help-0

[slate monolith]

u gotta wait 15 min

u didnt even wait 1

i read why u pinged, but thats still not a good reason. just do it tmrw or something

maybe go for physics server, this is like math

[random pelican]

dude thats geometry.

[lone sapphire]

what

[slate monolith]

wait what

do u mean 30 degrees

[random pelican]

yes I do mean that

[slate monolith]

i thought o was a physical variable

it sounds like a phyiscs question

is this from a geometry class

[random pelican]

dude im at 8th grade, dont even exist geometry class it is literally just named math but ye its prob geometry considering that it is literally A SHAPE OF A OBJECT

[slate monolith]

well okay, it just is worded really confusingly lol. I took a physics class this year and had similar problems

draw it out

idk what a prop or strut is

this is basically a word problem

[random pelican]

strut is strutury, prop = literally a prop

[slate monolith]

draw it out

[random pelican]

i cant draw it at the moment, dude my head is almost exploding of headache and that shit worth 10 points and is the last question

[slate monolith]

how much time u got

[random pelican]

i have 1 hour to send it, but i just want to sleep

[slate monolith]

hw or test

[random pelican]

its a hw that you need to send to teacher

that worth points

its 10pm rn, test at 10 pm would be crazyyy

[slate monolith]

well idk ur timezone lol

[random pelican]

lol, if you find someone that would be able to help me i would be grateful

[slate monolith]

the question doesnt even make sense imo

[lone sapphire]

yes just one info

one number info*

[slate monolith]

number is fine

i just dont know what they mean

too many words

dont make sense

[random pelican]

well, ig ima just leave it in blank and cry in the corner the rest of the summer

[slate monolith]

it would help with a diagram

[random pelican]

[slate monolith]

ur not gonna

fail the class

because of one assignment

[lone sapphire]

maybe he can find SOMEONE

[random pelican]

i am 3 points aways to reprove

[lone sapphire]

shit

[random pelican]

and i dont know if the others questions are right

[lofty hamlet]

Hi guys, is this channel free?

[lone sapphire]

no

we are trying to solve this

[lofty hamlet]

ok

[slate monolith]

no its paid

[simple pond]

Is that what you’re trying to find?

[random pelican]

yes yes yes

[simple pond]

Bc if so then thats easy

[slate monolith]

bruh

90-30

[simple pond]

All angles in a triangle add up to 180° and u already have two angkes

[slate monolith]

60

its just the digram thats hard

[random pelican]

oh ok so 30 + 90 = 120, 180-120 = 60

[simple pond]

Yes

[random pelican]

ok ty

[lone sapphire]

@lofty hamlet free now

[silk coral]

Can a parallelogram be a trapezoid

[queen wigeon]

no

[slate monolith]

no

[queen wigeon]

by definition, parallelograms have 2 pairs of parallel sides, while trapezoids must only have one

[slate monolith]

^

[silk coral]

Thank you

[rocky dock]

i ended up with (x+3)^2(x+4)(x+2)

but it says im wrong

[placid zinc]

,w roots of xxx + 9xx + 26x + 24

[rocky dock]

so, im right?

or wrong?

[placid zinc]

Oh, it wants the roots other than x = -3

So just -2 and -4

[rocky dock]

hmm

yep

btw i thought if there was an additional -3 you should list it

was i wrong?

or does it depend on the wording of the question

[placid zinc]

There's not an additional -3

Or else this would be a quartic

[rocky dock]

but when i factored (x^2+5x+6)

i got (x+2)(x+3)

and they already provided me with a -3

ohhhhh

so they already gave me a zero for free

degree 3 polynomial...

only needed to find 2 more

thank you @placid zinc

[silk coral]

Do diagonals bisect each angle of a rectangle

[raw sorrel]

How to be good at math

[wraith cairn]

no

[silk coral]

Ok

Is it only if all 4 sides are equal

So square and rhombus

[wraith cairn]

I am not sure about the if and only if

but if it's a square or a rhombus then the diagonals will bisect the angle

I am not sure about the converse.

[silk coral]

Ah ok

[wraith cairn]

@silk coral the converse is true

the diagonals will bisect the angles iff it's a rhombus

[craggy dirge]

how did my teacher to from x^4y + 2y^2 - ln(x) to the bottom line

i mostly done understand why x^4 dy/dx and 4y dy/dx is there

[placid zinc]

Let's do an easier question. What's d/dx of x³y?

You first have to make sure that you product rule

@craggy dirge

[craggy dirge]

@placid zinc 3x^2y i think

[simple pond]

Correct

[placid zinc]

No haha. Can't just ignore the y. Remember to employ the product rule.

[craggy dirge]

uh

one second

lol

[simple pond]

Wasnt The answer was right because x^3 goes to 3x^2 by the power rule

[placid zinc]

d/dx of x³ is indeed 3x²

d/dx of x³y is not 3x²y. d/dx doesn't ignore y

[slate monolith]

y isnt a constant

[slate monolith]

its another variable

[craggy dirge]

idk maybe im misunderstanding

[slate monolith]

yeah so the calc is wrong

it thinks y is a number

y is a function of x

[placid zinc]

I didn't ask you to use a calc lol. What's the product rule?

