help-10

[grave flicker]

0

[timid silo]

what is floor(0.01)?

[grave flicker]

its 0

oh

so the limit is

0

[timid silo]

but now lets look at the left side limit

what is floor(-0.1)?

[grave flicker]

it becomes -1

[timid silo]

yes

[grave flicker]

ooooo

[timid silo]

and so does floor(-0.000001)

[grave flicker]

so now its dne

becayse

so for the first one

the limit dne because

on the right side

the limit is 0

but left side -1

right?

[timid silo]

yes

so we know that f and g match the needed conditions

[grave flicker]

ooo and now we can multiply

f and g(x)

[timid silo]

yeah, but if we multiply we can use the same argument again with left side and right side

[grave flicker]

yeah so we wouldnt be able to multiply them?

oo

[timid silo]

we can still do floor(6x)*floor(6x)

[grave flicker]

i plugged in

0 for the first one

and got 0

which is a valid limit

so it does exsit for the first one?

[timid silo]

not quite, you cant just plug it in

[grave flicker]

?

[timid silo]

if we now think again what floor(-0.000001) * floor(-0.000001) is?

[grave flicker]

it is -1 and 1

= -1

oh wait

im tripping

its 1

[timid silo]

yes, so the left side limit of f(x)*g(x) is 1

and the right side limit?

[grave flicker]

so

we do

1 * 1

= 1

oh wait

no

one sec

im moving to fast

wait it is 1

so it does exist

[timid silo]

why would it be 1?

floor(0.0001) * floor(0.0001)

btw thats the floor graph

[grave flicker]

0 * 0

= 0

[timid silo]

yes

[grave flicker]

so 1 and 0

left is 1 right is 0

[timid silo]

so it still doesnt exist

[grave flicker]

yeah so it

i was just abt to say

OHH so the first one

would be incorrect

wait so if the first one dosent exist

then the last one dosent either

because its the same thing i think

[timid silo]

always keep in mind we only approach 0, but never ever does x hit exactly 0

[grave flicker]

so the limit would be 0

ok for the second one

when looking at the function

[timid silo]

second should be easy

[grave flicker]

if i did

6/0.01

i get 600

if i do negative i get -600

[timid silo]

na doesnt need to think compicated there

[grave flicker]

?

[timid silo]

its just 6/x, and x goes to 0, can that really approach any value?

[grave flicker]

it cant

[timid silo]

yeah, it goes to infinity / -infinity actually

and whats the product of f(x)*g(x)?

[grave flicker]

well i got -36/x^2

[timid silo]

and does that approach anything?

[grave flicker]

they do not

so dne

[timid silo]

yeah

[grave flicker]

so it means that

it also cant be the 4th one

because its the same thing

[timid silo]

yeah

[grave flicker]

so then we are left with the middle

which has to be the answer

now my only question would be why though

[timid silo]

well we also have the bottom one

can you see why f(x) and g(x) themself diverge?

[grave flicker]

diverge?

wdym

[timid silo]

i mean limit doesnt exist

[grave flicker]

for the bottom 2?

[timid silo]

oh, lets just start with the middle one

[grave flicker]

alright

[timid silo]

piecewise functions, its good to look at left side and right side limits there too

[grave flicker]

so on the left side

the limit is

-1

and on the righjt side

its 1

[timid silo]

yeah

[grave flicker]

for f(x)

and for g(x)

on the left side its 1

so

actually

the limit

would exist

for this equation

because if you multiply -1 and 1 and 1 and -1

they are the same thing

[timid silo]

yeah

[grave flicker]

ok and now the 4th one

[timid silo]

f(x)*g(x) is actually just constant -1

[grave flicker]

-1 is the limit

[timid silo]

4th is easy, what about bottom?

[grave flicker]

for the 4th one they both dont have limits

the bottom is the same as the top?

[timid silo]

not quite, but similar concepts

g is now the ceiling function

[grave flicker]

?

OMg

I FORGOT i just learned floor

i didnt even notice that

[timid silo]

ceil(5.3) = 6
ceil(9.8) = 10
ceil(2) = 2
ceil(-1.9) = -1

[grave flicker]

this thing

LOL

Ok got it

it rounds up

to the nearest whole number

[timid silo]

can you see what the right side and left side limits of ceil(x) are?

[grave flicker]

let me look

um

6 * 0.01

so for the left

it dne

its -1

i mean

for the right

[timid silo]

like
ceil(0.00001)
ceil(-0.00001)

[grave flicker]

for the rights its 0

[timid silo]

whats ceil(0.00001)?

[grave flicker]

0

[timid silo]

ceiling

[grave flicker]

1

[timid silo]

yeah

and ceil(-0.00001)?

