help-26

[fiery badge]

All parabolas are similiar btw, if you don't have a scale for numbers then the parabola is all parabolas

Just a fun fact lol

[neon iron]

Something like that

[fiery badge]

Oh well since you know the point (4,2)

just plug in x = 4, y = 2 and then solve for a

or any other point

[neon iron]

What do you mean plug in

[fiery badge]

works just aas well

[pastel oracle]

substitute 4 for x and 2 for y

[neon iron]

So it would be 2=(4-4)^2+2

?

[mortal crag]

yep

u can find a

[neon iron]

And what’s a for

I can’t remember

[mortal crag]

iirc it indicates the opening of parabola

if a>0 then it opens upward

[topaz sinew]

@neon iron Has your question been resolved?

[neon iron]

So how do you solve for a

[topaz sinew]

@neon iron Has your question been resolved?

[topaz sinew]

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[silent lichen]

could anyone help me figure out how this book is able to derive the last term in eq. 9.1.6 (cos term)

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@silent lichen Has your question been resolved?

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@silent lichen Has your question been resolved?

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[latent bear]

i’m not sure what to do here

or how to set it up

I was thinking midpoint but it’s not asking me for it

[simple jacinth]

first find the slope

rise over run

[latent bear]

I don’t know how

[simple jacinth]

$y2-y1/x2-x1$

[thorny flame]

the_legend

[simple jacinth]

the 2 and 1 are not the power

[latent bear]

oh I remember that

[rigid nimbus]

$\frac{y_2-y_1}{x_2-x_1}$

[simple jacinth]

use this to find the m in

[thorny flame]

otheol

[simple jacinth]

y= mx + c

[simple jacinth]

thankyou

[simple jacinth]

did you got it

[latent bear]

I got 0.33333

[rigid nimbus]

Be careful

Subtracting a negative

[latent bear]

0-(-2)/-6-0

?

[simple jacinth]

try to keep it in a rational number form

your answer is correct

noiw in y = mx +c

[rigid nimbus]

Indeed

[simple jacinth]

we need c

[latent bear]

I see so it would be -1/3 then

[simple jacinth]

substuting any point from the given two

as y

say

[latent bear]

I don’t understand

[simple jacinth]

i will take first point

in that

y = -2

ATQ

now using y=mx+c

-2 = 1/3(0)+c

c= -2

we got all the values

[latent bear]

what is c

i’m not familiar with that

same thing as y=mx+b

[simple jacinth]

yes

[latent bear]

I see

[simple jacinth]

both are the same thing

the equation is

1/3x-2

[latent bear]

so you took a y value from a point and -1/3 and plugged it into y=mx+b

[simple jacinth]

i took the value of y from the y point of any two point and 1/3 its the m part and x from the point you took y from

[latent bear]

?

[simple jacinth]

yes

[latent bear]

but I thought if I did -1/3(0) it’ll just be 0

[simple jacinth]

yes

[latent bear]

so how would I add it to -2

because I multiply then add it to both sides right

[simple jacinth]

i did not andorstant

[latent bear]

i’m sorry?

[simple jacinth]

see

-2 is on lhs and

[latent bear]

yes

[simple jacinth]

o-2 is -2

so -2 is also on rhs

equality

[latent bear]

would my answer just be 1?

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[solid island]

\begin{flalign*}
    \int \frac{4x^2 + 2x - 1}{x^3 + x^2}  &= \int \frac{4x^2 + 2x - 1}{x(x^2 + x)} &&\\
     4x^2 + 2x - 1 &= \frac{x(x^2 + x)A}{x} + \frac{x(x^2 + x)B}{(x^2 + x)} \\
     4x^2 + 2x - 1 &= (x^2 + x)A + B(x) \\
     4x^2 + 2x - 1 &= Ax^2 + Ax + Bx
\end{flalign*}```

[thorny flame]

Juan

[solid island]

hi guys im studing partials fractions (integrals)

[hollow plover]

Cool

[solid island]

but i dont know if this is correct haha

[solid island]

this is ok?

[hollow plover]

Hey

[solid island]

hey cairo how are you doing !

[hollow plover]

Why didnt you took out x²

@solid island i am fine bro

[solid island]

how?

[hollow plover]

https://brilliant.org/wiki/partial-fractions/

After i explain you, go through this page ok

[solid island]

the thing is that i dont have numbers

i just have letters

[hollow plover]

See we have (4x²+2x-1)/x²(x+1)

[solid island]

ohhhç

you are right

i just took one single x

instead of 2

[hollow plover]

Now we will write it like
(4x²+2x-1)/x²(x+1) = (Ax + b)/x² + C/(x+1)

Next you can do ?

