help-0

[alpine sable]

?

[violet panther]

No…

[alpine sable]

okay

it says tangent at 3, 6 passes through origin

this means you can draw a line from 0, 0 to 3, 6

[violet panther]

Ohh okay

[alpine sable]

the slope of this line is 2 right?

[violet panther]

Yes

[alpine sable]

and make the f'(2) equal to 2

and find k

-2 I guess

yeah -2=k

can you complete the rest?

oh we already finished it

aight

[violet panther]

Wait

How to get 2 in the f’(2)

I understand that dy/dx is equal to 2

[alpine sable]

we already found the value of f'(2)

by another method

what I do is just to put 2 there

[violet panther]

The textbook answer said k is equal to -4

[alpine sable]

I am going to check

[violet panther]

I got it until here

[alpine sable]

sorry

f'(3) is what we found

because the x value is 3 there

I drew it give me a second

[alpine sable]

this channel is busy

damn u being cringe

ight bet

?

[violet panther]

But how to get k=-4?

At the end?

[alpine sable]

oh that

we know f(3)=6 and f'(3)=2

[violet panther]

If f’(3)= 2(3) plus k, then the k will be -6?

[alpine sable]

yeah

we can find k here

f'(3)=2=2 . 3 + k

got it?

[violet panther]

Where f(3) came from?

I’m sorry for asking you a lot of question

[alpine sable]

the function passes through (3, 6)

that means, when you put 3 you get 6

to the original function which is f(x)

not f'(x)

[alpine sable]

np im here till you understand

[violet panther]

Am I correct?

[alpine sable]

tf is $\frac{dy}{dx}=2$

[ocean seal]

junait

[alpine sable]

you cannot say that

[violet panther]

I thought the slope is 2?

[alpine sable]

yes the slope is 2 but it is 2 only at the point 3, 6

[violet panther]

Oh okay

[alpine sable]

if you say dy/dx=2 that means the slope is always 2

wherever you look

[violet panther]

Ah ya

[alpine sable]

I suggest you learn the basic idea of derivative and where it comes from

[alpine sable]

if you know it very well, you will solve them much faster

[violet panther]

Ya I agree, my class started to learn this today

[alpine sable]

f(3)=x^2+kx+c this statement is incorrect

that looks like the function is depending on y or something other than x

but the rest is okay

[violet panther]

Could you show me the working how to get k=-4?

[alpine sable]

ok

[violet panther]

Thank you so much

[alpine sable]

firstly, this function you drew here is not f(x)

the graph I mean

erase it

[violet panther]

Ok

[manic forge]

can anyone help with algebra work?

[alpine sable]

this channel is occupied, you better go another channel

now we know f(3)=6

[violet panther]

Yes

[alpine sable]

we know f'(3) is 2

if you imagine a line there

the slope is 2 right?

[violet panther]

Ya

[alpine sable]

f'(x) function always gives you the slope at the point you write in x

instead of x I mean

okay

[violet panther]

Yes

I’m following

[alpine sable]

we wrote 3 and we got 2

we can do the same thing for f'(x)=2x+k

[alpine sable]

do it

are you a hundered percent confident about functions?

[violet panther]

Ooo?

I got it

[alpine sable]

yes yes

you found k

[violet panther]

Woooo

Thank you so much!

Sorry to hold you so long

[alpine sable]

integrate the f'(x) and rest is easy

[alpine sable]

it's okay

[violet panther]

I really appreciate

[alpine sable]

np, good luck

[ionic pilot]

hi

[devout kite]

hey

[ionic pilot]

can somebody solve this
find K somehow that alpha * beta= 3
(k-1)x^2 + 5x -8= 0

ik the formula p= c/a
but 8 cant be divided to anything to be 3

[glass lichen]

$\frac{-8}{k-1}=3$

[ocean seal]

Mosh

[glass lichen]

since the roots 2 at a time is c/a

[ionic pilot]

my problem is 8/n cant be 3 :\ its like almost 2.6 and k will be 3.6

[tight locust]

yes it can

i think you will see it better if i tell you this

$x = y \implies 1/x = 1/y$

[ocean seal]

EndTimes

[glass lichen]

have you done anything to do with fractions by chance?

[static saffron]

i am currently trying to explain why $\phi(\vec r) = \frac{\sigma R}{\epsilon r} (r+R - |r-R|)$ is constant for $r<R$ and for $r>R$ is proportional to 1/r. I dont really have a good explanation though. Anyone else?

[ocean seal]

derdotte

[zealous basalt]

why isnt this working?

[static saffron]

this channel is in use...

[static saffron]

people really dont read

[static saffron]

is still an open question..

[ionic pilot]

Guesing all the way
Thanks for your help and time i moved on to next questions

[uncut depot]

what will be the answer to root 3 * root of root 3

is it root 3

[static saffron]

you probably have learned what the laws for square roots are. Try them

[uncut depot]

yea, i tried im not sure if its the answer

so is that right?

√3 * √√3 = √3?

[buoyant kayak]

no

[placid zinc]

√[3]√√[3] doesn't simplify very well

[uncut depot]

oh

[buoyant kayak]

you can still get an exact answer fairly easily

[uncut depot]

how do i do that

[buoyant kayak]

change the roots to exponents and see what you can do from there

[placid zinc]

Oh hehe it does simplify pretty well

[uncut depot]

what's the answer?

[buoyant kayak]

that's for you to figure out

[buoyant kayak]

did you try this?

[uncut depot]

yea ig

[buoyant kayak]

and what did you get?

