help-0

[oak chasm]

Find a #questions channel where they last said they're done or the last timestamp is 30 minutes ago or more.

@shy oasis When do you have to turn it in?

[wanton shard]

quick question

is this right?

[oak chasm]

@wanton shard Sorry, channel is busy.

[wanton shard]

oh ok ok mb

[shy oasis]

11:59

by that time

[oak chasm]

How far away is that?

[shy oasis]

is 11:00 for me

[oak chasm]

Oh, OK.

x + 0 = 12

What can be simplified here?

[shy oasis]

x=12

[oak chasm]

Right.

[shy oasis]

it becomes that cuz the zero is not there anymore

[oak chasm]

Anything plus zero is that number.

[shy oasis]

yes

[oak chasm]

So, the x intercept is (12 ,0).

What about the y intercept?

[shy oasis]

wait what

[oak chasm]

x + 6y = 12

[shy oasis]

theres no 12 on my graph

only up to 9

[oak chasm]

Well, it goes up to 10, but we'll handle that.

What's the y intercept?

[shy oasis]

whats the equation again

sorry

[oak chasm]

x + 6y = 12

[shy oasis]

6y =12

[oak chasm]

Good.

[shy oasis]

y=2

[oak chasm]

OK, so the y intercept is (0, 2)

So, two points are (0, 2) and (12, 0).

Now another point on that line will be halfway between them.

So, what's halfway between their x coordinates?

[shy oasis]

i cant put 12,0

its only up to 10

[oak chasm]

Right.

Now another point on that line will be halfway between them.

[shy oasis]

ok

[oak chasm]

So, what's halfway between their x coordinates?

[shy oasis]

my friend got (2,5)

[oak chasm]

OK.

Now another point on that line will be halfway between them.

So, what's halfway between their x coordinates?

[shy oasis]

(2,5)?

idk

[oak chasm]

No.

What are their x coordinates?

[shy oasis]

(12,0)

[oak chasm]

No, 12 and 0.

So, what's halfway between those?

[shy oasis]

im not sure

[oak chasm]

What's their average?

[shy oasis]

who?

[oak chasm]

OK, add them together and divide by 2.

[shy oasis]

add what together??

[oak chasm]

12 and 0.

[shy oasis]

6

[oak chasm]

Do you see how 6 is halfway between 12 and 0?

[shy oasis]

yes

[oak chasm]

OK, what's halfway between their y coordinates?

[shy oasis]

4

1

[oak chasm]

Yes.

So, a point halfway between the intercepts is (6, 1).

[shy oasis]

ok thats it?

[oak chasm]

That's also on your line.

Mark the y intercept.

Mark (6, 1).

[oak chasm]

OK. Let's go back to a minute ago.

I said to mark the y intercept.

Did you mark the y intercept?

[shy oasis]

is it 12,0

[oak chasm]

No.

The y intercept is on the y axis.

Where x is 0.

That point has x as 12.

So, that's not the y intercept.

What is the y intercept?

[shy oasis]

my friend sent me the 1d part

[oak chasm]

I don't really care what your friend did.

What y intercept did we get?

[shy oasis]

6

[oak chasm]

No.

Look at your paper.

[shy oasis]

yes

[oak chasm]

What are the two intercepts you got?

[shy oasis]

0,2

[oak chasm]

Right, that's the y intercept.

Did you mark it on the graph?

[shy oasis]

yes i did

[oak chasm]

OK, we got the midpoint between the intercepts.

(6, 1).

[shy oasis]

yes

[oak chasm]

Did you mark that on the graph?

No, you didn't.

Look at (6, 1) on your graph.

[shy oasis]

like that?

[oak chasm]

Yes.

[shy oasis]

so im good?

[oak chasm]

Yes.

Now make the line.

If you need to, add more guidepoints.

[shy oasis]

ok ty

i added you on discord

@oak chasm

[oak chasm]

OK.

@shy oasis Is that the last question?

[shy oasis]

yea

[oak chasm]

OK, you need some practice with order of operations. You don't have to do it right now, but here's some video lessons and practice problems: https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-arithmetic-operations/cc-6th-order-of-operations/e/order_of_operations_2.

[shy oasis]

honestly i understand it know

because of you

[oak chasm]

It'll help you to figure out how to do (1/2 x² + 3y - 6) + 6.

Yeah, but we only covered part of it.

[shy oasis]

oh ok

[oak chasm]

They also have an algebra course at Khan Academy if you need to review stuff.

[shy oasis]

ok

[alpine sable]

I want to learn Venn Diagram

[shy oasis]

did u accept it yet?

@oak chasm have a great night

or day

idk where ur from

[oak chasm]

You too. Sorry, have to go.

[shy oasis]

gn

[ionic jewel]

simplify the top

notice that the co-efficients are the sum from 1 to n of the integers

[solemn oar]

Yea actually I did simplify

But the problem in coming afterwards

I m a bit confused how to solved the next step

[ionic jewel]

what did you simplify it to?

[solemn oar]

I simplified
[X]=x-{x}

I simplified everyterm of greatest inter to it

[ionic jewel]

can you write down your simplified form, I dont understand

[wind bane]

they did [x] = x - {x} where {x} is the fractional part of x

[solemn oar]

Hmm? Should I send the pic how I simplified

[ionic jewel]

oh wait am i reading the problem wrong

is [x] not equal to (x)

[solemn oar]

Noo

Its greatest integer function

[ionic jewel]

which is floor right

[5.5] = 5, right?