[solid island]

well, the thing is that i dont know how you take a C

its because of the x^2

now we have to pass the x^2(x+1) multiply to (ax + b) and C

to cancel with the denominator

[hollow plover]

If the base is

A quadratic

We need to take the above expression as a first degree polynomial

[hollow plover]

And we need not think what if the base is cubic because there is a theorem that states any polynomial can be factorised into quadratic and linear terms

[hollow plover]

Yeah correct , and then put values of x , or compare both sides to find unknowns A,B,C

[hollow plover]

I recommend this page to.everyone because its very helpful 🙂

[solid island]

one question

you are doing this

    \int \frac{4x^2 + 2x - 1}{x^3 + x^2} &= \frac{A}{x} + \frac{B}{x^2} + \frac{C}{x + 1}

[thorny flame]

Juan
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[hollow plover]

Yeah

[solid island]

or you are not?

@hollow plover

[hollow plover]

yeah

Im doing this you are right

[solid island]

i think i need to google more and i will check better that website

thanks cairio

[hollow plover]

See here there is a quadratic at deno, so the numerator is taken Bx + C

[hollow plover]

Yeah you will learn about the repeated fraction things too from that

and will surely clear all your doubts

Ok bro bye , have a good day

[solid island]

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[slender sonnet]

This is a opend up prism the base is a square need the volume

[hazy pumice]

What do you think the dimension of the square is?

[slender sonnet]

2?

Is the side right

So the base area is 4

No?

[hazy pumice]

No

Look at the vertical dimensions

[slender sonnet]

Ohh 1?

[hazy pumice]

If the height of the figure from the bottom square to the top is 7, and the whole figures height without the two squares is 5, how tall must each square be?

[slender sonnet]

So 1^2*5?

[hazy pumice]

Yes

[slender sonnet]

So the volume is 5?

[hazy pumice]

Yes

[hazy pumice]

Yes

1x1x5 = 5 units^3

[slender sonnet]

Can you help with one more?

[hazy pumice]

Ok

[slender sonnet]

It’s a geometry

[hazy pumice]

Lol, don't say it like that

[slender sonnet]

This is a square o is the center of the circle aswell BD diagnal is 4sqrt2 need to find EB

From this the squares side is 4 right?

[hazy pumice]

No

[slender sonnet]

Wdym no it is

[hazy pumice]

Use Pythagoream Theorem

[slender sonnet]

Its 4

[hazy pumice]

What is (4sqrt2)^2 ?

[slender sonnet]

32

[hazy pumice]

Double it

[slender sonnet]

64

[hazy pumice]

Take the square root

[slender sonnet]

Dude its 32

[hazy pumice]

Make up your mind also no

Sqrt(64) = 8

[slender sonnet]

Please use a calculator

[slender sonnet]

This is 32

[hazy pumice]

$\sqrt{{(4\sqrt{2})}^2 + {(4\sqrt{2})}^2} = 8$

[thorny flame]

Melvin Eugene Punymier

[slender sonnet]

The diagnal is 4sqrt2 not the sides

[hazy pumice]

You just told me the side length of the square is 4

[slender sonnet]

Dide the diagnal is 4sqrt2

[hazy pumice]

Oh

[slender sonnet]

The what is the side of the square

4 right

[hazy pumice]

Ok ok

So then 32 = 2x^2

And yes indeed

Side length is 4

[slender sonnet]

Ok i need EB

[hazy pumice]

Did they give you the radius?

@slender sonnet

[slender sonnet]

Nope

@hazy pumice

[hazy pumice]

Oh

I feel silly

[gritty birch]

you can just work out the radius

[hazy pumice]

The diagonal is the radius

[slender sonnet]

Why is that?

[hazy pumice]

Draw the opposite diagonal. What do you notice?

[slender sonnet]

Got it got it

I feel dumb

For not realizing taht

[hazy pumice]

Oh good, it's not just me

[slender sonnet]

Well anyways thanks

[hazy pumice]

You're welcome

[slender sonnet]

.close

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[candid dove]

if for some given data;
a,b,c,d,...,n; (N terms)

the mean is
(a+b+c+...+n)/N

it's mean deviation would be;

[candid dove]

right?

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[candid dove]

.reopen

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✅

[candid dove]

oh yeahhh it was standard deviation

[teal gust]

yeah

[candid dove]

but i found where i was going wrong over n over

[teal gust]

mean^2

[candid dove]

the mean has to be squared and then subtracted

yaaa

[teal gust]

yeah

[candid dove]

tyy :D

[teal gust]

lol

[candid dove]

xD

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[neon iron]

hi i solved this and only got cos theta equal 48.2 and 331.8 but dont know howw to get the other answer theta equal 0 and 180

[modern rock]

show working

[neon iron]

ok

[modern rock]

jesus

can u explain how u got from line 3 to line 4?