[uncut depot]

uh

[buoyant kayak]

ya didnt try it did ya

[uncut depot]

i did

but

the answer looks kinda idiotic to me

[buoyant kayak]

what is your answer?

[uncut depot]

⁴√3

the last part

[buoyant kayak]

very close

[placid zinc]

Let's say r < R. Then |r - R| = R - r
All of the r will cancel in this case.

Let's say r > R. Then |r - R| = r - R

[uncut depot]

wait what

idk

[buoyant kayak]

what did you change $\sqrt{\sqrt{3}}$ into?

[ocean seal]

a disappointing son

[uncut depot]

⁴√3

[buoyant kayak]

right

[uncut depot]

is that wrong?

[buoyant kayak]

and you changed $\sqrt{3}$ into...?

[ocean seal]

a disappointing son

[uncut depot]

nothing

i just left it

[buoyant kayak]

that should be changed into something

using exponents

you're multiplying $\sqrt{\sqrt{3}}$ by $\sqrt{3}$

[ocean seal]

a disappointing son

[uncut depot]

is it 3^1/2

[buoyant kayak]

yes

[static saffron]

yeah did it a second ago myself. Thank you though 🙂

[buoyant kayak]

now, use exponent rules

[uncut depot]

so its 3^1/2 4root3?

[buoyant kayak]

yes, but you can simplify that

[uncut depot]

okay

[buoyant kayak]

what is $\sqrt[4]{3}$ using exponents?

[ocean seal]

a disappointing son

[uncut depot]

uhm

3^1/4?

[buoyant kayak]

yep

so now you have $3^{1/2}\cdot 3^{1/4}$

[ocean seal]

a disappointing son

[buoyant kayak]

can you simplify that?

[uncut depot]

i don't think so

is it possible?

[buoyant kayak]

it is

[uncut depot]

how

[buoyant kayak]

$a^b \cdot a^c = a^{b+c}$

[ocean seal]

a disappointing son

[uncut depot]

so its 3^3/4?

[buoyant kayak]

right :)

[uncut depot]

alright

nice

[vestal aspen]

Hey

Yo

[severe star]

What does i mean here

[vestal aspen]

what

[severe star]

Its a compund Interest formula

Anyone knows what i stands for here

[wild shard]

interest maybe

[zealous basalt]

why is this wrong?

[storm lava]

i think it counts it as wrong cuz you didn't write y=

[zealous basalt]

oh god

you're right

I spent 45 minutes looking for what I did wrong

[storm lava]

😉

[sour dove]

Dang dude I"m sorry. You are correct though, so nice job!

[zealous basalt]

thx!

[modern dagger]

Hi. How can I represent this expression as a sum of three squares: $$\lambda_1^2 + \lambda_2^2 + \lambda_3^2 + 6 \lambda_1\lambda_2 + 2 \lambda_1\lambda_3 + 2 \lambda_2 \lambda_3$$?

[ocean seal]

OleG

[modern dagger]

I can represent it only as $$\lambda_1^2 + (\lambda_2 + \lambda_3)^2 + 6 \lambda_1\lambda_2 + 2 \lambda_1\lambda_3 $$, but this is only 2 squares.

[ocean seal]

OleG

[wide raven]

ive not yet completely solved the question

but i can tell that $\lambda_1$ and $\lambda_2$ are of same sign

[ocean seal]

Sabertoothed Rat

[wide raven]

@modern dagger

do you have any moe info?

[modern dagger]

No

[wide raven]

ok then

[glossy garden]

hey so if you flip 100 coins and take the sum of the number of heads, is it statistically the same thing as randomly generating a number from 0-100?

[unkempt dew]

Nope

[odd helm]

Hey could someone help me with something in #help-2?

[topaz atlas]

Umm guys how do u calculate a probability?

[glass lichen]

depends on what you're given

[unkempt dew]

Probability for what

Yo mosh

Can you help me

[glass lichen]

no

[crude moth]

Guys im so lost what is my teacher trying to tell me

[buoyant kayak]

not the slightest clue

looks like an incomplete question

[calm anchor]

She must have typed something wrong

[crude moth]

Okok I’ll email her

[calm anchor]

Im having trouble with b)

The function y = x^2 - 8x + a is given.
How do we choose a so that:
a) the graph passes through the point (2, 6)
b) the minimum value of the function becomes -6
c) the minimum point of the curve is on the x-axis
d) the curve does not intersect the x-axis?

Yea got that

But what about b?

Im guessing you should calculate the line of symmetry

Which is 4

And then plug that into x

y = 4^2 - 8•4 + a

y = a - 16

And then plug in -6 into y

• 6 = a - 16

a = 10

[crude moth]

Like arent both of these options correct?

[fast mantle]

ABCD is a square. P, Q and O are the mid-points of AB, BC and AC respectively. AQ intersects PO at R. If AD = 9 cm, then the length of AR is??

[calm anchor]

@crude moth I have no idea about your question

@fast mantle gonna try yours

[fast mantle]

i didd

want me to send?

[robust epoch]

This is probably really simple, but how would one scale a normalized set of [0, 1] to [-2.5, 1] ?

[fast mantle]

got anything yet??