[slate monolith]

and so you gotta use product rule

[craggy dirge]

f'(x)g(x) + f(x)g'(x)

[slate monolith]

^

d/dx y = y'

[craggy dirge]

so 3x^2(y) + x^3(0)>

i tyihkn

i cant type i broke my finger

[placid zinc]

Right! Or:
d/dx (x³y)
= d/dx(x³)y + x³ d/dx(y)
= 3x²y + x³ dy/dx

A big thing here is that d/dx (y) = dy/dx

Which is basically just a notation

[craggy dirge]

wait just to make sure

x³ dy/dx = 0 right

[placid zinc]

y is capable of changing with x, so dy/dx might be a function

So no. It doesn't need to be 0. If it is, y is a constant

The calculator didn't know that y can change, so it ignored y. The calculator is dumb and often doesn't know what you really want

[craggy dirge]

oh ok i see

so i understand teh first 2 variables

its just the power rule

but why is 4y dy/dx there

does that mean 2y^2 d/dx = 4y dy/dx

[slate monolith]

yes

[placid zinc]

So new question!
d/dx (y²)

There's a usual way to deal with this. Just take the derivative as if y was instead x, but then throw a dy/dx out front:
d/dx (y²) = 2y dy/dx

[craggy dirge]

whats this rule called

[placid zinc]

This is actually the chain rule:
du/dx = (du/dy)(dy/dx)

Where u = y² here

[craggy dirge]

oh wtf

i think i get it now

ty!

[wise jewel]

can someone please explain what the hell is going on here

[placid zinc]

Np, hope it helps! Feel free to ask if you have anything else

[wise jewel]

what i currently understand is that the primary objective is to get it from standard form into vertex fornm

and i understand everything up until right after they factor out a

"To complete the square, take the square of half the x-term"...what does that mean?

[glass lichen]

(b/2)^2

[placid zinc]

I also don't like how they did it haha

[wise jewel]

@glass lichen where'd you get b/2 from? wouldn't it be (b/a)^2

[glass lichen]

I just explained "take the square of half the x term"

(b/2a)^2, yeah

[placid zinc]

You understood this:
a(x² + b/a x) + c

Next thing you can do is this:
a(x² + b/a x + b²/4a² - b²/4a²) + c

See how that works? This is a trick we call "adding 0" and it doesn't change the equation

[jagged trout]

https://www.youtube.com/watch?v=C206SNAXDGE

[wise jewel]

i dont understand where the b^2 / 4a^2 comes from :/

[placid zinc]

That's okay! As long as you understand why we're allowed to do what I did

It will become clear in a sec

[wise jewel]

oh ok

you're too nice ur gonna get real annoyed with me real quick because it takes me 987234 years to grasp basic stuff like this LOL 😭

[placid zinc]

This is probably by far one of the most complicated things you've had to do, a lot of people struggle with it

[wise jewel]

❤️ ❤️ ❤️

[placid zinc]

That's okay, if you get the adding 0, you are doing well so far

[wise jewel]

so BASICALLY its: "a(x^2 + [b/a]x + 0) + c" ?

what you wrote out that is

[placid zinc]

So we're here:
a(x² + b/a x + b²/4a² - b²/4a²) + c

The big deal is that the first three terms are always a perfect square quadratic. It factors like so:
a((x + b/2a)² - b²/4a²) + c

And yes that's basically what I wrote out

[glass lichen]

$a(x^2+\frac{b}{a}x)+c \ a(x^2+\frac{b}{a}x+(\frac{b}{2a})^2-(\frac{b}{2a})^2)+c$

[ocean seal]

Mosh

[spice fiber]

i need help

with

this

i dont understand

this

[placid zinc]

We're full on this channel, haha. But I'll help you in a different channel

[wise jewel]

hmmmm

[spice fiber]

aw

[wise jewel]

in "a((x + b/2a)² - b²/4a²) + c" what're you factoring?

[placid zinc]

Try expanding (x + b/2a)² and you'll get the previous line

Specifically, we factor like this:
x² + b/a x + b²/4a² = (x + b/2a)²

.
To repeat the whole thing, we have this:
a(x² + b/a x + b²/4a² - b²/4a²) + c

And apply that factorization on the first three terms:
a((x + b/2a)² - b²/4a²) + c

[wise jewel]

im still not sure what is going on exactly... 😅

hm

maybe i can watch the vid linked earlier

and try to come back to this?

if u dont mind 🙂

[placid zinc]

Sure thing! Take some time with it, but trust me it will click

[wise jewel]

OH

I understand how they get a(x^2 + [b/a]x + b^2/4a^2) - b^2/4a^2 + c

!!!!!!

LOL you deleted your message...did i get something wrong??? 😅

[placid zinc]

You clicked something else lol

[wise jewel]

LOL

well...its progress at least 😅

let me keep watching and see if i figure out the factoring too

I GET THE FACTORING NOW

the guy in the video says that factoring the quadratic will ALWAYS look like this no matter the equation

and i followed what it shows and sure enough it lines up with what is shown in my book

so ig its just a case of memorizing how to do that...?

[placid zinc]

A little bit yeah haha

That's where the "half it and square it" comes from. That gives the factoring

[quiet crown]

It's easy peasy

What two numbers add to 4x and times to 2^2 or 4

[wise jewel]

2?

[quiet crown]

ye

[alpine sable]

I'm trying to self-teach myself up to calculus, any tips/recommendations? I'm near the algebra 2 level and I'm looking to be better.

[placid zinc]

Khan academy is a good resource for hs level

1.5x speed exists haha

[wise jewel]

ok huh?? why is it saying to add and subtract (b/2a)^2????

i thought you were just supposed to take the square of half the second x term?? which would be (1/2[-2])^2 which = + 1 which is what they got for the inside of the parenthesis. Shouldn't you then subtract 1 outside the parenthesis to maintain equality? why do they do "-3 + 7" when it should be "f(x) = 3(x^2 - 2x + 1) - 1 + 7" and again where on earth does (b/2a)^2 come from??? just when i thought i had grasped this concept too...

[ionic jewel]

its because theres a 3 outside the parenthesis

your way works if a = 1

so to maintain the equality when you add 1 inside the parenthesis, you have to subtract 3 from outside

because remember, the inside one is being multiplied by 3

[wise jewel]

ohhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh

ofccccccc

damn

hahahaha, ok, i got it now 😄

tyyyy!!!!!!!

gonna go to sleep now

brain is fucking fried

actually ill try one more practice problem of this

so first, im gonna do

f(x) = x^2 - 5x - 12

then group the x terms to get

f(x) = (x^2 - 5x) -12

(1/2[-5])^2 = 6.25

so that means f(x) = (x^2 - 5x + 6.25) -6.25 -12

which --> f(x) = (x^2 - 5x + 6.25) -18.25

is that the answer?