[neon iron]

cuz i cancel sine

[modern rock]

how did u suddenly get 0=-2/3 * cos(theta)

[neon iron]

OhhHhh

[modern rock]

anyways thats besides the point\

i would advise against multiplying and dividing by cos and sin

[neon iron]

Ok so what to do

[drowsy rampart]

well, multiplying is fine

dividing is what is dangerous

first fix your algebraic errors and then ill explain the "trap"

[modern rock]

yes mb, meant to clarify that. What he did was multiply then divide

[neon iron]

3sincos = 2sin?

[drowsy rampart]

good

what would you do next

[neon iron]

sin(-2 plus 3cos)=0

[drowsy rampart]

eyy there you go

[neon iron]

Oh

[drowsy rampart]

remember, ANYTIME you feel like dividing both sides of an equation by some expression E

you have two choices

either move everything to one side and factor (this is safer and recommended)

or you can just divide through by E

but now you must remember to go back and consider the cases where E = 0

this is more dangerous because most people forget

it is easier to split and manage, but you cannot forget that E=0 is possible

[neon iron]

ok ty

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[vapid oracle]

How do I prove this

[half edge]

What have u tried

[vapid oracle]

I started with sin²∅+cos²∅

Idk what to do next

[half edge]

What did u get when u expanded the parentheses

||Inb4 fresh dream||

@vapid oracle

[vapid oracle]

?

[half edge]

.

[vapid oracle]

I got this

[half edge]

Ok here’s the thing

[vapid oracle]

Oh

[half edge]

So now what should u do

[vapid oracle]

(sin∅+cos∅) (sin∅+cos∅)

?

Idk

[half edge]

Yes

Now expand that

[vapid oracle]

Using foil?

[half edge]

Yea

[vapid oracle]

I got it?

[half edge]

Yea

The line before the last line

Why is it = 11

Or are those “

[vapid oracle]

Oh

My teacher said it's just as easier way

To rewrite the other side

[half edge]

What’s that symbol?

[vapid oracle]

"

Or smth

[half edge]

Ah ok yea

Alr u need anything or no

[vapid oracle]

Na

Thx for the help

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[sullen briar]

Answer key says 1440, I’m getting 432, what am I doing wrong?

[sullen briar]

<@&286206848099549185> please I need to sleep soon and I’m cramming for a test help 😭

[unique whale]

How did you try to calculate the task? I don't quite understand what you wrote to the right of the task

[sullen briar]

4P2 is for how many different ways the people who only sit facing forwards have

the thing below shows the possible cases for the remainign 3

being all 3 sit backwards, 2 sit forwards 1 sit backwards and 2 sit backwards and 1 sit forward

[simple jacinth]

use permutaions

[sullen briar]

i did.

[simple jacinth]

use this

[sullen briar]

4P2*4P3

[unborn kiln]

After the 2 people sitting forwards there's 6 seats left to sit 3 people

[sullen briar]

and all fo that jazz

[sullen briar]

so would it be like 6P3

[unborn kiln]

Ye

[sullen briar]

OHHH I SEE

[unborn kiln]

,w P(4,2) * P(6,3)

[thorny flame]

Results provided by WolframAlpha

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

Requested by akumaenjeru

[sullen briar]

ok wait

another question

actually nvm

thx yall

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[frosty bay]

hey

[topaz sinew]

Please don't occupy multiple help channels.

[frosty bay]

.close

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[white igloo]

Find the area of the triangle determined by the y-axis and the geometric representation of the graphs of the two functions.

[white igloo]

My mistake, forgot about the letters

I can't really understand, which one will be the triangle determined by the y-axis and the geo representations of the two functions

[dim pulsar]

Shoelace theorem

[white igloo]

I am in middle school

what the h is that

[dim pulsar]

Uh it's a theorem which calculates area of polygon with points

[white igloo]

oh

umm, I guess no one stops me using it in an exam, right?

[dim pulsar]

Very useful

[dim pulsar]

Yes

[white igloo]

Could you give me the definition of the theorem?

[dim pulsar]

U can memorize it

It's a formula

[white igloo]

the formula **

my bad

[dim pulsar]

https://artofproblemsolving.com/wiki/index.php/Shoelace_Theorem

Very simple formula too, especially with less points

[white igloo]

do you have any other ideas, beside this theorem? I will memorize this, and if we don't have any other methods I will use it

also, my problem is that I can't understand which one is the triangle I am looking for

[dim pulsar]

Well I mean it's the simplest idea but u could draw the triangle

[dim pulsar]

Look at where the lines intersect the y axis

[white igloo]

this would be the triangle

?

[dim pulsar]

Yes

[shut coyote]

You jus need to find the area of this triangle?

[white igloo]

my mistake again, forgot about the letters, again

[white igloo]

yes

[shut coyote]

Alright you know the formula for the area of a triangle right?

