help-10

[coral willow]

I cant seem to find anything about this topic online

F is the transformation function (eg. F = (rcos(a),rsin(a),z)^T

<@&286206848099549185>

[tranquil basin]

.reopen

[obtuse pebble]

@coral willow Has your question been resolved?

[timid silo]

jacobian?

[cunning burrow]

So you want go from finding grad f in rectangular coordinates to cylinderical coordinates?

[coral willow]

But isnt that just calculating the jacobian matrix?

I mean that part of what weve been taught too, but i only knew of it as the matrix used in formulas and nothing more

[coral willow]

Yep

Thats for a scalar field

For a vector field (eg flux) youd want to preserve the surface integral in both coordinate systems

Stuff like that

Or divergence of vector field in physical and local coordinates, (for use in Volume integral)

[obtuse pebble]

@coral willow Has your question been resolved?

[obtuse pebble]

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[celest valve]

Solved and got 17cm, answer key says 22.7cm
Plugged in my answer to 1/2(ab)sinC to see if the area checks out, and got exactly 158cm^2
Plugged in the answer from the answer key and the area is way off
Can someone pls help and verify idk what I’m doing wrong

[timid silo]

,w sqrt(42158/(3sin(55 degrees)))

hmmmm

,align
A &= \f12 \m\sin{55\degrees}PR\cd QR \
158 &= \f12\m\sin{55\degrees} \f34 QR \cd QR \
QR^2 &= \f{158\cd 2\cd 4}{\m\sin{55\degrees} \cd 3} \
QR &= \s{\f{158\cd 2\cd 4}{\m\sin{55\degrees} \cd 3}}

[timid silo]

oh

i didnt divide by sin(55)

[warm shale]

Results provided by WolframAlpha

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Requested by qylooo

[timid silo]

yeah okay can you show what you wrote?

step by step

[timid silo]

what you put in the desmos is like pretty off from the expression above

[timid silo]

hol up

why 3x and 4x?

what is x representing

[celest valve]

I think I put in 3QR as 3x and 4PR as 4x

But now that I think abt it then it’d mean 3x = 4x 💀

How do I go about this question then

[timid silo]

yeah

i already wrote it above but like

you see how what you have is like [
A = \f12\m\sin{55\degrees}PR , QR
]
yeah?

[celest valve]

Yea

[timid silo]

yeah

so you wanna figure out QR

but problem is that we dont know PR

we can solve that issue by finding an expression of PR in terms of QR

makes sense right?

[celest valve]

Yeap

[timid silo]

yeah so remember that the question tells you [
3QR = 4PR
]

[timid silo]

can you solve for PR in the above equation

[celest valve]

Ohh so PR = 3/4 QR

[timid silo]

yaaas

so like

[timid silo]

change PR with 3/4 QR here

and solve normally

ill leave rhe rest to you its just algebra

[celest valve]

Alr gimme a sec

Got it, thank you !!

.close

[obtuse pebble]

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[timid silo]

noice

[obtuse pebble]

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[rancid hedge]

I dont know how to start with this question.

[rancid hedge]

should i find the expectation of Y and use the two values that the X takes on.

I got a to be 0 when its supposed to be 1/4

[obtuse pebble]

@rancid hedge Has your question been resolved?

[obtuse pebble]

@rancid hedge Has your question been resolved?

[rancid hedge]

https://tenor.com/view/chika-chika-fujiwara-chika-dance-silly-dance-anime-gif-18531305

[rancid hedge]

https://tenor.com/view/daniel-craig-yassify-namufilms-blairgif-gif-12824114076396553184

https://tenor.com/view/dance-daniel-craig-belvedere-belvedere-vodka-gif-27100770

.close

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[golden jolt]

i need help plz 4 d

[golden jolt]

why is it true ?

[viral blade]

is there a specific point in there you think it shouldn't exist?

[golden jolt]

1

[golden jolt]

cuz its not attached to - 1 and 0

[viral blade]

1 isn't in the set (-1,1)

[golden jolt]

but how its exists

[viral blade]

the limit doesn't exist at x=1

but d is still true, because 1 isn't in (-1,1)

[golden jolt]

can you plz explain why it isnt in (-1,1)

[rancid hedge]

because its an open interval?

[viral blade]

yeah

(-1,1) is the set of numbers between -1 and 1, not including -1 or 1

[-1,1] would include -1 and 1

[golden jolt]

okay thx alot

[viral blade]

np

[golden jolt]

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[strange harbor]

I need help on question 5c and 5h please

[strange harbor]

for 5c so far ive got 7sqrt(2) over 2

[icy granite]

that's correct

what did you try for 5h

[strange harbor]

5sqrt(7) over 7

[icy granite]

that looks correct too

[strange harbor]

do i need to do anyother steps than that?

