help-19

[thick pine]

OH

[cold swift]

sin(pi)=0

[thick pine]

nice

[cold swift]

so essentially what we figured out was what we needed to input into sine

to get 0

but since our input in the sine is 6x

we have to set 6x equal to the values we found

and solve for x

and that’ll be the answers

[thick pine]

oh sweet thats not too hard

THANK YOU SO MUCH

[cold swift]

yw!

[thick pine]

.close

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[mystic saffron]

prove that α || β

[quick river]

what did we know

[mystic saffron]

?

[quick river]

only 120 degree?

[mystic saffron]

everything we known is in picture

[quick river]

oh sorry

[mystic saffron]

well you see idk how to cal like single lines

the black ones

they are the same

[quick river]

I think the condition are too less

I need at least one more angle at B

[mystic saffron]

we got 3 angles tho?

[quick river]

why 3 angles

only two

oh wait

you mean these two are equal?

[mystic saffron]

i made them by color

[quick river]

did we know they're all equal to 60 degree?

[mystic saffron]

all we know that there is that 120 black angle and two equal red angles

thats it

[quick river]

then it is solved

[mystic saffron]

?

[quick river]

wait a minute lemme label them

It's hard to tell you rn

[mystic saffron]

alr

[quick river]

oh wait we needn't

so we knew that $\angle cb() = \angle ABb$ right?

[clever fjord]

e_waste

[mystic saffron]

i think you mean the red angles

yes

[quick river]

cuz $\angle Bbc + \angle cb() = 180^\circ$

the cb() means the red angle below

[mystic saffron]

c is the line or segment or whatever its called in english

that goes thro both lines right?

since you typed it as small c

[quick river]

You look at Bb

[clever fjord]

e_waste

[quick river]

so $\angle Bbc + \angle ABb = 180^\circ$

[clever fjord]

e_waste

[quick river]

proved.

[mystic saffron]

tf

is

Bbc

[quick river]

the one that is equal to 120

[mystic saffron]

that is BDC

[quick river]

holy shit it is BDC

[mystic saffron]

yes men

[quick river]

never mind

[mystic saffron]

bbc like big black curtains

[quick river]

you understand?

[mystic saffron]

or smth

yes

white boy

thanks

[mystic saffron]

would it be so a||b?

@quick river

since we need to prove that a || b

[quick river]

yes

it belongs to the parallelogram axiom

[mystic saffron]

okay thanks white man

wtf

chinese boy

has access to internet

.close

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[dawn coral]

yeow can anyone do my homework😭😭

[mystic saffron]

Yes, but we expect you to

1- be more specific about what question you need help with, as we cant assist you with an entire page of questions at once

2- explain what you are confused by and if you have tried anything so far

[dawn coral]

confused by quite literally everything

i sleep in this class and i never attend school

but i’m failing so i need to atleast turn some things in

[mystic saffron]

https://youtu.be/Ft2_QtXAnh8?si=clBS4evOXJd7ifac

Give this video a watch then? very informative and relevant to what you are doing. Try taking notes as you go

[timid cairn]

You can at least fill out the chart

[dawn coral]

alright

i’ll try

[odd edge]

@dawn coral Has your question been resolved?

[idle patio]

hi

can you please help me with the cauchy theorem?

[odd edge]

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[heavy flax]

@fleet frost sorry i was in class so couldn't respond, what did you mean by plugging in rounded numbers?

[heavy flax]

oops

@sharp tusk

my bad

what do i round it to?

5th decimal place or something?

[sharp tusk]

rounded numbers are 6,9,2 isnt it

given in the question

[heavy flax]

it told me to approximate

oh i just plug in 6 9 2 and 11?

well, just 11 for everything

since sqrt121

[sharp tusk]

L(x,y,z)=f(a,b,c)+fx(a,b,c) (x-a)+fy(a,b,c)(y-b)+fz(a,b,c)(z-c)

where, for this question,
a=6
b=9
c=2

[heavy flax]

alright thanks

[sharp tusk]

Then you put the normal values here

[heavy flax]

yeah i'll try that rn, let me just set up the equation again...

wait @sharp tusk isn't it just 11??

[sharp tusk]

no

[heavy flax]

the xyz's cancel out

[sharp tusk]

it shouldnt

can you show your work?

[heavy flax]

(6-6) (9-9)

[heavy flax]

here

[sharp tusk]

Oh no

[heavy flax]

the numbers inside the brackets cancel out to 0

i don't plug in 6/9/2 for those?

[sharp tusk]

After founding L(x,y,z) you put the original values there

for x,y and z

you are trying to find L(2.03,8.98,1.99)

[heavy flax]

so i plug in 2.03, 8.98 and 1.99 for the place where it almost cancels out to 0?

