help-0

[buoyant kayak]

@haughty falcon

[haughty falcon]

One message removed from a suspended account.

[wise hound]

I just need formula of x=1 under reflection

[haughty falcon]

One message removed from a suspended account.

[buoyant kayak]

no

[haughty falcon]

One message removed from a suspended account.

One message removed from a suspended account.

[buoyant kayak]

you didn't distribute the negative all the way through

the negative is distributed onto each term

[haughty falcon]

One message removed from a suspended account.

One message removed from a suspended account.

[buoyant kayak]

well, if you're adding a negative...

what are you really doing?

[wise hound]

.

[haughty falcon]

One message removed from a suspended account.

[raw shard]

@wise hound reflection across the y or x axis

y gets you the same thing, x reflection gives you -1

[alpine sable]

How I did @raw shard.

3b

[haughty falcon]

One message removed from a suspended account.

[marble storm]

would anyone know how this is wrong

[buoyant kayak]

adding a negative. what is 10+(-5)?

[haughty falcon]

One message removed from a suspended account.

[buoyant kayak]

so what did you really do to 10 when you added -5?

[haughty falcon]

One message removed from a suspended account.

One message removed from a suspended account.

One message removed from a suspended account.

[buoyant kayak]

exactly

you subtracted

[haughty falcon]

One message removed from a suspended account.

One message removed from a suspended account.

[buoyant kayak]

👍

[haughty falcon]

One message removed from a suspended account.

[wise hound]

x

[haughty falcon]

One message removed from a suspended account.

One message removed from a suspended account.

[wise hound]

@raw shard x

[raw shard]

so x = -1 @wise hound

[elder glacier]

what

[raw shard]

@alpine sable thanks for the explanation, pretty cool

[wise hound]

Thanks

May God bless you!!!

May God give you supernatural powers in your next life!!!

May you live long enough!

[fierce frigate]

nvm

found it

this tho

[alpine sable]

A = 28 is of only 1 face?

[fierce frigate]

i do not know

it may be area

but i need help with this one more

[toxic geyser]

can someone help with this ;n;

[alpine sable]

Square - sum of triangles

[fierce frigate]

what agnlges/

angles?

oh triangle

[raw shard]

no one said anything about angles lol

[fierce frigate]

what triangle?

[raw shard]

the 4 triangles in the picture

[alpine sable]

This is kinda funny.

[raw shard]

get the area of the circle and subtract the area of the 4 triangles added together

[fierce frigate]

oh

damn

the timer is up

[raw shard]

why did i say circle lol

[fierce frigate]

(its an exercise)

[raw shard]

i meant square

oof

[fierce frigate]

not a quiz

[toxic geyser]

I’m just lost in this problem completely 😔✋

[alpine sable]

Is there any wEiRd property of mirror included with this?

[fierce frigate]

if this?

[alpine sable]

Or should I assume it to be an ideal mirror?

[toxic geyser]

yeah an ideal mirroir

we kinda neglect the réflexions because the laws because they’re not useful here

[alpine sable]

Then I guess the answer should be 0.5.

[toxic geyser]

the whole thing just doesn’t make sense

[alpine sable]

Can you show the actual question from the book?

This might have a translation mistake or something.

[toxic geyser]

oh yeah it’s just in French

[alpine sable]

Did you translate using Google?

Or actually send the French version.

[toxic geyser]

Un homme de 1,50m est debout à 3 m d’un enfant. L’enfant devant lui est placé à 1,5m d’un miroir et mesure 0,5 m de haut. La distance entre les yeux de l’homme et le sol est de 1,45m et la distance entre les yeux de l’enfant et du sol est de 0,45m.

[alpine sable]

And do you have the answer as well?

[toxic geyser]

Quelle serait la hauteur du plus petit miroir accroché sur le mur, qui permettrait au chien de se voir au complet?

it’s a criterion B for the IB ;n; so not until the next class

[serene pilot]

I’ve learnt francais for six months

[alpine sable]

Don't give answers so directly.

Spoon feeding bad.

[raw shard]

they kinda did but kinda didn’t

[alpine sable]

They gave answer but not the method haha.

