside

[cedar ether]

For $a=0$, we obviously have $x\leq 1$. Maybe restrict ourselves to positive $a$ first.

[potent lotus]

sunside

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[onyx matrix]

I want to prove if $x$, $y$, $\in$ R $x>1$ and $y>0$, then exists $n \in N$ s.t $x^n > y$

[potent lotus]

Mia

[onyx matrix]

what I have:
by contradiction, for all$ n \in N, x^n \le y \implies y $ is the upper bound of $E = {x^n: n \in N}$. R has the least upper bound property, $\implies \exists a \in R s.t SUP(E) = a$. $x>1 \implies a - x < a$ , so $a-x$ is not an upper bound of E $\implies \exists n \in N$ s.t $x^n > a-x \implies x^{n+1} > a$ which contradicts $sup(E) = a$

[potent lotus]

Mia

[onyx matrix]

This is just my first time really working with proofs, I'm a little worried about my assumption that there exists n st x^n > a-x. Does this proof work?

[calm coral]

@onyx matrix Has your question been resolved?

[graceful dust]

that part seems ok

[onyx matrix]

great thank you

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[eager acorn]

Is this question wrong?

Answer is given A

[alpine stone]

,w plot cosec(x) from pi/2 to 3pi/2

[potent lotus]

Results provided by WolframAlpha

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

Requested by alonelybean

[alpine stone]

That seems to be the case

[rigid kettle]

what??

its clearly neither

[alpine stone]

Well if we ignore what's going on in the middle

[rigid kettle]

definition of increasing quantifies over that stated set in this case. Even ignoring the dubious pt, the defn fails.

[alpine stone]

Ah actually yeah nvm

I'm dumb

@eager acorn It's A indeed, recall the definition of an increasing function

[jade fractal]

yeah it's A

[calm coral]

@eager acorn Has your question been resolved?

[hushed tartan]

also you can check using derivative

take the derivative of each of the given functions and study the sign of each of the derivatives

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[spare pecan]

sry, I was away then forgot about it @remote mural

[spare pecan]

tbh Idt I understand the question well, I understand what a mealy machine is, but what does it mean to compute a reduction

[remote mural]

Basically, it means that the machine must take w as input and compute f(w) where f is a reduction from L to L'

[spare pecan]

but there are many reductions possible, and mealy machine is deterministic, so we have one output

[remote mural]

It just has to compute a reduction

The hard part is finding such a reduction

[spare pecan]

[remote mural]

Any reduction will do

[spare pecan]

oh

weird

I found a reduction then, we just switch the first symbol from the string

[remote mural]

Well there you go

[spare pecan]

f(1w)=0w
f(0w)=1w

[spare pecan]

thanks

[remote mural]

I learned FLT in the equivalent of a day just for this

I don't regret it

It's a dope field

[spare pecan]

too pro

[remote mural]

@spare pecan Don't forget to .close

[spare pecan]

yee

.close

[calm coral]

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[remote mural]

.It's kind of like programming languages where once you know a lot of them new ones just look like a mixture of those you have already seen but with somewhat new notation and you can almost learn it by just glancing at it

[calm coral]

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[bleak peak]

Idk I can use curve sketching

Is there any more effective way to do?

<@&286206848099549185>

Nobody help...

[calm coral]

@bleak peak Has your question been resolved?

[bleak peak]

<@&286206848099549185>

Is my question too diffcult?

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[loud ivy]

https://cdn.discordapp.com/attachments/808386688308477962/1162777729545031851/IMG-20231014-WA00004.jpg?ex=653d2c26&is=652ab726&hm=9cf7092e6c778222b0123adc560b2aa63539db1690f2733cd507fa8e961c8615&

[loud ivy]

what would be the answer for this? I wasn't given an answer choice but here's my thought process:

|A u B u C| = 80

|A| = 60

|B| = 50

|C| = 35

|A n B n C| = 0

so the two way intersections in total should amount to 65 right?

I'm assuming the venn diagram looks like this

the maximum value of |B n C| = 35

and since there's an intersection |B n C| can't be 0

so all the options except 0 is the answer (imo), can someone confirm?

[calm coral]

@loud ivy Has your question been resolved?