[sharp tusk]

Yes

[heavy flax]

like this?

[sharp tusk]

Yes that seems right

[heavy flax]

thanks

got it

[sharp tusk]

you are welcome ^_^

[odd edge]

@heavy flax Has your question been resolved?

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[wintry viper]

how do i answer this?

[wintry viper]

im super confused

do i just do n = k

n = k + 1

n = k - 1

then cube them all

[leaden oracle]

Just substite in (x+n)^3 where x is a multiple of 9 and n from 0 to 8 so you will find the remains of each remainder

[wintry viper]

but it wants me to show for all cubes numbers

so should it just be for k or just any integer

[odd edge]

@wintry viper Has your question been resolved?

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[untold valley]

I was wondering where I went wrong with this question

[untold valley]

I ended up with the yp being -xe^x+lnx(xe^x)

the correct should be this

[sharp oak]

xe^x is part of the homogenous solution, and doesn't add anything to the particular solution

Your answer is "correct" in the sense that this yp does indeed satisfy the DE. It does have a redundancy though

[untold valley]

I am not entirly sure how my prof got the solution she did

since my goal was to match her solution since I am studying for an exam

[odd edge]

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[timid tapir]

dv/dt = 2dr/dt
i took the first derivative making it
4pir^2 = 2dr/dt
not sure where to go from here

[narrow cove]

Unless I'm misinterpreting your workings, dv/dt isn't 4pir^2, that's dv/dr

Might find that when you use the chain rule to turn dv/dr into dv/dt, dr/dt comes into play

[timid tapir]

Oh

Okay hold on

alright i'm back sorry my dad was calling me

[timid tapir]

so dv/dt = dv/dr * dr/dt

[narrow cove]

Yee

[timid tapir]

dv/dt = dv/dr * dr/dt
dv/dt = 4pir^2 * ...?

how would i go about calculating d of r with respect to t?

[narrow cove]

But you also know dv/dt = 2dr/dt

dv/dr * dr/dt = 2dr/dt

[timid tapir]

i'm not sure i follow

[narrow cove]

You're happy that dv/dt = 2dr/dt from the question?

[timid tapir]

Oh is that wrong

[narrow cove]

No, that's right, we need that information lol

You've correctly identified now that dv/dt = 2dr/dt and also that dv/dt = dv/dr * dr/dt

[timid tapir]

Wait i'm confusing myself now

[timid tapir]

i see

[narrow cove]

We know dv/dr = 4pir^2

It's effectively simultaneous equations it just looks scary because it's derivatives

Substitute dv/dt = 2dr/dt into your second equation

And you get 2dr/dt = dv/dr * dr/dt

[timid tapir]

oh okay i see

[narrow cove]

So 2dr/dt = 4pir^2 * dr/dt

What could we do next?

[timid tapir]

uh a little silly question i because i think i'm confusing myself

i know i wrote dv/dt = 2dr/dt
but i'm seeing it now and why isn't it 2dv/dt = dr/dt? the volume is supposed to be increasing at 2x the rate of the radius not the other way around right?

[narrow cove]

Ye the rate of increase of volume (dv/dt) is twice the rate of increase of radius (dr/dt)

Say dv/dt = 2, we know that is twice as big as dr/dt, so dr/dt is 1

[timid tapir]

right, i get that

[narrow cove]

If 2dv/dt = dr/dt that would imply dr/dt was twice as big as dv/dt

Plug some numbers in and see what happens

[timid tapir]

alright, give me one sec, sorry for being stupid haha

[timid tapir]

Oh, i see what you mean now, i had the wrong idea

[narrow cove]

If you were stupid you wouldn't currently be doing calculus so I wouldn't be worrying about that lmao

[narrow cove]

So back to where we were, 2dr/dt = 4pir^2 * dr/dt

What next

[timid tapir]

we could divide both sides by dr/dt?

or 2dr/dt

[narrow cove]

Exactly, assuming dr/dt =/= 0

2 = 4pir^2, and now we are free of calculus and just need to solve for r

[timid tapir]

r = sqrt(1/2pi)?

[timid tapir]

Important thing to note, thanks

[timid tapir]

hoping i don't mess up on basic arithmetic

[narrow cove]

yee

[timid tapir]

i see, so the final answer is r = sqrt(1/2pi)?

oh wait simplest surd form

so multiply it by 2pi/2pi

[narrow cove]

I just left it as $\frac{1}{\sqrt{2 \pi }}$

Latex is not on my side

[clever fjord]

TayBee

[timid tapir]

Oh i see

[narrow cove]

Never enough brackets

[timid tapir]

is that the simplest form though?

