help-10

[shell prairie]

its actually just putting negative integers in p

and find where it starts and ends

which is -11~-5

idc if this method is bad

the question itself is ass

ima do other ones

.close

[obtuse pebble]

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[silver plover]

hello

[silver plover]

is this correct for fog?

[timid silo]

yeah, looks fine

although I wouldn't say that fog is undefined

its just defined on the empty set

[silver plover]

ms says this

for fog

it says cannot be defined

[timid silo]

ah ok then

ig it depends on the definition of function

[silver plover]

@timid silo

[timid silo]

it doesnt say that a function has to have a nonempty domain

[silver plover]

so is my initial answer correct then

[silver plover]

^

[timid silo]

yes

but I personally wouldn't say "fog is undefined"

just that fog: empty -> empty

but thats me being pedantic

[silver plover]

i dont really get

what the green means

and how theyve got to that

[timid silo]

it comes from that ^

[silver plover]

X and Y r domains

where has 'range of g(x)' come from?

[timid silo]

range of f is in Y

(fixed)

[silver plover]

is f(x) the range of f?

[timid silo]

yes

[silver plover]

so here can we say 'the range of g, which is g(x), does not intersect with the domain of f?'

@timid silo

[timid silo]

the set is all x in the domain of g such that g(x) (which is in the range of g) intersects with the domain of f

and yes, since it doesnt exist, there are no such x, ie empty

[silver plover]

ive edited my lecture notes

does this sound better?

[timid silo]

almost

the intersection is in Y

we want a set in X

so its the preimage of the intersection

[silver plover]

ok i see

[silver plover]

now for gof, ive done this so far

idk how to write the domain as a shorter format now

[timid silo]

what is the range of f?

and what is its intersection with the domain of g?

[silver plover]

lets sub in -2 into f(x)

that gives 11

that intersects in the set [1, infinity)

but

if we sub in 0 into f(x), which gives us 1

but 1 cant be in the set, since 0 is not included in the interval

so there isnt an intersection here

[timid silo]

this might give you some intuition ^

[timid silo]

no, the intersection should be everything here

[silver plover]

wdym

[timid silo]

intersection of (1,infinity) with [1,infinity) is (1,infinity)

which is the range of f

[silver plover]

ye

[silver plover]

is the domain of gof (1,infinity)?

ugh idk i give up

[timid silo]

no

[silver plover]

can i explain my reasoning plz

so u can see

what im doing wrong

so domain of f is (-infinity, 0)

[timid silo]

(1,inf) is this thing in red

we need to find the blue thing on the left

ie, we need to find all x such that f(x) is in (1,infinity)

which is (-inf,0)

if in doubt, draw some venn diagrams

[silver plover]

@timid silo i keep getting this

[timid silo]

thats fine

the intersection is in the middle

we need to bring it back to the left

[timid silo]

^

[silver plover]

yh this is the part now where im stuck

[silver plover]

i dont get that sry

im fine up until intersection

oh wait

[timid silo]

do you understand this picture?

[silver plover]

ye

ie, we need to find all x such that f(x) is in (1,infinity)

i just dont get

how that is

-inf 0 ()

[timid silo]

its the domain of f since f is onto

[silver plover]

idk if i understand

imma just practice

and see what happens

imma do a few more examples now

[timid silo]

hm ok

[silver plover]

is it normal for students to find this concept so hard to get their head round

or am i just thick lol

[timid silo]

nah its normal to be confused about compositions

its much easier to explain with a whiteboard and a bunch of gestures

so maybe its worth asking your teacher

[silver plover]

finding the domain of this example

have i written everything correct so far?

[timid silo]

yea

[silver plover]

is the range if g [-1,1]?

ye it is lol

[timid silo]

yup

[silver plover]

is the intersection correct?

[timid silo]

yes

[silver plover]

so we need to now find all x s.t. g(x) is in [-1,1]

[timid silo]

yes

[silver plover]

and thats real

[timid silo]

correct!

[silver plover]

numbers

SUIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII

SUIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII

LESGO
LESGO
LESGO

@timid silo last example then im done sorry to bother u for so long

doing gof instead now

does it all seem fine so far?

[obtuse pebble]

@silver plover Has your question been resolved?

[silver plover]

dw @timid silo got it now

appreciate ur help buddy

.close

[obtuse pebble]

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[obtuse pebble]

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[knotty lodge]

can a polynomial have no roots in real and complex numbers

[warm canopy]

Sure, the polynomial f(x) = 5 has no roots

[knotty lodge]

with coefficients*

quadratic

[knotty lodge]

that's not a polynomial tho

[warm canopy]

Sure it is, what's your definition of polynomial?

[knotty lodge]

my bad

i meant characteristic polynomial in linear algebra

[daring glacier]

what's the doubt?