[placid zinc]

That's not in vertex form so no

[wise jewel]

oh shoot

ur right

[placid zinc]

You're missing the final step

[wise jewel]

i have to put the exponent outside the parenthesis

[placid zinc]

What's the perfect square factorization?

[wise jewel]

(x + 6.25)^2?

[placid zinc]

It will be (x - 2.5)²
which expands to
x² - 5x + 6.25

.
Hint, x² + ax + something
factors to (x + a/2)²

[wise jewel]

ohhhh you're right

so the finals answer should be f(x) = (x - 2.5)^2 -18.25

[placid zinc]

Yaya!

[wise jewel]

yayyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy'

that thing u said is important

i should prob remember it 😅

the hint

WHEN TURNING STANDARD FORM QUADRATIC EQUATION TO VERTEX FORM:

1. group x terms

2. factor out gcf

3. take the square of half the second x term and add it to the inside of the parenthesis, then maintain equality by subtracting its equal outside the parenthesis
   • if a = 1, you can put the number itself, but if a > 1, then do a * #

4. put the first x term's exponent outside the parenthesis, this can be done via factoring.
   • Hint: x² + ax + something factors to (x + a/2)²

this is what i wrote for myself, would this be right?

[slate monolith]

Aka complete the square

[wise jewel]

Hahahah right 😅

Why do I make everything so much more complicated then it needs to be???

My brain is so weird

[alpine sable]

there are somethings here that seems like an ancient language

lol

[halcyon nova]

https://cdn.discordapp.com/attachments/800889689238011917/857826862423343124/image0.jpg

Helppp

[slate monolith]

Use tan and pythag

[ionic jewel]

r*cis(theta)

[umbral pulsar]

graph the number in complex plane, then use tan to find the angle with +ve x-axis

[celest hatch]

Answer will be 6(cos30 +isin30)

[umbral pulsar]

bruh

don't give them answers

just give hints

[celest hatch]

ohk ..sorry i m new here @umbral pulsar

[umbral pulsar]

ok, so remember now onwards

[celest hatch]

yup

[radiant ferry]

https://docs.google.com/forms/d/e/1FAIpQLSeWHoDbchL_tMZkgFMCR4nxnEcyTUfvo0Th1P6YMpjgfLtqAQ/viewform

yo help me fill this form

[umbral pulsar]

what is it?

a test?

[radiant ferry]

what food you like

idk its some dumb thing the school wants me to get like a few hundred responses

[umbral pulsar]

https://tenor.com/view/disappointed-face-palm-seriously-exasperated-gif-7304550

[halcyon nova]

Wrong answer

[umbral pulsar]

measure angle from +ve x axis

[celest hatch]

ufff..then what is correct

[celest hatch]

yeah.. my bad

🙂

i measured the wrong

[slate monolith]

wtf

thats nsfw

well, almost

i mean...

fr tho

[strong furnace]

<@&268886789983436800>

[slate monolith]

@strong furnacewhy ping mods

they no likey

[strong furnace]

nah they like being pinged

makes them feel "important"

[slate monolith]

hmmmmmmmmm

so what abt spam ping

[strong furnace]

thats a report ping not a spam ping and I was told to report trolls some time ago that is why I ping mods

[tall wing]

yeah idk they’re not here

i suppose i can try banning them still

er

im not on computer so i dont think i can

[slate monolith]

do u like being pinged

wtf

[tall wing]

wrf

uh

[slate monolith]

wait so who banned them

[tall wing]

where did they go

[slate monolith]

into the shadow realm

[tall wing]

oh namington got it

[slate monolith]

no but like

[tall wing]

ty

[slate monolith]

to what extent do they like pingies

[tall wing]

pinging us is fine

btw

[slate monolith]

ok good

[tall wing]

you can also use modmail

[slate monolith]

some servers have instabans

if u ping mods

[night geyser]

if someone posts literal porn

do ping us

[slate monolith]

but that wasnt

[night geyser]

yes it was.

[slate monolith]

they technically had clothes

alr

[tall wing]

yeah that was pretty bad lol its def worth instaban

[slate monolith]

ty for getting rid of it

[night geyser]

also, if a server instabans for pinging mods, that server is not run by competent people.

if the mods dont want to get pinged they can just disable pinging the mod role

trust me, im an expert in moderating while incompetent.

[slate monolith]

there was a big server and i asked for help

and like 10 sec ban

there was a timer lol

[slate monolith]

good to know 👍

[slate monolith]

check dms

[timid yoke]

anyone knows?

[rugged lynx]

-15 added to the difference of 7

[echo cape]

The menu of a small restaurant lists 2 soups, 5 meats, 3 desserts, and rice. How many different meals consisting of one soup, 1 meat, 1 dessert, and rice are possible?

[nova widget]

if you just had one type of soup, one type of meat, but 3 desserts and rice, how many combinations could you have?

[nova widget]

you can then repeat this for the other meal components

[nova widget]

(a) for the quadratic equation, you can think of the pythagorean theorem, then plug the values into the formula $a^2 + b^2 = c^2$ \
\
(b) try to use your equation in (a) to find $x$, then you can find the base and height of the triangle, with that, you can use $\frac{1}{2}bh$ to find the area

[ocean seal]

g-e-o-m-e-t-r-i-c

[nova widget]

we can assume that the triangle is indeed a right-angled triangle, so that you can use the pythagorean theorem to help you confirm that the two walls meet at a right angle

[timid yoke]

thank you so much

[dry thunder]

can someone help me with this:

Sum of the digits of a two digit number is 9. When we interchange the no's if it found that the resulting new number is greater than the original number by 27. What is the 2 digit number?