[narrow cove]

I mean I think it's more simple than what you get if you rationalise lol

[timid tapir]

Yeah i was just about to suggest that

[narrow cove]

And also is it really rationalising as you end up with pi on the bottom regardless XD

[vapid needle]

or just sqrt(2pi)/2pi

[vapid needle]

pain

[narrow cove]

Ye if your teacher is scared of surds on the denominator then this is the way

[vapid needle]

ye

[timid tapir]

you multiplied by 2pi/2pi right?

[vapid needle]

by the square root

on top and bottom

[timid tapir]

oh yeah, forgot to include that

[vapid needle]

that's probably the most simple forme

or you gonna do

(2pi)^-1/2

ye

do that

[timid tapir]

sqrt(1/2pi) x sqrt(2pi)/sqrt(2pi)
= sqrt(2pi)/sqrt(2pi)^2
= sqrt(2pi)/2pi works

according to the website

is my working alright?

should've probably used the latex thing, not sure how to though

[vapid needle]

this is more fancy

it's just beautiful

[timid tapir]

problem seems to be solved thanks tay!

[vapid needle]

how do yu use this latex thing

[timid tapir]

well it's more so what my teacher prefers tbh

[timid tapir]

i think $ is its command symbol

other than that i have no clue

[timid tapir]

thank you too nrf!

[timid tapir]

is my working correct for this though?

[vapid needle]

$(2𝝿)^-1/2

bruh

[narrow cove]

$ either side, https://tug.ctan.org/info/undergradmath/undergradmath.pdf for a little bit of syntax

[vapid needle]

$(2𝝿)^-1/2$

[clever fjord]

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

[vapid needle]

it didnt read the pi

rip

$(2pi)^-1/2

$(2pi)^-1/2$

there

[narrow cove]

$2\pi ^{-\frac12}$

[clever fjord]

nrf

TayBee

[narrow cove]

[vapid needle]

yes

[narrow cove]

Greek letters need sneaky \ beforehand, they're all on that sheet

I did forget the brackets around the 2pi but we all know they're there in spirit

[odd edge]

@timid tapir Has your question been resolved?

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[velvet cedar]

how

[vapid needle]

for 2 lines/ functions to be perpendicular

the product of their slope needs to be -1

for example f(x)=2x and g(x)=-1/2x

get it?

[velvet cedar]

imma be honest not rlly

do i put the equations of the line like isolate y

[vapid needle]

you know what a slope of a function is right

[velvet cedar]

no i dont

sorry

[vapid needle]

idk if I can help you then sorry

[velvet cedar]

why

[vapid needle]

you have to know what a slope is

[velvet cedar]

obv ik what a slope is

[vapid needle]

f(x)=6x

what's the slope

[velvet cedar]

6

[vapid needle]

good

now you have a line passes through 3;9 right

[velvet cedar]

yuh

[vapid needle]

so x=3 and y=9

[velvet cedar]

oh so

find slope using the formula

like

[vapid needle]

ye

find the slope of the first line

[velvet cedar]

its 0 no?

[vapid needle]

let me check

[velvet cedar]

i think its the first one

bc i got -2/0

[vapid needle]

how does a line have 2 different images for the same point

[vapid needle]

that's undefined I got it aswell

[velvet cedar]

huh

[vapid needle]

like

[velvet cedar]

wait so

is it the first

[vapid needle]

f(3)=9 and f(3)=7

how

[velvet cedar]

what are u talking ab

[vapid needle]

1 point has 2 different images

and its a single line

[velvet cedar]

i dont get what u mean but is the answser the first one then

nvm it is

[vapid needle]

nvm

its the first i think

ye it is

wanna see how I did it

[velvet cedar]

na i got i gng

[vapid needle]

word

good luck with ur stuff

[velvet cedar]

preciate it

[odd edge]

@velvet cedar Has your question been resolved?

[odd edge]

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[drifting pine]

Can someone help me with part b

[proper obsidian]

Help me please

[drifting pine]

Try a

Also, if a help thing is taken, don’t ask your questions in it, find an unclaimed one

@proper obsidian

[proper obsidian]

Uhm ok

[drifting pine]

<@&286206848099549185>

[mystic saffron]

I think HL

I didnt knew about it 💀

Its like RHS rule

[drifting pine]

.close

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[proper obsidian]

THANKSSS

[odd edge]

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[odd edge]

Please don't occupy multiple help channels.

@proper obsidian Has your question been resolved?