[fresh parcel]

use the opposite of the normalization formula

scale 0, 1 back to -2.5, 1

im not too sure though

[robust epoch]

I'll give that a shot, IDK why i'm brainfarting here. 😒 ty

[fresh parcel]

alr

lol

[robust epoch]

@fresh parcel glsl float scale(float v, float mn, float mx, float a, float b){ return a + ((v - mn) * (b-a) / (mx - mn)); } gosh it was so simple. I was doing (v - a) on my first assumption. thanks, idk why I didn't think to look at the norm func again

[robust flax]

doesnt the assumption make the conclusion follow immediately or am i missing something

[tardy plank]

can someone explain to me how this 1st partial derivative was derived?

[raw shard]

it’s just normal derivative rules, but y is a constant

can’t really explain it more than that

well, y is treated as a constant

[verbal marsh]

What is the sum of all odd natural numbers between 100 and 1000?

[fresh parcel]

so you want to find the sum of the odd numbers from 101 to 999

correct?

[alpine nacelle]

sum of all = sum of odd + sum of even

[verbal marsh]

Including those two yes

[fresh parcel]

so basically you can add 1 to each number and then divide it by 2

[verbal marsh]

what formula should i use

im learning arithmetic sequence

[fresh parcel]

just google: arithmetic progression sum formula

it shouldnt be too hard to find

this problem is just understanding a formula and applying it

[verbal marsh]

Will try, thx

I am kind of ashamed I wasnt able to figure this one out immediatelly

[simple orbit]

my question is where did f(y) come from

and why is the answer log(x) if f(y) is correct

I would understand if it's f(x)

is this a typo or am I understanding this wrong?

[raw shard]

@verbal marsh you could use the fact that the first n odd numbers added together equal n^2

[alpine sable]

Is anyone familiar with the formula n(n+1)/2 being the sum of the first n positive integers

[raw shard]

channel is occupied, go to a different channel please

[calm anchor]

Nopp :(

[fast mantle]

i got it

dw abt it

thank you!

[spare hill]

this question is already solved

i'm wondering if someone can help guide me on how the equation for the phase was formed?

[burnt blade]

Hi just familiarising myself with terminology

If set A is not an improper subset of set B, then set A cannot be equal to set B, right?

[simple orbit]

<@&286206848099549185>

[raw shard]

post your question again so it’s at the bottom @simple orbit

[simple orbit]

https://cdn.discordapp.com/attachments/490557019623915520/898656723915644988/unknown.png

my question is where did f(y) come from
and why is the answer log(x) if f(y) is correct
I would understand if it's f(x)
is this a typo or am I understanding this wrong?

[alpine sable]

Don’t think this would make any sense if f(y)dy was replaced by f(x)dx

[simple orbit]

the reason why I say I would understand if it was f(x) is because f(x) is 1 if it's between 0 and 1, which would explain the log(x) result

but...what is f(y)?

or is it the same function?

[alpine sable]

if I define a function rule like f(x) = 2x^2 + 1 I could write it as f(y) = 2y^2 + 1 instead

$\int_0^{\log(x)} f(y)dy$ is a function of $x$. What would $\int_0^{\log(x)} f(x)dx$ mean?

[ocean seal]

Botnuke

[alpine sable]

what if I name it $h(x)=\int_0^{\log(x)} f(x)dx$. What is $h(2)$?

[ocean seal]

Botnuke

[simple orbit]

0, right?

[vague coral]

wrong notation

[alpine sable]

well yea it's intentionally wrong

[simple orbit]

Im sorry I don't get what's wrong

[celest anvil]

so what's the process for this problem

[alpine sable]

$f(2)$ is a constant

[ocean seal]

Botnuke

[alpine sable]

is that what you want to integrate over?

[simple orbit]

I mean

f(2) is 0

oh wait

I get it

wait no

[sweet orchid]

Hi someone help me

[simple orbit]

don't we integrate over a constant regardless?

since the answer is log(x)

isn't the only way that happens is if we integrate over 1?

@sweet orchid if I remember correctly a vertex is where two or more lines meet, so it would be T

[alpine sable]

ok let's try this maybe. If $g(x)=\int_0^{\log(x)} f(y)dy$, what's $g(2)$?

[ocean seal]

Botnuke

[simple orbit]

I don't know...what's f(y)?

that's the part I'm confused about

[alpine sable]

https://i.imgur.com/5FUDEhy.png this is f(y)

[simple orbit]

so it's not a different density function of Y?

[alpine sable]

it's the same old f

[simple orbit]

ok if it's not different that makes sense

ty

[simple orbit]

that would be XW and XY

the sides are the lines that form to make that vertex X

(I think, correct me if I'm wrong)

but I'm 99% sure it's XW and XY

[raw shard]

same

[sweet orchid]

@simple orbit oh I didn’t see ur answer lol

[simple orbit]

ok so ur asking how to find the sides right

what is the vertex

[sweet orchid]

W?

[simple orbit]

yes

now, sides are classified as a connection between two points

we have two points that are connected to the vertex, W

which are V and X

therefore, the lines are WV and WX

I usually write them as vertex first, dunno if that's standard convention

[simple orbit]

aight

can u find the sides by yourself now?

find the vertex

find the other point that connects with the vertex

that's a side

[sweet orchid]

Can gimme answer pls bc I don’t understand this math

[buoyant kayak]

this server is not about giving answers

[glass lichen]

do you know what a side is?

[simple orbit]

you found the vertex in the above question

now, what other points do you see?

[normal turtle]

<@&286206848099549185> help

[brittle estuary]

Please

Help with double integration

Dont know what to do..

[magic geyser]

stop multi posting

[fervent dust]

sorry

[brittle estuary]

Sorry

[magic geyser]

?

[simple orbit]

lol

[serene lake]

yo can I ask a question from sat here?