[wind bane]

yes

[solemn oar]

Yea I think its 6

[wind bane]

no its 5

[solemn oar]

Ohh shouldn't the value approach to the next number

[wind bane]

?

do u mind elaborating

[solemn oar]

Ohhhh righttt

Its 5 sorry

@wind bane did u get the answer to the question?

[wind bane]

im still thinking about it

[solemn oar]

Yup take ur time

[candid sluice]

Is n fixed

I dont see how the limit exists if thats the case

[wind bane]

same

i actually cant convince myself tho*

[candid sluice]

Just make x a big integer

[solemn oar]

What method did u apply

[candid sluice]

You get lim x -> infty of like Cx for some constant C

Im asking if the limit is supposeed to exist or not

[wind bane]

oh

[solemn oar]

Answer is x/2

[candid sluice]

The limit depends on x

So the limit should be n -> infinity

Or?

[wind bane]

just $$\frac{\sum_{k=1}^n\lfloor kx\rfloor}{n}\cdot\frac{1}{n}\geq\frac{\lfloor x\rfloor}{n}$$

[ocean seal]

c squared

[wind bane]

by AM-GM

so as x tends to infinity, your limit diverges

[candid sluice]

Lol that works too

[wind bane]

if n is variable, thats a different story

[candid sluice]

For that you can note that the numerator is bounded by the sum of all integers up to n + n

[solemn oar]

Okay can any of you sum up the solution
I actually cant get it like this

[candid sluice]

This should work

[wind bane]

so if n is fixed and x --> infinity, then the limit diverges because of this

[ionic jewel]

their solution is that your problem andor answer is wrong looks like

[candid sluice]

For the limit when n -> infinity

Ok too many cooks

[solemn oar]

??

[candid sluice]

Ill leave this to you guys

[muted gust]

Anyone wanna fry there brain by answering the 3n+1 equation

[wind bane]

no go ahead and explain it pappa lol

[ionic jewel]

thought you were saying it diverged with this

[wind bane]

nobody wants to try to solve collatz conjecture lol

[solemn oar]

Sorry I m might sound dumb but I cant help with anything here
I can just tell that sandwich theorem is applied in it

[muted gust]

As it should its too trivial

[wind bane]

obviously

[muted gust]

Im new to math and my school is just teaching domain functions and relations idk shit

I understand the graph but nothing else

[solemn oar]

Guyss help?

[wind bane]

thats cool. were trying to help kaizen tho

[muted gust]

Ight

[candid sluice]

The version of the problem that you gave is wrong given the answer that you gave to be correct

[muted gust]

What the question

[candid sluice]

So im assuming that the problem is to look at the limit when n tends to infinity

[solemn oar]

Yesss sorry

Its n tends to infinity

I didnt see the mistake

Sorry for the trouble

I m soo soo sorry

[candid sluice]

When this is the case, we note that the numerator can be written as a $\left(\sum_{i=1}^n ix\right) + \sum_{i=1}^n {ix}$

[ocean seal]

Pappa

[candid sluice]

Now the first sum is easy to evaluate and ill leave that to you

[solemn oar]

Hmm hm okay

[candid sluice]

So now we want an upper and a lower bound for the second sum

Note that the fractional part of ix is at most 1 and at least 0

[solemn oar]

Yup

[candid sluice]

So when the numerator is as large as possible that sum is n

And as small as possible, it is 0

Now calculate the limits in both of these cases and you should be able to conclude by the squeeze theorem

[solemn oar]

Okayy thankss I got it 😁
Thanks for ur time

[candid sluice]

Np

[hot crag]

hey so im doing a question

find the equation of the vertical line passing through (-1,5)

can anyone help

[royal anvil]

can some1 help me understand Pythagoras theory

[hot crag]

u mean Pythagorean theory

[royal anvil]

yes

[wind bane]

there isn't really a function describing this

[hot crag]

wdym?

[wind bane]

do you know what the vertical line test is?

[hot crag]

no

i just want to know how to solve this

isnt it like y=mx+b

[wind bane]

thats exactly my point. what slope would you use to even get a vertical line?

[hot crag]

wait so do i find the gradient first?

[wind bane]

you literally cant

its a vertical line

the gradient is rise over run. there is no run. its rise over zero

[hot crag]

so how do i solve it?

im so confused

[wind bane]

oh wait. i may have misinterpreted this

[ionic jewel]

says eqn not function

answer is ||x = -1||

equations dont have to pass the vertical line test in general

[wind bane]

meh i hate that

[ionic jewel]

see x^2 + y^2 = r^2 or whatever

clearly an equation, not a function

[hot crag]

find the equation of the vertical line passing through (-1,5)

so what

is x=-1

the answer

??????????????
]

[ionic jewel]

I already posted the answer above, but the thought process is that vertical lines take the form x = c, where c is a constant

and the provided point has the x value of -1

[hot crag]

dont you first have to do y=mx+b and then put (-1,5) in it

[ionic jewel]

no, thats for lines that actually are functions

this is not a function, and wont fit in that form

[hot crag]

it says i need to find the equation tho

[ionic jewel]

a vertical line is the only time a line cant be written as y = mx+b though

yes, x = -1 is an equation

[hot crag]

so how should i write it down

just write x=-1

[clear vessel]

Can someone explain to me how to find the minimum or the maximum point of a quadratic equation? I used to be able to do it but I’ve forgotten

[ionic jewel]

-b/(2a)

where the quadratic is written ax^2 + bx + c

[clear vessel]

wait what

Is that the X value for the point?