[odd edge]

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[lavish spade]

need help with those 3 on the table

[rose mist]

is that 16 to the power of -3/4?

seems a little blurry just want to confirm

[lavish spade]

yes

same with the 16^1/4

[vapid needle]

question 3 or 4

im guessing 3

[lavish spade]

yea

[vapid needle]

ok so

you know the power rules right

[lavish spade]

sort of

[vapid needle]

for example

(x^y)^z

$(x^y)^z$

[clever fjord]

nrf

[vapid needle]

yeah this

@lavish spade

[lavish spade]

nah

[vapid needle]

bruh

its x^(y×z)

[lavish spade]

ok

[vapid needle]

now you use it

you have 16^(-3/4)

we notice that -3/4=-3/2×1/2 right

[lavish spade]

yea

[vapid needle]

now you have the power as a product

[vapid needle]

so you can put it like this

which one is easier

(16^1/2)^-3/2 or (16^-3/2)^1/2

[lavish spade]

16^-3/2^1/2

[vapid needle]

how would you do it

do you know what 16 to the power -3/2 is

or 16^1/2

[lavish spade]

yea

[vapid needle]

wym

whuch one do we know

16^-3/2 or 16^1/2

[lavish spade]

16^1/2 is 8

[vapid needle]

no

x^1/2 is sqrt x

the square root is basically power 1/2

[lavish spade]

so 4

[vapid needle]

yeah

now what do we get?

[lavish spade]

for what

[vapid needle]

like the whole yhing

we haw (16^1/2)^-3/2

what do we get now

[lavish spade]

4^-3/2

[vapid needle]

right

now what's -3/2

you always need to search for that 1/2

[vapid needle]

in terms of a product lf 1/2 × x

[lavish spade]

1/8

[vapid needle]

wym

like

multiply something by 1/2

to get -3/2

in other words; solve the equation 1/2 x= -3/2

[lavish spade]

-3

[vapid needle]

righy

so now what do we get

[vapid needle]

from here

[lavish spade]

4^-3

[vapid needle]

-3 multiplied by something

to get -3/2

we had 4^ -3/2

[lavish spade]

1/2

[vapid needle]

yeah

now re write the whole thing

[vapid needle]

from here

[lavish spade]

4^1/2

[vapid needle]

you keep forgetting the -3

[lavish spade]

whats that gotta do with anything

[vapid needle]

run it back

you have 4^-3/2 right

[lavish spade]

ye

[vapid needle]

now whats -3/2

as a product

you solved it earlier

[lavish spade]

-3

[vapid needle]

so ur saying

-3=-3/2

[lavish spade]

no

im lost

[vapid needle]

-3/2=1/2 x

do you agree with this

[lavish spade]

yea

[vapid needle]

you solved for x earlier right

[lavish spade]

yea

[vapid needle]

and we got x=-3

so -3/2=-3×1/2

then we can imput it into our thing

we get

4^(1/2 × -3)

right

[lavish spade]

yea

[vapid needle]

do you remember the rule we used

we said that x^(yz)= (x^y)^z

now we have x as 4

y as 1/2

and z as -3

[lavish spade]

yea

[vapid needle]

make 4^(1/2 × -3) as (4^y)z

how would you do it

its (4^1/2)-3

4^1/2 is 2 because sqrt 4 is 2

so you get 2^-3

which is 1/2³

which is 1/8

[rose mist]

wtf...

isn't it easier to recognize that 16 = 2^4

[clever fjord]

misha

[rose mist]

the same approach can be used for the other one

[clever fjord]

misha

[vapid needle]

idk if he knows the 1/4 power

root of 4

oh yeah u right

[rose mist]

to solve 1/4, again recognize that 16 can be written as 2^4

[clever fjord]

misha

misha

[rose mist]

we need this to be equal to 1/4

[clever fjord]

misha

[rose mist]

now we can infer that 4x = -2

x = -1/2

[clever fjord]

misha

[odd edge]

@lavish spade Has your question been resolved?

[vapid needle]

I'm sorry but you looked a little scjizophrenic 😭

[odd edge]

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[mellow tide]

Help.

[odd edge]

Please don't occupy multiple help channels.

[lavish spade]

how do you known that from that

above

[rose mist]

it is just comparison

[odd edge]

@mellow tide Has your question been resolved?

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[bright quarry]

Hi can someone plese help me find these surface area of these prisms?

[bright quarry]

i figured out H)

not sure about g tho

[dull fossil]

use pythagores to find that third side of the top triangle

and you know area of both the triangular bases would be simply 1/2 x 9 x 40

add the area of the 3 rectangles in that

[dull fossil]

42 x that third side u find

[bright quarry]

the 3rd side is the hypotenuse right?

[dull fossil]

yea

[bright quarry]

so its 41

long

[dull fossil]

yea

[bright quarry]

so then that bottom face is 41 x 42

[dull fossil]

bottom face?

that's a triangle

u mean the front face

[bright quarry]

yeah

sorry

[dull fossil]

yeah

we have 3 faces all rectangles of 41x42

and 2 triangles

ezpz

[bright quarry]

ah isee

[dull fossil]

wait no

other 2 rectangles have different lengths

[bright quarry]

yeah

40x42?