[brittle estuary]

I think it is for me.

[magic geyser]

np

no

[brittle estuary]

<@&286206848099549185>

[raw shard]

@serene lake you can’t even ask for help on a test

so that’s a huge no

[sleek elbow]

if its from an old sat its fine, no?

[raw shard]

yeah

[sleek elbow]

I would imagine it is

[raw shard]

i don’t see why not

but for a current test it’s no

[sleek elbow]

yup 👍

[candid atlas]

yo

is this correct

its correct right

4 and 6 are included in the interval of [0,8]

[raw shard]

i mean you can just plug the values in

[misty roost]

Yeah those are the roots

Not sure what it means to solve it graphically

[candid atlas]

lol

yea

[raw shard]

probably plot it

or use desmos

[candid atlas]

Im confused about why its asking graphically in the interval of [0,8]

[serene lake]

I mean the question on sept 2021 sat

the grades and qas is already out

[candid atlas]

this is the graph

[raw shard]

then yes

since it’s basically just a random sheet with questions at this point

[serene lake]

ok

`A function f has the property that if point with coordinates (a,b) is on the graph of the equation y equals f(x) in the xy-plane, then the point with coordinates (a+1, 1/3 b) is also on the graph. Which of the following could define f?
a.1/3(1/12)^x
b.12(1/3)^x
c.12(3)^x
d.1/3(12)^x

answer is B
Idk how to start on this problem to get the answer`

[raven chasm]

Can someone help me with this question

[nimble mulch]

How do I solve this

I got this, but I am unable to eliminate w(x) from the RHS

[jagged imp]

who says you need to? you can find w(2e^2).

[nimble mulch]

how tho, I couldn't get w(x) in terms of x either

this is what I got for the inverse function, couldn't isolate w(x)

[jagged imp]

you don't need an explicit formula for w(x) to find w(2e^2). you should be able to guess a y such that ye^y=2e^2

y being a sub for w(2e^2) to make it easier to see

[nimble mulch]

I can but is that something I can write down in a paper

I mean can it be considered the "proper" way to solve this problem

I guess I will just go with that, thank you. The final answer will be 1/(3e^2) right?

[jagged imp]

yes.

There's no reason it shouldn't be "proper"

[nimble mulch]

ah, appreciate it

[jagged imp]

guessing is perfectly find

you can think about why w must only take that one value at 2e^2 if you want

[alpine sable]

whats a good maths typer for linux?

[charred pier]

ok I dont see any fundamental flaw in my reasoning but it outputs 105%, what is going wrong

[fickle latch]

Just say it’s within a margin of error lmao

Also we don’t have enough information

[alpine sable]

this

[fickle latch]

What even is the question

[alpine sable]

give us the ex details

[alpine sable]

Topic: Reflect Figure over a Line (Level 1)

<@&286206848099549185>

@here

[humble ruin]

@silver tangle have you learned measure theory

[honest solstice]

just think of it like a mirror. For example point (-4,7) reflected across the -3 line would now be point (-2,7)

@alpine sable

[stoic cloud]

anyone familiar with "Desmos"?

[charred pier]

@fickle latch @alpine sable supposed to find the concentration in percent of O, C and H in X after it gets burnt

then get the empirical formula

[bleak basalt]

hello I really need help with #discrete-math

Im struggling hard with this homework

can anyone help me please?

its for discrete math. This is going to be hashtag #discrete-math

here I stand begging for help! Is anyone there, and can anyone give me some tips? im on both of my hands and knees, im trying so hard i hope someone helps me!

[clever tapir]

Where do I even begin

[bleak basalt]

wait, but im using questions-0 right now. im working on finding a match! is there anyone there?

the question is this:

[lime tangle]

channel occupied by @bleak basalt find another channel plz

[sour dove]

So it's the product of 4 consecutive integers, right?
So that means that numbers could be like 1, 2, 3, 4 or 10, 11, 12, 13, etc.

We don't know that that value is

but

[bleak basalt]

HEY that aint fair. i was using this one

[sour dove]

we know that the numbers are +1, +2, and + 3 respectively away from the source number

[sour dove]

What's the question asking for?

it's not stated in the form of a question

[bleak basalt]

oh yeah sorry about that. it is "prove or disprove the following statement"

[sour dove]

@clever tapir so take what I said and make a product out of your 4 "unknowns" and set it equal to 840

[sour dove]

okay so it says that x and y are rational number, x < y, but no other rational number exists between them, right?

[bleak basalt]

thats right. I am pretty sure its false, because rational numbers are infinite between them

[sour dove]

yeah exactly

[bleak basalt]

my problem comes in where, i just have no clue how to prove it or how to structure my proof

[sour dove]

so if x < a < y, but there is no a that is between them, then x has to equal y

you can prove by contradiction

[silver dew]

what is the average of x and y

[bleak basalt]

the average of x and y?

[sour dove]

oooh I didn't think of that. That's good

[sour dove]

so between x and y, where would the average between the two lie?

if x = 3/4 and y = 7/4, what's the average between the two, and where does it lie in terms of being greater than, less than, equal, etc

[bleak basalt]

so do i want to assume a specific value for x and y

?

[silver dew]

no just in general

you have it such that x,y >0 and x<y

[sour dove]

no, but the concrete example was supposed to show what @silver dew is saying

[bleak basalt]

okay so i start with "assume x and y are arbitrary and particularly chosen positive rational numbers such that x is less than y"

[silver dew]

write me the expression for the average of x and y

[bleak basalt]

x+y/2

[silver dew]

what observation can you make about x, y, and its average in terms of an inequality

[bleak basalt]

the average will be less than y

and I think it will be greater than x?

