help-10

[neon eagle]

They didn’t ask you to find that

[burnt thunder]

why did they do that

[neon eagle]

Don’t worry about that

[burnt thunder]

do i ignore

[neon eagle]

f(-x) happens to equal f(x) so it doesn’t even matter

[burnt thunder]

they do it in each question

[neon eagle]

They are the same thing

[burnt thunder]

ouh

so if its -f

everything

is multiplied

including x

[neon eagle]

Just times every term by -1

5 becomes -5

X becomes -x

Etc

[burnt thunder]

x^2-4=-x^2+4

[neon eagle]

Well not equals but when you -f it

Yes

[burnt thunder]

so x is negative in one

and not other

so

even?

f(x)=f(-x)

[neon eagle]

should be something like f(x) = x^2-4
-f(x)=-x^2+4

[neon eagle]

This is true yes

[burnt thunder]

yes

[neon eagle]

Yes it’s even

[burnt thunder]

okokkk

can we test second one

just to make sure

i got it 😭

plsls

[neon eagle]

are you in uni?

[burnt thunder]

no 😭

[neon eagle]

Senior?

[burnt thunder]

yea😭

[neon eagle]

k

Ok let’s do part b?

[burnt thunder]

yes okok

its

sin x

• x

[neon eagle]

f(x) equals that yeah

[burnt thunder]

yes

f(x)=sin x + x

so theres two x’s

so do i multiply both by -1

[neon eagle]

What are you trying to evaluate

[burnt thunder]

the second one

same thing as a

[neon eagle]

Yeah but f(-x) or -f(x)

[burnt thunder]

phh

first one

[neon eagle]

Ok

[burnt thunder]

f(x)= -sin x - x

[neon eagle]

Wot

[burnt thunder]

help

[neon eagle]

what happened to thi

[burnt thunder]

i did the

f(-x)

[neon eagle]

this is -f(x)

[burnt thunder]

how

i just multiplied

the x’s

with negative

[neon eagle]

Did you already realise sin(-x) is -sin(x)?

[burnt thunder]

yes

[neon eagle]

Oh good job

Then yes it’s right

Don’t skip working

[burnt thunder]

okok phew

mb

[neon eagle]

It’s hard for me to tell 😅

[burnt thunder]

lol my bad 😭😭

[neon eagle]

Ok and the second one

[burnt thunder]

ok so -f(x)

so u multiply everything

sin (-x) - x

[neon eagle]

Noooo

[burnt thunder]

help

[neon eagle]

rip

Um

[burnt thunder]

ow

help

[neon eagle]

You multiply everything by -1

[burnt thunder]

on sin

too

[neon eagle]

what you just did was replace x with -x

Which is the first one

[neon eagle]

This is for f(-x)

For this one you just multiply everything by -1

[burnt thunder]

yea

so

[neon eagle]

So it’s just -sin(x)-x

[burnt thunder]

well

that was

my next step…

i rhink

yea

u said

show the work

[neon eagle]

But the first step you replaced x with -x

You were meant to do that for f(-x)

[burnt thunder]

is that only for

that

ohh

help😭😭😭

[neon eagle]

it’s fine

[burnt thunder]

gosh

[neon eagle]

Just remember everything inside of the ( ) means you replace x with that

So f(-x) means you replace x with -x

[burnt thunder]

so f(-x)= -sin x -x

-f(x)=-sin x -x

[neon eagle]

yes

[neon eagle]

this one using sin(-x) =-sin(x)

To simplify it

you’re right basically

[burnt thunder]

which ways

better

because its the same answer for btoh

its odd?

[neon eagle]

Yes it’s odd

[burnt thunder]

so odd means

[neon eagle]

Wdym which way is better

[burnt thunder]

when its the same answer

for both?

[burnt thunder]

like which way

do i put it

[neon eagle]

what do you mean

[burnt thunder]

like what way do i keep it as

😭

[neon eagle]

Oh

[burnt thunder]

sin (-x)

or negative behind sin

[neon eagle]

Sin(-x) or -sin(x)

The second one but you show the first one in working

So you would write like

[burnt thunder]

ouhhkay

kokok

[neon eagle]

f(-x)=sin(-x)=-sin(x)

Oop I forgot the x

You know what I mean

Pretend the -x is there

[burnt thunder]

yeaa

im still kinda

confused

on

-f(x)

😭

[neon eagle]

oh

That just means you times everything by -1

So like (-1)(f(x))

[burnt thunder]

okok can u check

my work

for c

[neon eagle]

Sure

[obtuse pebble]

Channel closed

The owner is missing!