[dull fossil]

9x42 and 40x42 and 41x42

yeah

[bright quarry]

yes

ok thank you

[dull fossil]

[bright quarry]

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[topaz stone]

,rotate

[topaz stone]

Need help for b

[cobalt viper]

am I trippin or does it mean area of the tray

[topaz stone]

Idk 💀

Just need help for b and c lol

[cobalt viper]

volume is 3d

thats a 2d shape

so it must be area

[topaz stone]

Really...

[cobalt viper]

yea

[topaz stone]

Well if it's area wouldn't it be the same answer as A then?

[cobalt viper]

is it?

[topaz stone]

Idk

[cobalt viper]

check the answers

[topaz stone]

Just need help for b and c 😦

[cobalt viper]

how can you find the volume of thaht

theres no third dimension

[topaz stone]

<@&286206848099549185>

[cobalt viper]

volume as we know is length times width times height

theres no width 💀

[topaz stone]

.close

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[unique viper]

imagine we have a half circle with the diameter of 100, we'd want to draw a triangle which goes from the leftmost point to a point on the circumference then to the rightmost point and we'd want this to be as large as possible. How would i go about solving it? (ill draw a picture)

[chilly epoch]

Do you mean triangle with largest area?

[unique viper]

nope with the largest lenghts, from A to B then to C

like what would be the largest lengths possible

[swift rock]

if u want an triangle to be as large as possible , that does mean that it needs to have large area

[fluid tundra]

so largest perimeter?

[unique viper]

no just the lenghts (the number A to B to C to be as large as possible)

[swift rock]

ok so make equations from the given data

[unique viper]

yes but without going A to C

[chilly epoch]

you can take one side as x and then another side will be sqrt(100²-x²)

[fluid tundra]

then u say "maximize AB + BC"

[chilly epoch]

y=x+sqrt(100²-x²) maximise this func

[unique viper]

mb english isnt my strength lol

[unique viper]

tyty

[fluid tundra]

no worries i was just informing

[unique viper]

tyty

aight ty lot so much

.close

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[weak kindle]

How do i know if a quadratic equation is always positive at first look without doing any calculus?
Such as (2x^2 -x +1)?
Cause the only method i know is by checking the ∆ sign: if it's positive then the equation has 2 solutions, if equals to 0 then it has to solutions that are the same and when it's < than 0 it is always positive or negative.
Also, why can i say that is always positive or negative if < than 0?

[weak kindle]

That's just to speed up my calculus skills douring math tests

[tulip mica]

u can try completing the square to check if it is always positive or always negative or alternates

[modest nacelle]

What is the determinant?

[weak kindle]

you mean like checking if the expression is such (a+b)^2?
Cause this is only a particular case

[tulip mica]

nope

let me show for 2x^2-x+1

[weak kindle]

The discriminant of the expression i gave is negative, so it means that the expression is always negative OR positive but since the sign of 2 is positive then the expression has x € R

[tulip mica]

(√2x)^2-(2)(√2)(1/2√2)(x)+1/8+7/8

= (√2x-1/2√2)^2+7/8

We know that, (√2x-1/2√2)^2 >= 0

thus, (√2x-1/2√2)^2+7/8 > 0

thus, (2x^2 -x +1) > 0

[weak kindle]

Yea, that's a good other way to solve it and it's cool but it requires quite more calculus than calculating ∆

[tulip mica]

yup this is one way

there are other ways too i think

[weak kindle]

My questions are:

1. Is it possible to determinate if a quadratic expression is always positive without any calculus?
2. Why ∆ < 0 tells me that the expression is always positive or negative? I mean, what does ∆ < 0 mean?

[modest nacelle]

∆ < 0 means that the function has no root (i.e. there are no x so that f(x) = 0)

[weak kindle]

Yes, well, then the problem is even earlier than imposing f(x) = 0.
I mean, when i ask when f(x) > 0, my knowledge says to pass from f(x) > 0 to f(x) = 0 to determinate if f(x) has solutions for which f(x) > 0.
Why?

[tulip mica]

this method does not involve calculus tho

this is just pure manipulation

[weak kindle]

it's easier to calculate the discriminant

[tulip mica]

true

[weak kindle]

"This is because the points where the function crosses the x-axis (where f(x) = 0) can help us identify intervals where the function is positive or negative.
By finding the solutions to f(x) = 0, you are essentially identifying the x-values at which the function changes sign."
That's what GPT said

and it makes pretty sense

[tulip mica]

∆ just helps us to calculate the roots of the quad equation, if ∆ < 0 then √∆ is an imaginary number which implies that no real roots of the equation exist

[weak kindle]

OOOOOOOOOOOOOHHHHHHHHHHH, wait i got it

if ∆ < 0 then it means that the expression has no zeros, means that there are no interception with the x-assis, means that there are no sign changes, means that the function is always positive or always negative

DAMN

[tulip mica]

yes exactly

[weak kindle]

Damn, thank you guys for helping me understanding it

[tulip mica]

no prob

[weak kindle]

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[cobalt viper]

Could someone explain this answer to me? (the blue writing is the answer to the question but I don't understand it)

[weak kindle]

What don't you understand about it?