[dim pulsar]

,rotate

[dim pulsar]

Let fg be base

[white igloo]

bh/2 and ( ab * bc * sin(abc) ) /2

the letters are just random

[white igloo]

if the triangle is not equilateral or smth

and heron, if we have natural numbers

soo, ( FG * ET ) /2 where ET is perpendicular on FG

[shut coyote]

Yeah

[white igloo]

FG IS 4, ET 1, 4 * 1 / 2, and it's 2 u^2

but the area should be 4 u^2

am I wrong somewhere

[dim pulsar]

EG is not 1

The height is 1

[white igloo]

a typo, my mistake

but still same answer

[dim pulsar]

Ngl I have no idea

[white igloo]

so

[shut coyote]

Area should be 2

Cus bh/2

B being 4 and h being 1

4/2=2

[white igloo]

yea, but in the textbook says that it should be 4u^2

[shut coyote]

Ohhh

[white igloo]

F : [-2;3] - > R, f(x) = 3x-1, g: (-3;4) -> R, g(x) = -x+3

[shut coyote]

U being units right?

[white igloo]

um, yes

[shut coyote]

Alrigh that makes sense

The u^2 would just be a unit of measurement

Don’t worry about that

[shut coyote]

Not sure where you got the 4 from though

[white igloo]

the answers of the exercises are in the back of my notebook

[dim pulsar]

Is there an explanation

[white igloo]

no

that's what I hate about them

just the answer

well they could be wrong, but also they couldn't be

[shut coyote]

Did you plot these correctly?

Maybe the scale might have been wrong

[white igloo]

it's my first time using geogebra

F : [-2;3] - > R, f(x) = 3x-1, g: (-3;4) -> R, g(x) = -x+3

I used the 3x-1 and -x+3

to make the grapf

I don't really know if that's what I am supposed to do )))

[shut coyote]

Yeah the linear equations look about right

I’m 99% sure 4*1/2 is 2

[white igloo]

wait

soo

to determine the intersection of 2 functions

E

in this case

[dim pulsar]

Set the equations equal to each other

[white igloo]

Gf U Gg <=> 3x-1=-x+3

x = 1

[dim pulsar]

Yes

[white igloo]

inverse U there

good

so the x would be one

[shut coyote]

Yep

[dim pulsar]

And when x=1, y = 2

[shut coyote]

And plugging that in f(1) = 3(1)-1

Oops

So yeah the point would be (1,2)

[white igloo]

oh, than there is nothing wrong about how E is placed

but I am very confused

[shut coyote]

Fr

[white igloo]

guess I will just ask my teacher, the textbook might be just wrong

but I have this thing when it comes to math that I ask myself so many questions

maybe I am wrong somewhere

thank you very much for helping me :D

[dim pulsar]

I think the graph is wrong

Alr

[white igloo]

u mean the exercise?

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[acoustic hawk]

74th question

am just confused how to begin with this

[gritty birch]

whenever there's reciprocal and roots, always write it the form of x to the power of something

[acoustic hawk]

thanks

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[whole glacier]

how come he moves sqrt(2) into the division even tho it is always atop in the parenthesis?

[craggy haven]

really hard to read but

$\frac{\sqrt2}2 = \frac{1}{\sqrt2}$

[thorny flame]

hayley

[whole glacier]

the formula is for electric field strength (vectorial) on a point charge Q

[whole glacier]

what really? how does that work?

[craggy haven]

uh try it and see for yourself?

cross multiply?

rationalize the denominator?

take your pick

[whole glacier]

you mean take (sqrt(2)/2 ) * 1/sqrt(2)?

[craggy haven]

no... i mean multiply both sides by ✓2

[whole glacier]

ohhhh

makes sense now that i done it

thanks bro

exit

end

quit

idk the word for it anymore

finish

abrakadabra

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[whole glacier]

.close

never knew

[craggy haven]

you can

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[inner garnet]

hi how/what method did they use to get it such that the det of the big 3x3 matrix is the sum of the det of all those 3x3 matrices

[topaz sinew]

@inner garnet Has your question been resolved?

[inner garnet]

<@&286206848099549185>

[teal gust]

https://youtu.be/h4OSG8A556c?si=4ndz0jGxiWBSRUkr

this should give you an idea

[inner garnet]

ohhh okok i get it

thank u!

[stiff stag]

yo

nvm

[inner garnet]

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[frosty bay]

hey

[frosty bay]

are the numbers on here x or y axis

[loud oasis]

x axis if there's a dx, y axis if there's a dy

[frosty bay]

how do i find the area under the second grey area

like b c bit

i know the coordinates

[haughty wren]

You‘d integrate that function from B to C

On the x axis if you prefer, but the variable choice doesn‘t matter

[frosty bay]

but its not under the curve so how does it work

[haughty wren]

Flip it upside down if you want to have something under the curve. But integration doesn‘t just integrate "under the curve", it‘s "between the curve and the x axis"

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[fiery mirage]

2000 = 8000 * 0.67^t
i know what t is (~3.5), and i understand that this involves logarithms, but i don't understand how

[ivory wave]

is this from a word problem and you need simplify for t?