[knotty lodge]

the question was

a matrix always has a eigenvector in real or complex numbers

i said true cuz a charistic polynomial must have at least one complex root

am I correct?

[daring glacier]

yea

[knotty lodge]

ok nice

Is ||uv|| the same as u||v||

fok

is magnitude of CV the same as magnitude of V then C

[sharp pecan]

what V then C?
what if V=-C

[kind hawk]

$\norm{cv} = \abs{c}\norm{v}$ if $c$ is a scalar

[warm shale]

Denascite

[knotty lodge]

yea

is that true?

[kind hawk]

yes by definition of what a norm is

[knotty lodge]

it's properties of dot product right?

sorry,

property of scalar multiplication

[kind hawk]

no it's a property of the norm

[knotty lodge]

oh ok

[obtuse pebble]

@knotty lodge Has your question been resolved?

[obtuse pebble]

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[unkempt lotus]

How would I go about solving something like this? What problem is this called?

[unkempt cosmos]

Haha we got a question at the same time 😂

[unkempt lotus]

I beat you

Lol

[unkempt cosmos]

I know how to solve your stuff

[unkempt lotus]

that would be dope

what's it called? so i can look it up on Kahn academy

or u can help me if u want but not necessary

[unkempt cosmos]

I would just use distributivity

[unkempt lotus]

so like (x^2+6x+5)(3x+6)?

[unkempt cosmos]

Ill write it down on paper wait a sec

[unkempt lotus]

kk

[unkempt cosmos]

Oh wait

What is the question

I know how to solve it with complex numbers

[unkempt lotus]

idk i think it was just multiply .. what are those lol

i think it asks to just simplify

[unkempt cosmos]

Maybe this?

[unkempt lotus]

need english plz

nah man

[misty folio]

sorry, not of any help to the chat but what app is this? looks magical.

[unkempt cosmos]

Photomath

[unkempt lotus]

that might be it

idk

i need help tho

[unkempt cosmos]

@misty folio do you know how to solve my question

[unkempt lotus]

dude can u plz make aa new help

i need help with mine

[unkempt cosmos]

You can try Wolfram alpha

[unkempt lotus]

.close

[obtuse pebble]

Channel closed

Closed by @unkempt lotus

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[unkempt cosmos]

Thats another mathematics website

I'm sorry 😅

[unkempt lotus]

.close

[unkempt cosmos]

.open

[spiral knot]

you already have a channel

check help-11

[unkempt lotus]

dude i always legit run into a problem using this server

like for example this time someone took over my help channel

lol it's never ending

[unkempt cosmos]

Ill go on there

Bro relax im sorry

It was just a coincidence

[unkempt lotus]

its fine just go somewhere else

yes and ur supposed to just make a new one it happens all the time

[unkempt cosmos]

Gl with your question

[unkempt lotus]

thx

[obtuse pebble]

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[rapid lava]

I need help

[rapid lava]

A mass of 0.5 kg of ethyl alcohol occupies a volume of 0.000633 m3. Calculate:
a) What is its density?
b) What is its specific weight?

🥲

[alpine raven]

do you know the formula of the density ?

[rapid lava]

p=m/v

density equals mass divided by volume

[alpine raven]

then, you know how to do your exercise

[rapid lava]

no

i don't know

[alpine raven]

your exercise gave you the mass and the volume, what is the problem

[rapid lava]

oooo

And what about specific weight?

[alpine raven]

Im pretty sure you have the formula for this

[rapid lava]

nop

[alpine raven]

google it

[rapid lava]

but thanks, I guess I'll have to know the formula and do what it says

[rapid lava]

yep

thanks

[alpine raven]

np

[obtuse pebble]

@rapid lava Has your question been resolved?

[obtuse pebble]

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[obtuse pebble]

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[hidden spindle]

the final for this class is in 20 min and i have no memory of doing this lol

[tranquil quiver]

what have you tried

[stable rain]

:c

[hidden spindle]

i know i need to get to the quadratic formula but i dont know how

[stable rain]

denote cars rented w some var

[hidden spindle]

C = cq+F
R = pq
P = (p-c)q+F

[stable rain]

find exp for income

..

whats what

[tranquil quiver]

what

[hidden spindle]

those are the cost revenue and profit functions

[tranquil quiver]

they managed to get three variables

[stable rain]

u cant just introduce 4 vars

5

[hidden spindle]

bro im not

[tranquil quiver]

we don't care about those

[stable rain]

n not say what they r

[hidden spindle]

those are the cost profit and revenue functions

[tranquil quiver]

Only the income function

[hidden spindle]

yes you do

[tranquil quiver]

Nah

[stable rain]

dog

u getting taught

[hidden spindle]

dog youre wrong

[stable rain]

im out

[tranquil quiver]

😱😱

[stable rain]

LOL

[hidden spindle]

its business calc

[tranquil quiver]

dawg if I'm wrong why don't you solve it

[stable rain]

@tranquil quiver ur cue to leave

take it

[tranquil quiver]

🌞🌞

[reef raven]

where did u get all these variables fam

[hidden spindle]

those are the cost revenue and profit functions

[reef raven]

bro what

where did you get those from

[hidden spindle]

...