[grave flicker]

1

wait

its 0

[timid silo]

yes

so,
floor(x) right is 0
floor(x) left is -1
ceil(x) right is 1
ceil(x) left is 0

[grave flicker]

so dne for both functions

[timid silo]

what happens if we do floor(x)*ceil(x)?

[grave flicker]

now if you multoply them

let me plug in a var real quick

floor(0.001) = 0 * ceil(0.001) = 1

so it wouldnt exist

i mean

it would be 0

im dumb

now with negatives

floor(-0.001) = -1 * celi(-0.001) = 0

1 *0 = 0

so 0

[timid silo]

so?

[grave flicker]

so the limit does exist

its 0

[timid silo]

good

[grave flicker]

Omg

dude

thx so much

[timid silo]

np, it can be a bit unintuitive

[grave flicker]

Yeah no man i appreciate it so much

wow i understnad it a lot more now

.close

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[woven tartan]

Hi! I'm following along in a video and I'm very confused how they got from the top expression to the bottom expression. Is there some trig identity they used or smthing?

[cedar lichen]

They took the integral

Probably via integration by parts, if I had to guess

Or maybe there's a formula online for it

[woven tartan]

Ye I understood that I just didn't get how they took it

I'll try by parts and see if I get the same thing

[obtuse pebble]

@woven tartan Has your question been resolved?

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[ashen wharf]

I am trying to figure out how to simplify rational expressions. The problem I have is (x^2-36)/(6-x)

[robust sleet]

Factorize numerwtor

[ashen wharf]

Thats where im confused

When it comes to division I get all messed up

[robust sleet]

What u got

[ashen wharf]

Nothin I honestly just faked my way through hs so far not knowing how to simplify division

[robust sleet]

Can u Factorize numerator

[ashen wharf]

6-x

No dont think so

$(x^2-36)/(6-x)$

[warm shale]

Tree

[robust sleet]

https://youtu.be/bHTzg7vZneA

Watch tgis

[ashen wharf]

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[obtuse pebble]

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[still vault]

Why is A = 1/4?

[kind hawk]

it's not

A=0

[still vault]

Thats what i was thinking

Im solving non-homogeneous linear 2nd order derivative equations

and i am trying to follow my professors notes

but i couldnt understand why A was 1/4

[kind hawk]

the RHS should only be 4e^(-x)

but then still A should be 1/3

hmm

[still vault]

A is used to denote any multiple i guess or 'C' number

that satisfies this

[kind hawk]

well but 1/4 doesn't satisfy it

[still vault]

Oh i know, not arguing the result

[kind hawk]

can you show all of the question?

[still vault]

its not a question, its from my theory textbook

sec

[kind hawk]

well then all of the problem. better?

[still vault]

To translate

The characteristic polynomial is :
λ^2 -5λ +6 = (λ-2)(λ-3)

therefore the solution to the homogeneous is
yh = C1e^(2x) + C2e^(3x)

We observe that r = -1 is not a root of the characteristic polyomial (such as that e^-x is not a solution to the homogeneous, and doesnt zero out the differential equation).

Therefore x^k = x^0 = 1.

In addition there is not a polynomial on the RHS (we assume q(x) =1)

So we that in mind we search for a solution of the form
Yp = Ae^(-x)

[kind hawk]

yep ok

they just made some typos

should be 1/3 and then everything checks out

[still vault]

Question, when i see these do i divide from LHS to RHS to find the A?

cause by the same notion i could divide both sides by 4

[kind hawk]

well you have the equation 12Ae^(-x)=4e^(-x)

solve that however you want

[still vault]

Wait

[kind hawk]

divide by e^(-x) to get 12A=4

[still vault]

is it only 12Ae^(-x) = 4e^(-x)?

not 12Ae^(-x) = 4Ae^(-x)?

if thats the case you are right

and that makes much more sense

[kind hawk]

yeah they just made a mistake when going from one step to the next

RHS should always only be 4e^(-x)

[still vault]

Thank you

now to move to Laplace transformations ^^ and hopefully pass my exams

.close

[obtuse pebble]

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[kind hawk]

gl

[still vault]

Thank you ill sincerely need it

[obtuse pebble]

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[thorn kelp]

IMMSORRYY

[thorn kelp]

PLEATE UNKUTE ME

[kind hawk]

?

[long plinth]

.close

[obtuse pebble]

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[crystal basin]

<@&286206848099549185>

[tulip edge]

The bottom area of a cube-shaped container is 121 dm². How many liters of water does this container hold?

