help-28

[high mural]

🥲

[raw scarab]

lmao but yeah no worries

can ask anytime

[high mural]

Ok

Thank you

[raw scarab]

https://tenor.com/view/lewis-hamilton-bored-f1-waving-legs-reaction-gif-4824109469932584092

[high mural]

I'm watching this now

Because I can't solve book exercises by myself lol

[raw scarab]

yeah its no problem

but then try doing all the sums without reffering after watching this vid

[high mural]

Okk

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[high mural]

.reopen

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@high mural Has your question been resolved?

[high mural]

Can you tell me the meaning of this sign ^

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[tender thicket]

is this a theorem of probability?

Pr(A & B | C) ≤ Pr(A | C)

[static bramble]

idk about a theorem, but P(A & B) ≤ P(A) is a pretty elementary fact in general

irrespective of the exact probability measure

[tender thicket]

yeah that does make sense

are you positive P(A & B) ≤ P(A) translates over to Pr(A & B | C) ≤ Pr(A | C)?

[static bramble]

P(.|C) just represents a different probability measure than P(.)

[tender thicket]

makes sense

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[plush heart]

someone can explain why √y?

[plush heart]

for (b)

log(a) x^2/√y

[umbral dome]

,, y^{\frac 12} = \sqrt{y}

[glossy valve]

cloud

[plush heart]

if y=9, then 4.5 = 3?

[umbral dome]

no... $y^{\frac 12} \ne \frac 12 y$

[plush heart]

sorry can u explain to me why y^1/2 = √y

[glossy valve]

cloud

[umbral dome]

https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:exp/x2ec2f6f830c9fb89:eval-exp-rad/v/fractional-exponents-with-numerators-other-than-1

maybe more relevant: https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:exp/x2ec2f6f830c9fb89:rational-exp/v/basic-fractional-exponents

[plush heart]

i seeee

[plush heart]

oh yeaa this is better and explain moree, ty!!

[full forum]

@plush heart Has your question been resolved?

[plush heart]

@umbral dome do u know why (c) from - 1 to log(3) 3?

ik it is because of base of the log is 3, but is it just like that?

look at 1(d)

[plush heart]

look at 1(d), how to do that?

[shy edge]

change 2 to log

den others juz follow the given example

[plush heart]

log(4) √x + log(4) 2 - log(4) y^3

[shy edge]

well not exactly right

[plush heart]

since log(a) a

then log(4) 4?

so where 2 go

[shy edge]

and

[plush heart]

i see

so it become square

so if the question is + 3

[plush heart]

then it would be log(4) 4^3?

[shy edge]

yes

[plush heart]

i see, tysm!!

just learn log yesterday

[shy edge]

from indonesia?

[plush heart]

Malaysia

[shy edge]

wait no

same

lmao

[plush heart]

ahaha

just finished school then otodidak addmath

[shy edge]

oo

form 4 already?

[plush heart]

nah

im 06

who will get spm result at 27/5

[shy edge]

okok gl

[plush heart]

never take addmath in spm but it seems fun

[shy edge]

eh it helps alot in college i would say

[plush heart]

yeaa

[shy edge]

add maths fun

[plush heart]

hope ill get accepted to matrix

[plush heart]

fr

[plush heart]

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[naive monolith]

hi i’m stuck on part b, I have no idea where to start

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[naive monolith]

<@&286206848099549185>

[naive monolith]

<@&286206848099549185>

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[spice vector]

Hi, why the integral is incorrect in my process?

[shrewd hamlet]

how did u integrate from cos^-3 to cos^-4

[spice vector]

oh wait

That's dumb🤣 Thank you

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[little marten]

every variable here is real and positive digits

i need help

[spiral vigil]

start with e

[little marten]

i already found e, which is 6

sorry forgot to tell you

[spiral vigil]

neat! ok so what can you find next?

[thick hedge]

minecraft math ?

[spiral vigil]

rewrite it with 6 in place of e if it helps

[little marten]

roblox

so

2a = 6 and 6 + x = w

so a = 8?

[spiral vigil]

remember that digits might be carried

[little marten]

yea

8+8 = 16 and i carry the 1 into 1+6 =w

so w = 7

[spiral vigil]

ok great

what next

[little marten]

and 6y + 3 = 10x + r

based on the multiplication

[spiral vigil]

3?

[little marten]

i bring 3 since 6*6 = 36

[spiral vigil]

ah. yes.

[little marten]

and 6r + x = 8

[spiral vigil]

you might find it helpful to rewrite the problem with your substitutions

[little marten]

aight. ill do it

r = (8 - x)/6

soooo

y = ( 10x + ( ( 8 - x ) / 6 ) - 3 ) / 6

idk how to use the bot thingy

,help

[glossy valve]

A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!