[tranquil quiver]

what's the income function

[reef raven]

like

u need a legend for those variables

[hidden spindle]

(30x + 1)(200-5x)?

[reef raven]

lemme try and solve this rq

[tranquil quiver]

is this

even related

[reef raven]

😭

[hidden spindle]

isnt that the income function

[tranquil quiver]

where the numbers come from

[hidden spindle]

the problem???

[tranquil quiver]

well if you believe that's the income function you can go ahead and maximise it

[hidden spindle]

is that how you find the income function?

[tranquil quiver]

i don't know what you are asking

You just gave me an income function I don't know what x even represents

[strange sparrow]

Ok let's make y the profit and x the number of dollars they charge

[hidden spindle]

this is stressing me out more than failing my test in 2 minutes is going to

[tranquil quiver]

why profit now

we don't even have a way to find the cost

[tranquil quiver]

you have a test in 2 minutes?

You should get help earlier next time

[hidden spindle]

!!!

[strange sparrow]

So y=(480-(x-20)*10)*x

I'm not sure js that right

[hidden spindle]

dude I ask with like 20 minutes of time

[tranquil quiver]

please stop

[strange sparrow]

Wait

[hidden spindle]

except people argued about it for 20 minutes

and now we're here

[tranquil quiver]

don't solve the question for them @strange sparrow

[tranquil quiver]

okay

[strange sparrow]

I don't think that's right actuallg

Sorry

[tranquil quiver]

Let's be basic here

[hidden spindle]

dude are you kidding me

[tranquil quiver]

No

[hidden spindle]

i was literally asking how to start it

[strange sparrow]

Ok so there's 480 cars right

[tranquil quiver]

let p represent the price per car

[hidden spindle]

im out of time and dont watching people argue over this

.close

[obtuse pebble]

Channel closed

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Use .reopen if this was a mistake.

[tranquil quiver]

😱😱

[reef raven]

smh

[strange sparrow]

Wait is the rate of 20 dollars a day for one car only

[reef raven]

(480-10x)=(20+x)

[tranquil quiver]

don't come for help and be so unwilling to listen to the people trying to help you 🙏

[obtuse pebble]

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[proven siren]

Hey, what was the name of the identity that simplifies this formula ?

[alpine raven]

?

[neon eagle]

Isn’t this the sum of the first x natural numbers

But like written dumb

[proven siren]

yes

[neon eagle]

ok there u go it’s just the sum of the first x counting numbers

[proven siren]

are there a formula for instead of subtracting i we subtract 2*i ?

[neon eagle]

dude

isn’t this just 0

yea it’s just 0

For all x

in N

[sharp pecan]

why is it 0

for x=1

we get 1-2?

for x=2 we get 2-4

so the first 3 are already going negative

[warm shale]

Mehdi_Moulati

[neon eagle]

wait am I dumb

[sharp pecan]

real

[neon eagle]

No ur wrong

for x=1 u get 1-1

Which is 0

[warm shale]

Mehdi_Moulati

[sharp pecan]

thats the sum from 0 to 1, I was going over the individual steps

[neon eagle]

yea sum of first x counting numbers

[sharp pecan]

to show you that its not the same

[neon eagle]

What?

Could you give an example where it isn’t 0

see?

[sharp pecan]

I see the problem

[neon eagle]

There isn’t one

[proven siren]

Thanks, for the help

Should I close the channel?

[neon eagle]

if u don’t need help yeah

[proven siren]

Yeah, I found what I was looking for 😄

.close

[obtuse pebble]

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[restive storm]

idk how to solve (b)

[neon eagle]

what does the area under the v(t) graph represent?

[obtuse pebble]

@restive storm Has your question been resolved?

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[leaden ibex]

currently studying my past solutions, can someone tell me how I got (1/2)(pi) as b

[neon eagle]

What’s the question

[leaden ibex]

use local linear approximation

to estimate the equation on line 1

[neon eagle]

what

What is line 1

[leaden ibex]

like the equation on the top most of the screenshot

here

[neon eagle]

Ok ok just googled wtf that is

lemme look now

U messed up on line 2

[leaden ibex]

what

[neon eagle]

U differentiated f(x) wrong

[leaden ibex]

i got full points for this though

[neon eagle]

Wait did u

oh wait nvm u skipped steps

nvm

Is this ur test paper

it’s so neat bro

[leaden ibex]

thanks

[neon eagle]

Ur confused about how u got pi/2v

[leaden ibex]

yes

i forgot how i got pi/2

as b in y = mx + b

[neon eagle]

wtf this is a different local linear approximation to the one I read on google

can u show me the one ur using?