[hardy widget]

I think you're supposed to wait before pinging cause it says this

[worn swan]

yes

[hardy widget]

Note that all sides of a cube have the same length

[worn swan]

its againt the rules

against

[hardy widget]

So, we can use the bottom area ||to find the side length using the formula for the area of a square||

[tulip edge]

why he pinged

[hardy widget]

Then, we can use that to find the volume of the cube itself

Anyway, I gtg now, but hopefully it helps 🙂

[worn swan]

who would now

[tulip edge]

:v

[worn swan]

know*

[obtuse pebble]

@tulip edge Has your question been resolved?

[obtuse pebble]

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[burnt cipher]

was asked to find the electrical potential, now something is unclear to me

this is how i wrote the way to the answer which is wrong

i cant understand why

[random ocean]

where do we need to find potential at centre?

[burnt cipher]

yes

here is the written answer

[random ocean]

the distance would be droot2/2

cause droot2 is length of the diagonal

[burnt cipher]

wait shit not just root 2 x d

ohhhh

omg embarrassing

[random ocean]

lol its alright

[burnt cipher]

thanks @random ocean

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[obtuse pebble]

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[robust vortex]

ok so I tried many combinations and it didnt work

[robust vortex]

#3 problem

[random ocean]

ur name and ur school names are visible, if i were u i would crop and resend

[robust vortex]

idc

[kind hawk]

Don't cheat on tests

[robust vortex]

its a take home test

bruh

open note

[kind hawk]

In what world is open note the same as asking other people for help

[nocturne minnow]

Open note doesn't necessarily mean open internet and everything

[robust vortex]

bruh wtf

[upbeat plinth]

are u expected to do it without outside help?

[robust vortex]

the teacher said you could search up stuff

cringe

[upbeat plinth]

as in ask other ppl for help

[robust vortex]

Uess

yeyeyes

s

[upbeat plinth]

hmm i highly doubt that

i think u can only consult ur notes, etc, not ask others for help

[robust vortex]

omfg, it literally did the problem. I even asked this server a few days ago and no one could find a answer

thats why im asking

[upbeat plinth]

sry that doesnt change what i think the instructions are

muted for 24h, should cover the length of the test

.close

[obtuse pebble]

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[harsh glacier]

Someone else shared their homework with me and this diff eq problem sounded unfamiliar. How are they supposed to do this?

[harsh glacier]

[f'] = M^x L^y T^z
How would one write x, y, and z in terms of a, alpha, b, beta, c, and gamma?

I assume that's what they're asking for

[velvet spade]

I haven't seen a question like this before, but can you use the definition of the derivative?
[f'(x) = \lim_{h \to \mathbf{0}} \frac{f(x + h) - f(x)}{h}]

[warm shale]

Samsamson33

[stable rain]

go to another channel samson

[timid silo]

im not sure if this definition applies to multiple dimensions

[velvet spade]

I'm replying to the person who asked the question

[stable rain]

oh im dumb :c sry

[harsh glacier]

I don't know how that would work 🤷

[velvet spade]

it's not multivariate, so I think the dimensional analysis should be the same at least

[harsh glacier]

The (time) derivitive of something like position is velocity, so it could change the dimensionality, right?

[velvet spade]

divide the dimensions of the numerator and the denominator to get the dimension of the derivative

[harsh glacier]

Hmm ok

I guess h has the dimension of the dependent variable

[velvet spade]

it has the dimensionality of x

[harsh glacier]

Oh true!

Thanks

[velvet spade]

np

[harsh glacier]

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[obtuse pebble]

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[frosty plaza]

how does x(sqrt(x+4)+2) simplify to the one below

[frosty plaza]

ignore the top where it says answer -1

[meager granite]

because look at the top

you have 4-4

so you’re just left with x

and it just so happens that you have an x in the denominator

so they cancel out

[scenic sundial]

^

[frosty plaza]

okay so x = 1

where do you get x = 1 from

if x cancel out

[fathom plank]

What is x/x

[meager granite]

the answer is 1/4

I don’t know what software your using but it’s odd

[frosty plaza]

1

okay i get now

[fathom plank]

Yeah and thats where the 1 on top is from

Its not on the bottom for simplicity in writing

[frosty plaza]

its the teachers pdf

thanks

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[timid silo]

im mainly confused on what the solid youd get after you rotate the semi circle is

[obtuse pebble]

@timid silo Has your question been resolved?

[mint bronze]

Let's imagine rotating each line individually

If you rotate the straight line about the y axis, what surface would you get?

[timid silo]

youd get an empty cone

[mint bronze]

Yeah, exactly and how about the parabola?