[grave elm]

Have you already found b?

[little marten]

nope

[grave elm]

I can help with that then

[spiral vigil]

you should be able to find r as well fairly easily

[grave elm]

so first thing to note is r + t = r

therefore t = 0

that's from the addition

[little marten]

yup

[grave elm]

I mean last digit of b*e is t

finally correct

[little marten]

lol

[grave elm]

and t is 0

so last digit of b*e is 0

that means b*e is a multiple of 10

e = 6, so 6b is multiple of 10

do you know what's b?

[little marten]

60

[grave elm]

6b must be multiple of 10, do you understand why?

[little marten]

oh

[grave elm]

consider the prime factorization

[little marten]

no i dont

[grave elm]

okay ill repeat it

by the 2nd line of multiplication, we get that last digit of e*b is t

[little marten]

okay i understand that

[grave elm]

and we have that t = 0 and e = 6

[little marten]

true

[grave elm]

so last digit of 6b is 0

[little marten]

oh

oka

okay

[grave elm]

meaning 6b is multiple of 10

but 10 = 2*5

so 6b must have 2*5 in its prime factorization

6 already has 2, but it doesnt have 5

so 5 must be in prime factorization of b

but only one-digit number with 5 in its prime factorization is 5

so b = 5

and indeed, 6*5 = 30, so it has 0 as its last digit

[little marten]

ooooooh]

yea i totally missed that part

huh

guess i have to use this trick for the next one

[grave elm]

now with knowing b, you can fully utilize the second line of multiplication and find the remaining numbers

[little marten]

prime factorization, got it

hang on

5y + 3 is multiple of 8

should i just 8-3?

[grave elm]

Do you mean it's last digit is 8?

[little marten]

yes

[grave elm]

well, thats true, but it only tells us that y is odd

note that 5 * rye = eat

now think about what r can be

consider just the number of digits

[little marten]

oh eat =680

mb

[grave elm]

oh tahts true too lmao

that simplifies it a lot

[little marten]

136

thank you!

[grave elm]

np

[little marten]

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[chilly beacon]

Hello

[chilly beacon]

Are u there?

. close

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[worn tree]

So I saw this come up in a physics server and I'd like to know what justifies the rewriting of $g^{-1}\partial_{\nu}g$ as $\partial_{\nu}\log g$. I know it's simple chain rule, but wouldn't you also need $g^{-1}$ and $\partial_{\nu}g$ to commute in order for $\partial_{\nu}\log g$ to be a "sensible" rewrite?

[glossy valve]

Vanitas Daemon

Vanitas Daemon

[worn tree]

I'm pretty sure that $[\partial_{\nu}g, g^{-1}] \neq 0$ in general.

[glossy valve]

Vanitas Daemon

[keen vector]

why wouldn't they commute

isn't it just multiplication

[worn tree]

No, g is a metric tensor here.

i.e. a real symmetric, nondegenerate square matrix

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[worn tree]

Oh I didn't read the rules properly. My bad.

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[near snow]

whst the method

[velvet sedge]

https://tutorial.math.lamar.edu/classes/de/separable.aspx

good resource on solving problems like this (separable odes)

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[young python]

helllo

[young python]

I need help

answering a few question from my failed concepts

<@&286206848099549185>

[full forum]

Please post images (such as PNGs or JPGs) of the question rather than other filetypes such as PDFs which have to be downloaded. Non-image downloads can potentially contain viruses or other security risks.

[low echo]

Bro its better you provide screenshots

as there can be danger of malware

[young python]

oh

the pics are on my phone

i will send the ss

[low echo]

Ofcourse

[full forum]

It is suggested that you limit yourself to one question per help channel, opening a new one once your original question is answered and your original channel has been closed. This is to make your channel easier to follow for potential helpers and can bring attention to the fact that your question has changed.

[young python]

can we start with this one

<@&286206848099549185>

[opaque nova]

do you know what a domain is?

[young python]

nope

[opaque nova]

it is fine

[young python]

i forgot since this was taught in the beg of the year

[opaque nova]

in your case, every function f(x) can take an input, and give an output

right?

domain is all possible values that x can be, such that f(x) has a defined value

[young python]

Sure

[opaque nova]

Therefore, say:

$$f(x)$$ = $$\sqrt{x}$$

do you have an idea the domain of f(x)

[young python]

Not rlly

[glossy valve]

violet

[opaque nova]

what do you get if you input a negative value

[young python]

A neg number?