[burnt thunder]

,rotate 270

[neon eagle]

Yes

[burnt thunder]

do i put negative

under the x

in 1/x

[neon eagle]

Only thing I would change is for 1/(-x)+x I would just make that -1/x+x

[obtuse pebble]

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[faint verge]

i did it wrong

and then i realized

and now im trying to fix it

the third line idk how to fix

WAIT

i did it wrong again

fgrhyy643er 1 minute

nvm i got it

.close

[obtuse pebble]

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

@boreal spire Has your question been resolved?

[spare rain]

first question?

[verbal niche]

so you're just taking the derivative of $sin(\pi)$

[warm shale]

Joshii

[verbal niche]

do you know your trig identities?

can you set those up please?

and we'll go from there

sum identity for sin

$sin(\pi+h) =$

[warm shale]

Joshii

[verbal niche]

hm?

are you trying to prove the derrivative?

algebraically

yes but if ur teacher wanted you to just solve the derivative they would of given you

$f(x)=sin(\pi)$

[warm shale]

Joshii

[verbal niche]

find

$f'(x)$

[warm shale]

Joshii

[verbal niche]

right

but they gave you the newtons quotiant

maybe they want you to work it out algebraically

you only know its cos(x) because you were told thats the derrivative of sin(x)

yes

so lets do that

sub in the sum identity for trig

for sin(pi+h)

mhm

also lets sub x in for pi

it'll make things easier

so we have

$\frac{\sin{x}\cos{x}+\sin{h}\cos{h}-\sin{x}}{h}$

[warm shale]

Joshii

[verbal niche]

oh wait that was the identity for cos

not sin

sin is this

$\frac{\sin{x}\cos{h}+\sin{h}\cos{x}-\sin{x}}{h}$

[warm shale]

Joshii

[verbal niche]

well no you want to keep going

and take out the h somehow

im tryinbg to think about it one sec

i know this is for sure the first step though

i think the next thing we should try is breaking it into 2 or three limits

mhm

$\frac{\sin{x}\cos{h}}{h}+\frac{\sin{h}\cos{x}-\sin{x}}{h}}$

[warm shale]

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

[verbal niche]

this looks more promissing to me

than -sinx/h

well look you could do

$\sin{x}\frac{\cos{h}}{h}+\frac{\sin{h}\cos{x}-\sin{x}}{h}}$

[warm shale]

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

[verbal niche]

oh wait it would be much more helpful if we switched the sinh and cos x

like this

$\frac{\sin{h}\cos{x}}{h}}+\frac{\sin{x}\cos{h}-\sin{x}}{h}}$

oops

[warm shale]

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

[verbal niche]

and look we can do this

$\cos{x}\frac{\sin{h}}{h}}+\sin{x}\frac{\cos{h}-1}{h}$

[warm shale]

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

[verbal niche]

do you see why we can do this btw? @boreal spire

hm?

so far just the sum

have you heard of squeeze theorum?

how?

dont u need to show work?

https://www.youtube.com/watch?v=VMNX2xGffzU heres an in depth video if you want proof of the derrivative btw

but i think the way you did it is the way your teacher wants you to do it then

it makes more sense why she put pi there

[obtuse pebble]

@boreal spire Has your question been resolved?

[obtuse pebble]

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[distant shell]

how can i find weighted average?

[obtuse pebble]

@distant shell Has your question been resolved?

[obtuse pebble]

@distant shell Has your question been resolved?

[obtuse pebble]

@distant shell Has your question been resolved?

[obtuse pebble]

@distant shell Has your question been resolved?

[obtuse pebble]

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[inner helm]

can anyone help me fill this table

[wraith path]

plot it on a graph

and find turning points

boom

idk what restrictions there are lol idk why there would be any

wtf

how do u have a max and minimum number of turning points

the max is 3 oh

nvm

it means how many turning points are at a peak and how many are at a decline

how many local mins and maxs basically

should be 3 no?

idk graph it

what are restrictions

tf

[wide rose]

for a?

[obtuse pebble]

@inner helm Has your question been resolved?

[inner helm]

Uhm..

what

they are correct

what do I write for minimum turning points?

[inner helm]

a is correct right?

oh so 0 for all?

[lone echo]

nvm, its a language thing. i thought they were referring to inflection points, not local extrema

[inner helm]

ohh

Can someone verify

[wraith path]

wtf

im so confused

how could there be 0 minimums and 7 maximums

??