[opal trench]

yknow those black hole diagrams

[timid silo]

idk how to explain but it would look like an empty cone sort of thing

[timid silo]

yea like this

[mint bronze]

Yeah it would look like a cone with a curved side and a cusp at the centre, not an asymptote like a black hole, but yeah

[opal trench]

yeah pretend it ends in a point lol

[mint bronze]

Yea, and just combine those surfaces in your mind to picture the solid

It's a cone with curved interior

[obtuse pebble]

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[ornate iron]

How do i do this? (this is alg 2 i dont really know the concept and im trying to learn cause ive been in this class for 2 weeks and have trouble paying attention and understanding because i made the mistake of cheating in 8th grade when i was doing alg 1)

[obtuse pebble]

@ornate iron Has your question been resolved?

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[obtuse pebble]

@loud forum Has your question been resolved?

[obtuse pebble]

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[left goblet]

can someone help me

[left goblet]

i forgot how to do it but i've done it beofre

just a refresher

[nocturne minnow]

What does it mean to be a midpoint?

[left goblet]

be inbetween the other variables

or in the middle

[nocturne minnow]

Meaning that both halves will be the same, correct?

[left goblet]

i think so

probably

[nocturne minnow]

Midpoint, has the prefix mid, meaning middle

So if J is in the middle of CT then that means CJ and JT are equal

[left goblet]

yes

[nocturne minnow]

Do you know how you can create an equation with that info?

[left goblet]

i can do the algebra, idk how to set it up tho

[nocturne minnow]

.

CJ and JT are equal

Can you create an equation based on that?

[left goblet]

i dont think so

sorry

[nocturne minnow]

If they are equal, that means you can set them equal to each other, correct?

[left goblet]

yes

[nocturne minnow]

So then with that info, can you create an equation now?

[left goblet]

so both of the equations will be the same?

[nocturne minnow]

Yes

[left goblet]

i got it

thx

[obtuse pebble]

@left goblet Has your question been resolved?

[obtuse pebble]

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[stray trellis]

How do I know if a matrix exists just by knowing what the nullity of it is?

[royal shard]

your matrix is not determined by the nullity

not 100%

[stray trellis]

Like for example, I have a question here asking if a 4 x 9 matrix with a nullity of 3 truly exists

how would you go about this question?

[royal shard]

a 4 x 9 matrix has 4 rows

a matrix with nullity of 3 has 3 rows of zeros

[stray trellis]

yes, so the last row would be zeros

right?

[royal shard]

the last 3 rows would be zeros

[stray trellis]

I still don't understand

can you please explain

[royal shard]

do you know how to calculate the nullity?

[stray trellis]

yes

[royal shard]

how do you do that?

just so we are on the same page

[stray trellis]

by reducing the matrix to REF

then finding the rank

and minusing that from the number of columns

is that right?

[royal shard]

almost

this works for quadratic matrices

for m x n matrices we take the lower one of m or n

from that we subtract

this is also the same as counting the rows of zeros in ref

on another note:
a 4 x 9 matrix has a maximum row rank of 4
since row rank=column rank, the maximum rank of this matrix is 4
a matrix of such size can have any rank less or equal to this maximum rank

[stray trellis]

therefore the question that i've got here is correct because it's less than 4?

as in a 4x9 matrix exits with a nullity of 3?

[royal shard]

yes

[stray trellis]

makes sense

[royal shard]

the simplest one would be a matrix with 3 rows of zeros and one row with at least one entry not equal to 0

[stray trellis]

oh okay, perfect! thank you!!

[obtuse pebble]

@stray trellis Has your question been resolved?

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[stray trellis]

I'm not too sure how to go about this question. Not too sure what they mean by element?

[nocturne minnow]

The numbers, symbols, or expressions in the matrix are called its entries or its elements

[stray trellis]

do we sub in odd values for k or do we just leave it as k?

so 2 elements of k, 2k, 3k or 4k?

[nocturne minnow]

I think something like this

[obtuse pebble]

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[west bone]

Hi, I need help to show work on a geo question about angles and angle relationships.

[obtuse pebble]

@west bone Has your question been resolved?

[stable rain]

um

what is angle 2 in terms of x

and what is the sum of angles on a line

@west bone

[obtuse pebble]

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[timid silo]

i got a question like this in the chapter linear equations but the teacher didnt teach us about these sequences, could someone help me explain how i would complete this question without just counting and counting

[timid silo]

its just like this question

[stable rain]

ok so can u find a formula for how many dots are in the nth figure?

[stable rain]

what is the difference between each term?

[timid silo]

do you know the concept of a series?