[icy granite]

that's the simplest it'll go

[strange harbor]

so it doesnt matter if the radical is still in tbe denominator ?

[icy granite]

there's no radical in the denominator

it's 2 and 7, they're not radicals

[strange harbor]

oh yeah you're right

tysm again

.close

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[copper cape]

Ummm

[copper cape]

Hello?

Something's wrong, i can feel it

[timid silo]

should be 13 instead of 11

[copper cape]

13 : 1
11 : 0

Need more 3 people to proof it

XD

[obtuse pebble]

@copper cape Has your question been resolved?

[whole dock]

Should be 13 yeah

[marsh geyser]

Yes, it’s 13 don’t overthink it, it’s just a mistake from the textbook or a typo

[obtuse pebble]

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[nimble gulch]

i have a problem

[nimble gulch]

my solution:

i am confused

[royal basin]

hmm hold on

i think you overcomplicated this

[nimble gulch]

that's my specialty

[royal basin]

you called your given point A and found two points B and C lying on the intersection of the two given planes

and then you found the normal vector of... plane ABC?

why?

[nimble gulch]

whay is the alternative ?

[royal basin]

1. vector BC is already the normal of the plane that you want
2. or you could simply cross product the normals of the two original planes

and not fuck with any of this point-finding bullshit

so <2, 1, -2> × <1, 0, 3>

[nimble gulch]

ok i get this , but can you find the mistake in my calculations i am very interested what i did wrong

plz

[royal basin]

i don't want to dig through it sorry

[nimble gulch]

ok no worries

.close

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[tall venture]

you spend 0.65 for one pull
64% to get 1.60
23% to get 0.01
13% to get 0.03
how to calculate the average return?

[high lily]

have you done stuff with expected value?

[tall venture]

idk lol, english is not my native language

[high lily]

try looking up "expected value"

[tall venture]

= 0.64 * 1.5 + 0.23 * 0.01 +0.13 * 0.03 ?

[high lily]

* 1.6 not 1.5 based on what you originally typed

[tall venture]

yeah okay so thats the formula?

[high lily]

yeh, pretty much
then subtract the intial investment / cost of a pull
for the average return

[tall venture]

Alright tysm!

.close

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[kindred valley]

magnitude of first vector is 5 units

10/5 = 2
2(3i + 4j)
= 6i + 8j

[glass pasture]

thanks

.close

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[atomic salmon]

Someone help pls🙏

I keep solving and getting it wrong

[marsh geyser]

Don’t send files

[atomic salmon]

How do I show questions?

[marsh geyser]

Copy the image here

Copy and paste

[atomic salmon]

Where?

[marsh geyser]

You can do it with images too

It’s like copying text

Discord accepts images as copied input

[atomic salmon]

I don’t understand how to do that tho but could u help with that qs pls I am so desperate I have an exam Ty.

[marsh geyser]

Post your question

[atomic salmon]

Where?

On the help forum

[marsh geyser]

Here

[minor cairn]

here

[timid silo]

take screenshot of the image u shared and send it here

[atomic salmon]

Here

[minor cairn]

that doesnt work

[timid silo]

subscribed to your channel

[marsh geyser]

That is a file

[atomic salmon]

How do I send as an image?

It doesn’t let me

[minor cairn]

thanks sir 🙏

[timid silo]

no problem.

[marsh geyser]

Just take a screenshot and paste here

[atomic salmon]

https://cdn.discordapp.com/attachments/903430332324405288/1195733595415916606/IMG_4451.png?ex=65b510b0&is=65a29bb0&hm=784733045229781606c8923a1bb24b51aa0ca3cf1f40cb080559d4442466de20&

[marsh geyser]

Again

[timid silo]

lol

[atomic salmon]

I rlly don’t get it omgggg😭

[marsh geyser]

Then write your question

[marsh geyser]

With text

[atomic salmon]

Okay

So it’s about trapezoidal rule

[timid silo]

send it to me in messaging

if u are comfortable

I can forward it here

[atomic salmon]

Okay I will try

Integral-3 on top and -6 in the bottom the question is 10/1+x dx

Do u get it

And n=3

And it’s ab trapezoidal rule

[timid silo]

$\frac{10}{1+x}$

right?

[warm shale]

samyak

[timid silo]

wth lol

[atomic salmon]

Ur image isn’t opening but yes ur right

10/1+x

[timid silo]

alright, I understoor the question

[atomic salmon]

Integral -3 top and -6 bottom , n=3

Trapezoidal rule should apply,y

[timid silo]

u want numerical answer or algorithm?

or python code

[atomic salmon]

Numerical answer

[timid silo]

alright, so the formula for integral using trapezoidal method is I = h*(y0 + sum(y1 to yn-1) + yn)/2

h is given as b-a / n

where b is upper limit, in your case -3. a is lower limit, in your case -6

and n ofc 3 as u said

and yn is given as yn = yn-1 + y(x0 + n * h)

understood?