[raw shard]

they repeated what i said but in a visual way

well the person said their time was up anyways

so i guess it didn’t matter that much

[viscid junco]

you calculate the area of the entire square

then aubscract the white triangelles

this is what to do when you see irregular shapes

[alpine sable]

Welp, since we are confused anyway. Let's just guess the answer is 0.5 and hope for the best.

[toxic geyser]

Still thank you very much ! :))

[alpine sable]

ÜwÜxygen is crying?

[toxic geyser]

😭😭😭

[toxic geyser]

omg it’s genius but so

[raw shard]

@serene pilot huh?

[alpine sable]

Not my original tho' xD

It was actually from a teammate in Pokémon Unite.

[bold panther]

-6 i think

[stuck delta]

omg thank you

i appericate it ❤️

i was stuck on this one

[alpine sable]

https://cdn.discordapp.com/attachments/832850906030407700/895143374468833331/unknown.png could someone help me

[bold panther]

gotta find the equation of the lines first also one of the signs is wrong

[alpine sable]

ah ok

[viscid junco]

you know something is wrong when y is both bigger than -2 and -1

this rarely happens in linear programming

[bold panther]

once you find the three equations of the lines you can then determine the sign for them. Note that the dotted line is strictly greater than or less than while the straight non-dotted line is used to represent >= or <=

[alpine sable]

Brushing up on calc I, I found the second order derivative of $x^2tan(x)$ but I forgot how to evaluate it

[ocean seal]

Bouldering

[alpine sable]

I’m supposed to evaluate it at $x=\pi$, my handwriting is pretty messy

[ocean seal]

Bouldering

[rough plinth]

Something like this

The right edge got chopped a bit but ig you didn't miss much

[alpine sable]

Alright thanks

Good to know I did it mostly correct just gotta make sure I’m simplifying

[scenic sand]

does anyone understand how to solve this?

I dont know what the question wants me to do in order to solve it

[solemn juniper]

looks like it just wants you to evaluate that function at small values of x

so try doing x=0.1, x=0.01, x=0.001 and see if it converges to some answer

[scenic sand]

oh it wanted me to that

[solar widget]

hello can anyone tell me what topic this is? i just wanna know what to search up on yt

its something to do with functions

[alpine sable]

functions

composite functions probably

[solar widget]

ohhhhh

alright man

ty imma search that on yt

[alpine sable]

is arctan the same thing as tan^-1?

[bright coyote]

Hey

Can I have help with my homwork?

is it allowed here?

Hello?

[rough plinth]

This honestly could be anything. If you could provide more context that would be nice. Though your best bet would be composite functions like @alpine sable mentioned

[rough plinth]

What is your doubt?

[bright coyote]

If ∠BAC = 30°, find ∠ACD

[solar widget]

this help?

[rough plinth]

Yup, composite

more like, just functions

[bright coyote]

That sounds advanced

[bright coyote]

I think ACD should be 30 but not sure

[rough plinth]

Cool story

What do we want?

ACD huh

K

[bright coyote]

yea

Is ACD = 30?

[rough plinth]

Yes

[bright coyote]

oh okay thnkyou

[rough plinth]

Forgot the relation property

Alternate something

[bright coyote]

alternate interior angles

[rough plinth]

There we go

[stone minnow]

Yes I think

[alpine sable]

thanks, just wanted to make sure i was using the right notation for my homework

[rough plinth]

Try beginning with the 5n term

sub n = 2k + 1, since n is odd, like you mentioned

What do you get?

In fact, sub n everywhere

Add them up

K

can you factor something?

lol np

Notice the 2 upfront

?

Perfect!

Nothing

if anything is multiplied with 2, regardless of what its nature is (odd or even) will always result in an overall even number

Pick any number

K

I see

[queen raven]

how do i solve using complete the square

im lost

this is what i got so far

this is the equation

ive been on this question for an hour

[stone minnow]

Is the R.H.S. zero

[queen raven]

yeah

i made it = 0

[rough plinth]

No worries

Just do this

[stone minnow]

Ok
Then you may use the quadratic formula or simply factorize it

[queen raven]

cant

[rough plinth]

2*(12k^2 + 17k + 6)

[queen raven]

the question says i need to use complete the square

[rough plinth]

2*r

where r = 12k^2 + 17k + 6

and any number of the form 2*r is even. Done

[stone minnow]

Oic ...
Then sorry that I haven't learnt this yet 🙏

The original expression is 24k^2 + 34k + 12 right

[rough plinth]

Simplifying the expression after substitution gives me 24k^2 + 34k + 12: Is what you said, correct?