[fiery mirage]

ah yeah, sorry for little context. it's from a word problem yeah, t is what i need to figure out in it

[ionic oar]

try isolating t

also write 0.67 as 2/3 perchance

[fiery mirage]

i thought i was onto something here but nope 😭 wasn't even close to the answer

really no clue how to isolate t properly :v

[ionic oar]

log of a negative number is haram

in any case, you were meant to divide by 8000

not subtract

[fiery mirage]

ooooohhh

wait

[ionic oar]

[ \f 14 = \left ( \f 23 \right )^t ]

[thorny flame]

Sadie Carnot (η > 1)

[fiery mirage]

i see

[ionic oar]

now you can take the log

[fiery mirage]

but isn't 8000/8000 = 1?

am i dumb or

[ionic oar]

you have 2000 on the other side

2000/8000 = 1/4

on the right yes 8000/8000 = 1

[fiery mirage]

what happens with that 1

[ionic oar]

whats left is 0.67^t or, (2/3)^t

[ionic oar]

just didnt write it

1*anything = anything

[fiery mirage]

OH. THAT MAKES SO MUCH SENSE thank you

i was thinking completely wrong

so it's basically something like this, THANK YOU

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[whole glacier]

i want to find the length of the Hypotenuse through finding DeltaX. alpha/2 and a/2 are given, why do i use the tan(alpha/2) = (a/2) / DeltaX? how does that work?

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[rich star]

How do i do functions like Regression analysis?

[rich star]

Like how do you use F(x)=Kx+M

[gilded musk]

whats the question bro

to know u need to know what k , x and m stands for

[rich star]

Im not that good at english so i may have said it wrongly but you know correlation and regression analysis how do they work?

[gilded musk]

yes but show me your question so i can understand it better so i may help u

[rich star]

Its in swedish

[gilded musk]

aha

ok

jag kan hjälpa dig bättre

då

lol

[rich star]

Aha är du svensk lmao

[gilded musk]

bro du måste lära dig engelska lille bror

[fiery mirage]

har du också NP img eller?

[rich star]

Jag kunde inte regression på engelska

[rich star]

A

[gilded musk]

vänta ska göra klart min uppgift så hjälper jag dig

[rich star]

Jag kan det mesta som man ska i boken som statistik geometry och det andra

Dock regression är jag hemsk på

[static scarab]

regresjonen skal vel bare gjøres med f.eks geogebra?

[gilded musk]

vilken år är det?

[rich star]

2

[gilded musk]

gymnasiet eller 9an?

[rich star]

Gymnasiet

[gilded musk]

aha lol

hjälper dig snart brb

[rich star]

Vi använde inte geogebra, utan miniräknaren

[fiery mirage]

ajt men lycka till bror, jag e helt körd, kan knappt någonting 😭

[static scarab]

ahhh bare jeg som ikke kan svensk

[rich star]

Nej du klarar det säkert

Men asså 3 prov på en dag asså kom igen broder min

4 timmar på sig jag är kokad och bränd

[fiery mirage]

wtf? jag har bara NP o inga andra lektioner. men a jag får hoppas d, blir fest om jag får E 💀

[rich star]

Inshallah det blir E asså

Hoppas på högre men kommer bli glad för ett E

[rich star]

Nej jag menar asså NP det är 3 del prov har inget efteråt

[gilded musk]

bro kolla på en video den här är legit skit lätt lol

tar 3 min och fatta

är det matte 2c eller 2b?

[rich star]

Jag vill inte ha svaret jag vill veta hur man löser ut de

[rich star]

2b

[gilded musk]

ok men ta reda på det jag sa till dig

vad det är för definition för de

för k

x

och m

[rich star]

Ok 👍

[gilded musk]

trodde det var 9an matte lol

läser ingenjör just nu tänkte lol vilken matte är det här xD

[rich star]

Lol men tror du att regression kommer vara A frågor eller E frågor på NP?

[gilded musk]

det finns enkla och svåra

[rich star]

För att regression behöver väl miniräknare

[gilded musk]

men vet ej för jag hade 2C

läste natur

den var 1C för oss om jag minns rätt

[rich star]

Nu fattar jag

Det är skit enkelt

Wtf

😂

[gilded musk]

ja bruv

[rich star]

.close

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[gilded musk]

ekonomer nu för tiden xD

[rich star]

Jag går samhälle xD

[gilded musk]

jag går industriell ekonomi inom ingenjör lol

[rich star]

Tänker gå på tekniskt basår

Behövs för civilingenjör

[gilded musk]

aaaa

[rich star]

Är för sent att byta program nu

[gilded musk]

aaa

men läs bara basår

så kommer du fatta

men fokusera på matten då lol

[rich star]

Ja du

[gilded musk]

om du inte kan grundera

du är körd

[rich star]

Då är man kokad

Men tack för hjälpen dock!