[silver dew]

lol

Q

E

D

[worthy hawk]

hello quick question, can i consider these as the same thing or are they different?

[bleak basalt]

huh? what does
Q
E
D
mean??

[silver dew]

it's just a latin abbreviation when your proof is done

$x < \frac{x+y}{2} < y$

[ocean seal]

gramschmidtty

[bleak basalt]

oh okay so just by showing that there is an average that is between them, that is the proof. BUT, dont i then have to prove that the average is indeeeeeed betweeeeen them?

[tired drum]

Help please

[jagged imp]

yes. Just making absolutely sure, the exponent on the numerator is applied to 1, not -1 right?

[worthy hawk]

in both the numerator is -1 and the denom is 5

[bleak basalt]

hey watch it you guys, this room is occupied!

[jagged imp]

That's not what i asked. :( I'm just making sure its meant to be $-1^x$ and not $(-1)^x$

[queen mural]

i need help

[ocean seal]

Sneaky

[jagged imp]

if it is, you're correct, they're the same

[bleak basalt]

dont i have to prove that x+y/2 is between x and y? i am not sure how to do that

[silver dew]

@bleak basalt the average of two numbers is the midpoint

[worthy hawk]

it is (-1)^x

[jagged imp]

then you should write that. We'll continue in #calculus

[bleak basalt]

okay and so for my justification would i just write "by definition of average" or "by definition of midpoint" or something like that?

[silver dew]

you can just start with x < y then add x to both sides

what does that give you?

[tired olive]

Howzit. What knowledge do you have for the problem/what may you assume? The average will do the job, but what you want is a direct consequence of the Density Theorem.

[bleak basalt]

we just have to justify or prove everything that isnt given in the question

we can use theorems but must write "by definition of x" and stuff like that

[silver dew]

i'm showing you how to do it

take x < y and add x to both sides

[bleak basalt]

okay

let me do the math real quick

okay, im getting "2x < x + y"

[silver dew]

divide both sides by 2

[bleak basalt]

okay it should be x < x+y/2-OH i see what you did there!

this will be helpful

[silver dew]

do the same thing, but add y to both sides

you'll show that the average is between x and y

then

Q

E

D

[bleak basalt]

wait but how do i prove that x + y/2 is also a rational number?

[silver dew]

it is the very definition of a rational number

[bleak basalt]

are they closed under aditipon im guessing?

[silver dew]

x and y are both rational

it follows that (x+y)/2 is rational

[alpine sable]

https://cdn.discordapp.com/attachments/719800714544807989/898416947631366144/satmath6.png

[silver dew]

@alpine sable do you know how to complete the square

@alpine sable https://www.youtube.com/watch?v=WrH1Z-SuhhQ

first thing you need to do is make sure the leading coefficient is 1. so first divide both sides by 5, then follow the video.

[tired olive]

Under standard addition and multiplication, the rationals are a field (an Archimedean field). Adding two rationals is a rational and multiplying two rationals (dividing by two, if you really want to do it that way), is a rational.

If you know the result that the rationals are dense in the reals, then this is a trivial question. I suspect that, perhaps, you are unaware of this. Is this the case? If so, then you will certainly need to follow the method given to you by @silver dew

[lime tangle]

why dont u make i = root(-1)

then you would have

[alpine sable]

see this is not my work, this is my friends but i barely know this type of stuff

[bleak basalt]

yes ive never heard this term "dense in the reals"

[lime tangle]

actually first factor stuff

$\frac{3-5i}{2(4+i)}$

[ocean seal]

IAMTHEFARMER

[lime tangle]

then replace i with root(-1)

then

[tired olive]

OK, then take the average. It will do the job.

[lime tangle]

you rationalize

the denominatoe

$\frac{3-5\sqrt{-1}}{2(4+\sqrt{-1})}$

[silver dew]

3rd line left side is a perfect square

it will always be that way when completing the square

[ocean seal]

IAMTHEFARMER

[lime tangle]

@alpine sable

[alpine sable]

ty

[lime tangle]

then rationalize the denominator

(ie: multiply by

$(4-\sqrt{-1})$

[ocean seal]

IAMTHEFARMER

[lime tangle]

what will make u cancel out the denom roots

[alpine sable]

oh

[gray crypt]

Hey! Sorry to disturb anyone. But would someone be willing to assist me with my Math homework?

[lime tangle]

it is bad pratice to have sqrts at the denom

for what

[lime tangle]

sure

[gray crypt]

I'll wait till soft is finish

[lime tangle]

ok

@alpine sable $x^2-4x+4 \implies (x-2)^2$

[ocean seal]

IAMTHEFARMER

[lime tangle]

cuz its a perfect square trinomial

[silver dew]

@alpine sable do you know how to factor?

[lime tangle]

how do you find perfect sq trinomials?

you divide the middle turn by 2 and squre it

if that equals to ur last term

its a perfect square trinomial

ok

[silver dew]

you have to learn how to factor

[lime tangle]

what dont u understand

because in completing the square you need to balance the equation

you cant be taking out a number randomly

and not balance it

on the other side

[gray crypt]

Whatever you do to one side, you do to the other.

[silver dew]

there doesnt even need to be an equal sign. without it you can +13-13. but i'm saying that this method is only going to be confusing to you if you dont know how to factor.