[timid silo]

4 and 5

[timid silo]

nope

i tried the artithmetic sequence thing

OK assign each cube a number

say a1 a2...

but that didnt work because it wanst a arithemitc seqenece

yup

[timid silo]

k

it's a geometric series

[stable rain]

ok these are the square numbers

[timid silo]

oh

i didnt learn that yet

an arithmetic series is a series where the difference between two consecutive elements are equap

all we did in linear relation chapter was just plotting things in a number line

[stable rain]

try writing out the next few terms of each pattern

[timid silo]

geometric series is one where the ratio of two consecutive elements are the same

[timid silo]

so for both of the questions i use the geometic sequence formula?

one sec

[timid silo]

i did

i decided to stop after awhile

the first question is geometric

the second is arithmetic

because itll take me a whole lot of time if i keep subtracting 4 and 5

there is a general term

for arithmetic series

is you assign each element an index

[timid silo]

i see i tried the formula though but because i was trying to find the common number idk how to do it

it will be $a_n=q+(n*r)$

[warm shale]

Zermelon

[timid silo]

see the difference between two consecutive elements

can you do that

i dont understnad

what do you mean by consecutive elements

355,351

it's 4

right

yep

now we know the r in $a_n=q+(n*r)$

[warm shale]

Zermelon

[timid silo]

is this the geomettic formula?

or the arithemetic

seqenece

that is the arithmetic

i dont remember an r

isnt it this

yes

they are the same

I just moved the terms around

try to do it your way

so your professor/teacher doesn't remove points

they didnt even teach us about this formula

im currently taking a quiz online

and these questions showed up

but the teacher never taught us this

like a school related quiz?

if so talk to whomever assigned you the quiz them

yea its for marks

k

but theres a time limit rn

so if u dont mind could u help me

oh

I can't help you

oh

that is not allowed here

wait what

academic dishonesty is not allowed

in the rules

oh

i didnt know that

sorry

well now you know

i see

ill just come back later after im done the quiz

thanks anyways

np

.close

[obtuse pebble]

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[stark belfry]

Not sure if I did it right

Last answer was x^2 -2x - 9

And ik I got 9 wrong

[robust sleet]

(x-3)^2-2(x-3) you did this?

[stark belfry]

Yea

[robust sleet]

what's (x-3)^2

[stark belfry]

I got x^2 + 9 - 2x - 6

X^2 + 9

I think

[robust sleet]

That's not (x-3)^2

[stark belfry]

Really

[robust sleet]

Yeah

[stark belfry]

It isn't x squared and then 3 squared

?

[robust sleet]

(x+a)^2=x^2+2ax+a^2

No

[stark belfry]

That's x-3 tho

I am so confused

[robust sleet]

What?

[stark belfry]

Where did that equation come from

[robust sleet]

My head, you have never seen it?

[stark belfry]

No

Well maybe

But I don't remember it

Lemme try and solve it using that equation

I got x^2 - 8x+ 3

• 15

Instead of 3

I'll try it

It was right

[stark belfry]

Thank u

.close

[obtuse pebble]

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[obtuse pebble]

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[outer rune]

how do i solve this?

[hardy widget]

D, the closer the points you're using to find the secant line are to the point where you're taking the tangent, the better the approximation

[outer rune]

okay thank you 🙂

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[stark belfry]

So on the example they gave in like the notes section the points were marked

I know that from that middle point it'll be increasing or decreasing to negative or positive infinity

But how would I find that middle point

[desert sinew]

Try check “completing square” in your textbook or in google. I am sure there will be standard and clear explaination on how to resolve for quadratic equation max/min problem 🙂

[stark belfry]

Uh it's like video notes

[velvet spade]

do you know how to find the vertex of a parabola?

[stark belfry]

I do not

[velvet spade]

so, every parabola that has a vertex at the origin is of the form y = a x², for some constant a

if you translate this by (h, k), you get y = a (x - h)² + k

which is the equation for a parabola with a vertex at (h, k)

[stark belfry]

Hm

[velvet spade]

you want to find h, the x-value of the vertex (the "middle" point)

[stark belfry]

So I'd like the equation they gave me and then take the corresponding values and put it into y= a(x-h)^2 + k

[velvet spade]

yes, you want to get it in that form

a method for doing that is called "completing the square", which is what jimmy1234 was refering to

[stark belfry]

Hm

Lemme Google how do I complete the square

[velvet spade]

the idea is you can rewrite the equation as follows:

y = a (x - h)² + k
y = a (x² - 2 h x + h²) + k
y = a x² - 2 a h x + (a h² + k)

your equation is f(x) = x² - 12 x + 0

which means a = 1, - 2 a h = -12, and a h² + k = 0

does that make sense?