[nova widget]

find the volume of the sphere, and calculate how much of each metal is needed to craft the sphere

[alpine sable]

how would i find volume

[nova widget]

use a formula?

[alpine sable]

which

[nova widget]

the formula for finding the volume of a sphere ?

[alpine sable]

i see

ok

[nova widget]

We can take the original number to be $\overline{AB}$.
$\overline{A} + \overline{B} = 9$

[dry thunder]

thanks :))

[west raven]

"how u all that good at that"

[spice fiber]

what is 1 + 2???

[vale wigeon]

http://lmgtfy.com/?q=what+is+1+plus+2

[vast lance]

what does part c mean? i don't get how it affects the probability

[jagged imp]

in the first part she has to eat an entree, main and desert

but for c she could just eat a main, eat a main and a desert, eat a main and an entree or eat all three

[vast lance]

oh

how would i find out the probability for those

[thorn kindle]

@vast lance its really just an extra option

Call it "none"

[vast lance]

huh

[thorn kindle]

Add the none option to the tree

[vast lance]

ohh

[thorn kindle]

For the dessert and entree

[vast lance]

okay

[thorn kindle]

Do you know the definition of dot product

[halcyon nova]

No

So what’s the first thing I should do

[thorn kindle]

Why are you doing this lmao

If you dont know what a dot product is

[halcyon nova]

Cus it’s the hw

[spare fern]

Sussy baka moment

[minor crypt]

[vague coral]

read your lessons

[halcyon nova]

😭

[minor crypt]

he's right though

[thorn kindle]

Your teacher gives you he you don't know how to do 🤔

[placid zinc]

If
v = ai + bj
u = ci + dj

Then u•v = ac + bd

[minor crypt]

he probably just doesnt feel like going through the material

[vague coral]

[minor crypt]

asking discord is easier

[halcyon nova]

It’s not clear

[minor crypt]

well then ask your questions

what part of it don't you understand?

[halcyon nova]

What equation do I use

[placid zinc]

Google is your friend when all else fails, come to us when that fails too

[minor crypt]

this one^

[halcyon nova]

Ok

[vague coral]

let him read a book

[halcyon nova]

I don’t use a book

[placid zinc]

Yikes everybody get on the pile

[minor crypt]

[ivory otter]

Hey

so

can someone help me understand how to multiply matrices 3bluebrown way

[placid zinc]

I don't know 3b1b way but

That's by far the easiest way

[ivory otter]

i think this is the way yes

[placid zinc]

Put the matricies corner to corner, this gets you the size. Then dot product like above

[minor crypt]

why has no one shown me this ffs

[ivory otter]

ye but

[minor crypt]

[ivory otter]

im thinking

do i repeat

lemme show you my question

[minor crypt]

do you know how much time I've spent multiplying matrices

[placid zinc]

Yeah I didn't know of this method either. But now we do!

Not like I'm multiplying matricies all the time

[alpine sable]

help pls

its not (0,0) or 3pi/2

[ivory otter]

dang i get it now lol

thank you

but

last question

do i multiply each row from Matrix A with every column of Matrix B

[placid zinc]

Like if you wanted the top right entry, you'd dot the row to its left with the row above

[ivory otter]

ye but

the numbers that i have circled

[placid zinc]

So far so good. The next entry is 5

[ivory otter]

do i multiply the 1 0 with every element of matrix thats above

going by columns

do you understand what i mean?

[placid zinc]

I mean you'll eventually have to, yes

[ivory otter]

wdym eventually

i mean rn

so like this:

1x3 + 0x4

then

1x9 + 0x2

then

1x5 + 0x8

[placid zinc]

Oh no

[ivory otter]

then

[placid zinc]

1x9 + 0x2

For middle upper entry

[ivory otter]

wait i messed up there

i meant 2

[placid zinc]

Yeah that's all correct

[ivory otter]

ok

[placid zinc]

Then 0x3 + 1x4 for bottom left

[ivory otter]

yes

ok awesome

[placid zinc]

Yeye. Just continue and complete matrix

That's the product

[ivory otter]

thank you!!

[placid zinc]

Np! Good luck with the others. Feel free to ask if you need anything else.

[alpine sable]

can someone walk me through this

ive taken the second derivative of the function already but im still confused

[placid zinc]

So you know that f"(x) = -4sin(x) - 4sin(2x)

[alpine sable]

yes

[placid zinc]

And we just want any zeroes of that

[alpine sable]

yup

[placid zinc]

Obvious one, when x = 0

That might actually be the answer haha

[alpine sable]

right, it wont accept it though unfortunately

[placid zinc]

Okay so next. We need a better way to get zeroes

[alpine sable]

i only know of the unit circle

[minor crypt]

0 is the smallest x-value, no?

[alpine sable]

still not sure why 4pi/2 is a critical point either

[placid zinc]

0 = sin(x) + sin(2x)
0 = sin(x) + 2sin(x)cos(x)
0 = sin(x)[1 + 2cos(x)]

So we care about when
sin(x) = 0
Or
cos(x) = -1/2

[alpine sable]

it wont accept it for some reason

[minor crypt]

I'm pretty sure the teacher meant the open interval ]0,2pi[

[alpine sable]

yeah

[placid zinc]

Yikes took me a while to type that out correctly

See the edit

[minor crypt]

cos(x)=-1/2
x=-pi/3

which is not within the interval

[placid zinc]

So there's a zero when x = 2π/3

[minor crypt]

oh yeah right

[placid zinc]

Watch out cos(-π/3) = 1/2

I almost just did that myself kek

[alpine sable]

man this crap is confusing lol

[minor crypt]

[alpine sable]

how would there be a zero on 2pi/3 tho

when i plug it in it gives -sqrt3

[placid zinc]

Into the second derivative?