[ionic jewel]

wait

you said quadratic

[clear vessel]

yes

Ive completely forgotten

Absolutely forgotten everything ffs

So for example,

y=2x^2 + 7x + 12

To find the minimum point

[ionic jewel]

then the vertex is at -(7)/(2(2)) = -7/4

[clear vessel]

What is vertex again?

[ionic jewel]

either the min or the max

depending on which the parabola has

[clear vessel]

if I were to find the coordinates how am I to do that

[ionic jewel]

well you know x = -7/4

[clear vessel]

Oh

[ionic jewel]

so what f(-7/4)?

[clear vessel]

The. I just substitute it in

For the Y value

[ionic jewel]

yes

[clear vessel]

Thanks so much man

I was so confused haha

[ionic jewel]

👍

also once you get to calculus (for generally finding min and max of any function), the keyword is critical points

assuming that first question wasnt about calc

[clear vessel]

All the online tutorials had dy/dx

Or something

[jagged imp]

yeah thats calculus

[ionic jewel]

yeah the calculus way is finding the critical point(s)

is the 16 the entire bottom or just the right

[novel grove]

how do i express this formula as a function? there are 2 inputs

[ionic jewel]

(16+x)(v) = 112

i dont think its enough information without knowing the entire bottom

[jagged imp]

if thats the case then its either not enough information or it means that 16yd is the whole bottom

[terse bay]

idk how this works

[clear vessel]

basically you can factorise ( b^4 a^4 ) - ( a^3 b^5 ) into (b^4 a^3)(a-b)

[terse bay]

yeah but how

[clear vessel]

Its hard to explain it over text

but ill try my best

[terse bay]

u can use the bot

[clear vessel]

no idea how im new lol

[terse bay]

me too help

[clear vessel]

if you times b^4 a^3 by a

you get b^4 a ^4

[terse bay]

$(b^4a^4)-(a^3b^5)$

[ocean seal]

EDEN

[terse bay]

wait so

[clear vessel]

$a(b^4 a^3)

[terse bay]

are you just basically taking out an a-b

[clear vessel]

$a(b^4 a^3)$

[ocean seal]

qWeb

[clear vessel]

yeah quite literally lol

and then on 2nd part

$b(b^4 a^3)$

[ocean seal]

qWeb

[clear vessel]

and if you minus each one you get

basically its

https://cdn.discordapp.com/attachments/490557019623915520/876737048214663178/522639996587343882.png take away https://cdn.discordapp.com/attachments/490557019623915520/876737217349951488/522639996587343882.png

first take away 2nd

then you get

[edgy depot]

i can miss sister

[clear vessel]

$(a-b)(b^4 a^3)$

[ocean seal]

qWeb

[clear vessel]

got it

[terse bay]

wait what

[edgy depot]

i got you hunty

[clear vessel]

basically its a(b^4 a^3) - b(b^4 a^3)

$a(b^4 a^3) - b(b^4 a^3)$

[ocean seal]

qWeb

[alpine sable]

i can help u with that

[clear vessel]

= $(a-b)(b^4 a^3)$

[ocean seal]

qWeb

[terse bay]

OHHHHHHH

[edgy depot]

thats tea mama but idc

[clear vessel]

omg I teached someone lets go

[terse bay]

[edgy depot]

sis idk wym

[clear vessel]

[edgy depot]

im from greece

omg no mama

[ripe remnant]

Is someone here from Oceana

I need a person tomorrow

[gray isle]

<@&268886789983436800>

[edgy depot]

i wish i could sister

help

[ripe remnant]

But why not

[sly mantle]

b&

[ripe remnant]

Ur not the real nicki Minaj

[edgy depot]

yes i am?

[ripe remnant]

Can u unban those two cuz I feel sad for them

[alpine sable]

can someone exain why its out of 4 cards and not 5?

where?

@alpine sable

I mean, there are only 4 aces, jacks etc in a deck

so like, you first chose which of the 4 aces you hand will have

then which 3 out of 4 jacks

[alpine sable]

it states there consistin of 5 cards

yes

but do you understand what I wrote next?

not talking to u stfu

go in the channel where no one is asking questions

[brittle nimbus]

how would you use poisson approximation to calculate the probability in dice rolls?

[gray oxide]

Occupied?

I guess not

$$P(x) = x^2-16x+60 $$

[ocean seal]

!callidus

[gray oxide]

How do I write this in a factor form like this

K(x-a) (x-b)?

Where do I start?

[placid zinc]

If you've never seen factoring methods before, I suggest YouTube as a video can teach this one faster then I can.

[gray oxide]

Ok thank you :)

[placid zinc]

But in general you want to find two numbers that have a product of 60, and a sum of -16

[gray oxide]

What's the name of this i don't know the English term

[placid zinc]

"Factoring quadratics"

[gray oxide]

Dude..... You are litterly an angel thank you

[placid zinc]

Haha happy to point you in a good direction. Feel free to ask if you have any questions about it

[long siren]

is there a way to write a function in desmos i can use recursively that gives me this result? here are the first 4 iterations

[gray oxide]

Is there a shorter formula than this?

[compact hornet]

f(i)=a(f(i-1)+b*f(i-2)), i>=3

i>=2, not >=3
f(0)=a, f(1)=a(a+b)

[swift pendant]

Hey, can someone help me solve this without trigonometry:
ABC is an isosceles triangle. BC= 25cm and angle bAC = 90 degrees
i) what is the length of AB

[alpine sable]

have you tried anything with it?