[leaden ibex]

im pretty sure I also asked for help here

[dark stirrup]

Your tangent line is y=-2x+b

[leaden ibex]

wait lemme find it

[dark stirrup]

Your x coordinate is pi/4

[neon eagle]

L(x) = f(a) + f '(a) (x - a).

This seems easier

[dark stirrup]

f(pi/4)=ln(2cos(pi/4)^2)=ln(2(sqrt(2)/2)^2)=ln(2*(1/2)=ln(1)=0

[dark stirrup]

So y=-2x+b must contain the point (pi/4, 0)

So 0=-2(pi/4)+b

b=pi/2

[leaden ibex]

ahhhhhhhhhhhhhhhhhh

i see

thanks

forgot how i did it

[dark stirrup]

Hope this isn't hard to read. I do not know latex

[leaden ibex]

haha

yep i still understood it :))

thanks man!

[neon eagle]

Bro you should learn it

it’s so useful

[dark stirrup]

I use microsoft word then just paste the result. Formatting math in discord is a pain in the booty

[neon eagle]

just latex it

[dark stirrup]

At least in word, I get real-time viewing of the formulas as I make

one day I will try

[neon eagle]

U do in latex do?

Too*

[dark stirrup]

I'm old.

I do not embrace the new

[neon eagle]

U should it’s really easy

I learnt it in like a day

[leaden ibex]

thanks guys bout to close this now

.close

[obtuse pebble]

Channel closed

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[neon eagle]

yes

[dark stirrup]

It ain't easy for old farts to learn stuff

https://tenor.com/view/grampa-simpson-gif-19674842

[obtuse pebble]

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[zenith ibex]

Hello i'm doing an geometry exercise but i'm stuck

[zenith ibex]

I have three shapes and I need to get the area and the perimeter

for the first two, I cut them into smaller pieces and measured them separately

But I don't know how I can do that with this shape

[timber fox]

think outside the shape I guess

[zenith ibex]

how ??

these parts are easy to measure but I don't understand how to measure the sides

oh wait I understand you now

[timber fox]

👍

[zenith ibex]

I can see it as a rectangle and substract the triangles

👍 👍 👍 👍 👍 👍 👍 👍 thanks clark

.close

[obtuse pebble]

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[solar sundial]

hello

[solar sundial]

just a quick question

if a game has the option to either win or lose and the house has a 50% chance of winning higher than the player what are the probability of the player winning 21 times in a row

[timid silo]

8 times

[obtuse pebble]

@solar sundial Has your question been resolved?

[obtuse pebble]

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[meager root]

Question says to "Add or subtract as indicated"
Where do I start? I have the answer but I have no clue how to get there.

[meager root]

(x^2-7x+32) / (x-4)(x+4)(x+1)

[tardy epoch]

Show your work

[meager root]

I don't have any work, that's why I need to know where to start. I just have 4 answers and I know which one it is due to answer sheet. But the answer itself doesn't give me any clue as how to get there.

[tardy epoch]

Oh okay

[meager root]

Something about common denoms?

[tardy epoch]

Do you know how to factor either denominator?

[meager root]

hmmm

oh maybe using the ac method??

can i can factor the RHS with that?

[tardy epoch]

Try the method and write the factorization here

[meager root]

I can multiply 4 and 1 to get 4, and add them to get 5. So it'd become (x+4)(x+1) ?

[tardy epoch]

Yes that is the correct factorization for the denominator of the second term

[meager root]

ok, so the RHS now looks like 8/(x+4)(x+1)

and then the denom of the LHS can be factored to (x-4)(x+4)

[tardy epoch]

Yes

[meager root]

this looks good so far?

still not sure where to go from here

[tardy epoch]

Find the greatest common denominator. Then multiply the first term in the top and bottom by something that gives you the greatest common denominator. Similarly the second term

[meager root]

The GCF of.... 8? or or 1, 4, and 8?

or is greatest common denom diff than gcf?

[tardy epoch]

Yes they're different

[meager root]

im just tryna find the GCF within the denoms?

so 4 and 1?

[tardy epoch]

I might have been calling it the wrong thing

https://youtu.be/udkEiFJVE5s

They call it LCD

[meager root]

lemme see this vid real quick

ok so just focusing on the denom, the LCD would be 4x?

cause that's the smallest common factor between 1 and 4?

and theres no variable with a higher power?

and then I need to find somethin to multiply the LHS by in order to get 4x?

