help-13

[cyan swallow]

Yea right

What happens to the 1 thats meant to be there like (a + b)^2 (1+ (a + b)^2)

Why isint that 1 on second line

[clear umbra]

?

where was there a 1

[cedar kiln]

@cyan swallow Has your question been resolved?

[cedar kiln]

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[rough dove]

Hello

[rough dove]

@crimson sedge

Okay so i found out what elementary Matrices are

[crimson sedge]

[crimson sedge]

can you now translate rows operations like R2 -> R2 - R1 using them?

[rough dove]

Ok so what im confused about is that if its a 3×4 matrix should we use a 4×4 identity matrix or a 3x3

[crimson sedge]

elementary matrices will always be square

[rough dove]

Yes

[crimson sedge]

okay lets see

[rough dove]

But like my question is

Like here its a 3×4 matrix so
When getting the elementary matrix
Should we use the 3x3 identity matrix or 4x4

[crimson sedge]

,w ((1,0,0), (-1, 1, 0), (0,0,1)) * ((4,4,0, 8), (4,4,-4, 15), (-4, 4, 4, -8))

[wraith dagger]

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Requested by 0enzi

[crimson sedge]

of the size of the coefficient matrix most times

[rough dove]

Wdym coefficient matrix

[crimson sedge]

do you what a coefficient matrix is

[rough dove]

So according to that it is correct

[crimson sedge]

for the first operation looks like so

[rough dove]

The co-efficient of the matrix?

Like the constant before

[crimson sedge]

yh so 4 4 0
4 4 -4
-4 4 4

for here

without the augmented part
8
15
-8

[rough dove]

Yeah and now doing the elementary row operation
4408
00-47
-444-8

And using this elementary matrix we get the same

[crimson sedge]

also you shld remember when matrix multiplication works and doesnt work

[crimson sedge]

very good

[crimson sedge]

for example if i had a matrix of 3x3 and 4x4 can i multiply them?

[rough dove]

It works when column of A is same as row of B correct?

[rough dove]

No you can't

[crimson sedge]

yh the inner dimensions are not the same

2x3 3x1 would

[rough dove]

But for here we have a 3by4 and a 3x3 elementary matrix so the only way we can multiply is when put it on the left

Correct?

[crimson sedge]

yes good

3x3 3x4

you would do matmul like

E9 E8 .... E1 M im not sure if you saw that from strang

[rough dove]

So the way we know is by looking at the original matrix which identity matrix to use for the elementary matrix

[rough dove]

Huh?

[crimson sedge]

the elementary matrix will always be on the left

[rough dove]

Yes

[crimson sedge]

all of these elementary matrices you came up with

[crimson sedge]

.

[rough dove]

Ok so for example if its w 5×3 matrix we use a 5x5 identity matrix for the elementary matrix?

[crimson sedge]

how would you order them when doing matmul

[rough dove]

Not yet

[rough dove]

What's matmul🥲

[crimson sedge]

matrix multiplication

[rough dove]

According to the row operations we do?

[crimson sedge]

did you see the way strang ordered them

in the video i sent you

[rough dove]

I didn't see it full , i first started to learn from the textbook

[crimson sedge]

but first lets start by naming each of matrices

E1 for the first operation
E2.. and so on

[crimson sedge]

.

E9 E8 ... E1 M right

[rough dove]

I don't quite get what you're asking me

You mean that we start from E9 when we're doing the matmul

[crimson sedge]

yh

[crimson sedge]

M is the matrix we want to reduce

[rough dove]

Yes

So when we're using elementary Matrices to reduce we start from E9?

[crimson sedge]

you multiply E9 with E8 and so on

it would've be more handy if you looked at that part of the vid

[rough dove]

Tbh im so confused

So first here's the elementary Matrices

From E1 to E9

[crimson sedge]

btw have you filled in each of them

[crimson sedge]

this part is for finding matrix P

the product of all of these

[rough dove]

Filled in?

[crimson sedge]

on this thing

[rough dove]

Not yet
Why tho

[crimson sedge]

w/e moving on

[rough dove]

Azin am i on the right track or that's not how we supposed to do E1 to E9

Is the pic clear?

[crimson sedge]

see this part

actually here's this vid with the timestamp

https://youtu.be/QVKj3LADCnA?list=PL49CF3715CB9EF31D&t=1908

[cedar kiln]

@rough dove Has your question been resolved?

[rough dove]

Nope

So

You're saying P

[rough dove]

Is like the multiplication of all E1 up to E9?

[crimson sedge]

did you see the vid

[rough dove]

Yes

[crimson sedge]

the answer to this?

[rough dove]

But we start with E9

[crimson sedge]

yes

[rough dove]

So E9×E8×E7...

We will get P

[crimson sedge]

yes

[rough dove]

And that P can be used to Multiply By M

We get the Echelon form

[crimson sedge]

not sure if there could've been a way faster way to get P but yh

[crimson sedge]

very good

[rough dove]

So there's a faster way!