[long siren]

The definition of function 'f' cannot depend on 'f'.

sigh

[swift pendant]

I think I'm supoussed to solve this using the Pythagoras theorem
c^2 = a^2 + b^2

[alpine sable]

yes you can use it, but let's move to #help-9

[swift pendant]

kk

[long siren]

desmos doesn't like recursive functions

thank you anyway @compact hornet

[compact hornet]

sorry for misunderstanding

[alpine sable]

<@&286206848099549185>

[lone heart]

From

#❓how-to-get-help

Rule 4

If your question has not been answered for a minimum of 15 minutes, you may use the Helpers tag once. Please do not try to bump your question using this ping unnecessarily. Do not abuse this ping. Do not individually ping users with the Helpers tag without their express permission.

[vale wigeon]

@alpine sable what's troubling you with these?

[alpine sable]

so for c, i am getting 5 + i / 26

[vale wigeon]

parentheses?

did you mean (5+i)/26?

[alpine sable]

yes

[vale wigeon]

okay yes, and what's the issue?

[alpine sable]

the textbook answers say its meant to be 1/26

[vale wigeon]

the imaginary part of (5+i)/26 is 1/26, that's right

[alpine sable]

oh

ohhh

ok

soryr

just a misunderstanding

thnaks

@vale wigeon Hey, when i'm conerting a complex number to cartesian form, am i allowed to make the value inside the cos and isin brackets negative

for example is my argument was -1.05, could i put it in the brackets as both pi+-1.05 and -1.05, or just the first option

[vale wigeon]

?

not really sure what you're asking here

[alpine sable]

Okay, so for a

the modulus is arctan (7/(-4))

which is -1.05

i mean argument

sorry

the modulus is 8.06

[vale wigeon]

oh you mean trigonometric form

[alpine sable]

so can i put that as 8.06[cos(-1.05)+isin(-1.05)]

[vale wigeon]

the angle inside both functions needs to be the same of course

[alpine sable]

or does it have to be 2.09

2.09 is pi + -1.05

[vale wigeon]

adding pi is inappropriate

you would be adding 2pi rather than pi anyway... and that's if your class takes arguments to be between 0 and 2pi instead of -pi and pi

[alpine sable]

okay, so does -1.05 work for that problem?

cus the textbook says the argument should be 2.09

which is pi + the argument

[vale wigeon]

ah wait

hold on

[alpine sable]

alright

[vale wigeon]

oh you just used arctan without concern for the quadrant...

[alpine sable]

oh

so its in the sine quadrant

how does that change wht i do

[vale wigeon]

it's in the second quadrant

while the arctan gave you an angle in the fourth

add pi to compensate

[alpine sable]

ahhhh okay

and if it gave me an angle in the third, would i add pi/2?

[vale wigeon]

arctan never gives you an angle in the third quadrant

only the first or fourth

[alpine sable]

oh okay

i c

so these are the answers for this particular section of working

im a bit confused

[rugged tree]

What is confusing?

Is it 2.09?

[alpine sable]

principal values

[rocky spindle]

i have no idea how to do it

without knowing the fonction

[noble sinew]

not sure what you mean with without knowing the function. But using product rule and then a sub should do the trick for example

[rocky spindle]

i don't get it

[sage summit]

does it look like lim x -> a of (f(x)-f(a)) / (x-a) for some function f and real number a ?

[ocean seal]

Muzan Jackson

Muzan Jackson

[stark trail]

@rocky spindle

[rocky spindle]

no

[sage summit]

what if it was (x sinx - 0) / (x-pi)

[stark trail]

Ah yes it could be

So derivate xsinx and substitute x with pi might also work

[sage summit]

differentiate*

[stark trail]

Ok

[stark trail]

But I think doing this is faster than differentiate

[sage summit]

could be

[stark trail]

$\lim_{x\to\pi}\frac{x\sin{x}}{x-\pi}\
\lim_{x\to\pi}-x\left(\frac{\sin(x-\pi)}{x-\pi}\right)\
\lim_{x\to\pi}-x\
-\pi$

[ocean seal]

Muzan Jackson

[alpine sable]

hey so

If we can have R^n dimensional spaces, we also can have higher dimensions figures right?

Idk if figures is the correct word

so, how could we calculate the volume of a tesseract for example?

and what branch of math does it fall into?

[prime badge]

geometry

[alpine sable]

ah

just regular geometry?

[prime badge]

i think so

[alpine sable]

ah

also, if x^2 is the area of a square, x^3 is the volume of a cube. what does x^n represent? for n > 3

would it be correct to say
x^n. ∀ n > 3

[celest acorn]

Can anybody explain to me what is rate

[alpine sable]

Dm me

what

[muted gust]

what equation proves general relativity

physic papers are pain to make

[faint spade]

Hello can anybody help me with a problem?

[burnt meadow]

I need help with this question

[sleek elbow]

https://dontasktoask.com generally

in this case, the channel is occupied, so no

[faint spade]

Channel 2

[hollow pelican]

hi guys does anyone know how to solve this?

[nocturne cradle]

Hi all, I’m very new here. I need help calculating and summarizing the relationship in packing density between two differently sized cylinders. This is for the real life application of managing the waste stream for a covid-19 diagnostic testing lab. Currently there is a nationwide shortage of 30 gallon poly propylene barrels and my lab is trying to evaluate the difference in dry waste storage capability with a larger sized barrel (50gal). I tried googling a little but couldn’t really find a helpful explanation. Any help is greatly appreciated, and I can move to another channel!