[atomic salmon]

Okay

I think

I dint understand where u got the Yn formula from

[timid silo]

I gave u the formula and the meaning and formula of each variables used in the parent formula

[timid silo]

that is just the simplification of slope. It is dy/dx. dx is ofc h right? and dy is yn - yn-1

[atomic salmon]

Okay

[timid silo]

I can give u the proof, it's not that long

[atomic salmon]

No it’s fine dw abt it

[timid silo]

alright

[atomic salmon]

But the formula ik is x/n(f(X0)+(f(X1)…

[timid silo]

let me know if u need more help with the answer

[timid silo]

it should b-a/2 in stead of x

and the sum of f terms should be in numerator

[atomic salmon]

Yes I do pls

[timid silo]

otherwise the formula won't make sense, as in integral we are adding f(x)s and it should be in numerator

[atomic salmon]

Could u show me ur way of solving this qs I’d u don’t mind

If*

[timid silo]

sure. But can u give me 5 minutes?

[atomic salmon]

Cuz I understand how to do it I just keep getting it wrong

Yeah ofc no problem

[timid silo]

alright brb

back

[north cradle]

@atomic salmon file isnt working for me

can you send a screenshot?

[atomic salmon]

Yeah it isn’t rlly work for anyone it’s a screenshot the

Btw*

[north cradle]

on what device?

[atomic salmon]

iPad

[north cradle]

weird

try sending it from your gallery

or

use the plus sign on discord

and look for the image that way

[atomic salmon]

I did

And it didn’t work

[north cradle]

discord is having media issues

[obtuse pebble]

@atomic salmon Has your question been resolved?

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[obtuse pebble]

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[devout wind]

hi can anyone help me with this?

[upper shuttle]

Discord is having media issues. Please transcribe your issue in text so we can see your problem.

[devout wind]

decide for wich n element of N the inequality 2^n < n! is true and prove your claim by induction

[hexed gull]

dym from which element onwards

[devout wind]

so this is true for n>=4 but how do i prove it with induction

[hexed gull]

ah for n e N, misread

[hexed gull]

you start by showing it's true for 4

[devout wind]

yeah sorry

[hexed gull]

2^4 = 16

4! = 24

then induction assumption

assume 2^n < n! has been proven

under that assumption, can you prove that 2^(n+1) < (n+1)! is true?

if you do so, then you have shown that the inequality holds for n≥4

the last step would be to show that it's wrong for n=1,2,3 which is trivial

[hexed gull]

I'll put the solution as a hidden text below as I'm not certain whether I'll be back

attempt to solve it and when stuck or rechecking click on the message

||2^(n+1) = 2^n * 2 and (n+1)! = n! * (n+1). We already assume 2^n < n! and we know that 2 < (n+1) because n is already at least 4. These two inequalities imply 2^n * 2 < n! * (n+1)||

[devout wind]

so i need to show that is true and i expand it to 2^n*2 < (n+1)! and i switch 2^n with n! but now i'm stuck

[hexed gull]

hm maybe you can replace the 2

by an expression that would turn n! Into (n+1)!

2^(n+1) = 2^n * 2 < n! * 2

you are here and want a (n+1)! at the end

remember that (n+1)! = n! * (n+1)

[devout wind]

wait so i have n!*2 < n! * (n+1) i can devide both sides by n! and i'm left with 2< n+1 wich is true because n>=4

[hexed gull]

yop

you don't need to explicitly divide by n!

n! * 2 < n! * (n+1) would already be enough

since n≥4 is given as we start the induction at 4

[devout wind]

alright thank you very much

[hexed gull]

and now last step, disprove for 1,2,3:
2 < 1 wrong
4 < 2 wrong
8 < 6 wrong

[obtuse pebble]

@devout wind Has your question been resolved?

[obtuse pebble]

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[lucid drift]

when it asks to consider the function do i just plug each funtion into each roman numeral function? so each problem would have two solutions or??

Q1
Consider the functions
(i) 𝑓(𝑥) = 3𝑥 − 5𝑥'2 and (ii) 𝑓(𝑥) = 𝑥/x+3
For each of the functions find and simplify the following:
(a) 𝑓(𝑥 + ℎ)
(b) 𝑓(𝑥 + ℎ) − 𝑓(𝑥)
(c) 𝑓(𝑥 + ℎ) − 𝑓(𝑥)/ h

thats my question #1 as for question #2 , in this picture do i just find the piecewise of absolute value and plug into the whole function?