[lime tangle]

if it was positve yes

but its negative in this case

[lime tangle]

go to another channel and ill meet u there

[gray crypt]

okay

[lime tangle]

ill finish helping soft soon

@alpine sable do u understand factoring

cuz if u dont understand factoring then u need to go back to it

occupied

yes

because ur teacher is trying to check if the equation is a perf square trinomial

you will always be able to divide by 2

7.5/2 is not a perfect number

but itll still give u an answer

[buoyant kayak]

the (b/2)^2 thing is not to check if its a perfect square trinomial

it's to complete the square

[lime tangle]

how

(-4/2)^2 = 4

[silver dew]

adding and subtracting the (b/2)^2 makes the first three terms a perfect square

[lime tangle]

which is the last term

[silver dew]

thats the idea of completing the square

[buoyant kayak]

it's the last term because (-4/2)^2 MADE it the last term

[lime tangle]

which means its a perfect square

[buoyant kayak]

that's how you complete the square

[lime tangle]

thats not how i do it but ok

[buoyant kayak]

because you're not completing the square

[lime tangle]

there are many different ways

[buoyant kayak]

no, this is completing the square

there is one way

[lime tangle]

well

[silver dew]

when i say "adding and subtracting" i mean in the absence of an equals sign

[lime tangle]

variations of one way yes

[silver dew]

it doesnt need to be an equation

[lime tangle]

i know how to complete the square

[silver dew]

this technique is how to derive the quadratic formula

[buoyant kayak]

obviously not if you think (b/2)^2 is checking to see whether or not it's a perfect square trinomial

[lime tangle]

lol

i never used it

[buoyant kayak]

the equation is a perfect square trinomial because (b/2)^2 was used

[lime tangle]

ok

[lime tangle]

usually what i do is

x^2-4x = 13

x^2-4x + ______ = 13

[silver dew]

@alpine sable that video explains what to do. i initially said you need to divide the 5 out before you follow his example.

[lime tangle]

i divide 4 by 2 and i square it

thats my last term

therefore

x^2-4x+4-4 = 13

bring the -4 over

i have x^2+4x+4 =17

then

i factor

(x-2)^2 = 17

bring the 17 over

[silver dew]

@alpine sable factor out a 5 like this 5(x^2 + 4x + 1) = 0

[lime tangle]

(x-2)^2-17= 0 is the equation

@buoyant kayak u say i dont know how to complete square?

i know how

[buoyant kayak]

you didn't solve the equation lmao

[lime tangle]

doesent matter

[silver dew]

he was simply saying that the addition of (b/2)^2 doesn't mean you're "checking" to see if something is a perfect square

[lime tangle]

i am just trying to show u that i know how to complete the square

[buoyant kayak]

i don't care?

[lime tangle]

well u can use that way to check if its a perfect square actually

but i guess both work

[buoyant kayak]

you're making it a perfect square by completing the square

how is that hard to understand

[silver dew]

adding (b/2)^2 automatically makes it a perfect square

[buoyant kayak]

it's always going to be a perfect square

[lime tangle]

obviously

[buoyant kayak]

that's the entire point of completing the square

[lime tangle]

yes

i know

[silver dew]

it's almost as if you're saying "adding 2 to 2 makes it 4, but you can use the 2 to check that it makes it 4"

@alpine sable idk why you're subtracting

[lime tangle]

yes

like for example

this equation

[silver dew]

yeah that's pretty much a useless comment

[gray crypt]

Cmon guys take it easy with him

[lime tangle]

x^2-6x+9

6/2

squared= last term which means that the equation is a perf square trinomial

[buoyant kayak]

who cares?

[lime tangle]

i care

[raw shard]

aka the last term should be a perfect square

[lime tangle]

yes

[raw shard]

most of the time

[lime tangle]

$a^2 - ab +b^2$ or $a^2 + ab +b^2$

[ocean seal]

IAMTHEFARMER

[lime tangle]

sure

what r ur question

because

because

[buoyant kayak]

factor x^2-4x+4

[lime tangle]

x^2-4x+4 is factored

by dividing the 4 by 2

u get

(x-2)^2

[buoyant kayak]

bro what

[lime tangle]

in order to find what it is factored u divide middle term by 2

middle

by 2

that u dont touch

[silver dew]

@alpine sable review your methods for factoring quadratics please

[lime tangle]

or you can do product sum method

P roduct= 4 sum = -4

-2,-2

-2 x -2 = 4

-2+-2 =-4

[lime tangle]

pls do @alpine sable u seem lost

[silver dew]

@alpine sable gotta learn to be able to help yourself

otherwise whatever people tell you from here on out is just going to confuse you more and make you hate it

[lime tangle]

@alpine sable do u know product sum method

do u know any method

on how to factor quadratics

factor

$x^2-8x+16$

[gray crypt]

@alpine sable we know youre overwhelmed, but maybe watch a video on factoring. It's easy if you're dedicated.

[ocean seal]

IAMTHEFARMER

[lime tangle]

factor that

[raw shard]

(a+b)^2 = a^2+2ab+b^2

use this

[lime tangle]

u got the first bracket but not second bracket

find it

i will not tell you

no

can u show me how ur doing it?

?

show in bracket plz

yes

yes

after a million tries u got it

i want to see how u did it

how did u do it

[gray crypt]

you can also do (x-4)^2

[lime tangle]

what was the factoring technique u used

[lime tangle]

yes

?

thats a factoring technique?

what did u do then

divide what by what

[gray crypt]

hey farmer and soft, would it be cool if you guys can join and farmer can explain?