[inner helm]

tru

[lone echo]

a) has 2 turning points

[inner helm]

idk

[inner helm]

max or min?

[lone echo]

you would differentiate it and check how many roots the derivative has

[wraith path]

yeah i think u need to clarify what your teacher means by minimum number of turning points

is that not what this is?

arent u supposed to be doing that?

[inner helm]

I didn't study derivatives

[lone echo]

since it has 2 no matter the value of k, you'd have 2 min and max turning points

[inner helm]

tru

.close

[obtuse pebble]

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[brisk arrow]

what's the remainder of (x-1)^2 dividing x^100 + 1

[royal basin]

did you mean the other way around maybe?

dividing (x-1)^2 by x^100 + 1 will produce quotient 0 and remainder (x-1)^2

did you mean x^100 + 1 by (x-1)^2?

[brisk arrow]

x^100 + 1 divided by (x-1)^2

[brisk arrow]

yes

[royal basin]

right

and i take it you wouldn't want to do it the long way

[brisk arrow]

for sure, a intuitive and simple way is much prefered

[royal basin]

it'll be f(1) + (x-1)*f'(1)

where f(x) = x^100 + 1

[brisk arrow]

do you mind explaining how did you get that equality

[obtuse pebble]

@brisk arrow Has your question been resolved?

[obtuse pebble]

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[obtuse pebble]

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[brisk arrow]

What are the differences between expected value and weighted average in general?

They are quite similar in my opinion.

Therefore I think it is necessary to draw the boundary line**(.)**

1.When do I use expected value, and when **(do)**I use weighted average?

2.what are the purpose of these two things? What they stand for?

[obtuse pebble]

@brisk arrow Has your question been resolved?

[brisk arrow]

@Helper

<@&286206848099549185>

[errant lark]

Missing full stop. - line 3.
Missing helping verb "do" in the sentence after the comma splice. - line 4
A sentence always begins with a capital letter. - line 5
Wrong usage of the linking verb. "are" instead of "is". - line 5
Missing helping verb "do" in the second sentence of the line. - line 5

[frank monolith]

bruh

they pinged the role in the next try

[errant lark]

I suppose that expected value is a type of weighted average where weights are the respective probabilities of the random variable taking a value from the sample space.

[brisk arrow]

In my opinion, when there are probabilities involve, it is called expected value, otherwise it is called weighted average.

[errant lark]

Yes. That is what i said. It's given a special name when the weights happen to be the probability of occurrence of that particular unit/data point/sample point.

[brisk arrow]

Terrific, but why does it been named as expected value? Are we expecting something?

[errant lark]

Kind of. It gives us the expected value of any event.

[obtuse pebble]

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[errant lark]

E.g. let's say that there is a game. If you play it once, probability that you win $5 is 2/3 and that you lose $2 is 1/3.

[brisk arrow]

.reopen

[obtuse pebble]

✅

[errant lark]

You can find out how much money you are expected to win if you play the game n number of times.

Thus, it helps to assess situations and gain insights from data.

[brisk arrow]

The expected value of it would be 4

That means I “expect” to win 4 dollars per game

[errant lark]

When creating any games that require gambling or such, creators ensure that expected winning amount of players is such that they(creators) always land a profit.

[errant lark]

5 * 2/3 - 2 * 1/3 = 8/3 = $2.66

[brisk arrow]

How do they, creator, know if it is gonna to make them a profit?

[errant lark]

You are losing 2 dollars.

[brisk arrow]

Ohh

By the expected value

[errant lark]

Well, they make it. Don't they? They know everything behind the scenes.

For example - they have full discretion at how many winning lottery tickets are there among a thousand that are printed.

[brisk arrow]

Yes, they will be able to evaluate expected values. If the expected value bigger than 0 then technically those creators are winning, by organizing a gambling game.

[errant lark]

Yes. Sort of. If you are talking about expected value of earning of creator being positive, then yes.

Also, it doesn't have to be positive as well. I mean - as long as they are charging more than the expected winnings of player, they are in profit anyway.

Of course, they must be considering other expenses as well. You get the point though.

Now, i have to go. I'm sorry.

Hopefully, someone else will be able to continue if you have further questions.

[brisk arrow]

And I think I found out why it is called expected value rather than sort of an average. Since there is possibilities involves, so there’s more than one result. Yet, expected value is the result we are expected, that most likely to happen.