?*

[crimson sedge]

i said im not sure ive never done it on paper

probably not look it up

[rough dove]

Owh

Hmm

What's canonical form

[crimson sedge]

anyways i gtg

[crimson sedge]

if there's no other questions on this

[rough dove]

Aight ill do it and then send for you to confirm ok?

[crimson sedge]

sure

[rough dove]

Aight thank you so much!

[crimson sedge]

.coose

[cedar kiln]

If you are done with this channel, please mark your problem as solved by typing .close

[rough dove]

. close

.close

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[vague scaffold]

Covariance of variable X with Y is -143.8, with G is 4, and with K is 496. Additionally, it is known that the standard deviation of X is 4.4. What is the covariance of X with a variable D, which is defined by the formula D = (143K + 2.8G + 2X)?

The correct answer with a tolerance of absolute error ±0.06 is:

[vague scaffold]

i know that it should calculate with this statistical covariance, and X is 4.4^2= 19.36

i dont know how should i proceed futher

[tropic oxide]

you dont actually need that formula

you just need to know covariance is bilinear & that Cov(X,X) = Var(X)

[vague scaffold]

Still dont understand

[cedar kiln]

@vague scaffold Has your question been resolved?

[cedar kiln]

@vague scaffold Has your question been resolved?

[cedar kiln]

@vague scaffold Has your question been resolved?

[cedar kiln]

@vague scaffold Has your question been resolved?

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[crimson sedge]

not really sure what to do here lmao

im pretty sure you're supposed to get the factors of 1892 first

and then do smth with that

[cedar kiln]

@crimson sedge Has your question been resolved?

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[native atlas]

Hello I need a bit of help factoring x3+8x2+15x

[native atlas]

ahhh wrong problem

x^3+9x^2+15x

my result was

(x+0)(x+5)(x+3)

I began by setting it equal to zero and decieded that

oh wait

fuck I did synthetic division where it is not possible

since i dont have an a that isnt 1, right?

since i did p/q

[limber zephyr]

a would be 1

[native atlas]

yeah

when a=1 can i used p/q's?

to get factors? or is that something I cannot do

[limber zephyr]

I think you can

[native atlas]

so is my factoring correct?

ahhhh nvm

its x-3

not x+3

[limber zephyr]

I still don't think thats correct

if you multiply it together to try to get it back to the original it doesnt work

[native atlas]

since the 3 is the root I got from the quadratic formula after I used sythetic division of 0

8, not 9 i mistyped

[native atlas]

x^3+8x^2+15x

my apologies

Aswell as, I've now seen that the +0 is redundant

wait

no it wouldnt be x-3 would it?

hold on im a bit confused

running it back i believe that x^3+8x^2+15x factored is
(x+0)(x+5)(x+3)

just checked, this is correct

.close

[cedar kiln]

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[austere reef]

this is what ive done so far

[uneven matrix]

what the fuck?

no

[austere reef]

uhh

[uneven matrix]

$n^3 \in O(1.5^n) \rightarrow \lim_{n \to \infty} \frac{n^3}{1.5^n} = 0$

[wraith dagger]

nadav

[austere reef]

latex bot not working?

oh

[boreal epoch]

he just added space by accident

[austere reef]

uh this is what they did in lecture

[uneven matrix]

tthey proved it by fucking induction?

[austere reef]

i mean i was gonna try proving it with calculus

but it made sense with induction too

i was gonna try to use it

to show that

[uneven matrix]

the limit definition is most useful for calculations

[austere reef]

true i thought about that

for the second part

[uneven matrix]

if youre allowed to use the limit definition use that always pretty much

its as simple as calculating the lmit of n^3/1.5^n = 0 --> n^3 \in O(1.5^n)

[crimson delta]

well one of the classic ways of calculating that limit is with induction in the first place

[austere reef]

ik ik but the prof wants it in induction ;-;

[uneven matrix]

i mean usually in a class where you learn big O notation calculating that limit simply as "its fucking obvious" is acceptable

[crimson delta]

well obviously not in this case

[uneven matrix]

you could argue that calculating the limit is that simple but they dont want the limit defintion

anyway

[crimson delta]

calculating the limit isnt actually that simple. you just learned that exponential is faster than polynomial but have you ever tried to show that by hand? you would do a proof by induction

[austere reef]

full question

[uneven matrix]

yes but in my opinion doing that in a class wheer big O notation is relevant is just a big waste of time

[crimson delta]

cause understanding stuff properly usually is a waste of time

anyway

we want to show (k+1)^3 <= 1.5^(k+1)

[austere reef]

yeah

[crimson delta]

can you multiply out the left side

[austere reef]

k^3 + 3k^2 + 3k + 1

[crimson delta]

ok

we know k^3 is smaller than 1.5^k by induction hypothesis

[austere reef]

we know by IH that k^3 is satisfied so

do I set it to 1.5^k?

as in 1.5^k + 3k^2 + 3k + 1

[crimson delta]

if we can show that the remaining terms together are smaller than 0.5*1.5^k, then all together it is less than 1*1.5^k+0.5*1.5^k=1.5*1.5^k=1.5^(k+1)

[austere reef]

uh can you do that in latex

sorry where did you get 0.5 from?