[alpine sable]

yes

[minor crypt]

make sure you do sin 2x, so sin 4pi/3

[alpine sable]

still gives me -sqrt3

:/

[minor crypt]

[placid zinc]

Should not, that's definitely a zero

[minor crypt]

he's right, sin 4pi/3 is not zero

so we went wrong somewhere

if its not 0 then maybe there just is no solution?

[placid zinc]

,w -4sin(2π/3) - 4sin(4π/3)

[ocean seal]

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[minor crypt]

[alpine sable]

bruh

[placid zinc]

Y'all had me doubting

[minor crypt]

except you lied

[alpine sable]

brain hurts

also

[alpine sable]

i already have 4pi/3

AND ITS NOT A ZERO

confusion

[minor crypt]

2pi/3

[placid zinc]

Be careful with that calculator, 4π/3 is a zero

[minor crypt]

what is going on

[placid zinc]

Make sure you are correctly subbing it into
-4sin(x) - 4sin(2x)

[alpine sable]

i mean isnt sin(2 (2pi/3))=sin4pi/3

[minor crypt]

it is, but your x is still 2pi/3

[alpine sable]

yes

[minor crypt]

so what you'd write is (2pi/3 ; 0)

[alpine sable]

but somehow this is correct

??

[minor crypt]

because that's for x=4pi/3

[alpine sable]

but its not zero?

[placid zinc]

Oh, okay I see your confusion

[minor crypt]

therefore sin 2x= sin 8pi/3

[alpine sable]

yes

[placid zinc]

f(4π/3) is not zero.
f"(4π/3) = 0

[alpine sable]

hm

[placid zinc]

Now, we are currently talking about zeroes of the second derivative. But that picture is taking about the original function

[alpine sable]

ooh okay

so am i supposed to plug in the critical point into the original function? bc ive been plugging in the critical points into the derivative for the other homework questions lmao

and theyve been correct

[placid zinc]

To find what?

[alpine sable]

the point of infliction

[placid zinc]

Let x = c be a point of inflection
Then f"(c) = 0
And f(c) will get you the y-value of the poi

[alpine sable]

damn

i might be imagining things

[placid zinc]

f'(c) is nothing special

[alpine sable]

understandable

thank you

[placid zinc]

Np. Feel free to ask if you have any other questions

[thorn kindle]

If f: X -> Y is a function from N to N whose domain is the naturals 1 to 10, and whose function values are a random integer between 1 and 10 inclusive, what is the probability that f has a fixed point?

Hopefully i worded that right

[placid zinc]

You've listed three domains, haha.
f: X → Y implies X is the domain
"From N to N" implies N is the domain

.
Let S be the set of naturals from 1-10
You care about functions f: S → S

A good way to think about this problem is 10 different boxes, and 10 different balls. By putting the balls into the boxes randomly, you describe a function fully

Hmm. How to count the functions with a fixed point, though? Let me think.

[vale wigeon]

so really you meant f: 1:10 -> 1:10?

and the value of f at each input is uniformly distributed on {1, 2, ..., 10} independently of the others?

is that what you're going for?

||each number between 1 and 10 has a 1/10 probability of being a fixed point, so the prob of all of them failing to be fixed points is 0.9^10||

[placid zinc]

I haven't done enough probability recently

[thorn kindle]

I should also mention that no y value is repeated

[hardy geyser]

https://gyazo.com/0e8df8b7addd4bccce960014ddc3237c

i dont understand how?

[thorn kindle]

What is the domain of the square root function

[hardy geyser]

ugh what do u mean

[thorn kindle]

Over what interval is sqrt(x) defined

[hardy geyser]

umm

1-5 = -4? square rooted = 2?

[minor crypt]

cant take srt of negative numbers (complex 🤐 )

sqrt(-4) is undefined (for now)

[hardy geyser]

wait whatttttt

[vale wigeon]

sqrt(-4) is either not real or undefined

[minor crypt]

so z-5 has to be positive

[vale wigeon]

it's sqrt(+4) that is equal to 2.

[hardy geyser]

negative numbers cant be square rooted?

[vale wigeon]

until you learn about complex numbers, yes.

for now you cannot take the square root of a negative number.

[hardy geyser]

wait that make sense ohhh ty

what are complex numbers then

[vale wigeon]

they're what happens when you pretend sqrt(-1) is a meaningful thing to talk about

you'll learn about them in due time, but for now it'd only be a distraction

[hardy geyser]

ok ty

[vale wigeon]

do you have the exact problem statement in full

it just won't do any good if you keep making addenda like this and fumbling your question even further

[thorn kindle]

You have 10 boxes labelled 1-10 and 10 balls labeled 1-10. If the balls are put into the boxes randomly what is the probability that there will be at least one box whose value is the same as its ball?

[vale wigeon]

and the balls are put in such that there's one ball per box?

[thorn kindle]

Yes

[vale wigeon]

alright

you might wanna look up derangements then

they are closely related to your counting problem

[minor crypt]

1-P(no boxes with same number)=1-(9/10)^10

is that it?

@thorn kindle

[thorn kindle]

Ooh thats pretty interesting

Seems like the answer is really close to 1 - 1/e

So its just !10/10!

?

[vale wigeon]

one minus that

[thorn kindle]

Right

Really interesting stuff

The formula for the subfactorial is kind of surprising

[harsh acorn]

Prove that the integer n is a triangula number if and only if $8n + 1$ is a perfect square.

[ocean seal]

Hyl1s

[harsh acorn]

Can I get a hint?

[vale wigeon]

which direction would you like to start with?

"n triangular => 8n+1 square" or "8n+1 square => n triangular"?

[harsh acorn]

First one?