[brisk arrow]

It’s fine, you have well explained my question. Thank you so much!

[obtuse pebble]

@brisk arrow Has your question been resolved?

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Remember:
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• Show your work, and if possible, explain where you are stuck.
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[hallow socket]

hi

[hallow socket]

idek where to begin

[alpine raven]

expand the left side

[hallow socket]

this is what i was doing

its sendng

[frank monolith]

you didnt do anything

you just drew something

[hallow socket]

i was going to do it

so like 3x3 and then 3x2

yx3 yx2y

[frank monolith]

first do it.

then send the work

[hallow socket]

there

9x shld be in red tho mb

[frank monolith]

how is it 6y^2

[hallow socket]

yx2y = 2yy

does it not

i cant do maths

[warm shale]

Dyssrupt

[frank monolith]

then expand

do it this way

[hallow socket]

i havent been taught this way

[frank monolith]

this is the way

[hallow socket]

well im self-teaching myself maths coz we dont have a teacher

ima need some eleboration

[dire plinth]

dyk FOIL

[hallow socket]

nope

[hallow socket]

whats that

[dire plinth]

essentially this

first, outer, inner, last

[hallow socket]

right...

hol up let me try that

might not get anywhere tho coz this is the first time

[frank monolith]

dw try it

[hallow socket]

alr ill be back in 10

so

@frank monolith @dire plinth this is where i am rn

now what do i do w the dark blue

[frank monolith]

you are correct

[dire plinth]

last is wrong

[hallow socket]

oh

[frank monolith]

oh yeah

the -

[hallow socket]

whats the last then

ohh

mbmb

[dire plinth]

then just collect like terms

[hallow socket]

what do i do from now

oh

[dire plinth]

then A B and C are just the coefficients

[hallow socket]

like this?

so A= 9

B=6

C=2

[dire plinth]

uh

u added ur like terms wrong

[hallow socket]

oh

what do i do wrong

[dire plinth]

-6xy + 3xy isnt 9xy

[hallow socket]

I DIDNT SEE THE NEGATIVE

IM DONE

[dire plinth]

well now that u have that

just remember that the negative is part of the coefficient

so C for example is -2, not 2

[dire plinth]

mhm

[hallow socket]

Like that?

So A=9

B=-3

C=-2

[dire plinth]

yup

[hallow socket]

but how is it negative when in the answer it has a PLUS

[dire plinth]

wdym

[hallow socket]

here

in yellow

[dire plinth]

but like

[twilit tinsel]

how do you guys write like this so quick?

[dire plinth]

adding a negative number

= subtraction?

[twilit tinsel]

i mean i am sorry to disturb

[hallow socket]

wdym

[hallow socket]

yes

does it not?

[twilit tinsel]

• (-B)

[hallow socket]

so A=9, B=-3 and C=-2 WITH the negatives?

like do i put the negatives in my answer

[dire plinth]

yes

[twilit tinsel]

$\left3x + y\right\left3x-2y\right$

[warm shale]