[crimson delta]

well works out nicely together with the 1

[austere reef]

ooooh

this is the RHS right?

[crimson delta]

yes

[austere reef]

you mean like 1.5^k+1 = 1.5^k + 1.5^k/2

[crimson delta]

huh?

[austere reef]

nono i think i get it

sorry continue

[crimson delta]

lets look at the term 3k^2

[austere reef]

right

[crimson delta]

we want to compare it to 1.5^k somehow

[austere reef]

mhm

[crimson delta]

we know 3k^2 is smaller than k*k^2. which is k^3 and therefore smaller than 1.5^k

so thats nice

[austere reef]

right

[crimson delta]

but that's slightly too much

we want that the three remaining terms are together at most 0.5*1.5^k

[austere reef]

mhm

[crimson delta]

and with this current approach the second term itself already is 1.5^k

how can we fix that

[austere reef]

the second term

being 3k^2?

[crimson delta]

yes

[austere reef]

well

we can split it into k*k^2

and multiply by 0.5 to get k*k^2 0.5

we can sub in any arbitary value for k >= 24 right?

[crimson delta]

not really

[austere reef]

oh really?

[crimson delta]

we want to show that it holds for all k as long as they are big enough

[austere reef]

hm

so i cant do something like (24*k^2)/2

[crimson delta]

well 3k^2 is definitely smaller than 24k^2/2

[austere reef]

hm

[crimson delta]

if k>=6, then 3k^2 is smaller than k^3/2. is that what you wanted?

[austere reef]

uhhh

nah nvm my idea doesnt

[crimson delta]

because then 3<=k/2. so 3k^2 <= k/2*k^2

[austere reef]

work here

wait i think im lost

sorry right now we have

[austere reef]

and we want this

i.e.

[crimson delta]

yes

we showed 3k^2 <=k^3 <=1.5^k

which is a step in the right direction but too far

it would be nice if we had for example 3k^2 <= 0.2*1.5^k

[austere reef]

right since we want (1.5^k)/2

hm

[austere reef]

just to confirm

we're trying to get 3k^2 + 3k + 1 <= 0.5*1.5^k

[crimson delta]

yes

we are trying to do it term by term

[austere reef]

right

[crimson delta]

ok I am going to do the 3k^2 term cause I have to go

we know k is at least 24

which means 3<=k/8

which is 0.125*k

[austere reef]

right

[crimson delta]

so 3k^2 <=0.125k*k^2=0.125k^3 <=0.125*1.5^k

[austere reef]

right

for 3k+1

[austere reef]

can i do 72 is less than or equal to ...

some fraction?

for 3k?

[crimson delta]

why 72

3k is clearly smaller than 3k^2

[austere reef]

uhh

[austere reef]

?

<@&286206848099549185>

oooh

i ok so i get 1.5^k/8

• some term + 1 = 1.5^k/2

but i dont see how i'd do that with the + 1 there

<@&286206848099549185>

[cedar kiln]

@austere reef Has your question been resolved?

[austere reef]

this is where I'm at rn

<@&286206848099549185> save me ;-;

[restive ibex]

What's the question? I might be able to help but I might not

[austere reef]

uhh

im on part 1

[austere reef]

i wrote this so far

[restive ibex]

What's O and theta

Also what math class is this

[austere reef]

uh Cs class

[austere reef]

O is the notation

as in the runtime

[restive ibex]

I'll have to think about it

If I think of something I'll tell you inshaAllah

What class is this for?

[restive ibex]

Oh ok cs

What year of university?

Like I know math up until 2nd year calculus

[austere reef]

uhh

2nd year

[austere reef]

same

[restive ibex]

Ok well I'm not sure I'm the best person to answer your questions for 2nd year cs, I'm in grade 12...

Ad I can only code python

[austere reef]

nah no problem

[austere reef]

did part 2

just need

the first part

<@&286206848099549185>

[cedar kiln]

@austere reef Has your question been resolved?

[austere reef]

.close

[cedar kiln]

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[ionic wolf]

I highkey forgor how to sketch graphs from those fr

[floral arrow]

You may want to do B first

[ionic wolf]

Uhh f of x no sol

I don't think g has one either

Idk

Can I just graph it

And say I did that

To explain how I know

She would probably accept that

As an answer

Considering she considers "it has parenthesis" as an acceptable answer to the question is this in factored form

OK

[floral arrow]

I mean... you should probably understand how to find the roots of these functions by now

[ionic wolf]

Idk what that means

[floral arrow]

A root is a value of x for which f(x) = 0

A solution to f(x) = 0

[ionic wolf]

OK IVE DONE F AND G SO FAR

F is no solutions

G is 2 solutions

[floral arrow]

Yeah ok, what are these 2 solutions?