[vale wigeon]

okay

n = k(k+1)/2 for some integer k

see what happens when you look at 8n+1

[harsh acorn]

$8\frac{k(k+1)}{2}+1=x^2\rightarrow 4k^2+4k+1=x^2$

[vale wigeon]

no. do not start with the assumption that 8k(k+1)/2 + 1 is a perfect square

just simplify 8k(k+1)/2 + 1 on it sown

[harsh acorn]

okay

$8\frac{k(k+1)}{2} + 1=4k^2+4k+1$

[ocean seal]

Hyl1s

[harsh acorn]

oh, I see it now

,w factorize 4k^2+4k+1

[ocean seal]

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[harsh acorn]

yeah yeah I understand it

tysm

[prime mist]

is this free now

So I already Isolate y for x which leads to
$y=\sqrt{-x+8},:y=-\sqrt{-x+8}$

[ocean seal]

foreverbeginner

[vale wigeon]

this was useless

[prime mist]

nanii

in the end I found no solution jsut that..

[vale wigeon]

it's much easier here to integrate with respect to y

then you would have $\int_{-2}^2 (8-y^2 - y^2) \dd{y}$

[prime mist]

so i want to ask did i d osomethign wronggg

[ocean seal]

Ann

[vale wigeon]

in any case,

[vale wigeon]

this covers only the red curve

[prime mist]

oh

[minor crypt]

whats !10?

[stark trail]

Subfactorial

[minor crypt]

huh whats that

[minor crypt]

I know 10!=10x9x8x.....x1

[minor crypt]

wouldnt that just be 1 or -1

oh nvm

[bitter kite]

is anyone available?

[glass lichen]

clearly no one is available. . .

no one in the 30k odd people on the server is available obviously

[storm agate]

Can someone please explain and write the method to solve This? Just question 1 for now

[spring harbor]

(x+p)^2 = x^2 + 2px + p^2

Try to get the given expression in this form and then you can replace it with (x+p)^2

You can also add numbers to your expression; for example
1c) x^2 - 8x = x^2 - 2.4.x + 4^2 - 4^2 = (x-4)^2 -16

I added 4^2 because 8 = 2.p => p = 4

[craggy dirge]

how did this guy get 1 for t(1,0,-8)?

i understand how he got -8 because he just calculated the derivative

[whole prairie]

Can sqrt(2+x)-sqrt(2)/x be simplified? I’ve tried and cannot

Because I have lim->0 and can’t simplify

[wanton turtle]

Try rationalizing the numerator

[glass lichen]

interpret as a derivative

[whole prairie]

You can use derivatives for simplification in this scenario?

[wanton turtle]

Once you rationalize the numerator, the only thing remaining will be x, which cancels out with the x in the denominator

[wanton turtle]

You can directly substitute 0 instead of x after this

[glass lichen]

$\lim_{x\to 0}\frac{\sqrt{2+x}-\sqrt{2}}{x}$ is a derivative

[ocean seal]

Mosh

[whole prairie]

But doesn’t that make in undefined since it would be over 0?

[wanton turtle]

No, the x cancels out

Oh you talking about the original question?

[whole prairie]

Okay sorry if I’m getting this twisted but if I rationalize the numerator it would be multiplying both numerator and denominators by sqrt(2+x) right?

[glass lichen]

no

[wanton turtle]

No

[glass lichen]

sqrt(2+x)+sqrt(2)

[wanton turtle]

[whole prairie]

Okay

Thank you I will try that

[wanton turtle]

We are trying to remove the roots by using the (a+b)(a-b) = a^2 - b^2 identity

A general tip I can give for these limits with roots is to always rationalize

[whole prairie]

Okay thank you

[flat vale]

Anyway to get the range of any function?

[glass lichen]

if an inverse exists, then range of f is domain of f's inverse

[flat vale]

any function, even not one-to-one function

[glass lichen]

graph it

[woeful pulsar]

{f(x) | x in dom(f)}

[wispy olive]

Is there a way to find the x-coordinates- of a function/equation using the Quadratic Formula?

[glass lichen]

well not every function is a quadratic for one

[wispy olive]

Yeah.

But if it is.

[glass lichen]

and yes, you can find the domain of a function...

domain of all polynomials is R

[wispy olive]

How will that matter.

[glass lichen]

you're asking for x values......

[wispy olive]

Can we find these 2 points.

[woeful pulsar]

do you mean x-intercepts?

[wispy olive]

Using the Quadratic Formula itself.

[glass lichen]

yes..

[wispy olive]

Yes! Sorry I used the wrong word.

[wispy olive]

How?

[gray isle]

that's what the quadratic formula does

[glass lichen]

the quad formula tells you the roots if the quad is = 0

[wispy olive]

I mean with the quadratic formula you can find the vertex of the function/equation.

But how the x-intercepts?

[glass lichen]

??

[alpine sable]

they just told you

[glass lichen]

read this again

the quadratic formula tells you the roots

[gray isle]

either that or you think something else is the quadratic formula

[wispy olive]

Most probably I am wrong.

[ocean seal]

ℝamonov

[wispy olive]

Yes.

Wait.

Let me re-think what I am saying.

Most of the times later I realized I was being foolish.

Oh yes.

Sorry.

It was all my mistake.