[opaque nova]

if you input -4

you will get:

$$\sqrt{-4}$$

[young python]

F(-4)

[glossy valve]

violet

[young python]

Oh ok

[opaque nova]

which is not real

so

the domain for f(x) is

all Real numbers such that

x >= 0

[young python]

Deal

[opaque nova]

yes

now let f(x) = $$\frac{1}{x}$$

[glossy valve]

violet

[opaque nova]

what is the domain?

[young python]

Set of all real numbers

[opaque nova]

nope

set of all rea numbers EXCEPT 0

real*

[young python]

Ok

[opaque nova]

you got that?

because you cannot divide by 0

[young python]

Right

[opaque nova]

so the basic rules are:

cannot divide by 0
cannot square root negative number

that should be all you need

send one question at a time to ask, if you need to

do you want me to do the first one with you?

[young python]

Btw the reason I sent all of them at once is since the teacher will award bonus points on my grade by the end if the year

[young python]

Yes please

[opaque nova]

$$f(x) = \sqrt{x + 5}$$

[glossy valve]

violet

[opaque nova]

this is Q1

you notice the square root, what do you do?

[young python]

Square it to get rid of the root

Right?

[opaque nova]

No

Don't need to do anything

[young python]

Oh

[opaque nova]

you are not solving

You are finding what values of X will give a undefined value

I told you, that you cannot square root / cube root/ root a negative number

In what cases is x + 5 negative?

[young python]

When it is less than 0?

-5

[opaque nova]

My solution:

We notice that $$x + 5 >= 0$$, as we can only square root a positive number

Therefore $$x >= -5$$

The domain of f(x) is then all real x, such that x >= -5

[glossy valve]

violet

[opaque nova]

my bad, you should instead look at when the thing inside square root is positive

because you want to write what x you can input, not what you cannot input

[opaque nova]

Do you get this?

[young python]

Yeah

I believe the correct answer is 1,3,4,6?

Do you agree ?

[opaque nova]

which question

send the photo again

[young python]

The first

[young python]

...

It is multiple choice

[opaque nova]

it is referencing the whole collection of photos

so I do not know which

[young python]

Oh mb

[opaque nova]

just send the question, I will help

[opaque nova]

1, 3, 5 should be correct

how about 6?

$$g(x) = x^2 - 8x$$

[glossy valve]

violet

[opaque nova]

what is the domain?

[young python]

All real number except 8

[opaque nova]

think again

[young python]

.....

[opaque nova]

what is g(8)

is it undefined?

8^2 - 8x8

=0

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.reopen

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[torn jolt]

I don’t know how to find the equation of a parabola by looking at a parabola

[dark cobalt]

do you have an example

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[thick crystal]

how do they find area 3?

It looks like they're doing radius^2 multiplied by theta

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[thick crystal]

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[rancid token]

i don’t understand how to do question d

[rancid token]

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[prisma grail]

Can someone tell me what I’m doing wrong PLEAAAAASEEE! I’m so bad at math lol I need helppppp

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[barren merlin]

this is part of the last assignment i need to complete in order to graduate online high school and i can’t wrap my head around it. please tell me the regression equation and final answer. thank you so much in advance!!!!

[barren merlin]

<@&286206848099549185>

[sudden spear]

Do you need to do the linear regression by hand, or can you use a calculator?

[barren merlin]

calculator

[sudden spear]

There is probably a linear regression tool on your calculator that could help you find the equation for this set of data

[barren merlin]

i don’t have a calculator. i’m in a bit of a time crush and this is one of the last problems i need to complete in order to graduate. is there any chance you’d be willing to complete the problem for me? id be very grateful 🙂

crunch*

[sudden spear]

You can use Desmos to help you, if you have access to any electronic device

It has the capabilities that a calculator would

You would enter the table into Desmos with the table option, and then use the linear regression expression to try to fit an equation to your data

If you have a set of x-values x₁ and a set of y-values y₁ on Desmos, you can enter the expression y₁ ~ mx₁ + b to get values that would fit the equation y = mx + b

To predict the test score with a test grade of 69, you can plug in 69 into your y = mx + b equation and then solve for the other variable

[barren merlin]

where do i plug in 69 in that?

for x?

[sudden spear]

If x₁ are your homework grades and y₁ are your test grades, then you would plug 69 in for y

And then solve for x

[barren merlin]

put the info into desmos. do i need to round when i put in m and b? i assume the linear regression would be y=0.5x + 31.3

[sudden spear]

It wants you to round all of the coefficients to the nearest tenth

So I'd say yes

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@barren merlin Has your question been resolved?