[ionic wolf]

0

Or -3

[floral arrow]

Yes

[ionic wolf]

I think h is one solution

[floral arrow]

Which is?

[ionic wolf]

1

[floral arrow]

Yes

Is it easier to graph now?

[ionic wolf]

I used desmos to graph it

I don't remember how to graph from the equation

Except the first one

Idk

[floral arrow]

What does it mean in the graph if g(-3)=0?

[ionic wolf]

Idk

Y intercept

Idk

[floral arrow]

By definition, f(a)=b means the point (a,b) is part of the graph of f

[ionic wolf]

Oh

Does this look right @floral arrow

I think I messed up

[floral arrow]

If by rotation they mean couterclockwise rotation, then yes

[ionic wolf]

Positive is counterclockwise I think

[floral arrow]

Can't tell you, it's a convention

[ionic wolf]

Yay I got it right

Ty

.close

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[warped marsh]

can someone help me with what to sub with u here

[warped marsh]

oh wait

yea nvm i need help

im not sure how to get this

[humble karma]

I mean

ln(x)` = 1/x

You can definitely use that ..

[warped marsh]

yea but how do i get rid of the ten

cuz that would give me 10/x no?

[humble karma]

It`ll get rid of itself.

[warped marsh]

wym

[humble karma]

Just set u = ln(10x)

Go from there

[warped marsh]

thats what i did

[humble karma]

So you get du = 1/x dx

[warped marsh]

i got du=10/x dx

[humble karma]

How though?

[warped marsh]

oh wait

[humble karma]

You didn't do the chain rule correctly

Or something

[warped marsh]

yea i did it wrong

.close

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[odd sierra]

how do i find part c?

[odd sierra]

?

idk why the bot say that

[digital cliff]

end behaviour woop

[odd sierra]

oh

[digital cliff]

what happens as t tends to infinity

[odd sierra]

go down

[digital cliff]

go down?

[odd sierra]

oh

[digital cliff]

what does $e^{-0.046t}$ tend to

[wraith dagger]

AℤØ

[odd sierra]

uhh

[digital cliff]

remember that this is the same as $\frac{1}{e^{0.046t}}$ if that helps at all

[wraith dagger]

AℤØ

[cedar kiln]

@odd sierra Has your question been resolved?

[cedar kiln]

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[cedar kiln]

@meager bane Has your question been resolved?

[meager bane]

im unsure of how to solve b and c.
I am able to do the f(b)-f(a)/b-a but am unsure what f'(c) equals

<@&286206848099549185>

[cedar kiln]

@meager bane Has your question been resolved?

[meager bane]

<@&286206848099549185>

[cedar kiln]

@meager bane Has your question been resolved?

[cedar kiln]

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[maiden sequoia]

how do I do this?

[tropic oxide]

!status

[cedar kiln]

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

[tropic oxide]

do you know your way around basic trigonometry?

[maiden sequoia]

yeah

[tropic oxide]

ok right

can you sketch the ladder resting against the wall?

just as a right triangle

[maiden sequoia]

yeah alr did that

dk what to do now

[tropic oxide]

show me your sketch

[maiden sequoia]

im using a laptop i cant

but basically its a triangle as you said with 45 degrees and the height being 4m

[cedar kiln]

@maiden sequoia Has your question been resolved?

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[untold gate]

How do I calculate the derivative of this y_{3}=20510.59333e^{-0.04748631725x}+8.460537502

[buoyant latch]

Have you tried a calculator

[upper garnet]

whats the derivative of a constant and e^x?

[untold gate]

I know how to dervie it but its different to what i get on desmos

[upper garnet]

show your solution

[untold gate]

-0.073 is the derivative

[upper garnet]

what

[untold gate]

but i got 9.387

[upper garnet]

derivative of it at x=200?

[untold gate]

yes

idk why its -0.073

but its working for me

[upper garnet]

,w derivative of 20510*e^(-0.047x)

[untold gate]

i just have to show algebraically

[wraith dagger]

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[upper garnet]

,w -963.97*e^(-0.047 * 200)

[wraith dagger]

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Requested by fractalogist

[upper garnet]

it def cannot be positive lol

[untold gate]

yea its not

i 99% sure desmos is right

[upper garnet]

is this your derivative

[untold gate]

close

-0.0731

is it double derivative?

[upper garnet]

i meant without plugging x=200

[untold gate]

i got

9.387

waiy

-919.342

[upper garnet]

,w 20510.59333 * -0.04748631725

[wraith dagger]

Results provided by WolframAlpha

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Requested by fractalogist

[upper garnet]

use a calcualtor

[untold gate]

i got that

but how did desmos get to -0.0731?

[upper garnet]

coz thats the derivative at x=200

[untold gate]

so if i put into my calculator

the whole thing with x=200

i should get -0.0731?