[winter cargo]

take 1/(x+4) as common

[meager root]

sorry i dont get what ya mean by take 1/(x+4) as common

[meager root]

ah, so the common factors between the LHS and RHS being 1 cause both x and 8 share 1 as their greatest common factor?

and (x+4) being the part each side has?

[winter cargo]

yes

now u can do this

you can also directly do it

it will take just some more steps

[meager root]

why are ya multiplying by x+1?

[winter cargo]

to make the denominators common?

you can only sutract like fractions

[meager root]

you're multiplying the LHS by the denom from the RHS, and yer multiplying the RHS by the denom from the LHS? After ya took out (x+4)?

[winter cargo]

yes

since theyre coprime

[meager root]

ok so here the 1/(x+4) hasnt even been applied yet, yer just making common denoms?

[winter cargo]

yes

[meager root]

And ya were able to combine the LHS and RHS cause they share common denoms, and the subtraction between (x^2 + x) and (8x + 32) is there because it was originally subtraction between the two sides?

[winter cargo]

yes

8x - 32

[meager root]

8x-32?

[winter cargo]

yes

[winter cargo]

after subtraction -8x+32

since we did 8(x-4)

[meager root]

you mean 8x+32 yes?

i can see how everything's workin out now, but i dunno wym by 8x-32

[winter cargo]

you understand this step

?

[meager root]

yes

[winter cargo]

this one?

[meager root]

multiplying out from there

ooooooooh

no

just one part of it tho

OH!

wait i understand it

the positive and negatives changed cause you moved it?

[winter cargo]

yes

[meager root]

gotcha

[winter cargo]

-(8x-32) = -8x+32

[winter cargo]

then you get to this

[meager root]

i got it now, i didn't notice the change initially but i understand why that's happenin now

[winter cargo]

oh k

[meager root]

and i see where we'll get -7x+32 after x-8x+32, and where the (x+4) is coming from

(x^2-7x+32) / (x-4)(x+4)(x+1) lookin good 🙂

[winter cargo]

yes

now to simplify

[meager root]

we got x^2 - 16 originally and factored it to (x+4)(x-4) so I can get where that's from, the answer on the sheet doesn't simplify it but that is the simplest form yes

understood! 🙂

thanks for the help

[winter cargo]

k

welcom

*welcome

[meager root]

and thanks to riemann for the start

.close

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[warped hearth]

Hi, I need help. I'm not really sure what they mean by "Write this proportion as a percentage."

[warped hearth]

I understand everything else like the "Give your answer correct to 1 decimal place when appropriate."

pinged myself so i remember this channel

<@&286206848099549185>

Been 15mins so I pinged

[peak schooner]

hello i am one of the helpers how can i help you

lets join mathematics

[winter cargo]

theyre asking to write fraction of monkeys in percent?

23/164

to percent

[warped hearth]

Oh, so the answer is 14%.

Thanks

.close

[obtuse pebble]

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[grim herald]

my bad b

im not sure

if i use partial fractions it doesnt really help

and you cant really do long division

[timid silo]

I'm pretty sure you can do some shenanigans to split this into two fractions

[grim herald]

uh

[timid silo]

Like what if you added and subtracted 3 from the numerator?

Wait no

Add and subtract x - 3 from the numerator

Yes that should be it

So like

[distant moth]

Why not

[grim herald]

I dont think it helps

unless i did it wrong

[distant moth]

It does tho

[grim herald]

then i did it wrong

[distant moth]

Another way of doing this without actually doing long division is just subtracting and adding x

[timid silo]

[
\int \frac{x^3 + 3}{x^3 - x} \dd{x}\to \int \frac{x^3 +3 {\color{red}-(x+3)+ (x+3)}}{x^3 - x} \dd{x}
]
[
\to
\int \frac{x^3 +3 - x - 3}{x^3 -x} + \frac{x+3}{x^3 -x} \dd{x}
]

This has the same effect as long division

[grim herald]

oh

interesting

ah i see

okay okay

[warm shale]

♡LexQa♡

[grim herald]

.close

[obtuse pebble]

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[misty anchor]

Okii

[timid silo]

Okay

But ask your question

[timber fox]

[tardy epoch]

We're all on the edges of our seats

[timid silo]

They're going to drop the heat

Any second now..

[wild swallow]

[timid silo]

Omg snow is here now

[timber fox]

its to cool the heat

[mental plaza]

my channel is very hot

I need someone to come and cool it

[timber fox]

YOU ARENT GETTING THE REFERENCEEEE

[timid silo]

Anyways I will just

.close

[obtuse pebble]

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[obtuse pebble]

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[grand bane]

I forgot literally everything about equation of lines

[obtuse pebble]

@grand bane Has your question been resolved?