[gilded musk]

np

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[lavish seal]

what did I do wrong in this problem

[knotty ledge]

whats the interest rate?

[lavish seal]

3.56?

Or 0.036?

[knotty ledge]

you're correct in dividing by 100 to convert it to decimal but that wouldn't give you 0.036

[lavish seal]

What number is the interest rate then

Or what number should I divide by 12

[knotty ledge]

where are you getting 0.036 from?

[lavish seal]

3.56 as a decimal

Oh it should be 0.0356?

[knotty ledge]

yeah

[lavish seal]

Got it thanks

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[gaunt tendon]

Could anyone be able to help me with this? im honestly so confused and understand none of it

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[neon iron]

im self teaching math and I wondered if its a good idea to learn real analysis before finishing calc 2 (thats where im at atm) since you learn the same concepts but more rigoursly

[neon iron]

I plan to learn it after calculus either way

[glossy arrow]

Not really. Even though Calc 2 contains theorems that real analysis contain, it is not rigorous enough to prepare you to the proofs in real analysis.

I would say read introductory proof books, or start with elementary linear algebra, move on to advanced linear algebra (that contains proofs)

[quaint badger]

real analysis is not rigorous enough for real analysis?

[neon iron]

so I need linear algebra for real analysis?

[glossy arrow]

Yes.

[quaint badger]

i would disagree

[glossy arrow]

For example Hessian matrices require linear algebra. The proof that contains it stems from linear algebra.

[glossy arrow]

Well its not a dominant part of real analysis.

I mean its not bad to learn it first.

[quaint badger]

linear algebra is completely orthogonal to real analysis imo

no pun intended

[neon iron]

If its not that important to real analysis I can just learn the part needed when I stumble on it

[glossy arrow]

I would say learn more introductory proofs first.

Start with the simple definitions. Epsilon delta definition of limits, etc.

Get comfortable with the abstraction, then start to make your way up to real analysis.

[glossy arrow]

Elementary number theory proofs are kinda introductory

So you can start with those first

Just practice with proofs

Have you done proof writing before?

[neon iron]

Not really but my goal is to understand real analysis not really to prove its concepts by myself

[glossy arrow]

Real analysis is all about proofs.

So you are kinda contradicting yourself.

[neon iron]

But if its needed for understanding I can practice some proofs

So can I start with real analysis after I practice proofs or do I need to finish calc 2 and 3 first?

[glossy arrow]

I would say to be safe, do calc 2 and 3 first.

Practice thinking about "why" it is the case, when you are reading the theorems.

Start with thinking why the theorem is the case.

[neon iron]

thanks

[glossy arrow]

Np.

[neon iron]

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[vivid saffron]

Hello! This is a previous exam in Brazil translated to English. I am not understanding how am I supposed to solve this

[neon iron]

I need help with this question

I’m not sure how to do it

[vivid saffron]

<@&286206848099549185>

.close

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[crude pulsar]

I’m so confused could someone please explain how these questions are done?

[reef fjord]

,tex .exp rules

[thorny flame]

🫎MooseyMooseMooser 🫎

[crude pulsar]

Uh

Okay

[brittle wigeon]

was this a builtin you made

[reef fjord]

no

riemann made it

( a person on this server named riemann)

[reef fjord]

so, for the first one for example

$\f{\left(3^{\frac{1}{5}\right)^{10}}3^{-3}}{9}$

oops

[brittle wigeon]

can u give me the code or something

[thorny flame]

🫎MooseyMooseMooser 🫎
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[reef fjord]

note the rule of the power of power

what does that turn (3^(1/5))^(10) into?

@crude pulsar

[crude pulsar]

Uhh

2

@reef fjord

[reef fjord]

the power will be 2 yes

3^2

[reef fjord]

mhm

and the 3^2 in numerator and denominator cancel (top and bottom of fraction)

so you get 3^-3, which can be further simplified by negative exponent rule

[crude pulsar]

So is that my final answr?

[reef fjord]

what does 3^3=?

[crude pulsar]

27

[reef fjord]

yes

so your final answer is?