[cobalt viper]

the notation

its confusing

[weak kindle]

the derivative of f(x) is -3x^(-4), yeah?

[cobalt viper]

yes I get that

does tho for x not equal 0 mean that it equals every single value except 0?

because the graph is a hyperbola

[weak kindle]

x ≠ 0 cause f'(x) has x at the denominator (if x = 0 then you would have -3/0)

[weak kindle]

yeah

[cobalt viper]

ohh ok I get that now

[weak kindle]

then you have f'(x) = -3/(x^4), but x^4 is always positive.
But since you have a -3 on the top, the 'always positive' results in 'always negative'

you have something always positive at the denominator (x^4) (cause the exponent is even) but something that is always negative at the numerator (-3)

[cobalt viper]

oh

so therefore the derivitve is always negative

[weak kindle]

yes

[cobalt viper]

f'(x) < 0

why do they say for all x not equal 0

[weak kindle]

you can use geogebra program to better understand the 2 functions

[cobalt viper]

isnt f'(x) < 0 enough

yea I used desmos

[weak kindle]

f(x) has no Domain that says x ≠ 0 but the problem tells you that x ≠ 0 cause of the derivative Domain

[weak kindle]

it is

[cobalt viper]

ohh ok so I just add it in because its in the question

[weak kindle]

you can write f'(x) < 0 without saying x != 0

[weak kindle]

wdym?

[cobalt viper]

oh okay

[cobalt viper]

I add the x not equal 0 because the problem tells me the domain of the derivitive

[weak kindle]

yes (First Domain: x ≠ 0), but then you find out that f'(x) is always negative (Second Domain: x <= 0), so you intersect both Domains and you obtain x <= 0 and x ≠ 0, that you can sum up with 'x < 0'

[cobalt viper]

oh alright thanks

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[mellow axle]

What can i use to solve this integral?

I started with polynomial divison

But noticed it would take a while..

So i tried photomath, didnt work

Tried wolfram and got the solution i was about to do

What would be a better method?

The fact that Pi is in the answer makes me think it is using complex numbers

[plain ruin]

Like what

what if you split

into z⁹³/(z²+1) and 1/(z²+1)

idk

[rose mist]

is the answer 2 pi?

[mellow axle]

Yea

[rose mist]

z^93 is an odd function since raising an odd power of a negative number results in a negative number

z^2 + 1 is an even function

product of an odd and even function is an odd function

give me a moment while i write some latex

[clever fjord]

misha

misha

[rose mist]

this is just a standard integral which can be evaluated using the arctangent integral

[clever fjord]

misha

[plain ruin]

idunno how but i was right

[rose mist]

apply limits

[clever fjord]

misha

misha

[mellow axle]

Ooooohhh genius

[rose mist]

thank you

[mellow axle]

I tried a similar thing in the start

And thought the whole thing was odd

So everything would be 0

Why didnt that work?

Why do you need to split it?

[rose mist]

it might initially seem that the entire expression is odd because z^93 is an odd function, but the "+3" in the numerator changes the overall parity of the function

[mellow axle]

Why doesnt the +1 change it?

(In the denominator)

[rose mist]

that is because it is combined with z^2, which is itself, even

[mellow axle]

Hmmmm

I might have to look up how to tell if a function is odd or even

[clever fjord]

misha

[rose mist]

is that more confusing

sry

[mellow axle]

So why isnt it the same for the other

[rose mist]

raising an odd exponent keeps the sign

[mellow axle]

Oh the 3 isnt changed depending on if z is + or -

But z^93 is

[rose mist]

$$(-z)^{93} = -z^{93}$$

the negative sign remains when you raise an odd exponent

[clever fjord]

misha

[mellow axle]

So as a general rule

If its odd and there is + a constant

You have to split the function

[rose mist]

you should consider

yea

you want to prevent incorrect assumptions that an entire expression behaves as either odd or even based solely on just one component of the expression

[mellow axle]

Thanks for the help!

[odd edge]

@mellow axle Has your question been resolved?

[odd edge]

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[civic lintel]

i need help

[frigid canopy]

[civic lintel]

how he got (x+3)(2x-1)=0

cubic equation frm polynomial

[frigid canopy]

factorisation

[civic lintel]

how to do that can u teach me

[frigid canopy]

ok

[civic lintel]

can u plz do it fast i dont have much time

[frigid canopy]

wdym

this isn't a test, right?