Q2/
Write the functions as piecewise functions and simplify.
(i) 𝑓(𝑥) = |5𝑥 − 7|
(ii) 𝑓(𝑥) = |5𝑥| / x
(iii) 𝑓(𝑥) = 5 − 𝑥/ |𝑥 − 5|

(iv) 𝑓(𝑥) = |𝑥 + 2| / 𝑥'2 + 𝑥 − 2

[dusk widget]

for question 1, you've been given two functions

for each of them, you need to find and simplify f(x+h), f(x+h) - f(x), and [f(x+h)-f(x)]/h

there is no "solving" being done

[obtuse pebble]

@lucid drift Has your question been resolved?

[junior eagle]

Hey y’all I need help with analytic geometry

Is anyone up to help me

[obtuse pebble]

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[edgy needle]

excuse me

[edgy needle]

how do i do this proof

[timid silo]

what proof?

[edgy needle]

do i just do point b - point a = point c - point d

i mean

question ci

[timid silo]

AB=DC?

[edgy needle]

yes

i just did 2,4 = 2,4

do u think this is enough

[timid silo]

firstly show that the length of AB, i.e. the magnitude of AB is the same as that of DC

[timid silo]

ohh yes, that's enough too

[edgy needle]

ok thanks!

[timid silo]

other way, u can show that the magnitude is same

[edgy needle]

what is mafnitude

magnitude

[timid silo]

and then show that they make the same angle with x axis

[timid silo]

length of the vector

[edgy needle]

why dont they just call it length

can u tell i am self learning

[timid silo]

that way, the direction is also equal

[timid silo]

ik, but usually they use magnitude in maths

[edgy needle]

wait

[timid silo]

and length in physics

[timid silo]

yes?

[edgy needle]

so the letters like AB with the line on top

[timid silo]

ohh. Great. All the best!

[edgy needle]

mean a point?

[timid silo]

no, it means a vector

[edgy needle]

why can i write it as 2,4 then?

[timid silo]

that's a vector notation

[timid silo]

because a vector can be represented in a row or column matrix form

usually a column matrix is chosen

[edgy needle]

wait

[timid silo]

(2, 4) means that the vector has the component of 2 unit on the first axis and 4 on second

[timid silo]

yes?

[edgy needle]

so it is the same as this

[timid silo]

yes, that's a vector

[edgy needle]

oh wow

maths is confusing amirite

anyways, thank you

[timid silo]

well, you're chinese. U can do it

lol

[edgy needle]

WHAT

im not chinese

😭😭

[timid silo]

ohh, my bad

I am sorry, nvm

[edgy needle]

LMAOOOO

dont worry i am vietnamese

very close

but i live in australia

[timid silo]

ohh, I was close

still, u got asian genes. Dw, u can do maths

[edgy needle]

and i didnt inherit the genes unfortunately

[timid silo]

lol

[timid silo]

lmao

[edgy needle]

my dad was a calculus professor

....

[timid silo]

ohh

was?

[edgy needle]

in vietnam

[timid silo]

ahh

[edgy needle]

hes an engineer in aus

[timid silo]

ohh

nice

alright, I hope your doubt is solved

[edgy needle]

ok thank u

good night

or morning

or afternoon

[timid silo]

no problem

lol

[edgy needle]

.close

[obtuse pebble]

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[obtuse pebble]

Please don't occupy multiple help channels.

[stark jay]

How do i solve this?

[narrow vault]

try simplifying the integrand first

[stark jay]

How

1+ x^2(x^2+2)

After that?

[narrow vault]

keep simplifying

[stark jay]

1+ x^4 + 2x^2

[narrow vault]

good, now keep simplifying

[stark jay]

What else can i do?

[young narwhal]

F as in?

[stark jay]

?

[young narwhal]

Fa..

[stark jay]

What do you mean "F as in"

[stark jay]

??

[young narwhal]

Fac...

[stark jay]

???

[young narwhal]

You can do it

[stark jay]

Do what

[young narwhal]

Now you have to fac..

[stark jay]

What is "fac"??

[young narwhal]

You have to guess the word haha

[young narwhal]

Can you see?

You have to fac...

[stark jay]

I don't know what fac is

[young narwhal]

But i havent said the whole word xD

Fac doesnt mean anything as its not the whole word

Guess the word

Alright One more clue then

Fact...

[stark jay]

I dont know what is it

[young narwhal]

Facto...

[stark jay]

Still don't know what you wanna say, i am not english

[young narwhal]

Oh okay sorry

Where are you from?

[stark jay]

Greece

[young narwhal]

Ok so i meant to say factorize

Do you know what that is?

[stark jay]

Yes understood

But it was factorized

[young narwhal]

Ik but now you have to factorize again haha

It gets simpler

[stark jay]

With one included?

[young narwhal]

Yeah you dont see the remarkable identity?

[stark jay]

X*SquareRoot(1/x^2 + x^2 + 2)

After that?