[upper garnet]

yezs$

[untold gate]

oh ic

i forogt to get rid of the constant

mb

thank you

.close

[cedar kiln]

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[dapper apex]

Expand Fourier series for the function fx = π+x in the interval (-π,π)

[crimson sedge]

what have you tried

first determine if f(x) is odd or even

[dapper apex]

Umm.. that's later in my syllabus so I havent learned it yet

Is this much part correct?

[crimson sedge]

I'm pretty sure you have to find the coefficients of the cosine and sine terms here first

[dapper apex]

an and bn you mean?

[crimson sedge]

yes

[dapper apex]

But in full formulae a not is also needed?

Is my integration correct can u tell? Please

.close

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[signal haven]

i need help

[flat harbor]

what do you need help with mate

you can't just ask for help without a question

[cedar kiln]

@signal haven Has your question been resolved?

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[hidden crescent]

can someone explain this one :

[vale kraken]

whats it equal to?

[hidden crescent]

Nothing it is a fraction

[vale kraken]

u need to sinplify it?

[hidden crescent]

you must simplify

[hidden crescent]

yep

[vale kraken]

18x-12-40x+8

or as a fraction it would be

[vale kraken]

combine em btw

[cedar kiln]

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[hidden crescent]

i found 13x-1/12

[vale kraken]

(9x-6-20x+4)/24

[cedar kiln]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[hidden crescent]

no it's 26x-2 / 24

[vale kraken]

i think i meesed up somewhere

but if you think you got it right then thats alr

u in school?

[hidden crescent]

look 58x-4/48 is equal to 26x-2 / 24 and 13x-1/12

[vale kraken]

wait im dumb

[hidden crescent]

rn no

[vale kraken]

lucky

[hidden crescent]

nah

[vale kraken]

what grade u in

[hidden crescent]

i'm on vacation i'm french

[cedar kiln]

The original post of this help channel has been deleted, and it will abruptly close and possibly lock. (This is irreversible.) Please claim a new channel, and don't delete the first message of any future channel you claim.

[vale kraken]

oh makes sense

im in 9th

[hidden crescent]

i'm 9th grade

[vale kraken]

ayyy

nice

[hidden crescent]

and have a degree in physics

[vale kraken]

how?

huh

[hidden crescent]

where are you from

[vale kraken]

i struggle with physics

[vale kraken]

states

[hidden crescent]

i can fix that

[hidden crescent]

i'm really advanced in physics

[vale kraken]

i mean yea obv u got a degree

[hidden crescent]

and chimestry i give cours at university

[vale kraken]

rlly?

dayum

[hidden crescent]

yep

[vale kraken]

nice

[hidden crescent]

bc when i was young i love to learn physics online in 4th grade i had a 9th grade phyisics and chemistry level

[vale kraken]

oh nice

im a bit advanced in math

[cedar kiln]

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[vale kraken]

just a little bit

[hidden crescent]

me too but sometime i need to check my answer

[limber zephyr]

how much is just a little bit

[hidden crescent]

not that much

[limber zephyr]

wait hold up you said you have a degree in physics in 9th grade?

[hidden crescent]

1ère année d'études d'ingénieur en aérospatial

[vale kraken]

eh im in 9th but doing both 9th and 10th grade math

[hidden crescent]

1st year of aerospace engineering studies

[vale kraken]

holy

[limber zephyr]

in 9th grade?

[vale kraken]

yh

[hidden crescent]

yep

[vale kraken]

im in 9th

[limber zephyr]

WHAT okkkk

[vale kraken]

hes gonna help me understand

[hidden crescent]

what grade are u

[limber zephyr]

im 3 years ahed in math and that makes me feel sad

im in 8th

[vale kraken]

damn

im the least smartest here ig

[plucky owl]

Btw this isn't the answer, you did it wrong, show your work

[limber zephyr]

degree in physics tho?!?!

[vale kraken]

no not me

thats @hidden crescent

[limber zephyr]

oh

[cedar kiln]

This channel is only for on-topic discussion. Please take casual conversation to #discussion or #chill.

[vale kraken]

but wait resend the problem

[hidden crescent]

not bad

[vale kraken]

(18x-12-40x+8)/48

(-28x-6)/48

[hidden crescent]

what is the good answze

[plucky owl]

Can you show your work on that problem you did?

[vale kraken]

(-14x-3)/24

@plucky owl would that be right?

[hidden crescent]

nah it's on paper dude and i write with pencil

[plucky owl]

Take a picture of it

[plucky owl]

You made a mistake

Show your work

[vale kraken]

is my answer right?

[vale kraken]

^^

[limber zephyr]

show your work...

[vale kraken]

i did it mental

[plucky owl]

No

[vale kraken]

alr ima do it on paper

[plucky owl]

You weren't even the original asker

So please don't give out asnwers

[limber zephyr]

you dont have to go to 48 you can do 24

[plucky owl]

There's a minus between the fractions

Why did you add the terms?