[loud ivy]

<@&286206848099549185>

[violet torrent]

sorry i cant help :(

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@loud ivy Has your question been resolved?

[calm coral]

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[eager acorn]

b^2=ac
2logb=loga+logc
loga, logb,logc are in arithmetic progression

What to do next?

how make (loga base e => log n base a)

@brittle glade if you are interested

[calm coral]

@eager acorn Has your question been resolved?

[brazen rune]

g.p. is geometric progression, a.p. is arithmetic progression, what's h.p. again?

oh it's harmonic progression

well anw i had an idea abt how to solve this

if a b and c are in geometric progression that means you have a, b which is let's say a * x, and c which is b * x or a * x^2

if you take the log of a b and c

you get log a, log a * x which is the same as log a + log x, and log a * x^2 which is the same as log a + 2log x

so log a log b and log c are in arithmetic progression like you said

using log properties we know that loga of n = log n / log a

so using that

logb of n = log n / log b = log n / (log a + log x)

and logc of n = log n / log c = log n / (log a + 2log x)

log n is just a random constant

we can say that's like

1 or something

so you have the sequence 1 / log a, 1 / (log a + log x), and 1 / (log a + 2log x)

if you flip that it's an arithmetic sequence - log a, log a + log x, log a + 2log x

that means it's harmonic right?

@eager acorn

[eager acorn]

Yes harmonic answer

[eager acorn]

Can you write it over a paper in short. Because hard to understand @brazen rune

[brazen rune]

yeah sure

[eager acorn]

Thank you so much please

[brazen rune]

let me know if you are confused by a step

[calm coral]

@eager acorn Has your question been resolved?

[eager acorn]

I understand the whole process. I was inputting n into the log e process

But you said logn is just a number so this line solved the all thing in one second

[eager acorn]

.close

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[calm coral]

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[summer herald]

On which line did I mess up?

[novel turtle]

looks fine

[summer herald]

I figured it out
I wants me to plug in y

.close

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[grand rose]

How o you do part c

[grand rose]

this is the diagram I've drawn

AB is a diameter

radius is 13

[pure kayak]

you could call C (x,y) find the gradients of each line AC and CB, and you know the product of those gradients must be -1 since theyre perpendicular

thats one way at least

hm actually

[grand rose]

I've got an equation with 2 unkowns

[pure kayak]

yeah

lemme do some working so i can do it properly

aha

y=0

its on the negative x axis, so y=0

[pure kayak]

you only need to find x now using this

[grand rose]

oh yh

[pure kayak]

remember x is negative so take that solution

[grand rose]

🤦‍♂️

I miss the biggest clues

[pure kayak]

i missed it too

happens to us all

[grand rose]

.close

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[shy pelican]

hi

[shy pelican]

I dont even know where to begin

I feel like once i get the first few I'll be able to do the rest though

[calm coral]

@shy pelican Has your question been resolved?

[calm coral]

@shy pelican Has your question been resolved?

[calm coral]

@shy pelican Has your question been resolved?

[shy pelican]

I cant thank you enough. This was due in 4 hours and i gave up on it. I think i can do the rest by myself thanks to your help

[shy pelican]

.close

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[plush nest]

I can get the tangent unit vector

And i know the equation is the derivative of that over the magnitude of the derivative

But like

Im just doing it wrong

[calm coral]

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[plush nest]

Oops let me repost

Wrong question

#17

Can someone walk me thru it

I posted my work above

Should i plug in the value of t for the magnitude once i get the tangent unit vector?

And then only take the derivative of the top?

[spare beacon]

No

[plush nest]

So i gotta take that whole derivative 😭

[spare beacon]

Yes

[plush nest]

Pain

[spare beacon]

It's usually easier to find the unit binormal and get the normal via the cross product, but it varies per problem which is easiest

[plush nest]

Im just going to find it by taking the derivative

[calm coral]

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[gritty trellis]

If f(t) = sec(t), find f ″ (𝜋/4)

[plush nest]

You want the answer?

[weak rapids]

!nosols

[calm coral]

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.