[alpine sable]

,w 3+2

[ocean seal]

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[alpine sable]

,w {a+b+c+d= £7.11, abcd= £7.11}

[ocean seal]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
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Requested by Bucket#8932

[gray isle]

consider the the remainder when dividing by a quadratic polynomial will be in the form ax + b

[alpine sable]

,w {a+b+c+d=7.11, abcd=7.11}

[ocean seal]

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[gray isle]

#bots

[alpine sable]

,w {2.5+b+c+d= £7.11, 2.5bcd= £7.11}

,w {2.5+b+c+d= £7.11, 2.5*bcd= £7.11}

[ocean seal]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by Bucket#8932

[alpine sable]

,w {2.5+b+c+d= £7.11, 2.5xbcd= £7.11}

[ocean seal]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by Bucket#8932

[alpine sable]

Why won't @ocean seal understand?{2.5+b+c+d= £7.11, 2.5bcd= £7.11}

{2.5+b+c+d= £7.11, (2.5)bcd= £7.11}

,w {2.5+b+c+d= £7.11, (2.5)bcd= £7.11}

[ocean seal]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by Bucket#8932

[alpine sable]

,w {a+b+c+d=7.11, abcd=7.11}

[ocean seal]

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[gray isle]

<@&268886789983436800>

[true marsh]

here you can learn and do you homework

[alpine sable]

,w {£a+£b+£c+£d=7.11, £abcd=7.11}

,w {a+b+c+d=7.11, abcd=7.11}

[ocean seal]

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[tame falcon]

@true marsh Don't advertise here.

[alpine sable]

Hey guys I need to work out this equation {a+b+c+d=£7.11, abcd=£7.11} but it won't give me a simple answer. Can any of you help?

[gray isle]

what's with the £

[bronze dust]

can anyone explain me that transition from 2nd step to 3rd step, how did it take 18 common

[alpine sable]

@brittle pier I need help working out this. {a+b+c+d=7.11, abcd=7.11}

,w {a+b+c+d=7.11, abcd=7.11}

[ocean seal]

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[feral seal]

can someone tell me what is the use of this https://www.youtube.com/watch?v=wO61D9x6lNY

[alpine sable]

,w {1.2+a+b+c=7.11, 1.2abc=7.11}

[ocean seal]

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[gray isle]

well you have 2 equations with 3 variables...

[quasi canyon]

so
i gotta get perfect on my entire culminating assignment and bonus assignment and an entire other block to pass and todays the last day of math

help

help me

please

[quasi canyon]

@faint seal this does not help my case

[woeful pulsar]

Try drawing a diagram?

[faint seal]

Oh, you're an Evan Chen fan too? I'll give you the link to his Discord server if you want.

[woeful pulsar]

lol its fine i have enough servers

Okay maybe i should join dm me

[faint seal]

ok

[quasi canyon]

this is only the first page, its all grade 10 math so if someone is smart it shouldnt be that bad to do an entire like 2 months of work today

[woeful pulsar]

We cant really just give answers though but if you try working on them you can try posting your attempt and we might feedback

[faint seal]

Is this server really a homework help server? lol

[quasi canyon]

I didn't learn any of this I was busy doing other classes

and yeah

[faint seal]

then read up bro

[quasi canyon]

read what I have to get this all in in 1 hour and 18 minutes

[faint seal]

so you have 3 problems?

[quasi canyon]

I have 3 assignments

thats just the first problem

i dont like problems

math teacher should fix her problem on her own

i didnt even learn how to solve it im not a good worker for this job

[feral seal]

sounds to me like you are confused

[quasi canyon]

yes

you are correct

[faint seal]

ok, so these 3 problems are all addition and multiplication problems

I think you can do it, man

[quasi canyon]

the first one is the only one i dont know how to do

but this is all so tedious to do in 1 hour and 15 minutes so i wanted some help from someone in here

[faint seal]

bro if you don't know what a "first difference" is, then search it up

https://www.google.com/search?q=what+is+a+first+difference+in+math&oq=what+is+&aqs=chrome.0.69i59l3j69i57j69i59j0i67j69i60l2.1223j0j7&sourceid=chrome&ie=UTF-8

[quasi canyon]

i did

dint make sense

[faint seal]

"First differences are the differences between consecutive y-‐values in tables of values with evenly spaced x-‐values."

[quasi canyon]

the teacher explained it in like 20 seconds to me one time over call when she was walking her dog and it still didnt make sense

[faint seal]

read bro

[quasi canyon]

that still doesnt make sense

i did read

[faint seal]

so... 5-2 doesn't make sense?

cmon man

[quasi canyon]

3

[faint seal]

the x-values in the table are evenly sapced

and the consecutive y values are 2,5,8,11,14

[quasi canyon]

yep

[faint seal]

so...?

[quasi canyon]

so what?

what is it 2,4,6,8,10?

[faint seal]

no man

5-2=3

8-5=3

[quasi canyon]

well thats the difference

[faint seal]

11-8=3

[quasi canyon]

this doesnt make sense

[faint seal]

exactly

difference is subtraction

[quasi canyon]

oh

3

[faint seal]

yes

bro you gotta show some signs of learning it or else we're not gonna spoon feed you lol

[quasi canyon]

i didnt learn it

thats why i need help

i dont know if i should bother doing 2 culminatings and an entire block in 1 hour

or just retake math

because to pass i need to get all questions right on every assignment

actually 3 hours

without knowing alot of the stuff on them

[faint seal]

well sounds like you're in a pickle

but bro

[woeful pulsar]

You should probably retake ig because math builds on what you already know pretty heavily

[faint seal]

when we try to teach you we're expecting you to take something away

[quasi canyon]

oh okay

you explained differences better than my teacher so atleast i know how to do that now

[faint seal]

ok cool, then move on to the other porblems

do what you can

show us the work you did on the ones you cant solve

just keep going

if you get stuck, skip it and show us how you approached it

[quasi canyon]

this sounds like a better idea right now @faint seal

[faint seal]

in that case sure

[quasi canyon]

because my mark is 17% and its the last day

[faint seal]

but still try lol

[alpine sable]

Whats the value for the missing angles

[tribal oxide]

Can anyone explain why this is the answer

[limpid spade]

which function gives a negative inside the square root if u plug in - 2

[pallid olive]

hey

[wise jewel]

Good morning everyone

its a brand new day

[limpid spade]

raid?