Just take 2 on the outside

[stone minnow]

Then you can take 2 out as a common factor

[rough plinth]

Not exponent

Just 2

[stone minnow]

2 (12k^2 + 17k + 6) = 24k^2 + 34k + 12

[rough plinth]

K so

take out the -2 first

You get -2[t^2 - 7t/2] + 4

cool?

[queen raven]

by dividing everything by -2 or put it outside the bracket?

oh ok

[rough plinth]

Np

[stone minnow]

Yw~

[rough plinth]

Then do this

-2[(t - 7/4)^2 - (7/4)^2] + 4

Let this sink in

It's really crucial that you learn this technique well

Made a typo

Check again

[queen raven]

is the 7/4 cuz you have to plus b/2 then minus b/2

[alpine sable]

the reason we divide by 2 is because if you get the quadratic formula and rearranget it in the form of completing the square, you end up with b/4

inside the squared brackets

[rough plinth]

the (7/4)^2 is there to cancel the the extra (7/4)^2 coming out of the (t - 7/4)^2 part

[alpine sable]

^^

[queen raven]

makes sense

[rough plinth]

That's it

all that is equal to 0

-2[(t - 7/4)^2 - (7/4)^2] + 4 = 0

[queen raven]

so is it now: -2[((t-(7/4))^2) - (49/16)] + 4 = 0

[rough plinth]

You messed up the brackets

but yeah

[queen raven]

which would be -2[((t-(7/4))^2)] = -15/16

[rough plinth]

Not quite

[rough plinth]

Look at this again

(t - 7/4)^2 - (7/4)^2 = 2

[queen raven]

oh yeah

so (t - (7/4))^2=81/16

[sinful chasm]

could someone give me an example of a subset of real numbers that is bounded above, but has no suprenum

[queen raven]

(t-7/4-9/4)(t-7/4+9/4) @rough plinth

is that the factorised version

does that work?

[rough plinth]

Perfect

[tired drum]

Help please

Anyone?

[rough plinth]

Try writing the initial equation with z substituted

[tired drum]

Yeah done that

[rough plinth]

What did you get?

[tired drum]

Got it down to a^2-b^2 + 2abi = a - bi

[rough plinth]

right

add the terms

[tired drum]

There aren’t any like terms tho

[rough plinth]

real with real

[tired drum]

Oh okay

[rough plinth]

img with img

[tired drum]

What do u do after that

[rough plinth]

What did you get?

[tired drum]

a^2-b^2=a

And 2ab = -b

I got 2 equations

[rough plinth]

Perfect

Can you solve them now?

[tired drum]

Its just simultaneous equations right?

Yeah i should be able to

[rough plinth]

Take 2nd one first

Cancel out b

[tired drum]

Ye

[rough plinth]

And you're done. Congratz

[tired drum]

Thanks

[peak niche]

Can someone please help with 3a and 3b?

[rough plinth]

Do you know the concept of post and pre mmultiplication

?

[peak niche]

Maybe

Might be called something else where I go to school

I can manage b I think now

But proofs 😫

[forest garden]

yea proofs hurt

[peak niche]

Especially matrix proofs

[rough plinth]

This one's a 3 liner

[peak niche]

I remember how to do b

[rough plinth]

ABC = I

Pre multiply by A^-1

[peak niche]

Nvm

[forest garden]

Wait you can't multiply both sides of equation by B ^ -1 and it should be a proof ig?

[rough plinth]

You can

[peak niche]

My teacher says alot of the time if I prove using normal algebra that its wrong

[forest garden]

welp

[peak niche]

It's annoying

[forest garden]

I was just gonna say
ABC = 1 -> ABC * B^-1 = 1 * B^-1 => AC = B ^ -1

but then you said that lol

[peak niche]

Yeahhhh it's annoying

Like the algebra will make sense

But apparently it's "not proving"

[rough plinth]

This is not quiet right

You can't multiply in any order

[forest garden]

Hmm?