That's 18x - 40x

Not 18x + 40x

[cunning hazel]

lmfao(no hate)

[vale kraken]

what happens if you made them 24 instead of 48

[plucky owl]

You get the same answer

[vale kraken]

oh alr

[plucky owl]

With 48, you just have to simplify a bit more

[vale kraken]

true

[cunning hazel]

bro thats not the answer 💀

[plucky owl]

Did you not read what I said?

There is a minus in between the fractions

Why are you adding the terms?

[cunning hazel]

i thought he said he studies 1st year aerospace

[hidden crescent]

bc it's the same denominator

[cunning hazel]

💀

bro go revise integers

[plucky owl]

That still doesn't mean you add them if there's a minus sign

[cunning hazel]

and it would be -40x-8

[hidden crescent]

you are right

[plucky owl]

$\frac{18x-12}{48} - \frac{40x+8}{48} = \frac{18x-12-(40x+8)}{48} = \frac{18x-12-40x-8}{48}$

[wraith dagger]

CaptainNova22

[cunning hazel]

@vale kraken use .close if you have no more doubts

[hidden crescent]

but this give : 22x-20/48

[plucky owl]

Simplify it

[hidden crescent]

11x-10/24

[plucky owl]

Yes

[cunning hazel]

its -11x

[plucky owl]

Yeah -11x

[hidden crescent]

My bad

alright gentlement i got another one for you

[limber zephyr]

How would you start?

[cunning hazel]

take the lcm

[plucky owl]

First off, this isn't your channel @vale kraken opened it, continuing the previous converstation, so you need to open your own channel

[cedar kiln]

@vale kraken Has your question been resolved?

[cedar kiln]

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[crimson sedge]

if i find reciprocal of $\frac{x+2}{x-5} < 0$ do i need to reverse the sign of inequality ?

[wraith dagger]

bearcw

[crimson sedge]

then will $\frac{x-5}{x+2} > 0$

[wraith dagger]

bearcw

[crimson sedge]

i just want to know that ..

[crimson sedge]

can i take this as true

[cerulean sail]

If a number is negative[/positive] then its reciprocal will also be negative[/positive]

[crimson sedge]

i will show u my work in a moment

when i reversed the signs here (highlighted) i got the answer

original problem

[crimson sedge]

i also want to know can i solve a inequality like this?

i know how to solve how they showed

but i want to know can i solve like this too!!

[cedar kiln]

@crimson sedge Has your question been resolved?

[tough wave]

Taking the reciprocal of a fraction flips the inequality sign

Like 3<5 but (1/3)>(1/5)

[tough wave]

Yeah this is true

[tough wave]

This seems right. what you are doing is finding the critical points for these two rational functions, plotting them on the number line test for equalities in the 3 sections and you have your answer

[crimson sedge]

oh

ok

thx

[tough wave]

Welcome

[crimson sedge]

.close

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[potent flower]

A sphere is tangential to the planes xy , yz , xz and it passes through the point (1,-4,5). the radius of the sphere might be ....... units.

[potent flower]

a)6

b)7

c)8

d)9

how should I start

[cedar kiln]

@potent flower Has your question been resolved?

[cerulean sail]

[as a quick comment (sorry new OP!) but this isn't true: your earlier comment would imply that "as 5 > 0, you have 1/5 < 0", which it isn't...
issue comes around when multiplying by either (x + 5) or (x + 2), these may be positive (preserves the inequalities) or negative (reverses them). but another help channel for that one... (cc@crimson sedge)]

[potent flower]

<@&286206848099549185> s

[woeful cloak]

hi hamdy

what do you require

[crimson sedge]

Hi Hamdy

[potent flower]

.

[woeful cloak]

if the sphere is tangential to the planes xy, yz and xz then there are 3 points on this sphere's circumference whose coords are (x, y, 0), (0, y, z) and (x, 0, z) respectively

[crimson sedge]

I have a doubt in this question regarding the basics of calculus : Differentiation of cos(3x+5)

[woeful cloak]

what calculus

[crimson sedge]

The differentiation

[woeful cloak]

are you talking about this?

because this is analytical geometry

[crimson sedge]

Who u asking btw ?