[crude pulsar]

1/27

Can u help me with the next one too pls

[reef fjord]

sure

so the next one will require us to use distributivity and power of power rule

[crude pulsar]

@reef fjord

[reef fjord]

wait

you must apply distributivity again

you didn't apply it to (-4x^2)^-3

@crude pulsar

[crude pulsar]

I only applied it to the exponent

[reef fjord]

(-4)^1

[crude pulsar]

Wouldn’t it be -4 ^-3

[reef fjord]

yes

[reef fjord]

but you don't have (-4)^-3 here

[crude pulsar]

@reef fjord

[reef fjord]

yes, that looks good, now, you can apply negative exponent rule to x^-6 and quotient rule to y^6

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[tawny gyro]

public static void CreateTranslation(float xPosition, float yPosition, float zPosition, out Matrix result)
{
    result.M11 = 1f;
    result.M12 = 0f;
    result.M13 = 0f;
    result.M14 = 0f;
    result.M21 = 0f;
    result.M22 = 1f;
    result.M23 = 0f;
    result.M24 = 0f;
    result.M31 = 0f;
    result.M32 = 0f;
    result.M33 = 1f;
    result.M34 = 0f;
    result.M41 = xPosition;
    result.M42 = yPosition;
    result.M43 = zPosition;
    result.M44 = 1f;
}```

is this a correct interpretation of translations?

[tawny gyro]

this is what microsoft has, but I thought the x, y, and z should be in M14, M24, and M34

[quaint badger]

needs more context

[tawny gyro]

these are their definitions

https://github.com/MonoGame/MonoGame/blob/develop/MonoGame.Framework/Matrix.cs

line 1327

[quaint badger]

what do you want to translate?

[tawny gyro]

a vector3

[quaint badger]

and why is stored in the first three columns of row 4?

and how is translating anything?

[tawny gyro]

yeah I thought its supposed to be stored in the last column of rows 1-3

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[brittle void]

uhhhg think i figured it out

[brittle void]

im not 100 since its arithmetic vs geometric so i took a slightly educated stab

[abstract wadi]

it's arithmetic lol. a_n = a_{n-1} + k is how an arithmetic progression looks.

So you are right.

[brittle void]

ah

thanks!

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[fading lance]

I’m not sure if it’s independent or dependent or the send part but would P(X and Y) = 100%

[unborn kiln]

It says P(X and Y) is 0.24

That don't look like 100% to me

[fading lance]

Which one do you think is right?

[unborn kiln]

I'll just say

If they are independent events then
P(X and Y) = P(X) * P(Y)

[golden blade]

exactly so ask yourself if the equality holds what Akuma stated

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[lucid blade]

I dont know how to do this at all I need like a full run through ngl

[somber socket]

Isn’t the area of just (d1 x d2)/2

Because if a recall a kite is just half a rectangle

You see

like if you reflect the triangles

@lucid blade

[lucid blade]

I just multiply those 2 and divide it by 2?

@somber socket

[somber socket]

ye

[lucid blade]

why is that easy af 😭

[somber socket]

hardest part is finding the formula

[lucid blade]

how do I do these 3

stupid ah word problems

<@&286206848099549185>

heeeeelp

or im bouta blow

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[glass wolf]

can someone tell me what I'm doing wrong?

[normal tapir]

can you explain how you got 3 for #1

[glass wolf]

f(x) graph when x goes to 1 is 2 and g(x) when x goes to 1 is... oh. its dne-

[normal tapir]

yup

[glass wolf]

ahhhhhhh

thanks

[mental basin]

the limit of a sum is equal to the sum of limits

the right graph has no limit against x=1

so the overall limit also DNE

[marsh verge]

The first one doesn't work out as we are analyzing the limit approaching 1 from both sides for fx and gx, in gx the limit approaches a different point from either side, there for it does not exist, so the overall limit mist the "Does not exist"

[glass wolf]

gotchu, i realized

[south scarab]

I don't think the limit exists for #1

[mental basin]

the other answers seem correct

just the first one that's off

[marsh verge]

The rest seems correct

[south scarab]

All the rest is correct just #1 yea

[normal tapir]

guys i think there's an issue with his answer to question number 1. it seems the answer to lim f + g = 3 is incorrect.

[glass wolf]

yeah it worked when i put DNE

uh how do i close the channel when I'm done with the question, or does it automatically go to the next person who needs help

kinda new to this

[normal tapir]

.close

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[glass wolf]

ah

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[autumn sparrow]

Is this how I would draw the graph for sin=-1/3 (given that it's in quadrant 3)?

[autumn sparrow]

and if so, would the side length be -√8 or √8?

[sterile finch]

Looks good to me.

[keen venture]

The length of that side is √8, but the point on the x-axis it reaches is x = -√8

Lengths aren't crazy important in the unit circle, points are

[autumn sparrow]

so if I were to label it I would use -√8 and if it asked for the cosine ratio I would use -√8/3

[topaz sinew]

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[sterile finch]

Yes.

[topaz sinew]

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[topaz sinew]

@cedar surge Has your question been resolved?

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[topaz sinew]

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[coarse frigate]

honestly im not sure to use demand-side policies if they've been made redundant

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[coarse frigate]

<@&286206848099549185>

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@coarse frigate Has your question been resolved?