[stark belfry]

Oh I was getting confused with a

Gimme a sec I needa write it out

[velvet spade]

sorry, typo, a = 1

[stark belfry]

Alr

So
Y = 1(x+12)^2 + 0

[velvet spade]

(x+12)^2 = x^2 + 24 x + 144

[stark belfry]

What's that equation

[velvet spade]

that's just an equality

[stark belfry]

When it's( x + a) ^ 2

[velvet spade]

like if you expand (x+12)^2

[stark belfry]

I saw it earlier when I got help

[velvet spade]

ok, the trick is: see how (x + 12)² gives you x² + 24 x + 144?

where 24 = 2 × 12?

you can use that to find the value of h easily

[stark belfry]

Why though wouldn't it be 12 squared

[velvet spade]

(x + 12) (x + 12) = (x × x) + (12 × x) + (x × 12) + (12 × 12) = x² + 12 x + 12 x + 144

so 12 x shows up twice

[stark belfry]

Ohhhh yea I do remember that

So y = x^2 + 12x + 144

[velvet spade]

if y = (x + 12)²

no

[velvet spade]

x^2 + 24 x + 144

[stark belfry]

Yea 24 my b

[velvet spade]

now look at your equation: y = x² - 12 x

[stark belfry]

Then I plug y in

[velvet spade]

what value of "h" will get you 12 x after you expand (x - h)²?

[stark belfry]

?

[velvet spade]

so (x + 12)² gives you 24 x

as one of its terms

[stark belfry]

Wait

Go back a step please sorry

[stark belfry]

Like here

[velvet spade]

ok, say you have an equation y = x² + b x

[stark belfry]

Yea

[velvet spade]

you want to get it into the form y = (x - h)² + k

(forget about a for now)

[stark belfry]

Alr

But question

Didn't we already get that

[velvet spade]

what is (x + b/2)²?

[stark belfry]

We don't have x yet
And is b 0

[velvet spade]

just expand it

(x + b/2) × (x + b/2) = ?

[stark belfry]

X^2 + x(b/2) + (b/2)(x) + (b/2)^2

[velvet spade]

right

and what is x(b/2) + (b/2)(x)?

[stark belfry]

2(x)(b/2)

[velvet spade]

...which is?

[stark belfry]

(2x)(2b/4)

[velvet spade]

where'd the plus come from?

and 2b/4 = b/2

[stark belfry]

Oh idk

[velvet spade]

what's 2 (b/2)?

[stark belfry]

Ohhh

Its just b right

(2x)(b)

Or 2xb?

[velvet spade]

yes

wait no

2 x (b / 2) = b x

[stark belfry]

Huh

[velvet spade]

2 x (b / 2) = x × (2 × b/2)

[stark belfry]

Oh I just did 2 alone

[velvet spade]

so (x + b/2)² = x² + b x + (b / 2)²

does that make sense?

[stark belfry]

No

[velvet spade]

(x + b/2) × (x + b/2) = x^2 + x(b/2) + (b/2)(x) + (b/2)^2

and x(b/2) + (b/2)(x) = b x

so (x + b/2)² = x² + 2 x+ (b / 2)²

[stark belfry]

Okay so you went back and simplified it correctly

I think

[velvet spade]

hmm?

[stark belfry]

This

[velvet spade]

yes

[stark belfry]

Is this

[velvet spade]

and we have x^2 + x(b/2) + (b/2)(x)+ (b/2)^2

so that's x^2 + 2 x + (b/2)^2

[stark belfry]

So question

We did we plug x(b/2) + (b/2)(x) into there

Also still kinda lost cause there's like 100000 steps

Not sure how you remember all this

[tidal hawk]

ur qn was x^2 -12x right

what’s ur a, b and c value?

[stark belfry]

A is 1 ik that

Is b 0

B or c is 0

[velvet spade]

a x² + b x + c

[tidal hawk]

a is 1 and b is -12 and c is 0

[velvet spade]

and we have x² - 12 x

[stark belfry]

Alr

[tidal hawk]

do u get how we got that thingy

[stark belfry]

This?

[tidal hawk]

a is the coeff of x^2, b is coeff of x and c is just the number without x

[tidal hawk]

this

[stark belfry]

Yea ik

[tidal hawk]

oki

[stark belfry]

It's in the same format as that equation

So yea we did that

And then we were completing the square

[tidal hawk]

if u have ax^2 PLUS bx + c,, when u complete the sq,

a[(x + b/2)^2 - (b/2)^2 + c] and simplify and expand

if u have ax^2 MINUS bx + c,,

a[(x-b/2)^2 -(b/2)^2 +c]

[elfin cipher]

omg factorization

[stark belfry]

Hm

[tidal hawk]

look at ur eqn,, is the bx -ve or +ve?