I think it'll benefit you more soft

[lime tangle]

cant join VCs at the moment

[gray crypt]

ahhh okay

np

[lime tangle]

yes

good work

the trick is to know right away that it is a perfect square trinomial

the first term is perfect square and last is perfect square

$x^2-8x+16$ can be re-written as $x^2-8x+(4)^2$

[ocean seal]

IAMTHEFARMER

[lime tangle]

thats how you know

if the first and last are perfect squares, its a perfect square trinomial

so basically the question is telling you do

change $5x^2+20x+5$ into the form $(x-h)^2+k$

[ocean seal]

IAMTHEFARMER

[lime tangle]

how do you do that @alpine sable

complete the square

the former

yes

[buoyant kayak]

you do not complete the square yet

[lime tangle]

ok ok

you factor out 5

[raw shard]

yeah that

[buoyant kayak]

you can't complete the square if your a term has a coefficient other than 1

[lime tangle]

yes

[buoyant kayak]

no

needs a 5 in front

[lime tangle]

make sure its in brackets with 5 at front

[buoyant kayak]

also forgot an x

[lime tangle]

now u are at this stage

[silver dew]

i'm popping in and we're still on the part about factoring out the 5?

[lime tangle]

$5(x^2+4x+1)=0$

[ocean seal]

IAMTHEFARMER

[lime tangle]

no what do u do next

im not supposed to tell u

[buoyant kayak]

no

complete the square of the stuff inside the parenthesis

[lime tangle]

@alpine sable i would have factored first tbh i would have done this

$5x^2+20x =-5$

[ocean seal]

IAMTHEFARMER

[lime tangle]

then

factor out the

5

[buoyant kayak]

gets you the same exact thing

[lime tangle]

i know

yes

[buoyant kayak]

no

[lime tangle]

but u need to bring something over to the other side

@alpine sable

what do u bring to the other side?

wrong

$5(x^2+4x+1)=0$

[buoyant kayak]

this would be right if you used the correct equation

[lime tangle]

here u can visualize it better

@alpine sable what do u bring to the other side

oops

[ocean seal]

IAMTHEFARMER

[lime tangle]

ok

@alpine sable what do u bring to the other side

wrong

well

actually right

u got it right n

nvm

but what happens to the 5

good

so now u have

$5(x^2+4x)=-5$

[robust flax]

how can i calculate the mean? when these are continuous

expected value

[ocean seal]

IAMTHEFARMER

[lime tangle]

occupied

so @alpine sable what do u do next

because

you cant just take it out randomly

[gray crypt]

its fine

[lime tangle]

here is what happened

you multipled the 1 by 5

and brought it to the other side

distributive law

[raw shard]

no

[lime tangle]

$a(c+b+d) \implies ac+a(b+d)$

[ocean seal]

IAMTHEFARMER

[lime tangle]

distributive law

im showing u how i brought 5 to the other side

$5(x^2+4x)=-5$

[ocean seal]

IAMTHEFARMER

[lime tangle]

what do u think we do next?

ill give u hint

[raw shard]

this way isn’t as good as the normal way

confusing

[lime tangle]

what is the normal way

[raw shard]

i know how to do it and it confuses me lol

ok what was the original equation

i can explain it in a less confusing way

[lime tangle]

change $5x^2+20x+5$ into the form $(x-h)^2+k$

[ocean seal]

IAMTHEFARMER

[raw shard]

so factor out a 5

5(x^2+4x+1)

[lime tangle]

yeah i dont like the way either i do it another but anyway show your way i think soft will understand your way better

ill watch

[raw shard]

divide the middle term by 2 to see what the last term should be

well, the square root of the last term

4/2 = 2, so the last term should be 2^2 = 4

[lime tangle]

do u want me to do it in latex so that soft can visualize better?

[raw shard]

maybe

probably lol

[lime tangle]

ok so we are here now

$5(x^2+4x+1)=0$

[ocean seal]

IAMTHEFARMER

[lime tangle]

then

@raw shard proceed

[raw shard]

divide the middle term by 2, that will give us the square root of what the last term should be

we get 2, so the last term should be 2^2 = 4

so we’ll add 5(3)

[lime tangle]

ok so

ok

[raw shard]

and leave a -5(3) in there

[lime tangle]

wait i will write it

[raw shard]

5(x^2+4x+4)-5(3)

ok

[sour dome]

what we do ?

[lime tangle]

$5(x^2+4x+4)-5(3) = 0$

[ocean seal]

IAMTHEFARMER

[raw shard]

@alpine sable if you can’t tell, this is a perfect square polynomial

[lime tangle]

how dont u know what a polynomial is

[raw shard]

what we’re working with right now

whatever

anyways

this is in the form where we can express it in the form (a+b)^2

[lime tangle]

its in form of $Ax^2+Bx + C$

[ocean seal]

IAMTHEFARMER

[lime tangle]

like multiple variables

poly means variety or numerous

nomial means number

[tight locust]

yes

[lime tangle]

poly numbers

lots of number basically

[raw shard]

(a+b)^2 = a^2+2ab+b^2, and we have x^2+4x+4

[tight locust]

nomial actually means name

[raw shard]

can you see what b should be?

that wasn’t sped up at all

that was literally my next step

[buoyant kayak]

you didn't explain this at all you just kinda threw it in there

[raw shard]

substitute x for a

[lime tangle]

i see i always thought itmeant number but nomial as name makes more sense cuz variables are basically names

[tight locust]

if you've taken biology before that should be clear. look at the "binomial nomenclature"

[raw shard]

oops

[buoyant kayak]

this is a cluster of nonsense lmao

[lime tangle]

never taken it unfortunately

[raw shard]

at this point i don’t know when i should or shouldn’t explain what i’m doing lol

[buoyant kayak]

can i explain this?