Arrogant of me to assume everyone is from US also*

There is a US shortage

[alpine sable]

There's like 4 people interrupting each other in this channel

[burnt meadow]

Well I was first :P

[alpine sable]

Yeah I agree

What have you tried

[wild marten]

the meme about #help-0 is actually true

[wild marten]

yes, this one

lmao

[burnt meadow]

umm I've tried doing simutaneous

with sin as displacement

and cos as velocity

but I figured that was too complicated and there are simpler methods

[alpine sable]

Simultaneous sounds right to me

Although I haven't done physics in a bit

[burnt meadow]

x= a sin( kt) and v = ak cos (kt)

so do I simutaneously solve 4 different equations?

[alpine sable]

Well you're solving for k and a

Or k, a and t

[burnt meadow]

yeah

not t

just k and a

I don't know how to incorporate x and v in the same equation

cuz 20 = a sin (kt) when 30= ak cos(kt)

would these be simutaneously solved?

[faint spade]

It says that h>50m and i have to prove it

[alpine sable]

Occupied

I'm gonna have to think about this, it's been a while since I did shm

You might have better luck in discord.gg/physics

[faint spade]

Any way you could help me please if you are done with that? @alpine sable

[alpine sable]

Use another channel and someone might help

Read #❓how-to-get-help

[faint spade]

I tried #2

[muted gust]

if x is traveling 10 kph in a constant speed and z is running at 15 kph and y is undefined what is the speed of y

the distance between x and y is 2 and y and z is 3

[alpine sable]

12, if by distance you mean difference in speed

otherwise not enough information

[muted gust]

i was looking for the average speed of y

all of them are in a constant

[alpine sable]

x + 2 = z - 3 = 12 is the best I can do

[muted gust]

actually 12 is the correct answer

ok another one

this one is harder

hol on nvm im stupid

[burnt meadow]

Ok thx!

[fierce vale]

2+2=5

[muted owl]

Hi Could someone help me in this exercise?

Which of the following expressions is (are) rational (s)?

[alpine sable]

ii is 13.

To figure out if something is a rational, attempt to reduce the expression as much as possible

[plucky crow]

rationalise the denominators where you can and expand where you can.

[alpine sable]

how to find HCF?

[oak chasm]

@alpine sable Do you know how to find remainders after dividing?

[alpine sable]

i have helped

someone asked using my id

[thorn vortex]

It isn't 13

It is 10

[warped gulch]

hello @everyone

Solve these equations using Algebra Tiles.
4x^2 -5x-6=0

[gray isle]

algebra tiles? also don't ping everyone

[warped gulch]

oh sorry im new

yeah

that's basically the instructions the teacher gave

[gray isle]

wtf are algebra tiles supposed to be

[warped gulch]

ikr

but i tried to search it and watched vids but i didn't understand it

[gray isle]

you're probably better off looking at general methods for factorisation

i guess
https://www.sd43.bc.ca/Resources/ParentResources/math/10/Documents/factoring simple trinomails using algebra tiles.pdf
is semi-decent for "tiles"

[warped gulch]

OMG TYSM

[thorn vortex]

Nice try

[slim grove]

for the 2 questions x^2<-6x-12 and x^2>-12x-39, one answer is no solution and one answer is all real numbers

but both are not factorable

why does one have no solution and one is all real numbers?

[sterile isle]

can somebody tell me what i have to study to understand this

[surreal meadow]

sequences and series

they are usually taught in calculus 1

in the US at least

never mind, it's actually taught in calculus 2

although this is actually a little simpler than that, you'll probably learn how to solve this in precalculus
as long as you know what an arithmetic sequence is, you should have a general idea of how to approach this problem

[gaunt magnet]

really confused on 1 part

is 5/6 is the slope at y=-1

[surreal meadow]

usman, do you know what a derivative is?

[gaunt magnet]

yee so ill show how i got 5/6
f(x) = x^1/6 - 2x^-1/3

f'(x) = 1/6 x^ -5/6 + 2/3 x^-4/3

at x =1

f'(x) =1/6 +2/3

f'(x) = 5/6

and for -1

[surreal meadow]

why are you getting the slope for -1?

[gaunt magnet]

so then y = 5/6 (x - 1) - 1
when i will simplify that i get the answer 5/6x-11/6

cause it should be -1

[surreal meadow]

you'll have a point and a slope

so use the point slope equation

(y - y1) = m(x - x1)

[surreal meadow]

ah i see, yes that looks fine

[gaunt magnet]

yes and i got -1
(sqrt(1) - 2)/cuberoot(1)
= -1

like this now

$(sqrt(1) - 2)/cuberoot(1)$

[ocean seal]

Usman

[novel crag]

y-y1=d/dx(at x=1)(x-x1) , find x1 and y1 but putting x =1 in the equation

[modest crow]

can i distribute a limit among two functions that are added?

like can lt[f(x)+g(x)] be lt f(x) + lt g(x)

[glass lichen]

Yes, assuming both exist

[modest crow]

yes they do

thanc

[alpine sable]

\sqrt{}

\frac{}{}

and \sqrt[3]{} for cube root

[gaunt magnet]

f(x) = x^1/6 - 2x^-1/3

f'(x) = 1/6 x^ -5/6 + 2/3 x^-4/3

at x =1

f'(x) =1/6 +2/3

f'(x) = 5/6

and (sqrt(1) - 2)/cuberoot(1)
= -1
from there
y = 5/6 (x - 1) - 1
simplify
get answer 5/6x-11/6

[viscid quiver]

would anyone mind helping me with factoring polynomials in algebra 2?

I'm doing khan academy right now

[solemn flicker]

I can try

[viscid quiver]

alright

vc?