[tribal oxide]

To me, it looks both, thats why i dont understand ;-;

[limpid spade]

it's occupied

[pallid olive]

can someone help

[ionic jewel]

you can take the odd root of a negative number

for example sqrt(-8) is complex, but cube root of -8 is -2

[tribal oxide]

Ohhh

Thanks

Got it

[ionic jewel]

or more accurately, the odd root of a negative number has a real solution

[tribal oxide]

I see

[pallid olive]

i need it in full sentences

[limpid spade]

what?

[pallid olive]

i need the answer in full sentences

[limpid spade]

repost your question and I can't help

[pallid olive]

this 1

[ionic jewel]

males are taller lol

what do they even want you to write

[tribal oxide]

Can i dm u, i have a few more doubts regarding to other questions

[ionic jewel]

no

[limpid spade]

an essay of 800 words on why males are taller

[ionic jewel]

genetics but 800 times

[wise jewel]

can someone explain this to me?

before i checked the answer i said that it is easy to identify the vertex, axis of symmetry, AND the y-intercept in the vertex form

but they say it's easy to identify it in standard form?

all you have to do to find the y-intercept in a vertex form equation is substitute x for 0

[alpine sable]

the y intercept is the constant in ax^2+bx+c

[wise jewel]

what's the constant

[alpine sable]

and yes that is also true

[wise jewel]

c?

[alpine sable]

yup

[wise jewel]

ahhh

so technically it would be easier then ig lol

ty!

[alpine sable]

idk thats up to you I prefer the vertex form

oh yeah in the context of looking for the y-intercept standard form is easier

but generally speaking they aren't both hard?? idk but vertex form allows you to identify more stuff

[wise jewel]

yeah

also

i understand how they got the vertex and the y intercept

but how did they find (2, 0) for the third point?

[alpine sable]

what third point

That being the vertex/global maximum?

ok to find roots/zeros/x-intercepts of a parabola you'd use the quadratic formula

or get your expression

[wise jewel]

well

(2, 0)

[alpine sable]

and make that equate to 0

and solve for x

[wise jewel]

how did they find that

oh

[alpine sable]

Thats the roots

[alpine sable]

.

[alpine sable]

.

[alpine sable]

.

[wise jewel]

somake the quadratic equation equal 0?

[alpine sable]

.

[alpine sable]

yes

but you could use the formula

which is only applicable iff ax^2+bx+c=0

[wise jewel]

so -0.5(x + 2)^2 + 8 = 0

[alpine sable]

yeah

[wise jewel]

ohhh

wish they told me how to do that

ty!

[alpine sable]

or again you could use the quadratic formula

[wise jewel]

well you said its only applicable if ax^2 + bx + c = 0

how do i know that its applicable

[alpine sable]

Also to speed up things

[wise jewel]

the equation is in the vertex form

[alpine sable]

You could use the discriminant

to find how many solutions you have

so I wouldn't spend time looking for roots

[wise jewel]

idk what a discriminant is

[ocean seal]

Πολλά άτομα είναι

Πολλά άτομα είναι

[alpine sable]

Your discriminant tells you have many solutions your quadratic has

[ocean seal]

Πολλά άτομα είναι

Πολλά άτομα είναι

[wise jewel]

how do i know what a b and c are

[alpine sable]

Wdym

[glass lichen]

read

[ocean seal]

Πολλά άτομα είναι

[alpine sable]

idk how else you could explain this, but just read ig?

[wise jewel]

well

previously i was given three passthrough points

to substitute a b and c for

but i dont have 3 points now

[ocean seal]

Πολλά άτομα είναι

[alpine sable]

wdym

send the question over

[wise jewel]

i want to know how they know/figured out that the curve passes through (2,0). I understand how they know the curve passes through (0, 6) because that's simply the y-intercept. and I know how they figure out that it also passes through (-4, 6) and (-6, 0) because that's just mirroring the two other points.

[alpine sable]

As I said

Wait

I already answered you

[wise jewel]

I did -0.5(x + 2)^2 + 8 = 0 and solved for x but got 12

[alpine sable]

Nah

you did something wrong

[wise jewel]

i probably did my math wrong, but putting it in a calculator says that "x =6, x = -2"

but x = 2

[alpine sable]

2 solutions you have to have

[alpine sable]

are you sure?

you typed it wrong

6 is supposed to be negative

and 2 is supposed to be postivie

[wise jewel]

$solve:for:x,:-0.5\left(x-2\right)^2+8=0$

[ocean seal]

¿Black Hat? ͜..

[wise jewel]

omg im retarded

[alpine sable]

,w -.5(x+2)^2+8=0

[ocean seal]

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[wise jewel]

yeah i put a negative instead of a positive

my bad

[alpine sable]

[wise jewel]

but i still dont understand

how they got 2 x's

[ocean seal]

¿Black Hat? ͜..

[wise jewel]

but i dont know what any of that means

is g(x) and f(a) the same thing?

[alpine sable]

They could, they could not

can you send the question over

[wise jewel]

sure

[alpine sable]

or wherever that says that

[glass lichen]

$x^2=a\implies x=\pm\sqrt{a}$ is all it's saying

[ocean seal]

Mosh

[alpine sable]

you sent the same thing

[wise jewel]

thats the question

[alpine sable]

Yeah I know that

[alpine sable]

But i was talking about this

where does it say that

[wise jewel]

oh

here

one sec

once at the point

$\left(x+2\right)^2=16$

[ocean seal]

¿Black Hat? ͜..

[wise jewel]

should i take the square root of both sides?

[glass lichen]

yes

[wise jewel]

which would be x + 2 = 4

so x = 6

[glass lichen]

+/- 4

$x+2=\pm 4$

[wise jewel]

omfg

sorry x = 2

[ocean seal]

Mosh

[glass lichen]

cause $(-4)^2=4^2=16$

[wise jewel]

whats the point of the +-

[ocean seal]

Mosh

[glass lichen]

cause both are valid

and quadratics have 2 roots