[grand bane]

<@&286206848099549185>

[obtuse pebble]

@grand bane Has your question been resolved?

[winter cargo]

um slope rt?

[obtuse pebble]

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[obtuse pebble]

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[simple lagoon]

If M1 and M2 are the number of sexagesimal and centesimal minute of any angle, prove that M1/27=M2/50

[simple lagoon]

.close

[obtuse pebble]

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[hearty zephyr]

Hello

[hearty zephyr]

I have to find A^32 for a matrix A using Caley Hamilton theorem

The Matrix is:
1 0 0
0 -1 0
1 0 1

[alpine raven]

find an explicit expression for A^n

[hearty zephyr]

I have

[alpine raven]

,w [[1,0,0],[0,-1,0],[1,0,1]]^2

[warm shale]

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[alpine raven]

,w [[1,0,0],[0,-1,0],[1,0,1]]^3

[warm shale]

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[alpine raven]

,w [[1,0,0],[0,-1,0],[1,0,1]]^4

[warm shale]

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[alpine raven]

do you see the pattern ?

[hearty zephyr]

Yes

But I cant do that

lol

cuz this doesnt use the Caley Hamilton theorem

and Im stuck here

[alpine raven]

Ah, I didnt read the cayley hamilton part

wait

,w eigenvalue [[1,0,0],[0,-1,0],[1,0,1]]

[hearty zephyr]

This is the general expression for A^n that I thought you were talking about

Unfortunate

One of the eigen values repeats, 1 precisely

[alpine raven]

yea i kniw

know*

[warm shale]

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[alpine raven]

,w multiplicity of eigenvalue [[1,0,0],[0,-1,0],[1,0,1]]

[warm shale]

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

Requested by Ｈｅｒｅｌｓ#1420

[alpine raven]

welp

you said its 1 ?

[hearty zephyr]

yes

yes

[alpine raven]

then you can write the polynomial as :
$(X+1)(X-1)^2$

[warm shale]

Ｈｅｒｅｌｓ

[hearty zephyr]

[1 - l][1 + l][1 - l] = 0 is the characteristic equation

yes

[alpine raven]

Using cayley hamilton, you have :
$(A+I_3)(A-I_3)^2$

[warm shale]

Ｈｅｒｅｌｓ

[hearty zephyr]

Yes

[alpine raven]

its better to expand this

[hearty zephyr]

Yes

the expanded is l^3 - l^2 - l - I3 = 0

[alpine raven]

$=(A+I_3)(A^2 - 2A + I_3)$

[warm shale]

Ｈｅｒｅｌｓ

[hearty zephyr]

I tried doing it that way but takes way too many annoying computations

[alpine raven]

$=A^3 - 2A^2 + A + A^2 -2A + I_3$

[warm shale]

Ｈｅｒｅｌｓ

[alpine raven]

$=A^3 - A^2 - A + I_3$

[warm shale]

Ｈｅｒｅｌｓ

[hearty zephyr]

oh :0

[alpine raven]

dont forgot that all of this are equal to $O_{\mathbb{R}^{3 \times 3}$

[warm shale]

Ｈｅｒｅｌｓ
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[hearty zephyr]

What does that mean

damn lol im blind

[alpine raven]

Null matrix

[hearty zephyr]

mb

Yeah yeah

That is the theorem agreed

[alpine raven]

so $A^3 = A^2 + A - I_3$

[warm shale]

Ｈｅｒｅｌｓ

[hearty zephyr]

Yes

[alpine raven]

we can factor this I think

[hearty zephyr]

factor?

[alpine raven]

,w x^2 + x -1

[warm shale]

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[alpine raven]

hmm nah not important

[alpine raven]

normally we should see a pattern with this

[hearty zephyr]

pattern in the sense?

as to what variables to put together to sum upto 32

?

[alpine raven]

$A^4 = A^3 + A^2 - A$

[warm shale]

Ｈｅｒｅｌｓ

[hearty zephyr]

hm yeah

[alpine raven]

$A^{n+1} = A^n + A^{n-1} - A^{n-2}$

[warm shale]

Ｈｅｒｅｌｓ

[alpine raven]

but Thats not what i want

there is a better way

[hearty zephyr]

oke

:>

Im just sitting duck xd

Alright while you try to figure that out, Ill try another method for the same

[alpine raven]

$A^3 = A(A+I_3) - I_3$

[warm shale]

Ｈｅｒｅｌｓ

[hearty zephyr]

Hum hum?

I have something going here too :D

[alpine raven]

?

[obtuse pebble]

@hearty zephyr Has your question been resolved?

[alpine raven]

I cant find how

but we have the simplest expression of A^3

I cant do much simpler

[hearty zephyr]

Illshowo yqou

what I foubd

but

its wrong

:<

computational error

[alpine raven]

just show

[hearty zephyr]

but itsa good method

That's the idea atleast

[alpine raven]

what have you done with A^4 ?