[lime tangle]

explain as much as you can

[buoyant kayak]

alright lmao

[raw shard]

yeah

[buoyant kayak]

let's go back to the beginning

where we factored out a 5

[lime tangle]

let @buoyant kayak explain hes good

[buoyant kayak]

$5(x^2+4x+1)=0$

[ocean seal]

a disappointing son

[buoyant kayak]

so this is what we're at right now

now, i'm gonna put some more brackets to make things clearer

$5[(x^2+4x)+1]=0$

[ocean seal]

a disappointing son

[buoyant kayak]

so the stuff inside the parenthesis, x^2+4x, that's what we want to take a special look at. we'll be completing the square

[lime tangle]

perfect

[buoyant kayak]

so, using $(\frac{b}{2})^2$, we get $(\frac{4}{2})^2$ which is 4

[ocean seal]

a disappointing son

[buoyant kayak]

now just to make things more clear

we are adding this to both sides, you understand that, right?

we add this 4 we just got to both sides

in completing the square

[lime tangle]

@buoyant kayak why dont u have helper role

[buoyant kayak]

don't want it

[lime tangle]

ok

we do get pinged a lot

[buoyant kayak]

$5[(x^2+4x+4)+1]=0+4$

so now we're here

[silver dew]

thats incorrect

you have 5 outside still

[glad moon]

Can I get some help with this

[lime tangle]

nah its right

[silver dew]

you should just divide both sides by 5 first

no it is not.

[lime tangle]

seems good to me

[silver dew]

you have 5 on the outside, divide it out first

[lime tangle]

its the longer approach which is good

$5[(x^2+4x+4-4)+1]=0$ @alpine sable bascially son is doing this

[ocean seal]

IAMTHEFARMER

[lime tangle]

then multiply -4 by 5

and bring to other side

because we cant just put in a 4 randomly

we had $x^2+4x+0$ before

[ocean seal]

IAMTHEFARMER

[lime tangle]

therefore we need to do 4-4

to ake sure it stays at 0

then

multiply 5 by -4

and bring to other side

so now you have

$5[(x^2+4x+4)+1]=0+20$

[ocean seal]

IAMTHEFARMER

[silver dew]

divide the 5 out here

because

[lime tangle]

then

[silver dew]

i promise you're incorrect if you leave it here

[buoyant kayak]

no you're right, i messed up

[lime tangle]

$[(x^2+4x+4)+1]= \frac{20}{5}$

[ocean seal]

IAMTHEFARMER

[lime tangle]

thats how @silver dew wants it

which is good

[silver dew]

no i want the 5 gone lol

but yes

[lime tangle]

$[(x^2+4x+4)+1]= 4$

[ocean seal]

IAMTHEFARMER

[lime tangle]

now you can remove the square brackets

$(x^2+4x+4)+1= 4$

[ocean seal]

IAMTHEFARMER

[lime tangle]

then

bring one to other side

$(x^2+4x+4)= 4-1$

[ocean seal]

IAMTHEFARMER

[lime tangle]

$(x^2+4x+4)= 3$

[ocean seal]

IAMTHEFARMER

[lime tangle]

then factor

$(x+2)^2 = 3$

[ocean seal]

IAMTHEFARMER

[lime tangle]

then bring 3 over

[silver dew]

when you get to that step, the left side will always be $(x \pm \frac{b}{2})^2$

[ocean seal]

gramschmidtty

[silver dew]

the $\pm$ depends on the sign in front of b

[ocean seal]

gramschmidtty

[lime tangle]

yes

[buoyant kayak]

final answer is off by a factor of 5 because we can't just get rid of the 5

[silver dew]

yes you can, the right side was zero

[buoyant kayak]

no you can't

[silver dew]

yes you can

the right side was zero

[buoyant kayak]

we're rearranging a quadratic equation in a different form

we're not solving

that is not the answer

it's not the right choice lol

[lime tangle]

how do we do it then

[silver dew]

was it not an equation?

it was an expression?

[lime tangle]

i did it grams way

[buoyant kayak]

.

$5[(x^2+4x+4)+1-4]=0$

[ocean seal]

a disappointing son

[buoyant kayak]

$5[(x+2)^2-3]=0$

[ocean seal]

a disappointing son

[silver dew]

if the original problem was an equation set equal to zero, then the 5 goes away

[buoyant kayak]

$5(x+2)^2-15=0$

[ocean seal]

a disappointing son

[silver dew]

exactly

[buoyant kayak]

oh it's equals k

[lime tangle]

why did u bring -4 outside the bracket i dont think u can do that

[buoyant kayak]

?

[silver dew]

he's adding "zero"

[buoyant kayak]

it's inside the bracket

[lime tangle]

oh ok

didnt see sorry

[silver dew]

+4 - 4 on one side is the same as adding 4 to both sides

[lime tangle]

we arent gonna help u for ur entire assignment

[silver dew]

@alpine sable this channel spent like an hour on that one problem

please review your notes

[lime tangle]

we need to make space for others

[silver dew]

we cannot do the problems for you

as cliche as it sounds, it's really not "helping" you

[lime tangle]

sorry

but we need to be courteous

and let other people ask questions

i understand your frustration but plz review your notes

and ask your teacher for help

what!!?