[solemn flicker]

do you have any specific questions?

I can't do vc rn, sorry

[viscid quiver]

mainly just with some factoring

[viscid quiver]

it's fine

[surreal meadow]

what's the specific question?

[viscid quiver]

I just actually need some help with identifying quadratic patterns

like what formula does this equation use

or something along those lines

[surreal meadow]

that's still pretty vague

do you have any examples?

[viscid quiver]

can you vc?

I can share screen there

[surreal meadow]

can you send a screenshot?

[viscid quiver]

okay one sec

that is the kinda question I'm currently stumped on

@surreal meadow

[surreal meadow]

have you tried factoring it and seeing if it fits either pattern?

[viscid quiver]

let me try that right now

see that's the part I don't really understand

is the factoring part

[surreal meadow]

do you know how to factor?

[viscid quiver]

yes

I'm just confused on where to like start

like starting out by finding a gcf between the values?

[surreal meadow]

we're interested in the following patterns

(a + b)^2

(a - b)^2

(a + b)(a - b)

now, expand those expressions

and see what you get in terms of a and b

[viscid quiver]

oh okay

alright so (a + b)^2 gives us u^2 + 2uv + v^2 right?

[surreal meadow]

(u + v)^2 gives us that, yeah

[viscid quiver]

okay

[surreal meadow]

now before you expand the rest

@novel crag

give us a second

we're working through it

[surreal meadow]

see if the expression you have above

fits that pattern

[viscid quiver]

I think it does

[surreal meadow]

so what are the values of U and V?

[viscid quiver]

u = 3x^3

v = y

[surreal meadow]

yep

[novel crag]

Ohh

[surreal meadow]

so what would the answer be

[viscid quiver]

so the first answer is correct right?

[novel crag]

Nice

[surreal meadow]

yes

[viscid quiver]

ohh okay

let me try the next one

[surreal meadow]

we did this backwards

so you could notice the pattern

[viscid quiver]

ohh okay

so basically

[surreal meadow]

but once you get more comfortable with factoring and the patterns present, you can factor and then deduce the pattern

[viscid quiver]

oh okay

so for now, just do what I just idd

did*

how can I do a question like this?

so far I just defined each of the values in the most likely formula

u^2 - v^2

and I know that u = x^2 and v = 3

but how can I thoroughly check to see which pattern it is?

@surreal meadow

[surreal meadow]

well you know that if you expand (a + b)^2 you'll get 3 terms

and same with (a - b)^2

but you only have 2 terms

so that can't be it

[viscid quiver]

so it's impossible to have either of those patterns

but how can I check to see if the perfect square formula works or not?

[surreal meadow]

what do you mean by perfect square formula?

[viscid quiver]

oh wait

nvm

I meant the u^2 - v^2

formula

how can I check to see if that works

[primal ether]

do you mean (u+v)(u-v)

[viscid quiver]

oh yeah

how can I check to see if x^4 - 9 fits that formula?

[surreal meadow]

x^4 - 9 does

but what you are given doesn't

[viscid quiver]

oh wait

because it's +

not -

[primal ether]

yh

[surreal meadow]

exactly

it would work if u and v could be complex numbers

[viscid quiver]

ohh so no patterns would work

[primal ether]

yeah

[surreal meadow]

but we only want integer/single variable solutions

[viscid quiver]

ohhh okay

that makes sense

so I have to use a bit of logic for these kinda questions

[surreal meadow]

yes

[viscid quiver]

alright

[primal ether]

in another question if you had x^4-9, to realise it can be factored, you need to recognise that x^4 and 9 are both squares

its called difference of two squares

(only possible with a minus sign)

[viscid quiver]

yes I know that formula

thank you for letting me know about that though

how can I factor x^4 - 14x^2 + 49?

[alpine sable]

(x^2-7)^2

[viscid quiver]

since you can't have anything that multiplies to 49 and adds to 14x^2, but if it were just 14x, you could factor it as -7x - 7x

[viscid quiver]

can you explain how you got that answer though?

[primal ether]

expanding (a+b)^2 gives you a^2+2ab+b^2

[viscid quiver]

yes

[primal ether]

so if we compare it, -14=2ab and b^2=49

[viscid quiver]

ohhh

okay

I got it now

let me do this problem

alright, I got the question correct. Thank you to @primal ether and @surreal meadow !

[alpine sable]

you could always also solve the equation x^4 - 14x^2 + 49 by putting t=x^2 and getting t^2-14t+49=0 then you get t=7 then (t-7)(t-7) or (x^2-7)^2

[viscid quiver]

I understand the question now. Thank you to you too.

[unique latch]

876897402555080794

[misty path]

a right trialngle size would look something like this?

6,7,13

[surreal meadow]

that is not a right triangle

[novel crag]

If they are Pythagorean triplets , then am they do form right triangle

[surreal meadow]

i don't even think its a triangle

[misty path]

10,60,61?

[surreal meadow]

is there a more specific question you had in mind?

[misty path]

ill send a picture

i aint learn nothing in remote learning

[surreal meadow]

do you know the pythagorean theorem?

[misty path]

yup

c2 = a2 + b2

[surreal meadow]

yes, do you know what it means though?

[manic glade]

quick question that wont get in the way, whats the english term for opening brackets and manipulating the values around, can i say develop?

[surreal meadow]

please ask in another unoccupied channel

[misty path]

I know it works with 2d shapes

[surreal meadow]

look up the pythagorean theorem and what it means

[sleek elbow]

writing exponents is done like this a^x btw 🙂

[misty path]

I know but thanks for letting me know 😃

[sleek elbow]

oh okay 😄

[misty path]

a theorem attributed to Pythagoras that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.