[hearty zephyr]

The bottom right and left parts of the page

[hearty zephyr]

Helped in the computation of A^10 just under

And then I tried to get A^30 bottom left of image

[alpine raven]

the middle on the right page

[hearty zephyr]

The A^4?

[alpine raven]

yes

[hearty zephyr]

I'll retry on a cleaner page and compute slower this time

[hearty zephyr]

Yes it was used in the computation of A^10 just under A^4

[alpine raven]

nah you wrote :
$A^4 = A^3 +A^2 - A$

[warm shale]

Ｈｅｒｅｌｓ

[hearty zephyr]

Yes and I substituted in A^3

[alpine raven]

and after that, I dont understand what you did

[hearty zephyr]

From above

[alpine raven]

ah

$A^4 = A^2 + A - I_3 + A^2 - A = 2A^2 - I_3$

[warm shale]

Ｈｅｒｅｌｓ

[hearty zephyr]

Yes

[alpine raven]

I see

this method should work

you are on the right path

do it and find a recurrence relation

so you wont have to do this until A^32 ROFL

[hearty zephyr]

I wrote the recurrence relation at the right most side

It works

Got the answer too 👍

But I can't be using the recurrence I kinda have to do it up till 32

Thanks a ton ❤️@alpine raven take care

.close

[obtuse pebble]

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[hearty zephyr]

@proven crown repost your message after the botopens the channel

Head over to #help-0

Or #help-2

Now go to help-2

[obtuse pebble]

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[alpine raven]

np take care

[alpine raven]

.close

[obtuse pebble]

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[obtuse pebble]

Channel closed

Closed due to the original message being deleted

[wanton bluff]

Someone check this pls

[obtuse pebble]

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[edgy cargo]

Can anyone help me? My original answer was C but I'm having doubts because the questions states the number of students too, So now I think it's E.

[wanton bluff]

Bro why my questionn

[lost tree]

Average for all = (sum of marks of first 20 students + sum of marks of next 30 students) / tot. no of all students

[wanton bluff]

Yeah and my question got skipped like before

[lost tree]

Oh

The bot has assigned this to loltyler so maybe u shud get a new channel?

[fading quest]

dont delete your post when opening a channel, just open a new one

[wanton bluff]

Ok

[fading quest]

show your work

[edgy cargo]

i just found the average of 66 and 56

[edgy cargo]

ok ill try that

[edgy cargo]

wait wouldnt it be 60 then

if i tried ur way

[fading quest]

yep

[edgy cargo]

ah okay thanks

that helped me alot

since i had alot more questions similar to that

[edgy cargo]

i also have another question im kinda confused on if u mind helping me

[fading quest]

post it and ill see if i can help

[fading quest]

so what do you think you should do here?

[edgy cargo]

ig ill just add all the things up so 10+20+30 then divided by 3?

[fading quest]

not quite

so how many questions are there total?

[edgy cargo]

25

[fading quest]

and how many minutes did he spend in total?

[edgy cargo]

60

[fading quest]

and how do you find the average minute spent per question?

[edgy cargo]

60/25

[fading quest]

yep

now you simplify the fraction

[edgy cargo]

oh i was just overthinking it

thanks tho

[fading quest]

👍

[edgy cargo]

i understand it now

[fading quest]

in general when it comes to finding average you just need to find the total of each thing and divide them accordingly

[edgy cargo]

okay

[fading quest]

these questions are rather simple so just know that if things seem complicated, then you are probably doing something wrong and need to reread the question properly and find exactly what it is they want you to do

[edgy cargo]

mhm

.close

[obtuse pebble]

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[fallow widget]

,, x^2 +4x +12 = 0

[warm shale]

Merineth

[fallow widget]

How do i solve out x?

I can't do square root out of -8

[keen jungle]

Its a quadratic equation

you need to find delta first

[teal turret]

No real roots to this one

[next reef]

,w solve x^2 +4x +12 = 0

[warm shale]

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[next reef]

It has two distinct complex roots

[teal turret]

What quadratic formula did u use

[fallow widget]

PQ

[teal turret]

Oh

[teal turret]

Yes so have u learnt about finding complex roots?

[fallow widget]

Maybe, can't remember. I'll look into it

[teal turret]

Ok, because this sort of problem requires that knowledge

Unless u are told to write "no real solutions" or something similar because the formula yielded a negative under the radical

[fallow widget]

I looked it up and still don't fully understand it

The square root of -8 becomes 8i?

so x1=6 and x2=-10 ?

I have literally no understanding of this

.close

[obtuse pebble]

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[wanton kraken]

why does this happen?