[woeful cloak]

i'm with hamdy

i'm asking you

[crimson sedge]

oh

no its not analytical geometry

[woeful cloak]

because i think you're on another question lol

[dire geode]

!occupied

[cedar kiln]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[crimson sedge]

im learning the basics of differentiation

and came across a doubt

[woeful cloak]

oh so a double feature here

[potent flower]

okay bro feel free to discuss it but in another channel plz

[crimson sedge]

which channel

[woeful cloak]

@crimson sedge #help-25 is free

[crimson sedge]

sure

thank you

[woeful cloak]

np

[potent flower]

@woeful cloak back to our thing

what should I do

[woeful cloak]

alright so we have established that there lies three points (x, y, 0) (0,y,z) and (x,0,z) on the xy, yz and xz planes which touch this sphere

[potent flower]

yup

[woeful cloak]

the sphere passes through 1, -4, 5

[potent flower]

yes sir

[woeful cloak]

wait i'm just referencing smth

[potent flower]

زؤمخسث

.close

[cedar kiln]

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[cedar kiln]

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[crimson sedge]

tryna make the lhs equal to 0

whats the next step

[small knoll]

i am strugglgin

[valid yacht]

subtract it from both sides

[crimson sedge]

why would i subtract it

[small knoll]

i cant do this

[crimson sedge]

how does that undo it

[valid yacht]

the only way u can make something zero is by subtracting it from itself

[crimson sedge]

wrong channel go find help somewhere else

[valid yacht]

@small knoll pls make a new channel

#❓how-to-get-help

[crimson sedge]

oh so it would be

[valid yacht]

u dont really want to make lhs zero if you're trying to solve for x

[valid yacht]

if you're trying to solve for x, what u rather want to do is to keep x on one side and everything else on the other

isolate x

[crimson sedge]

im not soklving for x

im solving for roots

[valid yacht]

ah

what

[crimson sedge]

?

solving for the zeros

[valid yacht]

roots of?

[valid yacht]

now u have lhs zero

[crimson sedge]

oops i forgot to write down the i

there we go

ok yep thats all

ty

[valid yacht]

np

[crimson sedge]

.close

[cedar kiln]

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[crimson sedge]

For the principal complex logarithm, which is bijective and continuous over C, the relationship Log(z^z) = zLogz holds for some complex number z (≠0).
What about other branches, and in general?
I need some hints on this because I'm a bit clueless about this

[crimson sedge]

<@&286206848099549185>

[cedar kiln]

@crimson sedge Has your question been resolved?

[crimson sedge]

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

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[cedar kiln]

Please don't occupy multiple help channels.

[dire geode]

closed your other channel

[cedar kiln]

@nova walrus Has your question been resolved?

[nova walrus]

well noones responded anyway

so

[cedar kiln]

@nova walrus Has your question been resolved?

[cedar kiln]

@nova walrus Has your question been resolved?

[cedar kiln]

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[fickle sedge]

how do i turn this into factored form (y=a(x-r)(x-s))?

[crimson sedge]

factor out x

[fickle sedge]

and how do i do that..?

i'm not too rememberful with factoring

sorry

[crimson sedge]

ab-ac=a(b-c)

in your case, a=b

c=8

[fickle sedge]

.close

[cedar kiln]

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[mortal dew]

In the quotient inequality (2x+6)(-5x-20)/(30-6x) > 0, is the bracket open or closed on the -5x-20

[mortal dew]

like is it (-4,-3(U)5, infinite( or )-4,-3(U)5, infinite(

btw using ( instead of brackets cuz mine are broken

[high tinsel]

U do the limit of this fonction

Is it that this fonction is définit in -4

[mortal dew]

Man idk look I did a drawing( it’s poorly made ) but all I wna know is if the -4 is closed or open

[high tinsel]

If fonction is définit in -4 so open

Else close

[mortal dew]

so i was supposed to do it open

)-4,-3(U) 5, inf (

[high tinsel]

Nooo sorry xd

For me open it's ( xdd

[mortal dew]

ah

[high tinsel]

Sorry i'm tired xd

[mortal dew]

)4 = open
(4 = closed

(for me)

see the ball thingy

[high tinsel]

It's (-4,-3(U) 5, inf (

[mortal dew]

i see

[high tinsel]

Yes it's that sorry

[mortal dew]

so its like that cuz 2 > 0

on the (2x+6)

[high tinsel]

But you did définition if this fonction ?

[mortal dew]

i did not, i dont think i've learned about that still
but its a straigtht line

not like this one

[high tinsel]

Because f(-4) is définit

If this fonction is >0 with f(-4) so it's close

[mortal dew]

yoo i got it

yea its f(-4)

thats the fonction, yes

[high tinsel]

Oh what your level in school

[mortal dew]

9th grade

[high tinsel]

Oh i'm french xd how old re u

[high tinsel]

Yes so close

[mortal dew]

but i dont learn in english, the language barrier in math is quite challenging

[mortal dew]

15

[high tinsel]

Me too xdd

[mortal dew]

so if the fonction is negative on a >0, the bracket is closed

[high tinsel]

Oh okay u go learn that this years normaly or last years

[mortal dew]

i started learning this last month

[high tinsel]

No si f(x) existe or défine

If*

Because if f(x) >0 it don't négative

It's positive

This fonction is défine with f(x)>0 so if f(x)<0 so this fonction it's no défine so bracket open if not défine

[mortal dew]

so bracket closed if f(-4) because -4<0

wait contrary

[high tinsel]

No -4 but f(-4)

Wait

F(-4)=0

Or we Saïd f(x) défine with f(x)>0 or f(-4)=0 so f(-4) it's not define so bracket open

All your intervalle it's not define

Because f(-4)=0 f(-3)=0 and f(5) is not possible because WE can't devide by 0

[mortal dew]

ok i cant understand

mb

BUT i have another question

its more simple

imagine we have this function

f(x) = 5x + 2
y = 2
x = -2/5

can i multiplicate everything by 5 and still have the same proportion

[high tinsel]

What's y in your fonction ?