Ritvik.is-a.dev

$\left3x + y\right\left3x-2y\right$
```Compilation error:```! Missing delimiter (. inserted).
<to be read again> 
                   3
l.57 $\left3
            x + y\right\left3x-2y\right$
I was expecting to see something like `(' or `\{' or
`\}' here. If you typed, e.g., `{' instead of `\{', you
should probably delete the `{' by typing `1' now, so that
braces don't get unbalanced. Otherwise just proceed.
Acceptable delimiters are characters whose \delcode is
nonnegative, or you can use `\delimiter <delimiter code>'.```

[hallow socket]

oh

[twilit tinsel]

$(3x + y)(3x-2y)\equals(3x)^{2}-(2y)^{2}$

[warm shale]

Ritvik.is-a.dev
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[twilit tinsel]

who stole my equals again?

[hallow socket]

what are u tryin do fam

[twilit tinsel]

$(3x + y)(3x-2y)=(3x)^{2}-(2y)^{2}$

[warm shale]

Ritvik.is-a.dev

[twilit tinsel]

this is the final expression

[hallow socket]

thats not what the question is asking tho

[twilit tinsel]

according to (a+b)(a-b) = a^2 - b^2

[dire plinth]

uh

[hallow socket]

Uhm

[dire plinth]

wrong

[twilit tinsel]

oh i see

i got my own wrong

[hallow socket]

im gonna try taro's way lets hope its not wrong

GOT IT RIGHT

THANK YOU

AND I LEARNT SOMETHING

Look at me gi

[dire plinth]

difference of two squares only works when its (a+b)(a-b)

you have (3x+y)(3x-2y)

[hallow socket]

having to self teach a subject coz u dont have a teacher is lowk hard especially maths lowk

[dire plinth]

y is not -2y

[twilit tinsel]

yes here b not equals b

[twilit tinsel]

yes i can agree A = 9, B = -3 and C = -2

@hallow socketIs case closed?

[dire plinth]

and if u expand this

[hallow socket]

yall

what ab this one tho

[dire plinth]

you'll get 9x^2 - 4y^2

[hallow socket]

is there a way to solve this without graphing it?

[dire plinth]

parallel lines have an equal slope

[hallow socket]

right and here i the problem

what

is

slope!!

im not even gonna lie atp

dont i js graph it

[dire plinth]

dont have to

u have the form already

y = 4x + 9

when you have a parallel line

you haev

y = 4x + c

[hallow socket]

yes

[dire plinth]

c just determines if the graph translates up or down

[hallow socket]

so its b

[dire plinth]

and how did u get that

[hallow socket]

is it wrong

because u said 4x+c and there is only one + option, its not c and b is a negative / take away

[dire plinth]

idk if its right i havent worked it out myself

the proper way to work it out

is that your given a point that the line passes through

(2,1)

now

knowing this point

what is our x and our y

[hallow socket]

2, 1?

is it not

[dire plinth]

ye but you know which one is which right?

[hallow socket]

nope

[dire plinth]

remember that a point is always (x, y)

so x = 2, y = 1

now that we have this point

and our form

y = 4x + c

we can sub in

1 = 4(2) + c

[hallow socket]

ohhh yea i know the x and y part but idk which one is right

[dire plinth]

then solve for c

[hallow socket]

like the answr

[dire plinth]

1 = 8 + c
-7 = c

[hallow socket]

alr lets do this

oh

so it wasnt b

[dire plinth]

mhm

then once u put -7 back

into y = 4x + c

u get

y = 4x - 7

[hallow socket]

ur so smart

like when u teach it i get it

it all makes sense

[dire plinth]

im not smart compared to the other ppl in the server i just enjoy teaching what i know

and thats good enough for me

[hallow socket]

and u shld coz ur good at it

one more please then ill let u go but i wanna solve it and get it checked by u

[dire plinth]

mhm

whats the q

[hallow socket]

this is the question (i know the blue is wrong)

[dire plinth]

so what does perpendicular mean

[hallow socket]

a 90 degree angle

maybe

[dire plinth]

mhm

okay so

first thing

the line that we have

whats our gradient

[hallow socket]

1/3x-6

[dire plinth]

nope

thats mx + c

[hallow socket]

no

-3,0

[dire plinth]

nope

[hallow socket]

oh

wait

[dire plinth]

y = mx + c, where m = gradient, c = y intercept

[hallow socket]

idk how to solve gradient for fractions

im dumb we know we're getting their slowly

[dire plinth]

okay so

if we have

lets say

y = 2x + 3

whats our gradient

[hallow socket]

2

[dire plinth]

now

if i said

y = 0.5x + 3

whats our gradient

[hallow socket]

0.5

[dire plinth]

if i said y = 1/2x + 3

whats our gradient

[hallow socket]

1/2

[dire plinth]

exactly

[hallow socket]

im

so

done

[dire plinth]

so back to y = 1/3x - 6

whats our gradient

[hallow socket]

1/3

[dire plinth]

great

now

[hallow socket]

mega mind

[dire plinth]

when you have a perpendicular line

u have the formula

m1 * m2 = -1

[hallow socket]

i was never given a formula

this is a joke

anyways

yes

[dire plinth]

so you were

never given this

?

[hallow socket]

nope

[dire plinth]

well

okay

[hallow socket]