[young narwhal]

?? I mean this

This is what you have to factorize

[stark jay]

I did

[stark jay]

This is in a SquareRoot

[young narwhal]

Yeah but factorize it and see whats going on 😃

[stark jay]

I did factorize it

[stark jay]

.

After that what?

[young narwhal]

No thats wrong

Do you know (a+b)^2 ?

$(a+b)^2=a^2+2ab+b^2$

[warm shale]

tresbienmonsieur

[stark jay]

I know

Didn't think of it

[stark jay]

But this is still correct

[young narwhal]

Yeah but not useful here

[stark jay]

Solution is 12?

[young narwhal]

No

What did you get after factorizing

Yeah its 12 (i didnt see that you edited)

[obtuse pebble]

@stark jay Has your question been resolved?

[obtuse pebble]

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[shadow lava]

magnitude vs strength vs scalar

In summary, magnitude is a general term referring to the size of a quantity, strength often implies a degree of force or power and can be scalar or vector, and a scalar is a specific type of quantity that has only magnitude and no direction. These terms are used in different fields and should be interpreted based on the specific context in which they are employed.

none of these words represent direction, they all seem the same
can anybody explain why we have three words to basically mean the exact same thing?

[shadow lava]

wouldn't it be easier if we all agreed to drop two of these words and only used one? in all contexts, we would understand the meaning, no?

[past sand]

Are you asking why a language has synonyms?

[timid silo]

that's not really a math question

[obtuse pebble]

@shadow lava Has your question been resolved?

[tardy epoch]

Yes. Avid is an avid proponent of trying to force others of dropping words to not confuse him

[tardy epoch]

Please stop doing that

.close

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[flat pier]

Hello, I need help with exercise 33.3 please

Can you translate or you can do it?

[tardy epoch]

you should translate

[flat pier]

Ok

You have a vector u=(4,-1)
Point A(5,2)
Point P(k+2,-k²-5)

We have to determinate the values of k for which the vectors u and AP do an obtuse angle

[tardy epoch]

use the dot product

[flat pier]

Between u and AP?

Like this

.close

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[obtuse pebble]

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[quiet ice]

What are these questions called? Trying to find a video on the specific case. Polynomials?

[obtuse pebble]

Please don't occupy multiple help channels.

[brazen gorge]

rational functions

[quiet ice]

Perfect thanks

.close

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[rare comet]

Hello!

[rare comet]

im doing a pratice problem for liner algebra and im having a bit of trouble

so with this problem that gave us the answer but imhaving trouble getting there

so i understand that the matrix would look something like
1 1 2 -1
2 1 3 0
0 -2 1 2

and ik we need to have the diagnal to eqaul 1

and the surrounding numbers equal 0

the issue that im having is more so understanding the build up to that

so for example in row 2

1 1 2 -1
2 1 3 0 we want to make that 2 be 0
0 -2 1 2

i was doing something like r2= r1(r2)-2

[dark stirrup]

Not necessary, but it is one way to solve the problem, yes

[rare comet]

oh?

how so

[dark stirrup]

you could have something like
0 1 0
1 0 0
0 0 1

[rare comet]

ohhhh as long as the rows are 1?

[dark stirrup]

I forget the name for this kind of matrix, each row and column must have exactly one 1

[rare comet]

ik my professor said to have it diganal so i assumed that should have been the case

[dark stirrup]

There's nothing wrong doing it that way, and it's probably the safest choice. I'm just making you aware of the flexibility

[rare comet]

ok gothca thank you

but my main issue is more so solving the rows

[dark stirrup]

This sounds a little off.

[rare comet]

how so

[dark stirrup]

neither r1(r2) nor the 2 by itself sound like valid row operations

valid row operations would be $\$

1. swapping: $r_i\leftrightarrow r_j\$
2. multiplying by a nonzero scalar: $r_i\to \alpha r_i\$
3. linear combination: $r_i\to \alpha r_i + \beta r_j\$

[warm shale]

SWR

[rare comet]

how would you reccomed solving 2?

[dark stirrup]

Are you asking which row operation I would do on row 2 to make the first column zero?

[rare comet]

yup

im a bit confused "scalar"

[dark stirrup]

scalar is just any real number

[rare comet]

oh lol

[dark stirrup]

So "nonzero scalar" is any number except zero

[rare comet]

gotcha gotcha

[rare comet]

im not all to familar with this is all

the professor didnt really show us this

[dark stirrup]

Hmm.. Are you sure? These are the elementary row operations. This is precisely what the problem is asking you to do

How did you professor tell you to do it?

[rare comet]

let me send a picture as an example

i hope this helps

[obtuse pebble]

@rare comet Has your question been resolved?

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[royal basin]

there's a lot of stuff you forgor to mark there

like the distance from Sarah to the statue

[calm zephyr]

I don’t how to label it. That’s why I was asking

[royal basin]

which side of your triangle is the statue?