[civic lintel]

no i just wanna finish this topic fast

[frigid canopy]

ok

[civic lintel]

my exams in 2 week

[frigid canopy]

there are multiple ways

one is the quadratic formula

[civic lintel]

yeah plz teach

[civic lintel]

i dont understand nvm

[frigid canopy]

so say you have a quadratic expression

[civic lintel]

ill figure it out myself frm youtube thank u for ur time

[frigid canopy]

ok

[wild rune]

https://youtu.be/4v-EQIxqpMQ

[civic lintel]

wait leme watch this

[ivory hare]

factoring is gay

[ivory hare]

i hate it

[civic lintel]

If you not here to help please don't disturb

[wild rune]

not quite no

what two numbers multply to get -6 and add up to make 5

[civic lintel]

Can you please tell me what I did wrong?

Wait

Don't say the answer

[wild rune]

you chose 3 and 2 which isn't quite it

[civic lintel]

Oh i get it

Hold on

[ivory hare]

the two numbers at the centre must multiply to equal AC and add to equal B

[frigid canopy]

Mind it, don't use gay as a slur/ to insult something/ someone

[civic lintel]

-3,2??

Is it correct??

[wild rune]

hmm -3 + 2 = -1

we need it to add up to 5

what other factors of 6 are there

[civic lintel]

-3-2?

Yeah

If we do -3*-2 = -6

[ivory hare]

positive 6

[civic lintel]

And if -3,-2 = 5

Right?

[ivory hare]

-3*-2=6

[civic lintel]

😭😭

I give up how to do it??

[ivory hare]

what other factors of 6 r there

just list them all

[civic lintel]

I don't get it

[ivory hare]

1 and 6 r factors of 6

multiply them to make -6 and add them to make 5

[civic lintel]

🥲??

[fair token]

Kindly do not use "gay" as a pejorative in this server. Thank you.

[civic lintel]

Wdym

[ivory hare]

ax^2 +bx +c

two numbers must multiply to equal ac

[civic lintel]

Yeah I know that

[ivory hare]

and the same two numbers add to b

okay

[civic lintel]

3,2 right so

[ivory hare]

what two numbers multiply to -6 and add to 5?

[ivory hare]

there r more factors of 6

😭

[ivory hare]

THERE R MORE FACOTRS OF 6 RAHHHH

^

[civic lintel]

yes i did lcm got 3,2

3*2 6 right

[ivory hare]

OFHER THAN 3 and 2

[civic lintel]

idk

[ivory hare]

OVJEOSJJXXKSKSP

i’m going to

die

[civic lintel]

[ivory hare]

[civic lintel]

2,-3

?

awdakjdasisdiasdaisdasda

i go bye my mind not for math ill make some cheat'

i wanna cry

im stuck here for several hours

[ivory hare]

just

you’re so close

[civic lintel]

1,1 give 1

[ivory hare]

find x

[civic lintel]

-6

yes

[ivory hare]

-1*x=-6

6-1 =5

[civic lintel]

i see

so

the question is

how he get x+3 (2x-1

i dont know

[civic lintel]

yes

[ivory hare]

yes so now what is ur equation

[clever fjord]

faiyrose

[civic lintel]

Like this?

Leme try

Me mess up so bad

[ivory hare]

er

[civic lintel]

Don't laugh

[ivory hare]

ur close

x* what =-x?

[civic lintel]

🥲leme try

[ivory hare]

^

[civic lintel]

Im screaming inside

I'm so lost

[clever fjord]

faiyrose

faiyrose

faiyrose

[ivory hare]

[clever fjord]

faiyrose

[civic lintel]

Wait I'm processing 1 moment please

I'm terribly sorry for wasting your time .. but I don't think I'm capable of doing the maths..I'll take my leave I'm really sorry

How i don't even get a single thing here my mind will blow up I'm just embarassing myself here 🥹

[clever fjord]

faiyrose

[civic lintel]

Wait

🥲🥲

[clever fjord]

faiyrose

[civic lintel]

Why it's not like this I mean i don't get it.. before when i doing this kind of equations it's easy but now it's so complicated

[civic lintel]

Ya Allah i wanna cry

[clever fjord]

faiyrose

[civic lintel]

2,5,3

a= 2,b=5,c= -3

2-3

Yes

Okay understood

-6

Right?

5

6

-6

But we also need to find the 5 right

Okay

Ok

5

-1,6

Yes

3?

-3

Okay

-2*3

1*3?

-2

Okay

5

-1+6

Yes

Yes

[clever fjord]

faiyrose

[civic lintel]

I get this

2x

2x-1

Oh okay wait

Yes yes

Wait

Wait

Wait

Is it correct

Is it is it?