[rough plinth]

It has to be sequential

[forest garden]

ah

Welp then ignore my solution Oscar lol

[peak niche]

I can do my homeworks with my other (3) teachers but not with this one

She doesn't explain stuff well

That's 4 total maths teachers!

[magic geyser]

y is a great place to work

[astral solstice]

What approach is this so prove the p-q-equation?

[tired drum]

Why does Sin2x= -(root3/2)have 4 solutions?

[alpine sable]

it has infinite solutions

[tired drum]

I mean I with 0 - 360 degree domain

[alpine sable]

well why can't it have two solutions

[tired drum]

Bruh sorry my bad it’s 4 solutions lol

I get why it can have 2

I don’t know why it has 4

[olive sandal]

What's its use this symbol ∐ ?

[alpine sable]

because x lies between 0 to 360°
2x lies between 0 to 720°
so it covers the quadrants twice

[tired drum]

Ohhh

Thank you

[solemn bloom]

What is the period?

[alpine sable]

what does period mean, here ?

[tired drum]

It’s the wavelength

[tired drum]

It’s 6

[alpine sable]

Haww no

[solemn bloom]

it's for circular functions btw

[alpine sable]

12.5

[tired drum]

Wait what

How?

[alpine sable]

Is the graph between origin and x=6 EXACTLY the same between 6 and 12 ?

[solemn bloom]

what is the period of y=−3/5sinθ?

[alpine sable]

Do something on your own

[solemn bloom]

i was asking for help because our teacher didn't teach us but we're having a test

sorry for bothering

[undone siren]

Hi guys... This question has been bothering me for a day already.. Could someone recommend where could I insert the variable "r"? Thanks

[alpine rivet]

L

[undone siren]

L? what is that?

[alpine sable]

Excuse me

Is anyone able to help me quickly with some maths

[umbral hatch]

go on

[alpine sable]

So I’m doing angles

I’m in yea 7 sorry

But I’ll send picture

[umbral hatch]

cool

[alpine sable]

How do I find the answer to this

[umbral hatch]

what do u know about angles in a quadilateral

[alpine sable]

They all equal to 360

[umbral hatch]

so what u reckon u should do here?

[alpine sable]

What is the x

That’s what I’m not sure of

[umbral hatch]

u can form an equation

[alpine sable]

Question: Does Taylor series of ln does not work after some value?

[umbral hatch]

and then solve to find x

[umbral hatch]

what

[alpine sable]

So like? 3+4 =7. X =7?

[undone siren]

doent remove the equations

add them all as is

[umbral hatch]

not really

so treat the 3x+4... like individual numbers

[alpine sable]

Okay

[umbral hatch]

so if u add all of them

they will equal to 360

and now a equation has been formed

do u get it?

[alpine sable]

I still don’t understand sorry

[umbral hatch]

ok 1 min

[alpine sable]

Okay I am sorry for the trouble by the way

[undone siren]

After this help me with my question please UWU 🙂

[umbral hatch]

no its fine people come here to ask and answer

[alpine sable]

I was watching a 3b1b video about Taylor series and he said its series diverges after a point known as "radius of convergence".

[alpine sable]

ye

[umbral hatch]

k @alpine sable

u know how to solve 8x+5= 45

[alpine sable]

No

[alpine sable]

So, sometimes Taylor series does not work?

Can u teach me quickly how to do it @umbral hatch

[umbral hatch]

ye im finding an easy video for you

[alpine sable]

don't we usually use it when in
ln(1+x)
when x tends to 0 ?

@umbral hatch I just need quick explain to do it I done it before but forgot

[umbral hatch]

oh ok cool

so we have 8x+5=45

[alpine sable]

Okay

[umbral hatch]

now we use the fact that what u do to one side u do to the other

[alpine sable]

Yeah. Do you mean it works for every point in ln(x+1) but not ln(x)?

[umbral hatch]

so basically we have to isolate the x

[hoary fiber]

Sorry
Have screen time on my phone

Np
Thanks

[umbral hatch]

so lets do -5 on both sides

8x+5-5= 45-5

8x=40

[alpine sable]

No no i meant we usually use that when x is near zero so it works fine then

Wait

[umbral hatch]

can u guess what we do now?