[stark belfry]

Negative

[tidal hawk]

ya

when u complete the square

just divide the b value by 2

and that’s what’ll be inside ur parentheses

[tidal hawk]

^^ can try following this form

[stark belfry]

So
1[(x - 6) ^2 ‐ (-6)^2 +0

[tidal hawk]

yes

expand and ur done

Nono

inside the parentheses is -

remember ur b was -ve

-12/2 = -6

[stark belfry]

Oh yea

[tidal hawk]

ya

but ur right other than that

[stark belfry]

So
X^2 + (-6x) + (-6x) + 36 - 36

[tidal hawk]

nope leave it in completed square form

[velvet spade]

you may find this link helpful: https://www.mathsisfun.com/algebra/completing-square.html

[tidal hawk]

(x-6)^2 -36

[tidal hawk]

^^ u can also watch some yt vids on this

helped a lot for me 🥳

[stark belfry]

Yea im so confused

Ik we are like completing the square

[tidal hawk]

issok just need more practice (:

[stark belfry]

But don't we need like a ordered pair

[tidal hawk]

wdym by ordered pair?

[stark belfry]

For the vertex of the parabola

[tidal hawk]

u mean the h,k

[stark belfry]

Yea

Wait

[tidal hawk]

ya

[stark belfry]

Did we have that like a long time ago

[tidal hawk]

u have (x-6)^2 -36

no in this case u need complete the square for that

so ur min. point is (6,-36)

[stark belfry]

Wait -6 is h

Wait

[stark belfry]

He gave me this

[tidal hawk]

why -6?

[stark belfry]

Not negative

So a is 1

[tidal hawk]

we have (x-6)^2 -36 right

to find h, set x-6= 0

x= 6

[stark belfry]

Then we have (x-h)^2 + k

[tidal hawk]

so x coord of ur vertex is 6

[tidal hawk]

yesh

[stark belfry]

Hm alr

Then I don't need like k

Cause it just goes off into inf

[tidal hawk]

err what?

in this case ur k is -36

[stark belfry]

For increasing/decreasing interval notation

Well I do need k but not really

Unless 6,-36 is the constant

Which I don't think the vertex = constant

[tidal hawk]

it’s from -inf to -36 inclusive and -36 to inf I think

for decreasing and increasing

[stark belfry]

Wait

[tidal hawk]

not sure for that part,,

[stark belfry]

WAIT

[tidal hawk]

ya

[stark belfry]

It could be

I might be using the x value twice

Cause I did 6 to inf for increasing

Is that wrong

No I just chanced it it was right

[tidal hawk]

wait ya shd appear twice i forgot it’s related to x

i went to use y smh

[stark belfry]

Ty tho

[tidal hawk]

welcc!

[stark belfry]

U too ty

Savin dat link

.close

[obtuse pebble]

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[signal snow]

Yo yo

My physics question is still left hanging

[obtuse pebble]

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[quaint finch]

I worked out this question a long time ago, but I am reviewing it right now and I am left clueless.

[royal basin]

the marked price is 50% above the purchase price ($80)

do you understand how to calculate the marked price, ie what the price tag says?

[quaint finch]

yes

[royal basin]

ok, then do you understand the following line?

150% of $80 = $120

[quaint finch]

yes

[royal basin]

and do you understand the line that follows it?

[quaint finch]

no

[royal basin]

the jacket is sold for 30% off the marked price

so the sale price is 30% less than the marked price

do you understand how to calculate the sale price?

[quaint finch]

so I make 70 percent profit

that is why I have calculated all the profits in one part

[royal basin]

no

no, your profit margin isn't 70% at all...

[quaint finch]

for the second part?

to calculate sale price?

[royal basin]

the second part says:
sale price = 70% of marked price

this 70% has nothing to do with profit whatsoever

[signal snow]

Math question help

[royal basin]

@signal snow channel busy please move

[signal snow]

Aight

[quaint finch]

can't I calculate the sale price by taking 30% of 120 and then subtracting it to the value I get?

cuz that also gives me 84

alright

got it

.close

[obtuse pebble]

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[modest void]

Log_1/3 2x. How do I make the 1/3 base 3 ?

[plain stag]

There's a change of base formula

$\log_b(a) = \frac{\log_c(a)}{\log_c(b)}$

[warm shale]

Steakanator

[modest void]

So if I wanna make it base 3 it becomes log_3 (2x)/log_3(1/3) ?

[plain stag]

Yes

And the denominator can be simplified further

[modest void]

How ?

[plain stag]

By evaluating log_3(1/3)

[modest void]

So -1

[plain stag]

Indeed

[modest void]

Thank you so much

For the help

[plain stag]

Np

[modest void]

.close

[obtuse pebble]

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[deep dirge]

.reopen

A. Provide the appropriate information necessary for each arithmetic sequence to complete the table.

[deep dirge]

<@&286206848099549185>

[royal basin]

have you made any progress so far?