[calm zephyr]

The opposite

[royal basin]

i was expecting "the vertical", but ok yeah that's the opposite side.

you should also mark the right angle btw

and the vertex of the 61° angle is Sarah's eye

or her head ig. we don't care enough to distinguish between her height and eye level anyway

(not that they would differ by a lot)

do you now see where the 166ft distance should go?

@calm zephyr

[calm zephyr]

Yes I do.

One second

wouldn’t u subtract 6.5 from 166?

[royal basin]

dunno where 6.5 came from...

but also show your diagram & work.

[calm zephyr]

I meant 5.5 sorry

All i’ve done is this so far. Because I don’t know if I should subtract 5.5 from the height of the statue?

So it’s 305?

[royal basin]

where did 305 come from?

and also no you should not subtract

[calm zephyr]

tan61=x/166 = 299.5 and then I added 5.5 to get 305

[royal basin]

well

this 5.5 also counts towards the height of the statue doesn't it

and given you added it in

why would you then subtract it again and undo that

[calm zephyr]

No I said subtract before realizing you should add it

.close

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[unkempt lotus]

am i not underatanding what a linear equation is?

i got the slope and just did point slope to find the equation

not sure what im supposed to do here it said my answer was wrong

huh?

[tardy epoch]

<@&268886789983436800>

[unkempt lotus]

what are u doing man

[tardy epoch]

they'll get banned soon. just block and ignore

[tardy epoch]

how did you get 8 in 2x + 8

[unkempt lotus]

i got the slope as -2. did point slope so y - (-2) = -2(x-5)

then y = -2x + 10 - 2?

so y = -2x + 8

[tardy epoch]

oh you input 2x instead of -2x

[unkempt lotus]

oh

[unkempt lotus]

lol

my bad, thanks

.close

[obtuse pebble]

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[rustic fern]

how to show ? o g = g o ? = g to show there exists an identity for the group?

[unreal musk]

What do you think the identity for said group is?

[obtuse pebble]

@rustic fern Has your question been resolved?

[rustic fern]

f x = x?

i think they call it id x

so i just say ye cuz id x exists

?

this seems like obviousness

[wary vigil]

what are the conditions for a group

[unreal musk]

It kinda is

[rustic fern]

do i just say for inverse is the same thing but with -1 on top

[rustic fern]

Closed, Associative, identity, inverse

[wary vigil]

which have you proved and not?

[rustic fern]

all

but idk 100%

can u check?

[wary vigil]

yeah sure we can check

[obtuse pebble]

@rustic fern Has your question been resolved?

[wary vigil]

seems good

sorry for super late response

@rustic fern

[obtuse pebble]

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[obtuse pebble]

@iron cave Has your question been resolved?

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[uneven wren]

i have a question

[obtuse pebble]

Please don't occupy multiple help channels.

[tardy epoch]

close your other channel and

[obtuse pebble]

@uneven wren Has your question been resolved?

[obtuse pebble]

@uneven wren Has your question been resolved?

[tardy epoch]

.close

[obtuse pebble]

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[undone plume]

hello how do you solve the first one

[undone plume]

HELP!

[wary badger]

wherever u see x for f(x)

put the whole function g

so for part a

you would get -g(x)+2

but g(x)=(x+3)^2

so u get -(x+3)^2+2

does this make sense

[undone plume]

HELLO

hello

[wary badger]

hi

hello

[undone plume]

i have question

[wary badger]

do u get what i did

ok ask

[undone plume]

no

[rich mist]

😂

[undone plume]

wait

where did the f go

this is my friends

answer

[wary badger]

this is the same thing i did but obviously the inferior way

because f=-x+2

[rich mist]

Knief is just superior

[wary badger]

the input is (x+3)^2

[undone plume]

i don’t understand the inferior way 😢

[wary badger]

so f((x+3)^2) gives what they did

[wary badger]

couldn’t have said it better myself

[wary badger]

don’t need to they expanded and did nonsense

think of it like this

f(anything)

=-anything +2

[undone plume]

ohhhh

[wary badger]

for part a

[undone plume]

okay

one sec lemme try

[wary badger]

we’re letting anything=g(x)

[wary badger]

yes this works

me personally i just put (x+3)^2 in immediately

then expand if necessary

i’m not sure if ur teacher wants u to expand

it says simplified so ig

do understand the rest of them

[undone plume]

HELP!

[warm shale]

mikak

[undone plume]

what the heck

okay skip that

how do you do this

THIS IS SO HARD!

how did anyone even figure this out

[pure yacht]

do you know how to find the inverse function

[undone plume]

no 😢

[versed stratus]

hint:- $f^{-1}(f(x))=x$

[warm shale]

Why am. I here

[versed stratus]

aasuming the function is non-periodic, if it is, we have to consider a principal branch

[undone plume]

thank you for the hint

does anyone know what i did wrong

[pure yacht]

$0^2 = 0 \cdot 0 = 0 \neq 1$

[warm shale]

mikak

[undone plume]

ohhh

so it’s 0

[pure yacht]

ya

[undone plume]

yay

[obtuse pebble]

@undone plume Has your question been resolved?