[barren merlin]

so then how would i find the final answer

[sudden spear]

You would plug in 69 for y in your equation

then solve for x

$69=0.5x+31.3$

[glossy valve]

otheol

[sudden spear]

You would also need to round x to the nearest integer

[barren merlin]

how do i solve for x? i know i have to subtract 31.3 from both sides but that’s it

[sudden spear]

You would need to multiply both sides of the equation by some number to cancel out the 0.5

This number would be equal to $\frac{1}{0.5}$

[glossy valve]

otheol

[sudden spear]

Since this is the inverse of 0.5

And any number times its inverse (except for 0) is 1

Which would get rid of the coefficient of x

[barren merlin]

so 69 - 31.3 is 37.7. does 37.7 x 1/0.5 = 75.4?

so x = 75.4? or did i do the math wrong

[sudden spear]

I believe you are fine

[barren merlin]

says answer is incorrect

oh wait. needed to round the final answer to the nearest integer. not nearest tenth. i got it. thank you!

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[lunar acorn]

<@&286206848099549185>

[torn jolt]

Wait 15m

Nvm

[lunar acorn]

whoops a minute early

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[torn jolt]

how u use algrebra identity on this

[pine egret]

for the first one u can split the middle term

[rough plaza]

well, technically this question is not for identities

I would personally use "Cross-Multiplication method"

[torn jolt]

Oh ok

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[brittle parcel]

How do I solve this problem: "Find the volume of the body T, limited by the cylinder K : x^2+2y^2=2 and from the planes P_1 : z = 0 and P_2 : x + y +2z =2"

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@brittle parcel Has your question been resolved?

[brittle parcel]

@terse terrace

<@&286206848099549185>

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@brittle parcel Has your question been resolved?

[brittle parcel]

<@&286206848099549185>

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@brittle parcel Has your question been resolved?

[brittle parcel]

<@&286206848099549185>

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@brittle parcel Has your question been resolved?

[brittle parcel]

<@&286206848099549185> I think it's been 4 hours

[daring bay]

maybe open a new help channel so your question goes up?

[brittle parcel]

good idea

.close

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[polar hearth]

yo

[polar hearth]

i know that dcb is 120

and dec is 139

someone gv ans pls

[fading onyx]

what is <BDC

can you work that out

[polar hearth]

120

nvm

[fading onyx]

read again

[polar hearth]

sorry

idk how

[fading onyx]

because it's a parallelogram, <BAD + < ADC = 180° must be true

[polar hearth]

fr

so answer is

180 - 60 - 39?

[fading onyx]

what is <BAD

[polar hearth]

180-120

oh

shit

sorry g

its supposed to be 60

so 60-38

so 22

[fading onyx]

yeah now you're on the track

[polar hearth]

dec is 180-41

[fading onyx]

so now one last step

yup

[polar hearth]

so 180-22-139

19]

thx

[fading onyx]

gg

[polar hearth]

appreciate it

can i ask a quik thing

[fading onyx]

sure

[polar hearth]

opposite angles on a trapezium = 180 right?

so does that mean the 2 top angles are also 180

and 2 bottom

(together)

[fading onyx]

that is the only rule i'm aware of

[polar hearth]

ohh

[fading onyx]

and works as long as the sides i marked are parallel

[polar hearth]

are the 2 top equal then?

[fading onyx]

if the trapezoid is isosceles, then yes

only under that condition

[polar hearth]

ok thx

can u help 1 more thing

🥺

just check ofc

i thin k i got it

[fading onyx]

sure

[polar hearth]

umm bdc - 180 - 90 - 20

so 70

abd adc is 180-70 cuz angles strt line so = 110

then x = (180-110) /2

so 35

??

[fading onyx]

thats correct

[polar hearth]

thxx

[fading onyx]

how i'd go is

[polar hearth]

?

[fading onyx]

mark the angle ACD as x

[polar hearth]

ok

[fading onyx]

therefore CDB=2x

and 2x+20=90

[polar hearth]

i understood the 2 x part

not thew other

[fading onyx]

2x+20+90=180

[polar hearth]

yeah

basically same thing

[fading onyx]

yeah

[polar hearth]

ok thx

[fading onyx]

any other questions?

[polar hearth]

btw what r ur pronouns

[fading onyx]

idk

[polar hearth]

💀

[fading onyx]

what vibes do i give off

[polar hearth]

idk

[fading onyx]

yeah

[polar hearth]

i cant tell cuz were texting

maybe female cuz ur pfp is pink

anyway doesnt matter

have a nice day

byee

.close

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[tawdry grove]

uhhhhhhhhhh

[fallow coral]

what have you tried?

[tawdry grove]

what i have in green

[fallow coral]

have you tried plugging into the equations to see if the solution fits?

[tawdry grove]

like plug in x and y's and see which ones match?