Skskskwksksjsj

Me so happy

Yes but but why you used 6 instead of 2,3 like

Some people used 2,3 and the answer was not coming

That's why I was so confused

How u knew that we need to use -1+6

And btw I have alot of questions can you help me with that I'm really bad at math but the way you just explain was better than everyone even my school teacher

?

Yes

[sleek coyote]

my bad

[civic lintel]

Can I send you a friend request? If you don't mind?

I see.

Okay wait

2 no is polynomial

what close?

.close

[odd edge]

Channel closed

Closed by @civic lintel

Use .reopen if this was a mistake.

[civic lintel]

.reopen

[odd edge]

✅

[civic lintel]

ok

i see but still they way u teach me was so cool

[haughty scaffold]

do you need help with those?

[sleek coyote]

I can help with the last 2 when your done, but damn you really jumped difficulty ngl (sorry for barging in again 😭 )

[civic lintel]

well i m dumb sorry for that and thankyou for helping

[civic lintel]

okay

i dont

hmm idont know

[civic lintel]

ug questions idk how i passed alll my exams.. so far

[civic lintel]

yes wth cubic equations

[sleek coyote]

thats wild, i'll help with the cubic one after your done with fairyrose, because 3 people in one channel is a lot.

[civic lintel]

🥲🫂I'm perplexed

@icy vault I'm so sorry.. I know u are annoyed 😭

But can you please teach me

[clever fjord]

faiyrose

[civic lintel]

Identities what do you mean

🥲🥲

Umm i don't know

Can u teach me

[clever fjord]

faiyrose

[civic lintel]

Should I note down ?? This

[clever fjord]

faiyrose

faiyrose

[civic lintel]

Leme write it wait wait

[clever fjord]

faiyrose

faiyrose

[civic lintel]

I think all of them?

[civic lintel]

How how

Oh ok

I was writing everything down hehe 😝

[sleek coyote]

can i ask what grade these questions are ?

[civic lintel]

12th grade I don't know where you guys are from.. so it might be different.. for some people

[sleek coyote]

oh

to be honest understandable, most of those concepts are in 9th, 10th, and 11th grade

[civic lintel]

Yes yes so please help me wwkwkw

[sleek coyote]

watch this as she said, very good video

[civic lintel]

I see

Wait leme learn leme learn

Me watching

😭okay okay

So should I close the chat for now?

By typing close?

Okay

.close

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[civic lintel]

yes im doing that

[civic lintel]

.close

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[neon wagon]

how would u do this?

[neon wagon]

wait no im just dumb

nvms

sorry D:

.close

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[balmy dagger]

How can I use data about past occupied horizontal land mass/area in a city in creating an equation that predicts the occupied land mass after 20 years (using a statistical tool)?

[mystic saffron]

Do you have this data?

[balmy dagger]

Oh it's only assuming we have the secondary data (official records etc) already (since we're writing our methodology chapter and not the data collection part)

stuff is just really hard for me ion get it T-T

[mystic saffron]

Do you need to do any actual calculations?

[balmy dagger]

Not really, just more on how are we gonna calculate data once we got them lol

[mystic saffron]

Because if you don't, it should be trivial result in your specification, so it should be easy to find

[balmy dagger]

to be honest it's only the statistical tool or approach that I need :3

[mystic saffron]

Do you have any past papers or something?

[mystic saffron]

There is no way that you can calculate it based on this information. So I assume it some trivial result you suppose to know

Sorry, suppose to have in your spec

[balmy dagger]

not really :(( our related literature did use some spatial analysis model but I don't think it's needed in our case since we don't need geographic representations and allat

just the numbers

[balmy dagger]

realll

[mystic saffron]

What kind of math are you study on lessons?

So that's geography

?

[balmy dagger]

stats for our research T__T

idk which approach to use honestly

[mystic saffron]

Wait is it university level ?

You definitely need software for spatial analysis

[balmy dagger]

i'm still in high school :3 our research topic is so tuff

i'm like a year away from college :3

[mystic saffron]

What subject?
What specification?

[balmy dagger]

its field is mathematics tho

since we had to create an equation and allat

[river pagoda]

not an expert but can't you just create a Polynomial equation base on 20 yr past?

[mystic saffron]

That's sound wild. Because you can only assume general form of equation you won't be able to get particular one which satisfy minimal amount of criteria

[mystic saffron]

Bruh what

[balmy dagger]

i mean that's trueee

ig we'll have to disregard many other factors that can affect stuff

[mystic saffron]

Can you pick the region for your experiment?

[balmy dagger]

and just base it on

[river pagoda]

becuse is high school math so Polynomial is needed I think

[balmy dagger]

past data

[mystic saffron]

Log, e^x, In, 1/x^2,etc

[balmy dagger]

i'm in 11th grade in my country idk the equivalent of it in other countries tho :0