same as FOIL never seen it

[dire plinth]

anyway so we have one of our graidents

and we have to find the gradient of our other line

so we can put it into slope intercept form

our first gradient is 1/3

so we have

1/3 * m2 = -1

[hallow socket]

yes boss

[dire plinth]

so whats m2

[hallow socket]

give me a moment

[dire plinth]

(hint: isolate m2)

[hallow socket]

I wanna say 2

but idk where i got it from

so we're gonna go w 3!

idk how to isolate this isnt okay

[dire plinth]

how do we get m2 by itself

[hallow socket]

idk i worked it weirdly in my head and wanna say b

like i didnt do the m1 m2 method

[dire plinth]

wym

[hallow socket]

like i was going through my notes and worked it out and feel like its B

[dire plinth]

how so

[hallow socket]

because u need to distrute the -3 after simplifying it

[dire plinth]

wait where are we up to

what

[dire plinth]

im still here

[hallow socket]

coz m is slope

oh

i worked it out

[dire plinth]

oh alright

[hallow socket]

is it B tho

i dont trust myself personally

[dire plinth]

havent worked it out lmao

was gonna work it with you

[hallow socket]

ooh

uhm

thats okay

ill learn ur method

[dire plinth]

okay

[hallow socket]

lets do it!"!

trying to find m2

[dire plinth]

so in order to find the equation

we need two things

1. a point on the line

(we're given that)

2. the gradient

to find the gradient

we used the other gradient since its perpendicular

so we have the formula

1/3 * m2 = -1

[hallow socket]

yes

[dire plinth]

so ur unsure how to isolate the m2, yes?

[hallow socket]

yes i am

[dire plinth]

okay

if i said

2x = 4

how do u isolate x

[hallow socket]

divide 2

[dire plinth]

if i said

0.5x = 4

how do u isolate x

[hallow socket]

dicide 0.5?

[dire plinth]

mhm

[hallow socket]

v

then u divide 1/3

[dire plinth]

so if i have now

great

[hallow socket]

mega mind hello???

[dire plinth]

m2 = -1 / (1/3)

do you know the flip and swap?

[hallow socket]

ohh yes so its 3/1

[dire plinth]

mhm

so m2 = -1 * 3/1

[hallow socket]

3/1=-1

-1

[dire plinth]

huh

huh

[hallow socket]

no?

[dire plinth]

-1 * 3/1

[hallow socket]

oh

[dire plinth]

3/1 simplifies to 3

so -1 * 3

[hallow socket]

oh

yes

mb

[dire plinth]

so our gradient is -3

y = -3x + c

well ur right since b is the only one that has -3 as the gradient

are you wondering on how to solve for c though?

or not really

[hallow socket]

not really anymore coz it makes sense

thats all tho

[dire plinth]

but dyk how you get the -9?

[hallow socket]

not rlly but i will learn that a bit late

r

[dire plinth]

alright if you say so

[hallow socket]

coz i have to do something else rn asw

but thank you

[dire plinth]

np

[hallow socket]

for wasting ur time and actually helping me

[dire plinth]

ah all good

[hallow socket]

ur the best honestly hopefully u presue ur teaching career

.close

[obtuse pebble]

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[thorny sky]

Is this correct?

[obtuse pebble]

@thorny sky Has your question been resolved?

[thorny sky]

<@&286206848099549185>

[obtuse pebble]

@thorny sky Has your question been resolved?

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[rich holly]

,w y=(4-x^2)/(x^2-x-6) inverse

[warm shale]

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[rich holly]

where did I go wrong

i’ll swap the xs and ys later

how does it get 3x+2 in the numerator?

[warm canopy]

You should try going right back to the start and factoring the numerator

[rich holly]

ohhhh

[rich holly]

why is canceling x+2 possible?

[warm canopy]

What is that you mean by why

Like how cancelling works?

Or concern for division by zero

[rich holly]

this

[warm canopy]

The domain of the function can't include -2 as then we'd be dividing by zero, so we're okay to divide by x+2 to cancel

As long as you remember the function isn't defin3d at -2

[rich holly]

also here the domain is all real numbers except for -1, but why is the range for my original equation includes -4/5?

,w range y=(4-x^2)/(x^2-x-6)

[warm shale]

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[rich holly]

ah

[obtuse pebble]

@rich holly Has your question been resolved?

[obtuse pebble]

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[timid silo]

HLPPPP

[timid silo]

12x^3 + 12x^2

FACTOR THIS

i forgot

[midnight crypt]

what have you tried?

[timid silo]

i mean i havent learned this

well

[midnight crypt]

then pick up google and go learn it

[timid silo]

its limits

[midnight crypt]

oh?

[timid silo]

limits by factoring

wait

can u tell me step by step what happened there

this confuses me like this is the final stage i have to learn so i can perfect the exercise

how do i simplify it

[lyric crane]

ok ive got like 10 minutes but we'll see if that's enough

so basically