[keen vector]

more like plug in y and y' s but yeah

also y'' apparently

[tawdry grove]

wait

[tawdry grove]

how come i can do this

because there are y primes and y double primes

not just standard y's

[fallow coral]

you have already found y'

so you plug in that

[keen vector]

basically y is a function, not a variable

so ur really plugging in y(x), y'(x), y''(x)

and u want it to be true for all x

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[mild jackal]

Need help graphing this

i just need a picture of these 5 points graphed pls

[quick cairn]

polar coordinates ?

[mild jackal]

no

just those right there

i mean these are the polar

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[vale cipher]

I have no idea what i did here.

we did this in class like a week ago and i went on vacation so now idk what i did here...

can someone rexplain each step lol

[wise gate]

Have you studied logarithms?

[vale cipher]

nope.

this is gr 11 math

[wise gate]

You have the equation a^b = 1

Where a = x^2 - 5x + 5

and b = x^2 + 4x - 60

[vale cipher]

right and b should equal 0

[wise gate]

Now, if a and b are numbers, when does a^b equal 1?

[vale cipher]

when b is 0

[wise gate]

There are more solutions

For example 1^2

[vale cipher]

oh

[wise gate]

So a = 1 is another solution

And (-1)^4 too

But for example (-1)^3 not, because 3 is odd

(-1)(-1)(-1) is -1

[vale cipher]

yeah

[wise gate]

So you have three cases:

b = 0
a = 1
a = -1 and b an odd number

And there are no more solutions, you will have to believe that without proof

[wise gate]

So now you apply these cases to the problem

(x^2 - 5x + 5)^(x^2 + 4x - 60) = 1 if:
x^2 + 4x - 60 = 0, or
x^2 - 5x + 5 = 1, or
x^2 - 5x + 5 = -1, and x^2 + 4x - 60 is an odd number

[vale cipher]

oh i see

[wise gate]

And those three cases are here

The first two are just quadratic equations

[vale cipher]

but why did i write beside the x=3 that its odd

[wise gate]

And in the third one, you obtain x = 3 and x = 2, but then you have to see whether x^2 + 4x - 60 is an odd number

[vale cipher]

and and what if it is odd?

[wise gate]

Because 3^2 + 4*3 - 60 is odd

[vale cipher]

because you wrote a= -1 and b an odd number but this is for a

[wise gate]

No, it is for b

[vale cipher]

oh wait

yeahhh

WAIT

so x=3 is correct to use if a = -1

and x = 2 is not

??

[wise gate]

Wait

[wise gate]

I meant even

[vale cipher]

oh

[wise gate]

a = -1 and b an even number

Sorry

[vale cipher]

oh wait yeah yeah

[wise gate]

For example, (-1)^4 is 1

[vale cipher]

ok so x=2 is correct but x=3 is wrong

of a=-1

[wise gate]

^

[vale cipher]

dayum my teacher did NOT explain this properly

alr tysm i get it

.CLOSE

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[paper wedge]

How should I even do this

[paper wedge]

Neither 18 degrees or 36 have known values

[hollow sable]

they do

[paper wedge]

0,30,45,60,90

I don’t know 18 or 36

[hollow sable]

thats the point of the problem

[paper wedge]

So are you able to help me solve the problem?

That’s why I’m asking 😂

[hollow sable]

yeah try to find sin(36 deg)

[paper wedge]

Nice

To solve a problem, you just need to solve it

[velvet sedge]

,calc 360/36

[glossy valve]

Result:

10

[velvet sedge]

real

[hollow sable]

use addition and subtraction formulas

or geometric interpretation

the point is to think

[paper wedge]

💀

Bro I’m trying

If I use addition on 18 degrees, I get only one of the values that I know of

The second would be something over 5,

[hollow sable]

lemme see if there is a good way to find this using addition and subtraction

[paper wedge]

Alright

[paper wedge]

What’s this for? @velvet sedge

[hollow sable]

ok

so we have

x=18
then
sin(2x)=sin(90-3x)

because 2x=90-3x

so

sin(2x)=cos(3x)
now expand using addition formulae and simplify

[paper wedge]

Alr ima give it a try

Thank you

#realOne

Howd u get sin(2x)=cos(3x)?

[shrewd hamlet]

theres no way i wouldve ever thought of this

nice thinking

[paper wedge]

Ye lol

[hollow sable]

sin(90-3x)=cos(3x)

[paper wedge]

Oh I see

Sin(90-y) = cos(y)

This is hard ngl

I’m still stuck trying to expand it with addition or subtraction

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[crisp shoal]

What are lengths of horizontal line and vertical line of rectangle when the total length of bigger rectangle with sum of outer lines being 44 but the rectangles are all same areas

Left side has 3 rectangle and right has 2 rectangle rotated by 90°

[crisp shoal]

The bottom side has one side that is long with short one

Same for upper side

[lofty vine]

A Diagram would help

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@crisp shoal Has your question been resolved?