[misty path]

so it has to be either B or D?

[primal ether]

Yeah it's one of them

[heady tusk]

can someone help me with 3.1

you have to solve x

[surreal meadow]

do you know how to factor?

[heady tusk]

uhm yea

[tranquil parcel]

3andak dits fries

[heady tusk]

@surreal meadow what

[surreal meadow]

you want to factor that polynomial into (x-a)(x-b)(x-c)

or it might be (2x-a)(x-...

but you want to write the polynomial as the product of three terms (ax-b)

this way you can solve for different values of x that will make the polynomial equal to 0

[heady tusk]

how do I factorise with so many x's

@surreal meadow

[primal ether]

Use factor theorem

[heady tusk]

only used to doing it with 3

[heady tusk]

?

[primal ether]

So because x-2 is a factor (im assuming)

you divide the polynomial by (x-2)

with algebraic division or by inspection

[heady tusk]

what is the first factor?

[surreal meadow]

you're supposed to do that

[primal ether]

Sorry was looking at wrong q

[heady tusk]

hm?

[surreal meadow]

i.e., we're not going to factor it for you

[heady tusk]

ik

[surreal meadow]

it's best if you learn how to do it yourself

[heady tusk]

but can you just help me with the first one

then I'll get it from there

[primal ether]

Substitute values of x in until you get something that equals 0

[heady tusk]

if I know the first one I'll understand

[surreal meadow]

how did you do the question before this

it's the same thing

[heady tusk]

so the common factor is just x?

or x+1

@surreal meadow

[primal ether]

sub values of x in until the polynomial = 0

[surreal meadow]

http://web.math.ucsb.edu/~vtkala/2016/S/4B/FactoringCubicPolynomials.pdf

they'll explain it better than i can

[heady tusk]

what?

[primal ether]

Search up Factor Theorem

[heady tusk]

@surreal meadow yo I think I got it?

[willow wadi]

wow

[heady tusk]

now how do I solve the x

[heady tusk]

sarcasm?

[surreal meadow]

are you sure x=2 is a solution?

[heady tusk]

no? what?

@surreal meadow wdym

[surreal meadow]

oh i misread the question

[obsidian cave]

Looks good

[heady tusk]

now how would I solve x man? @obsidian cave

from there

[surreal meadow]

you have that (x-2)(x-5)(x+5) = 0

what values of x make the left side 0 ?

[heady tusk]

yes

x=2

x=5

x=-5

[primal ether]

yh

[surreal meadow]

that's your solution set

[heady tusk]

oh so there's answers

to x

[surreal meadow]

yes

[heady tusk]

solve x if g(x)= 0

@surreal meadow

3.2.2

[surreal meadow]

it's the same type of question

[heady tusk]

oh factoring

but this time the two sides aren't the same

so what type of factoring would I use

@surreal meadow

[surreal meadow]

wdym?

[heady tusk]

that's hwhat I have

but I can't take the common factor out of the two pairs

then group it together

like the prev question

so how do I do it now

@surreal meadow

[surreal meadow]

stop pinging me pls

[heady tusk]

soory

:(

that's my bad

[surreal meadow]

http://web.math.ucsb.edu/~vtkala/2016/S/4B/FactoringCubicPolynomials.pdf

if you want a quick method

then find a value of x that makes that equal to 0

and then divide the polynomial by (x-a)

where a is that value

[heady tusk]

it isn't in cubic polynomial form though

[surreal meadow]

usman this is occupied

[heady tusk]

like in the notes

[surreal meadow]

wdym

[heady tusk]

the notes doesn't support a method for that sum

question

[surreal meadow]

http://web.math.ucsb.edu/~vtkala/2016/S/4B/FactoringCubicPolynomials.pdf

[surreal meadow]

or do this

i don't know what your notes are

[heady tusk]

bruh

I meant this notes

[heady tusk]

.

[surreal meadow]

they describe how to solve this in there

[sudden hawk]

when i put the equation into desmos the graph isnt the same, idk what im doing wrong

[heady tusk]

that good max?

x=1 or x=3

[surreal meadow]

yes looks good

[wary stream]

It's probably the same, it's the y axis scale. In desmos, you're scaled to 20000, while the other plot, the max y is 10

[rugged brook]

Math HL Year 2 and we are doing a review and i don't remember anything :((

#5 a) where do i start?

[topaz scaffold]

Just plug the solution into the differential equation

With the derivative on the left hand side

[rugged brook]

So substitute y on the right side for the solution?

[topaz scaffold]

Yep

[surreal meadow]

i think they'd rather you show it works by integrating rather than plugging it in

that's what i recall from my hl class but i may be wrong

[rugged brook]

Yeah i tried to plug it in but idk if it's working out

I also tried integrating but i didn't get an e anywhere from 2x-y

[honest hawk]

Silly question here. Does anyone have any tricks to doing quick math such as finding the decimal for 2.5/75?
Currently studying for the MCAT, and this is simply just stuff i relied on my calculator to do.