[deep dirge]

Yes i answer 50 from 1 in common difference in scratch paper

And the rest is idk what's the answer

[royal basin]

Yes i answer 50 from 1 in common difference in scratch paper
...sorry, i don't understand you

[deep dirge]

Just look in the photo to understand it

[royal basin]

i don't know what "50 from 1" means and i don't know which of the 5 sequences it's meant to be for

[deep dirge]

The part 1 is i answer 50 from common difference

[royal basin]

so you mean that you put 50 here?

[deep dirge]

Yes

[royal basin]

this is incorrect.

show your scratch paper.

[deep dirge]

I throw them in 15 minutes ago

I forgot to mention to you sorry

[royal basin]

.-. great... so all we have is a mega wrong answer

and no work to show for it

that could be corrected

your arithmetic sequence has $a_1 = 3$ and $a_6 = 20$

[warm shale]

Ann

[royal basin]

$a_6 - a_1$ is equal to five times the common difference

[warm shale]

Ann

[deep dirge]

So i picture from the black board

While during class

That left one

[royal basin]

are you trying to ask a question?

[deep dirge]

No? Why

[royal basin]

then what are you saying?

you keep saying things that i just don't understand.

[deep dirge]

Its from arithmetic sequence that's why

[mental solstice]

we're not interested in the board, we're interested in what thought process and working you did to even get 50 in the first place

so show that, and a better discussion can take place

[inland spruce]

a(n+1) - an = d, like that

[royal basin]

on the one hand, too many cooks in the kitchen
on the other hand, OP is just posting nonsense after nonsense which is making me not want to help anymore

[deep dirge]

Ok i lied but i started to solve rn

Hello?

[inland spruce]

hey

@deep dirge where is your doubt

[deep dirge]

I started rn and i lied

I should've never lied in first place

[inland spruce]

forget it. now start

[deep dirge]

<@&286206848099549185>

[inland spruce]

@deep dirge where doubt

[deep dirge]

Idk

[inland spruce]

what are u going to find

d ryt?

what's the formula for it

[deep dirge]

I need to find the answer in the blank

[inland spruce]

you know a(n+1) - an = d?

[deep dirge]

And my teacher doesn't tell us the example that's why

[deep dirge]

Yes

[inland spruce]

they gave n = 6

they gave a1= 3

[inland spruce]

so tell me what's a6-a1 in terms of d

[inland spruce]

clue here

[deep dirge]

Wait? Im gonna solve it be right back

[inland spruce]

ping me

[deep dirge]

@inland spruce

@inland spruce

@inland spruce

@inland spruce

@inland spruce

[inland spruce]

stop bruh

I came

[deep dirge]

You said to ping me

Here i think this is it

[inland spruce]

not to mass ping lol

[inland spruce]

nooo

[deep dirge]

Then what is it

[inland spruce]

a is not 3

a1 is 3

[deep dirge]

Ok then

[inland spruce]

@deep dirge what all formulas you learned tell me

[deep dirge]

a(n+1)-an=d

[inland spruce]

any other

[deep dirge]

Sn=a+b(n-1)

an=n²+4

That's all

@inland spruce

[inland spruce]

ok

[inland spruce]

what is that

nvm

see From a(n+1) - an = d, we take 1 for example, then a(1+1) - a1=d

a2-a1 = d

ok?

@deep dirge

[deep dirge]

Then what's the d

<@&286206848099549185>

[inland spruce]

d is common diference

here n = 6

so a6-a1 = 5d

[deep dirge]

So that's the answer

[inland spruce]

20-3 = 5d

d = 17/5

understood? @deep dirge

[deep dirge]

Im clearly don't understand the solve

[mental solstice]

@inland spruce it might be better if you taught OP about arithmetic sequence from the start, because it feels like OP doesn't actually understand what's an arithmetic sequence

[inland spruce]

hmm, the problem is I'm busy

[inland spruce]

you can watch some good basic tutorials of arithmetic progression

in youtube

[deep dirge]

Ok

So the answer is 17/5

[inland spruce]

what is OP btw

[inland spruce]

I got that

[deep dirge]

Overpowered

[deep dirge]

So its correct or not

?

[inland spruce]

@deep dirge you can verify with others, that's what I got

[deep dirge]

Im gonna make a new one

.close

[obtuse pebble]

Channel closed

Closed by @deep dirge

Use .reopen if this was a mistake.

[inland spruce]

damn

[obtuse pebble]

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[oak scroll]

I know that
f'(a)=g'(a)
f'(b) = g'(b)