[obtuse pebble]

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[pure yacht]

!status

[obtuse pebble]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[spark stump]

is PQ the crossed area?

and if so, how do i find an integral to find tehe area

[pure yacht]

for which part

do you need help with finding area P or Q or both

[spark stump]

both

[pure yacht]

for Q

since it's between the two curves

if you find the area underneath e^x

you'll get this shaded area

so you would need to take away the area below e^-x

and just setup an integral from 0 to 1

[pure yacht]

do you see what areas you need to find to get P

[spark stump]

this?

[pure yacht]

well yeah but how would you go about finding it

by using other areas and subtracting them

[spark stump]

welll

whats the line?

y=e^x

so i do

y=y

e^x=e^-x?

[pure yacht]

why do you need to equate them

[spark stump]

to find interecetps

when they = each other

[pure yacht]

but we have the intercepts given

we just need to figure out the areas

[pure yacht]

like this green area would be $\int_0^1 e^x dx$

[warm shale]

mikak

[pure yacht]

but since that's not the area we're looking for we can subtract the small area underneath the curve e^-x

given by $\int_0^1 e^{-x} dx$

[warm shale]

mikak

[pure yacht]

and if we subtract the bigger area from the other we get area Q

does that follow?

[spark stump]

wgere'

where*

[pure yacht]

on the diagram

[spark stump]

oh

what is this point?

[pure yacht]

since e^x and e^-x are symmetric across the y-axis

[spark stump]

2,e?

[pure yacht]

it's -1, e

[spark stump]

ojh ye

oh ye

ok so green area would not be $\int^{-1}_{1} e^x-e^{-x}\mathrm{dx}$

?

[warm shale]

LW

[pure yacht]

no

[spark stump]

oh?

uh

[pure yacht]

just the green area is this

[spark stump]

doesn’t make sense idk why

why u use only e^x for green area

how come u don’t use e^-x for it

[pure yacht]

the green area is just the area under the e^x curve

it doesn't involve e^-x

i was just using it to demonstrate

that u get two different areas

one that's under e^x

and one under e^-x

and by manipulating them you can get area Q

[spark stump]

what

[warm shale]