[surreal meadow]

2.5/75-> 25/750 -> 5/150 -> 1/30

decimals are essentially fractions, and fractions can be simplified until the numerator and denominator are coprime

[rugged brook]

Idk how they can prove that as a solution

[honest hawk]

Sounds good. I often forget that you can make the fraction easier to deal with beforehand. Thanks

[surreal meadow]

they aren't treating y as a function of x there, just a constant

[topaz scaffold]

I don't think it's separable

The differential equation

[rugged brook]

Oh i see

Kinda

So what do i do with that y

[surreal meadow]

the integral calculator won't work for differential equations i don't think

[topaz scaffold]

I think you can do $\frac{dy}{dx} +y = 2x$

[ocean seal]

RipeOrange

[topaz scaffold]

Then multiple both sides by $$e^{\int 1 ,dx}$$

[ocean seal]

RipeOrange

[topaz scaffold]

Multiply*

Then you'll get $\frac{d}{dx}(y \cdot e^x)=2xe^x$

Which you can integrate

[ocean seal]

RipeOrange

[rugged brook]

Ohh wow okay tysm!

[topaz scaffold]

Np

[candid thistle]

If an angle bisector is also an altitude, would the two parts of the side that it split be equal?

Lemme sketch a quick diagram

a and b are angles, x and y are sides.

Another thing, am I then allowed to assume that r = s

Actually nvm I think I got something

I can just use AA similarity :P

[sudden hawk]

It's (5000, 2.57) in desmos but the other one doesn't have 5k

[leaden galleon]

Algebra 1:
What is 15x^5 x^8 / 90x^12 ?
Evaluate and explain pls

[ocean seal]

Eat water it's good

[candid thistle]

Could you start off with simplifying?

[surreal meadow]

look up the laws of exponents

[leaden galleon]

Like I’m learning this but I can’t understand it

I mean I understand the simple ones but not like that

[surreal meadow]

what about it is confusing?

[shut elk]

solve $x^5 \times x^8$

[ocean seal]

eis

[leaden galleon]

Oh

[candid thistle]

Perhaps rewriting would help?

[leaden galleon]

Perhaps

[shut elk]

eat water is right, group up the like numbers/algebraic terms.

[ocean seal]

Eat water it's good

[candid thistle]

Do you see what you have to do?

[leaden galleon]

Yea

[candid thistle]

Alrighty

[shut elk]

crypt, also, answer maximos question

it'll help you, he asked, what is confusing?

[leaden galleon]

?

Oh

[shut elk]

^^

budi, select an empty channel

and delete your question.

[leaden galleon]

Well, my teacher said that I had to simplify 15/90 which would be 1/6. But I really didn’t know what to do with the exponents on the top. I thought I had to add them but I know now that I have to multiply them

[low topaz]

what is 2+2

[candid thistle]

Keep in mind that exponents are just repeated multiplication.

[candid thistle]

Sorry, I cannot give a full answer. Do you know how to count to 10? That could be a start.

[leaden galleon]

XD

[surreal meadow]

it seems that you should review the laws of exponents, and like eat water said, exponents are just repeated multiplication

[leaden galleon]

Supposedly Mathway said that the answer to the question I asked was x/6

[low topaz]

no, i can only count to 5

[shut elk]

Crypt, also, consider what you're dealing with here. you are dealing with two things

the variable x and integers.

we can separate our concerns.

[leaden galleon]

Yea

[shut elk]

but, fundamentally, maximo is correct. solve this question then review laws of exponents.

[candid thistle]

Ahh, learn that then you can come back to troll later.

[low topaz]

ok

[low topaz]

its 4

2+2 is 4

[leaden galleon]

What do I do with the bottom though? It says I have to multiply 90 by x^12

[surreal meadow]

90 * x^12 = 90x^12

[shut elk]

no, what the denominator is saying is that there is a number 90x^2

[leaden galleon]

Bruh XD

[shut elk]

it's not instructing you of anything.

[ocean seal]

Eat water it's good

[shut elk]

^^^

[leaden galleon]

So it would be 1x^40/6x^12?

[ocean seal]

Eat water it's good

[candid thistle]

Review your exponent stuff, as maximo said.

[leaden galleon]

Multiplying the exponent 5 and 7

8

Didn’t you tell me to do that?

[surreal meadow]

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

[candid thistle]

No, you multiply the terms

[ocean seal]

maximo

[surreal meadow]

review exponent laws

[candid thistle]

but just because you multiply the terms doesnt mean the exponents get multiplied

This table looks useful:

[ocean seal]

Eat water it's good

[leaden galleon]

Like I said I know most of it but the quotient ones are just kinda complicated for me

[candid thistle]

Where the first thing is x a's and the second is y a's

[ocean seal]

Eat water it's good

[candid thistle]

Did you get that?

[leaden galleon]

Yes

[ocean seal]

Eat water it's good

[leaden galleon]

Yes

I understand that

[candid thistle]

Cool, then you could use that in your problem

[ocean seal]

Eat water it's good

[candid thistle]

ahh keep forgetting the {} for 12

[leaden galleon]

And I simplify 15/90?

[candid thistle]

Yeah

[leaden galleon]

K so it should be 1/6x^28?

[surreal meadow]

redo the x exponents

what's x^5 * x^8?

[leaden galleon]

X^40

[candid thistle]

Noo

[candid thistle]

.

[shut elk]

product rule.

[surreal meadow]

what's x^5 * x^8?

[leaden galleon]

X^13 🤦‍♂️

[surreal meadow]

good

and do the quotient rule like you did before

[leaden galleon]

So x/6?

[surreal meadow]

yep

[ocean seal]

Eat water it's good

[leaden galleon]

Nice

Thanks guys

[candid thistle]

np

[leaden galleon]

Sorry if i was being a complete idiot XD

[shut elk]

na, you weren';t

revise exponent rules

[leaden galleon]

I have trouble understanding things quickly