you're just using the distributive property of multiplication over addition

which is that a(b+c)=ab+ac

right

[timid silo]

OKAY

OHHHHH OKAY OKAY

its called distributive property of multiplication

[lyric crane]

so then 12x^3+12x^2=(12x^2)(x)+(12x^2)(1)=12x^2(x+1)

[timid silo]

why is it 12x^2 instead of 12x^3

[lyric crane]

because 12x^2 doesn't have a factor of 12x^3

so you can't divide that out

[timid silo]

mhmm okay

what if the exponent is 4

[lyric crane]

in algebra it's usually just shortened to the distributive property

[timid silo]

and the other one is 3

what should i use

[lyric crane]

then you would take out 3

because thats the maximum you can take out of both

[timid silo]

its always 3?

[lyric crane]

no

[timid silo]

i mean the max

[lyric crane]

it should be the biggest factor you can take out of every term

for example if you had x^2+x^3+x^5

[timid silo]

its 5

[lyric crane]

you would take out x^2

[timid silo]

oh

[lyric crane]

because you can only take out x^2 from the first term

[timid silo]

ohh okay

what about if its

x^4+x^5+x^6

[lyric crane]

well

what do you think?

[timid silo]

4?

[lyric crane]

yup

gj

[timid silo]

ight

thank u

but

[lyric crane]

np

[timid silo]

wait

[lyric crane]

?

[timid silo]

in algebra

what is it called again

distributive property

is there a distributive property of subtraction

[lyric crane]

uh

kinda?

i mean like -(a+b)=-a-b

[timid silo]

mhmmmmm

[lyric crane]

but that's because it's the distributive property of multiplication over addition

because there it's just a=-1

[timid silo]

ohh okay okay i get it now

thank u!

[lyric crane]

ok cool

bye

[timid silo]

byee thanks agaun

[obtuse pebble]

@timid silo Has your question been resolved?

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[wispy shadow]

regarding expressing the expectation value for some non-stochastic quantity, is the PDF = 1/N ?

[wispy shadow]

assuming N data points of course

[obtuse pebble]

@wispy shadow Has your question been resolved?

[obtuse pebble]

@wispy shadow Has your question been resolved?

[wispy shadow]

no, but i found my answer elsewhere

[obtuse pebble]

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[rapid remnant]

I need help

<@&286206848099549185>

[golden sand]

!15min

[obtuse pebble]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[rapid remnant]

Oh sorry

[obtuse pebble]

@rapid remnant Has your question been resolved?

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[rapid remnant]

No

[rapid remnant]

How?

<@&286206848099549185> iys been 15 min

[obtuse pebble]

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[dark idol]

-sqrt2 doesn’t work and thissay enter an exact answer with no rounding

[rapid remnant]

It's this

[unreal musk]

You've lost the channel (because you said you were done with it), you'll need to open a new one (and make sure you respond to the bot with ❌ if you aren't done)

[unreal musk]

How are you putting it in?

[dark idol]

Like that

[unreal musk]

As in for the one you did here, you were able to put this in, does it not let you write similar, but as $(-\sqrt{2}, 0)$ or is it rejecting that as well?

[warm shale]

@unreal musk

[dark idol]

That one worked

[unreal musk]

Yea that's what I'm asking - what does it show when you put in $(-\sqrt{2}, 0)$ for the first one?

[warm shale]

@unreal musk

[dark idol]

Nvm I put a space before comma and it worked

.close

[obtuse pebble]

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[timid silo]

little confused from how they got from L2 to L3

i know that sec is 1/cos so sec^2 is 1/cos x 1/cos

[frank monolith]

they expanded the tan too

tan = sin/cos

[timid silo]

is

1/sec^2 = cos^2??

[frank monolith]

yes

[warm shale]

Dyssrupt

[timid silo]

aaaah okay

thanks for your help i really appreciate it :))

[frank monolith]

np

[timid silo]

.close

[obtuse pebble]

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[obtuse pebble]

Please don't occupy multiple help channels.

[dark idol]

Help

[tardy epoch]

Well the radius is definitely bigger than 3

[wraith path]

i mean

only marginally

[tardy epoch]

The radius is the distance from the center to a point on the circle

Do you know distance formula?

[dark idol]

What part is wrong

[wraith path]

the radius is pi

[dark idol]

The 3^2 is the radius?

[tardy epoch]

Use this to find radius

[wraith path]

se the three points at the bottom to make a half triangle

and use a^2+b^2=c^2 to find your radius

use*

[dark idol]

I got 3.16

[tardy epoch]

!show

[obtuse pebble]

Show your work, and if possible, explain where you are stuck.

[dark idol]

@tardy epoch

[tardy epoch]

Looks right

Use the exact formula in your equation instead of rounding

[tardy epoch]

Notice the equation asks for r^2 and you've calculated sqrt(r^2)