[olive ginkgo]

You've got 5 small rectangles altogether

6 long sides and 9 short sides

And looking at the outside, you have 4 long and 5 short gives 44cm

So say 4l+5s=44

The areas of the small rectangles are sl, and 5 of them makes one big rectangle, of area (s+l)(2l)

So 5sl=2sl+2l^2

Does that help?

[crisp shoal]

Yes

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@crisp shoal Has your question been resolved?

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@crisp shoal Has your question been resolved?

[mint sequoia]

The final answer is length = 6 units and width= 4 units right?

[crisp shoal]

But is it only solved by brute force

[mint sequoia]

🤔 brute force?

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[rare dock]

do the side lengths need to be integers?

[crisp shoal]

No

[rare dock]

assuming what was said already is correct, you can use 2l(s+l) = 5sl to write l = …

and then substituting l into 4l + 5s = 44 should tell you what s is

[swift fulcrum]

역시 수능 수학은 어렵다

[waxen pagoda]

연립으로 푸는거 아닌가

가로 x 세로 y

위랑 아래는 x+y

왼쪽 오른쪽 3x,2y

왼쪽 오른쪽 같으니까 3x=2y

[crisp shoal]

There's too many solutions for 4l+5s=44

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@crisp shoal Has your question been resolved?

[compact zodiac]

Lol what

Didn't they solve it for you

[crisp shoal]

They found 4l+5s=44 but it is not enough to find both l and s

[compact zodiac]

4l + 5s = 44, and also 2l = 3s

[torn jolt]

fact

[rocky sentinel]

solve

[compact zodiac]

You can solve it yourself

[crisp shoal]

I solved it

[waxen pagoda]

Good Jod

[scenic veldt]

와 한국인이다

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[crisp shoal]

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[odd isle]

I have to proof that the lebesgue measure is distance preserving under isometries. Using the fact that the lebesgue measure is the only distance preserving measure under parallel translation with its measure of the cube [0,1]^n being 1

[odd isle]

I already know isometries are compositions of parallel translations and linear maps

that it preserves distance under parallel translation is given by the definition so I only need to show that the lebesgue measure preserves distance under linear maps

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[odd isle]

<@&286206848099549185>

[odd isle]

this is the solution I stitched together with all the resources I could find:

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[abstract flower]

how do I graph this correctly with the slope as a fraction of the slope?

[glacial pasture]

the slope as a fraction of the slope?

you can draw a line across from a point and a line up - creating a triangle with the main line

[abstract flower]

is what I have tried to do but it gives me an error. I have been trying to build on the examples

[neon fulcrum]

what did u try?

do you understand the question or?

what it's asking you to do

[abstract flower]

“(2.7) and ‘run’ (4.4) I want to know if I am, since the slope of 2/3
indicates that for every 2 units of progress in
𝑥
there is an increase of 3 units in
𝑦
y, which is clearly reflected in the graph.graphing well with respect,

see if I graph well

or can you solve the exercise for me?

[neon fulcrum]

no i dont think that's what is reflected on the graph

actually draw the lines, you're missing something

[abstract flower]

I think I have it

thks

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[last shuttle]

For the sphere $x^2+y^2+z^2=a^2$, why can't you parametrize it like $\textbf{r}(\theta, z) = \langle a\cos\theta, a\sin\theta, z \rangle$, with the z bounds just being $-a \leq z \leq a$?

[glossy valve]

tric

[last shuttle]

I can do it with spherical, but the cylindrical also makes sense because you use the shadow in the xy plane for the polar part and then your z-coord is a variable

[neon crystal]

that would make a cylindrical shell

the limits on z are different at different (x, y) pairs

for example at (x, y) = (a, 0), we need z = 0

[last shuttle]

But since z doesn't depend on theta or the radius, can't you just set z=0?

[red blade]

wtf

[last shuttle]

bro idk whats going on

[red blade]

doesn't z depend on r?

z^2 = a^2 - x^2 - y^2

[last shuttle]

oh uh

oh wait

[red blade]

x^2 + y^2 = r^2?

[last shuttle]

ok ok ok okokokk

dont hate im just stupid

i get it lol

[red blade]

no ur okay

sorry

i was confused too with ur work

[last shuttle]

The reason i was asking was because I was getting the right answer using a cylindrical setup with my integrals

was that just by chance?

for surface integrals

[red blade]

probably

[last shuttle]

well

thank you

💀

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[ripe sierra]

How do I approach this problem? I know how to do some of the mathematical steps but I want to be able to understand what I'm doing

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@ripe sierra Has your question been resolved?

[ripe sierra]

<@&286206848099549185>

[ember shadow]

just plug in those expressions for x and y, then compute x^2 - y^2?