[wanton kraken]

which property was it?

[royal basin]

$\log_a(b) \log_b(a) = 1$

[warm shale]

Ann

[royal basin]

or, if you like, $\log_a(b) = \frac{1}{\log_b(a)}$

[warm shale]

Ann

[wanton kraken]

ty @royal basin

.close

[obtuse pebble]

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[rough herald]

Find the smallest positive integer d such that there exists an integer n with n, n + d, n + 2d, n + 3d, n + 4d, n + 5d being all primes.

I honestly don't know where to start with this question

[rigid lintel]

well

d is at least 2

[rough herald]

yeah

[rigid lintel]

interesting question though

[rough herald]

but is there a way to prove

like

i dont know how to word this

but where would i start with this question

because im completely lost

[spice citrus]

don't think d can be odd

and n isn't divisible by 2, 3, 4 or 5

so it's at least 7

does there even exist a solution?

[rough herald]

is there a way to do this other than super repetitive guess and check

[rough herald]

not sure

[spice citrus]

looking mod 3 kinda looks like there isn't a solution at all

[rough herald]

if there isn't a solution is there a way to prove that there are no solutions

[spice citrus]

maybe if n = 0?

nvm

[rough herald]

how did you utilize mod 3

[spice citrus]

you can look at the cases where d is 0, 1 or 2 mod 3

and where n is 1 or 2 mod 3, n = 0 mod 3 can't be true because n + 3d would be divisible by 3

[rough herald]

wouldnt d have to be greater than or equal to 2

and also your previous message states that d cant be odd

[rigid lintel]

it is

[rough herald]

how would i go from there

like

is there a fast way to get the answer

[spice citrus]

I think the only case that works is d = 0 mod 3

[rough herald]

given all these conditions

[spice citrus]

maybe try 6 because it has to be even, if d were odd, one of the numbers would be divisible by 2

and thus can't be prime

[rough herald]

i tried n = 5

and the last num was 35

lmao

the rest were prime

[spice citrus]

yeah, also tried that, but then realized I wrote this message

[rough herald]

oh

true

[spice citrus]

n = 7 with d = 6 also doesn't work

because 25 fails

for d = 6, n = 11, 13, 17 and 19 don't work for the same reasons

25 or 35

[rough herald]

wait

i dont think d = 6 works

because

when you take the unit digits

its 1, 7, 3, 9 and 5

and numbers ending with 5 are always composite

[spice citrus]

then d = 12 it is

[rough herald]

d=12 doesnt work for the same reason

[spice citrus]

the bigger d is the less chance of there being 6 primes

[rough herald]

yea

wait what are the current conditions we have on d right now

must be even

what else

[spice citrus]

must be a multiple of 3 (I'm pretty sure)

checking all the cases d mod 3

[spice citrus]

does the same apply to d = 6k? where k is an integer?

[rough herald]

nope

im pretty sure not

it doesnt work for 12

but im fairly sure it may work for 18

let me check

wait no

it doesnt

wait if i can prove that there is no possible d

by stating these conditions

then the problem might be solved

@spice citrus do u think that there are no solutions to this question

[spice citrus]

not sure, the way the question is phrased kinda implies there should be

find the smallest integer, so there should be an integer

[rough herald]

im pretty sure there are no solutions

there is a number ending with 5 at least once for every d

when you start with 5 the lst number will end with 5 as well

[spice citrus]

maybe the statement that k is 0 mod 3 is wrong

[rough herald]

hmm

maybe

[spice citrus]

didn't look at it too carefully

[timid silo]

https://en.wikipedia.org/wiki/Primes_in_arithmetic_progression

green-tao says that there is a solution

and 2*3*5=30

[rough herald]

alright thank you

.close

[obtuse pebble]

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[ember sigil]

where did i go wrong

[kind hawk]

well for starters none of those sets should include 0

[ember sigil]

and

[kind hawk]

U(15) is not the set you wrote down

U(15) = {1,2,4,7,8,11,13,14}

<1> is not equal to U(15)

the powers of 1 mod 15 are just 1, 1, 1, 1, ...

then for 2 you have 2,4,8 and then 14

instead of 2,4,8 and then 16=1

not sure what your thought process for 4 was. the powers of 4 are 4, 16=1, 4, 1, ...

and well the rest is wrong too

[ember sigil]

btw do i need a binary table to prove this question? or not needed?

[kind hawk]

what exactly do you mean with a binary table?

your approach would be correct here

if the calculations you did were correct

[ember sigil]

Oooooh actually after binary operations, the rest of the topics goes over my head

anyway thank you for checking my work

.close

[obtuse pebble]

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[silver plover]

help please

[celest lodge]

what is your grade

[silver plover]

idk

[celest lodge]

are you a student