[obtuse pebble]

@dark idol Has your question been resolved?

[obtuse pebble]

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[twin imp]

Can someone do these with a 2 column proof

[golden sand]

!show

[obtuse pebble]

Show your work, and if possible, explain where you are stuck.

[twin imp]

I don't know where to start

<@&286206848099549185>

[obtuse pebble]

@twin imp Has your question been resolved?

[obtuse pebble]

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[compact walrus]

I'm working with the concept of derivatives, and this one is really messing with my brain.

[compact walrus]

I have to make the two drawings/sketches

[solar trellis]

derivative = slope of tangent

[compact walrus]

Yea, I know, but I believe the double differerentiation is messing with my brain, when trying to visualize the graphs as a drawing

[empty locust]

f'' >0 = concave up

so for f it would be concave up parabola and for f' it would be a positive slope

line

[compact walrus]

Is this a start?

[empty locust]

concave up

[compact walrus]

Yea i mistaked that

Would something like this be close to it?

[empty locust]

ya

[compact walrus]

The tell me to do the same for
$f'(0)=f''(0)=0$

[warm shale]

Schimmell

[obtuse pebble]

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[pale birch]

"which values of a gives one solution in this system of equations"

[fossil crag]

!status

[obtuse pebble]

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

[pale birch]

1

or maybe 2

i multiplied the top equation with -5

to get the same x

yeah thats it lol

[pale birch]

i think what im supposed to do is simplify this and then a can't be the same value as the other slope

but the problem is idk how to simplify

theres too many variables .-.

oh nvm i solved it

.close

[obtuse pebble]

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[night plume]

hello ,

[night plume]

im confused as to why there is (20-x) on the equation

[timid silo]

because they want 20 pounds of seed overall, and they have x pounds of seed A, so they only need 20 - x pounds of seed B

[obtuse pebble]

@night plume Has your question been resolved?

[night plume]

ic

[obtuse pebble]

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[spice chasm]

$\int_{3}^{9}\left(4-\sqrt{9-(x-6)^2}\right)dx$

[warm shale]

Jash

[spice chasm]

do i have to do u-sub

[meager gale]

idk bruh

open a help channel

im fully aware this is a help channel

[meager gale]

prolly my first though too

i dont see anything being multiplied.. so i dont see the point of IBP

no trig sub obviously

[spice chasm]

how do u even take derivative of sqrt(9-u^2)

[meager gale]

partial fractions dont make sense

[meager gale]

um what

[spice chasm]

ohhhh wait the answer is 24-(9pi)/2 i think

,w int from 3 to 9 of 4-sqrt(9-(x-6)^2)

[warm shale]

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Requested by jashxdlol

[spice chasm]

i think you can just find the area

[meager gale]

good job

[spice chasm]

ye so its just a semi circle pointing down centered at (6,4)

[meager gale]

right

u could also integrate like normal

idk

[spice chasm]

how tho

[meager gale]

its been a while

wait

lemme find a marker

[meager gale]

integrating circles without polar form is fking terrible.

i quit

im dnf LOL

[spice chasm]

bruh

[obtuse pebble]

@spice chasm Has your question been resolved?

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[obtuse pebble]

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[merry topaz]

on a chess board two squares are chosen what is the probability that two are not in same column and row

[timid silo]

The first choice can be any of the 64 squares, correct?

[oblique marlin]

I need to know where to start with something I'm playing with. I have a dataset that represents the distances between the words in a document. For instance, "Word A" is, on average, 3 spaces from "Word B" and 6 spaces from "Word C." At the same time, "Word B" would be 3 spaces from "A" but nine spaces from "C." Obviously, this would be nonsensical if I were to try to graph this on a line, but if I were to collapse down the data to an n-dimensional matrix, I would be able to create a point-cloud in a higher dimensional space. I asked GPT to explain this to me and it suggested doing something with the math surrounding a hilbert curve, but I think it was hallucinating. I just don't know where to start.

I really hope I did a good job of explaining what I'm trying to do here. Open to criticism if anyone thinks what I'm asking for is broken.

[eternal thistle]

The first rook eliminates always the same number of squares (source: linear algebra cofactors)

[obtuse pebble]

@merry topaz Has your question been resolved?

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.