[ripe sierra]

what about part b

[ember shadow]

what is the definition of a subset

[ripe sierra]

for A to be a subset of B, all the elements of A must be found in B

[ember shadow]

yes

so you take an arbitrary element of P. say, (x, y) in P

you want to show that it is in C

what is the condition for an element to be in C

[ripe sierra]

when x^2-y^2=4

[ember shadow]

yes

[ripe sierra]

for (x,y)

[ember shadow]

right. so how can you prove that

[ripe sierra]

the same steps as part a?

let x=e^t+e^-t

and y=e^t-e^-t

[ember shadow]

yes. I'd argue it isn't necessary to redo them

[ripe sierra]

what do we say? "since this satisfies the condition for C, x^2-y^2=4, then P is a subset of C"?

[ember shadow]

if I were writing it, I'd probably say "from part (a), since (x, y) was an arbitrary element of P and we showed that it is also in C, then P is a subset of C" or something like that

[ripe sierra]

ah okay

for the last part, do we choose any elements that are in C but not P?

[ember shadow]

yeah

[ripe sierra]

alright

thanks

[ember shadow]

yw

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[waxen quail]

quick question- this is part of the solution to a "find and classify stationary points" question. i dont understand the use for the last column?

[red blade]

That’s to tell if it’s a saddle point or not

[waxen quail]

helooooo

[waxen quail]

how exactly can i from this?

[red blade]

Yo yo

[waxen quail]

o

[red blade]

@waxen quail

Found something online to summarize!

[waxen quail]

ahh ty!!

ty again

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[vague quiver]

Guys my doubt is in this step
How the sign of inequality changed? [x]<-2
I think this should be instead [x]>-2

[vague quiver]

Guys?

[civic bay]

the best way is to think visually about the graph, you know this is a parabola opening upwards and you know that -2 and 5 are the two zeroes

that must mean that the vertex is between -2 and 5, and to find where the parabola is positive, you are either to the left of the leftmost zero or to the right of the rightmost zero

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[buoyant yew]

Why did they do 0.0013 x 60 x 60 ?

[frozen coral]

to find answer in seconds

instead of hrs

[buoyant yew]

but why 60 twice?

[frozen coral]

1 hr = 60 mins = 60 * 60 seconds

[buoyant yew]

oh my i am stupid

[buoyant yew]

thank you so much!

.close

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[tiny terrace]

Is this something a mod should be pinged for?

[frozen coral]

should be banned fr

[tiny terrace]

Seems gone

[rare dock]

i like how he agreed a mod should be pinged

[tiny terrace]

I know right?

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[violet lance]

i need to find where $A\cup B=\varnothing$

[glossy valve]

R4F43L1006

[paper acorn]

ok... can you translate third and forth option?

[devout valley]

Copy everything and do it in a new channel, though, because

[paper acorn]

oh yeah the bot is dead

[violet lance]

i just need verification if ㄱ is right

[violet lance]

okay

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[peak narwhal]

There is a step in solving this equation where i cannot follow what happens and based on what logic:

9x² - y² = 17

1. Rewrite in factors

(3x-y)(3x+y) = 17

2. Something happens I dont know how or why its possible but it does lead to solutions that are TRUE

(3x-y) + (3x+y) = 17+1

what happens between steps 1 and 2?

[minor crater]

pretty certain it's completing the square

actually nvm

[minor crater]

maybe provide more context?

[peak narwhal]

sure.
So its an exercise on my textbook.

This method im trying to understand the logic beheind why its allowed so i could maybe use it in the future:

after doing the leap from step 1 -> 2 It allows us to solve for x = 3 and we can substitute it to solve y = 8

i just ... Dont understand what happens between steps 1 and 2 😦

does this help at all?

[minor crater]

x and y are integers right?

[peak narwhal]

yea
Maybe actually jiust forget the method

how would we solve the exercise itself if the method above is not reasonable?

9x² - y² = 17 | (instructed specifically to use factoring)

(3x-y)(3x+y) = 17 | how do we solve this with logical steps.

You think perhaps this is more reasonable approach?

[minor crater]

ohhh

i get it

basically

i have no clue how you would see something like this immediately but

[minor crater]

since 17 is a prime, (3x-y) must be 1 and (3x+y) must be 17 or viceversa

basically one needs to be 1 and the other needs to be 17

[peak narwhal]

yea i follow this one yep
or -1 and -17

[minor crater]

yep

so adding them together gives you 17+1

[peak narwhal]

yea this one is the one that drops me from the horse.