[weak rapids]

please

[plush nest]

Oh okay

Sorry I was just looking at my question

[weak rapids]

@gritty trellis what should be the derivative of sec(t) wrt t?

[spare beacon]

I think for your closed question, the strategy to just brute force the second derivative is not smart vs using the cross product, but it's entirely up to you.

[split ferry]

yeah i'd do the same

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[lean axle]

So for question five I’m supposed to rotate the bounded region by y=2 but I’m a little unsure if I set it up right as it doesn’t make sense my volume is negative, can someone point out where I went wrong as I thought I was supposed to take each curves distance from the line of rotation

[little musk]

What are your curves

[lean axle]

y = x^8, and y = 1 around y = 2 sorry picture is blurry let me send a better one

[little musk]

you need to square the terms in parentheses, no? And your bounds might be from 0 to 1 since the two curves intersect at (1,1)

[lean axle]

hm yeah ur right they would be from 0 to 1 just graphed it on desmos and I just looked back at the formula they should be squared, but otherwise did I set it up right?

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[lean axle]

.close

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[deft notch]

I dont know what the question is asking

Can someone explaine what sample points and sample space are?

[pallid halo]

are you taking a class of some kind? does it have notes/book?

[deft notch]

Its just some excerpt that my math team teacher gave me

[pallid halo]

sample space = the set of possible outcomes

sample points = the outcomes

[deft notch]

ohh

[pallid halo]

an outcome would be like "3 on first die, 4 on second die"

[deft notch]

Ohh ok got it

[deft notch]

so sample space would be

6 ways on the first die, 6 ways on the second die?

[pallid halo]

yep

[deft notch]

Would that also be the sample points?

@pallid halo

[pallid halo]

yes, the sample space = the set of all the sample points

where each sample point is one of the outcomes

[deft notch]

ok thanks

[deft notch]

so the answer to my question is 36?

[pallid halo]

yes

[deft notch]

ok

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[deft notch]

.close

[calm coral]

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[slow venture]

If the points (1,3) (3,-2) and (-2,1) are on the graph of a one to one function f(x) find the value of f(1) +f^-1(1)

[slow venture]

What the hell does that even mean

[tawdry gust]

its saying that those three ordered pairs are points on a function

[slow venture]

So what do I do

[tawdry gust]

so you dont know thte function but you have f(1), f(3), f(-2)

and it wants f(1) + f^(-1)

[slow venture]

I don’t get it

[tawdry gust]

you can think of a function like this: you give it a number and it does something to it and spits back another number

take for example f(x) = x^2

if you put in 1 for x

you get f(1) = 1

or f(2) = 4

does that make sense?

[slow venture]

Yes but how does that help us

[tawdry gust]

okay lets start with one half of the question

whats it the value of f(1)

[slow venture]

Well idk

We don’t have a function

[tawdry gust]

yeah exaclty but you have ordered pairs: (x, y)

x is your input

y is your output

[slow venture]

Oh

3

[tawdry gust]

yes correct

but now theres this other question

f^-1(1)

so f^-1 is a inverse function

[slow venture]

So what do we do

[tawdry gust]

you can think of it like the "undoing" function

[slow venture]

Wdym

[tawdry gust]

think about it like this

if i give you a coordinate (x, y):

where x is the input

and y is the output

and i say my y is 3

what is my x?

[slow venture]

Well I don’t know the function

[tawdry gust]

from this one

[slow venture]

1?

[tawdry gust]

yeah exactly!

so we would say that (3, 1) is the inverse of (1, 3)

or another way is f^-1(1) is?

[slow venture]

1?

[tawdry gust]

close we are trying to find x in (x, 1)

what could our x be?

[slow venture]

-2

[tawdry gust]

yes

so f(1) + f^1(1) is?

[slow venture]

1

[tawdry gust]

yup

[slow venture]

Thanks

.close

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[reef island]

Hello! I have a few questions

[reef island]

could anyone walk me through this?

[calm coral]

@reef island Has your question been resolved?

[calm coral]

@reef island Has your question been resolved?

[civic dirge]

Do you have a normal distribution calculator or chart?

Imo, going through the answers quickly and seeing which line up is a pretty good strategy

[calm coral]

@reef island Has your question been resolved?