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[neon iron]

how is this a math problem???

also, it seems like you're cheating on an exam or something

[tender swallow]

this is not maths

[vague path]

Maybe relocation

Like if the government promoted relocation to areas where the industry is still active?? Idk

Im not sure

[topaz sinew]

@coarse frigate Has your question been resolved?

[tender swallow]

immigration/emigration?

[vague path]

no like domestic

Migration

[tender swallow]

oh

[topaz sinew]

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[neon iron]

for the ODE[
4\dnv2[y]t + 20\dv[y]t+y = 20, \q \6y0 = 10. \q \dv[y]t = \412
]
i get the general solution [
\6{y_c}t = 20 + A\6\exp{\8{\4{-5+2\36}2}t} + B\6\exp{-\8{\4{5+2\36}2}t}
]

[neon iron]

but like im surely doing something wrong here because like

this feels sus

[knotty ledge]

,w solve 4y''(x) +20y'(x) + y(x) = 20

[thorny flame]

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Requested by icaird

[neon iron]

these are the options so im evaluating the coefficients wrongly

somehow

[knotty ledge]

,calc 5/2 + sqrt(6)

[thorny flame]

Result:

4.9494897427832

[neon iron]

yeah

but like

about the coefficients

ok this seems like a precision problem

ok still not the same coefficients

[knotty ledge]

Did you use -4.95

[knotty ledge]

💀

Wolfie solves it fine

With rounding

[neon iron]

damn

[neon iron]

wait what are the coefficients

then

[knotty ledge]

,w solve a + b = 10, -0.05a - 4.95b = 0.5

[thorny flame]

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[knotty ledge]

Lol

[neon iron]

,w 500/49

[thorny flame]

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Requested by qylooo

[neon iron]

damn

rounding error

[neon iron]

ok so i guess number 1 here then

[knotty ledge]

It'd probably crunch it with it written explicitly too

Yeah I mean you van just look at signs and which one is closer to 10 lol

[topaz sinew]

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[neon iron]

hi i am stuck on tan^2(360- theta)-sin^2 theta = (1-sin^2 theata)(tan^2(360plus theata))

[versed cairn]

u can change those angles into theta only

make it easier

either use the formulas or use a unit circle

lets consider
tan(360-theta)

[neon iron]

is it 1/tan?

[versed cairn]

360-theta lies in quad 4

and in quad 4 tan is negative , also note that 2pi (or 360) is 1 revolution (or 1 complete circle) that means the value of tan repeats

[neon iron]

Ok

[versed cairn]

so tha(360-theta) can be written as -tan(theta)

for cos(90-theta)

check where the angle lies

cos doesnt repeat it values after 90 degrees btw but we can write that as sin

ill explain this via graph

[neon iron]

ok

[versed cairn]

explaing using the cos(a-b) formula is easier tbh

but ill try my best with this as well

dont mind the red line

cos 90 = 0 sin0 = 0
cos 89 = 0.017 sin1 = 0.017
cos 88 = 0.034 sin2 = 0.034

so on

so that means
Cos(90-theta) = sin(theta)

i hope u under stood it (ask again and ill explain again but better ig)

[neon iron]

ok i think im understand

[versed cairn]

samething with the rest

just remember if the angle is 90 , 270 , 450 , 630 etc then the trig flips (sin to cos , cos to sin , tan to cot , ccot to tan)

if angle is 180 , 360 , 540 etc then trig doesnt flip (sin is sin , cos is cos , tan is tan , cot is cot)

[topaz sinew]

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[topaz sinew]

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[stark panther]

not sure what it means by code value

[restive inlet]

i suppose they want you to do something like express those points as $20 + d_n$

[thorny flame]

ℝαμΩℕωⅤ

[restive inlet]

so instead of adding 19 two digit numbers,
you'd have
= 20 * 19 + (sum of a mix of 19 positive/negative one digit numbers)

[stark panther]

yeah i was thinking something like that

weird though

so i would do 6 -3 -1 + 0 -2 + 3 etc

then add that result to 380

[restive inlet]

yes

[stark panther]

ok thanks

.close

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[opal kayak]

why is math soo hardd?

[topaz sinew]

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[stiff stag]

it is not hard when you understand wat ur doing

[opal kayak]

idk but its pretty hard for me 😭

[stiff stag]

oh ur muslim

[opal kayak]

yea ngl

[stiff stag]

i will send u a link of this website its helpful

u can see my name lmao

salahudeen

😂

[opal kayak]

yea 😆

[stiff stag]

i sent u a link in dms sister

math is not hard

this man will break it down

he has all the steps

[sterile finch]

Higher level math is very unforgiving if you do not understand the prerequisite material.

[stiff stag]

that one ye

[sterile finch]

Learning the terminology is also beneficial. It not only helps you to contexualize a math problem in your head, it also enables you to ask a proper question when you need help.

[stiff stag]

right

idk why ppl skip textbook tho

tbh