[minor crater]

suppose 3x-y = 17 and 3x+y = 1
what does (3x-y) + (3x+y) equal to

[peak narwhal]

So if i try to write it on paper it looks really strange to me:

A*B = 17

A+B = 17 + (1 why how do i know) 😄

[minor crater]

suppose A = 17 and B = 1
what does A + B equal to

[peak narwhal]

17+1

[minor crater]

there you go

if you say A=1 and B=17 it will still be 1+17=17+1

[minor crater]

and i suppose we don't consider these because we have x^2 and y^2 are both positive and 9x^2 > y^2

[peak narwhal]

yea we always end up with positive numbers because of the powers of 2 is what oyur saying right?

[minor crater]

actually the negative values can also be checked here, they just happen not to be roots

nvm they are roots

[minor crater]

x = -3, y = -8 is also a solution

maybe they place a restriction on these values in the problem

[peak narwhal]

I will try to illustrate a little what is problematic for me here still

yea -3 and -8 also work

A*B = 17

Therefore A+B = 17+ A or? B? you see the ?

[minor crater]

in short we can perform this trick because 17 is prime, otherwise this wouldn't be possible / you would have to consider all divisors

[minor crater]

neither? both?

it is 17+1

because we don't know which one of them is 1 and which one is 17, but it doesn't matter in this case

$A+B = \underbrace{17}{A\text{ or }B} + \underbrace{1}{B\text{ or }A}$

[glossy valve]

artemetra

[peak narwhal]

ooo okay i think i get it

let me see

well yea ... a+b = 17 + ("the other")

and in this scenario it can only be 1 because 17 is a prime number (or -1 if the other is -17)

[minor crater]

yes

[peak narwhal]

Would it be a terrible trouble to ask if there would be a less "trick" way to solving this exercise?

actually i can do that on my own time this was plenty of help enough

Ty so much 🙂

[minor crater]

honestly, you'll arrive to this result one way or another

otherwise i don't really see a way tbh

[peak narwhal]

yea. Just a bit of a problem if i need to remember "tricks" to solve then sooon i have a full notebook of tricks and no way of remembering them consistantly hehe

[minor crater]

no problem!

[peak narwhal]

I'l close ty again

.close

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[agile ermine]

image of the point (1,7) after a dilation by a factor of 3 from the x axis, a reflection in the y-axis then a translation of 6 units in the positive direction of the x-axis is

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[tacit siren]

$g_k:A \subset R^n \rightarrow R^m$ bounded and continuous. Suppose the series converges uniformly and absolutely. Then any rearrangement also converges uniformly and absolutely, and to the same limit.

I don't have a question rn, I'll try to just rewrite the proof for the single variable case and ping if I get stuck

[glossy valve]

992HallucigeniaEnthusiast

[tacit siren]

Oh the single variable only proves absolutely

In this book

Okie no biggie

ok so for uniformly

I think it's pretty much the same proof but you write g_k(x)

W/e don't feel like writing it out to check if I'm wrong so neeext question

Give an example of discontinuous f_k converging uniformly to continuous f

maybe f_k = 0 if x = 0 and 1/k in (0,1]

yeah

Ok next

Prove that $\sum_{x = 1}^{\infty} \frac{\sin{nx}} {n^2}x^3$ defines a continuous function on all of $\mathbb{R}$

[glossy valve]

992HallucigeniaEnthusiast

[tacit siren]

Brb

ok guess I should review the relevant parts

Oh

Ez

Prove it's continuous on [-a, a] for arbitrary a by using weierstrass M-Test

Neeeext

Oh boi a 3 part problem

g(x) = |x| on [-1/2, 1/2]

Extend g so it becomes periodic

Define $f(x) = \sum_{x = 1}^{\infty} \frac{g(4^{n-1}x)}{4^{n-1}}$

[glossy valve]

992HallucigeniaEnthusiast

[tacit siren]

a.) sketch g and the first few terms of the sum

I might skip this

b.) weierstrass M-Test to prove f is continuous

c.) prove differentiable nowhere

imma take a break brb

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@tacit siren Has your question been resolved?

[tacit siren]

ok

[tacit siren]

f_2 and f_1

not gonna bother drawing n = 3

[tacit siren]

Oh wait

I f'ed it up

Forgot to sale down g(4x) by 4

[tacit siren]

ok hmmm

To prove it's not differentiable

Suppose it is

Then uhhhh

Show that it converges uniformly which implies you can differentiate term by term

But then show the limit of the derivatives

Isn't equal?

Well

The derivatives can't have equal domain

Cus at every partial sum u get more and more points that aren't differentiablr

So that won't work

Sooooooo

How do we formalize this

Ok hmmmst

gonna study an example in another real analysis book

Ok got it

Neeext problem

Actually U know what imma go take a shower

[tacit siren]

Back

Let A be compact subset of R^n