[alpine sable]

Hahahahaha.
Hours late again.

[alpine sable]

I’m trying to get it in my head quickly because it’s kind of confusing

[hoary fiber]

😅

[umbral hatch]

https://www.youtube.com/watch?v=M3e3U5bK_b0

[alpine sable]

Oh so

[umbral hatch]

this video explains it better than me

[alpine sable]

8x+5=45

U -5 from 45 and take of the +5

[umbral hatch]

yes

[alpine sable]

Making its 8x =40

[umbral hatch]

yes

[alpine sable]

And then divide it and u get 5?

[umbral hatch]

yesssir u got it

[alpine sable]

So x = 5?

yes

[umbral hatch]

now u have to apply that in your question

here u have to do an extra step of forming that equation though

[alpine sable]

https://youtu.be/3d6DsjIBzJ4
Watch after 19:55 till 1 minute more.

8x+5 so that’s

8 x 5 + 5 =?

[umbral hatch]

can u add all these expressions

[umbral hatch]

45

40+5=45

[alpine sable]

So that one is 45?

[umbral hatch]

no the answer of x= 5

[alpine sable]

Oh now we make the thing without the x?

[umbral hatch]

what value of x should be taken to make the expression equal to 45

that value would be 5

[alpine sable]

8 x 5 + 5 is that correct?

[umbral hatch]

correct for what?

no, if ur asked to solve for x

or find the value of x

[alpine sable]

I’m doing that we have to find the angles

[alpine sable]

Watched and i have watched it 3 times before

[umbral hatch]

ah yes if u have to find the angles

u do what u did

but what did u take for x?

[alpine sable]

5 for x

[alpine sable]

So now explain. It diverges so we cannot have ln(x) as a series properly?

Because 8x = 40

[umbral hatch]

no nono i was just using that to explain

https://cdn.discordapp.com/attachments/490557019623915520/895237174327382016/image0.jpg

[alpine sable]

Yea I know u were helping me with an equation of ur own

[umbral hatch]

yea

[alpine sable]

we can but only for a certain domain

Thank you

[umbral hatch]

u sure u got it?

[alpine sable]

Makes me sad.

Yes

Will u be able to help me with another question?

[umbral hatch]

just tell me ur answer soi can double check for u and sure

[alpine sable]

I’ll go and do that answer right now I’ll be back

[umbral hatch]

cool

[alpine sable]

Haha
Study further and once we understand it maybe can do something about it

[alpine sable]

Welp, how does calculators calculate it then?

If the domain is kinda wacky after x > 2?

Do they use log base 10?

@umbral hatch can u help me again with the steps of doing it again

[umbral hatch]

ya sure

[alpine sable]

3x + 4

We do 3+4 right?

[umbral hatch]

no

[alpine sable]

what calculators don't use taylor series to calculate it

We -4 from the equation

[umbral hatch]

u have to form the eqation using the fact that angles in quadlilateral add to 360

[umbral hatch]

u cannot solve 3x+4 it is an expression, in other words it is not given it is equal to something

what u have to do is

(2x-9)+(2x-10)+(3x+5)+(3x+4)= 360 as angles in a qualitateral add to 360

[alpine sable]

Yes

[umbral hatch]

all the different expressions represent a number

[alpine sable]

Yes

[umbral hatch]

do u get it now
?

[alpine sable]

Yea all the expressions are numbers

3x + 4 =

How do I get the answer?

[umbral hatch]

solve this

but first tell me do u get how i got that?

[alpine sable]

Got what?

The first one?

[umbral hatch]

that equation

(2x-9)+(2x-10)+(3x+5)+(3x+4)= 360

this

[alpine sable]

Actually none. It kinda shrinks the number first in order to fit it into the proper domain and then uses other algorithms and then only uses Taylor series. It's more than what we expected. Nice.

[umbral hatch]

also if anyone else can explain better than me please do

[alpine sable]

Yea u put all the questions in one because all the angles together equal 360

[umbral hatch]

now what we do is simplify it

and then solve

can u simplify it?

[alpine sable]

180

90

45

[umbral hatch]

wait what

[alpine sable]

22.5

11.25

[umbral hatch]

can u do 2x-9+2x-10

[alpine sable]

I don’t think so

[umbral hatch]

can u do 2x+2x?