thepersonwhomasteredhismathstats

\int
```Compilation error:```! Missing $ inserted.
<inserted text> 
                $
l.52 \int
         
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.

LaTeX Font Info:    Calculating math sizes for size <14> on input line 52.
LaTeX Font Info:    Trying to load font information for OT1+lmr on input line 5
2.```

[spark stump]

the green area.. why are we including parts mot in the yellow area?.

[pure yacht]

.

[spark stump]

please can you leave this channel unless you’re contributing something…

oh

[pure yacht]

you can just skip that step and go straight to this

but this isn't correct because the bounds of integration are wrong

area Q only goes from 0 to 1

$A_Q = \int^{1}_{0} e^x-e^{-x}\mathrm{d}x$

[warm shale]

mikak

[eager niche]

You could also use the linearity of integration to calculate three integrals then add / subtracted them as needed

[spark stump]

i don’t understand how the bounds actually work in integration to be honest

[pure yacht]

yeah

[pure yacht]

which i was trying to explain here but i'm bad lol

[spark stump]

it shouldn’t be that complicated… why isn’t Q just $\int^{1}_{0} e^x-e^{-x}\mathrm{dx}$

[warm shale]

LW

[spark stump]

like…

[pure yacht]

it is!

[spark stump]

IT IS?

DAMN?

actual?

[pure yacht]

yes

[spark stump]

ok NOW

THIS IS STARTING TO MAKR SENSE

FINALLY

[pure yacht]

it's the same equation but it's not from -1 to 1, it's from 0 to 1

[spark stump]

now i’m going to find P

[eager niche]

LW is right for Q

[spark stump]

without having to scroll up to see answer

so P

integrate from -1 to 1

those are bounds

[pure yacht]

it's a bit more complicated

bcos e^-x goes above e^x

from x=-1 to x=0

so you can't directly integrate it

like prior

[spark stump]

why would i need to consider e^-x again

brb

[eager niche]

||or just 2 times 0 to 1 on e^1 - e^x since it’s symmetrical||

[pure yacht]

yup

[obtuse pebble]

@spark stump Has your question been resolved?

[spark stump]

you’re not given it’s symmetrical…

[pure yacht]

if you have a function f(x)

then f(-x) is that same function but mirrored across the y-axis

in this case

f(x) = e^x

and f(-x) = e^-x

so they are symmetrical across the y-axis

[spark stump]

P would be $2\int^{0}_{-1} e^{-x} \mathrm{dx}$

[warm shale]

LW

[spark stump]

this!?

[pure yacht]

you're on the right track but not quiet

[pure yacht]

this would be that whole area

well doubled

[pure yacht]

this statement is really equivalent

to this whole area

the orange bit

but it's not P

there's one more step

to finding P

[spark stump]

wtf

P would be $2\int^{0}_{-1} e^{x} \mathrm{dx}$

[warm shale]

LW

[pure yacht]

no

[spark stump]

oh

[pure yacht]

go back to this and just think about it

you see this poorly-drawn rectangle

[spark stump]

yes

[pure yacht]

what's the area

[spark stump]

2e

[pure yacht]

yes

[pure yacht]

now you already have this area

[pure yacht]

given by this

so you can subtract one area from the other

and get an answer for P

[spark stump]

i don’t think so

i@ so confused

i’m

[pure yacht]

if you get area of the rectangle

which is 2e

and subtract the green area

given by what you said earlier

then you get

[spark stump]

I get the

[pure yacht]

$A_P = 2e - 2\int^{0}_{-1} e^{x} \mathrm{d}x$

[spark stump]

P

[warm shale]

mikak

[pure yacht]

which evaluates to 2

[spark stump]

BUT

[pure yacht]

oh?

[spark stump]

how do i know the green area???????

[pure yacht]

so this area is $\int_0^1 e^x dx$ right

[warm shale]

mikak

[spark stump]

????????????????????? no?

[pure yacht]

why not

[spark stump]

actually

yes

[pure yacht]

alr

[spark stump]

yeah so thats P

[pure yacht]

it's not P?

[spark stump]

BUT how do i actually find P using integration

OK

now im f=confused

[pure yacht]

we are using integration wdym 😭

[spark stump]

bruh

[pure yacht]

okokok

this whole thing

$\int_{-1}^{0} e^{-x} dx + \int_0^1 e^x dx$

[warm shale]

mikak

[pure yacht]

right..

[spark stump]

kms

this is supposed to be easy

[pure yacht]

and the area of the rectangle if you want to integrate it is just $\int_{-1}^1 e dx$

[warm shale]

mikak

[spark stump]

hmm

[pure yacht]

$\int_{-1}^1 e \mathrm{d}x - \int_{-1}^{0} e^{-x} \mathrm{d}x - \int_0^1 e^x \mathrm{d}x$

so that's area P

[warm shale]

mikak

[spark stump]

im confused as hell

[pure yacht]

hm

[pure yacht]

what about this doesn't make sense

[spark stump]

i hate math

[pure yacht]

:(

[spark stump]

uh

could you explain this solution instead?

[pure yacht]

yeah sure

[spark stump]

YAY

[pure yacht]

do you get where the two integrals come from

[pure yacht]

and why they're different

[spark stump]

bro

im on drugs

i get it now

[pure yacht]

lol alr

[spark stump]

I GET IT

its easy

BRO HOW DID I NOT GET THIS

@pure yacht actually

could you explain

why functions in the integrand

is

e-e^x

instead of e^x-e

[pure yacht]

why would it be e^x - x

im just wondering where that came from

[spark stump]

i mean

-e

[pure yacht]

ah

because the line y=e is above the line y=e^x

if you did it the other way around you would get a negative area

[pure yacht]

( between 0 and 1 )

[spark stump]

but then i just take the absolute value i will still get the area right

[pure yacht]

yeah

[spark stump]

AMAZING

thanks for the help

really apricated

[pure yacht]

np

[spark stump]

so

actually

it doesnt matter

as long as i tend the abs

take*

at the end

[pure yacht]

yeah

[spark stump]

right

easy'

thx

,w integrate e

[warm shale]

Results provided by WolframAlpha

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

Requested by fwgx

[spark stump]

,w antideritvative of e^x

[warm shale]

Results provided by WolframAlpha

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

Requested by fwgx

[spark stump]

HUH

??????/

[brazen viper]

@spark stump one of the ways to define e is it's the number such that d/dx(e^x) = e^x. So it stands to reason that you can run this in reverse, yeah?

[spark stump]

uh no

oh wait

nvm

i forgot

.close

[obtuse pebble]

Channel closed

Closed by @spark stump

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[deft bramble]

anyone good with inequalities? for a, b positive real numbers, prove a^4 b^3+a^3 b^4<=a^7+b^7

[deft bramble]

thanks :D

[royal basin]

!status

[obtuse pebble]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[deft bramble]

!status 1

[obtuse pebble]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[deft bramble]

1

[royal basin]

ok

[deft bramble]

sorry lol i'm kinda new to this

[royal basin]

try proving a^7 + b^7 - a^4 b^3 - a^3 b^4 >= 0 instead

(sorry typo)