[mortal dew]

b

f(x) = ax + b

[high tinsel]

Y=b ?

[mortal dew]

ye

if i multiply everything by 5 in order to eliminate the fraction (-2/5)

would the line be proportional to the original one

the graphic representation

[high tinsel]

Yes u Can in équation

[mortal dew]

so 2, -2/5 = 10, -2

in this linear function

[high tinsel]

Yes because it's équation linear

[mortal dew]

thanks a ton

fun fact btw, i went to france on july

i visited the palace of versailles and stuff

it was very cool

[high tinsel]

But u can't multipliate for 5

[mortal dew]

wait i can't?

[high tinsel]

Because before it's not the same fonction

U Can in thé équation for exemple

[mortal dew]

so i have to mark the point on the x line on -0,4

-2/5

[high tinsel]

U Can here

[mortal dew]

i can cuz its not an fonction

[high tinsel]

But if u multipliate for 5 this fonction it's not okay thé same fonction

[mortal dew]

oh ok

[high tinsel]

No it's the fonction

[high tinsel]

5x+2 and 25x+10 it's not equal

[mortal dew]

i understand

[high tinsel]

Okay cool

[mortal dew]

.close

[cedar kiln]

Channel closed

Closed by @mortal dew

Use .reopen if this was a mistake.

[cedar kiln]

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[vagrant breach]

Hello, I'm a bit stuck on the first part of this question, I feel like it should be really simple, i'm just not sure how to define the composition

[plucky owl]

<@&268886789983436800>

[vagrant breach]

Thanks

[wanton sail]

Damn dani you're fast

[wanton sail]

You might get better help in a topics channel like #advanced-algebra

Oh wait

Actually #category-theory exists

[vagrant breach]

Cheers mate, I'll close this

.close

[cedar kiln]

Channel closed

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[gilded remnant]

could someone check if the answer to f) is 4?

[cedar kiln]

@gilded remnant Has your question been resolved?

[gilded remnant]

this is my working

<@&286206848099549185>

[cedar kiln]

@gilded remnant Has your question been resolved?

[gilded remnant]

<@&286206848099549185>

[cedar kiln]

@gilded remnant Has your question been resolved?

Channel closed

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

[olive folio]

how do I solve for the value of f(x) that would complete the cubic function

[violet flume]

hmm well you could create a system

if you call the function $f(x) = Ax^3+Bx^2+Cx+D$

[wraith dagger]

jan Niku

[violet flume]

you actually know D

from f(0)

[olive folio]

How do I use that system

[violet flume]

the same way youd use any other system of equations

you have 3 unknowns

so youd need to create three equations from your table

you actually have an excess of information but thats fine

[olive folio]

how do I fill in the equation

[violet flume]

do you see how you know D?

if not thats a good first example of how to make an equation

[olive folio]

is D the f(x) in the table

[violet flume]

no

We want f(x) to be a cubic right

[olive folio]

yea

[violet flume]

that means that we should be able to find A B C and D such that

[wraith dagger]

jan Niku

[violet flume]

we just need to find out what these numbers are

[olive folio]

so I should know what D already is?

[violet flume]

you dont have to, its a good first example

youd do it like this

you start this process by looking for an x value that you know f(x) for

lets start with x=0

[violet flume]

next, you take your x value, and plug it into your f(x), here

so $$f(0) = A\cdot 0^3 + B \cdot 0^2 + C \cdot 0 + D = 0$$

[wraith dagger]

jan Niku

[violet flume]

the last =0 comes from the second column of the table, where x=0, we are given f(0) =0

[olive folio]

so D = 0?

[violet flume]

yea

because x=0 kills all the other terms

and we get D = 0

[olive folio]

yea i understand that

[violet flume]

okay

[olive folio]

so how would I do that but with x = 1

[violet flume]

now you can start here

$f(x) = Ax^3 + Bx^2 + Cx$

[wraith dagger]

jan Niku

[violet flume]

try repeating this process

whats the next x value to try

[olive folio]

x = 1

[violet flume]

what is f equal to there?

[olive folio]

im not sure

1?

[violet flume]

well start with the table, what does the table say f(1) is

[olive folio]

4

[violet flume]

okay

[violet flume]

what happens when you plug in x=1 here

[olive folio]

it should equal 4

[violet flume]

but, i mean, what is it equal to

take the equation, put in x=1

whats f(1) in terms of A B and C

[olive folio]

A(1)^3 + B(1)^2 + C(1)

[violet flume]

hows it simplify