[alpine sable]

Are they all 1 question

[alpine sable]

No

[umbral hatch]

u know like terms

[alpine sable]

U -2 from both

[umbral hatch]

<@&286206848099549185> i reckon its been time, perhaps you guys can explain better than me

[alpine sable]

And get xx?

[carmine lion]

sum of all 4 angles = 360

[alpine sable]

What is the sign for?

[umbral hatch]

not to me explain to @alpine sable

[carmine lion]

what sign

[alpine sable]

I know

Next to evaluate

[carmine lion]

the pi?

[alpine sable]

Yes

[carmine lion]

its like sigma

but multiplication

[umbral hatch]

erm channel in use

[alpine sable]

I see thank you

Sorry

[umbral hatch]

dont worry

https://www.youtube.com/watch?v=HB52UTcAv0g

try this video

[alpine sable]

To complex

Is it just u use the opposite

Symbol

[umbral hatch]

no not really

u can add 2x+2x

to give 4x

but u cannot add 2x+2

does that help

[alpine sable]

Yea kinda

But what does 3x + 4 equal if u can give me answer

And show me

[umbral hatch]

back to this
(2x-9)+(2x-10)+(3x+5)+(3x+4)= 360

[alpine sable]

How u did it would help

[umbral hatch]

2x-9+2x-10+3x+5+3x+4

add all the xs

[alpine sable]

4 x

[umbral hatch]

and then all the numbers

[alpine sable]

38

Added all the numbers together

[umbral hatch]

10x-10

[umbral hatch]

can u show ur working

[alpine sable]

2+9+2+10+3+5+3+4

[umbral hatch]

that is wrong

remember u cannot add an x and a number

[alpine sable]

Do I do the - and +

And not include the x

[umbral hatch]

erm

i think this will help

2x-9+2x-10+3x+5+3x+4

so what we do now

is arrange all the xs on one side

and all the number terms on one side

[alpine sable]

2x we don’t include that?

[umbral hatch]

what

[alpine sable]

I’ll ask my teacher tomorrow how to do it sorry for the trouble

Is it okay if u can give me the answer?

[umbral hatch]

dont worry it is more liekly that my explanation is bad

[alpine sable]

I’m not trying to call ur explanation bad

[umbral hatch]

i dont think im allowed to give u the answer directly

[alpine sable]

It’s just i don’t understand

[umbral hatch]

nah dont worry

[alpine sable]

Well then can u help me with some shapes?

[umbral hatch]

ill try

[alpine sable]

Sorry about the tape on the book

a

Has 130 on both sides

And 40 on the top

60 on bottom is that correct? @umbral hatch

[umbral hatch]

im really sorry i cant explain it in words

it will be terrible

[alpine sable]

No it’s okay

This is more simple

It all equals 360

[umbral hatch]

it is but i cant explain it

im sure someone else will volunteer to help u soon

[alpine sable]

Okay

Someone please help me

With these

[potent pebble]

d = 60 yes

[alpine sable]

Be the opposite of 100 is 100

[potent pebble]

on b?

[alpine sable]

And the other sides are 80 80?

Yea b

[potent pebble]

yes

[upper ember]

thats what i think

[alpine sable]

And c

Is opposite of 30 is 30

And the other is 150 each

[potent pebble]

yep :)

[alpine sable]

And d other both sides are 95 each?

[potent pebble]

i got 45 for k

[alpine sable]

How!

?*

[potent pebble]

360 - 135 - 135 = 90

if you half that you get 45

[alpine sable]

My bad

I did some maths wrong then

Thanks

[potent pebble]

no worries

[alpine sable]

For f

[scarlet atlas]

opposite angles are equal

[alpine sable]

Yes

For f the squares are 90

[scarlet atlas]

135

[alpine sable]

So double 90

[scarlet atlas]

180+45

[alpine sable]

180 + 45

[scarlet atlas]

subtract from 360

[alpine sable]

225

135

[scarlet atlas]

what classs are u in?

6/7 th?

[alpine sable]

7th sorry

[scarlet atlas]

why u sorry bro?

chill

[alpine sable]

Because I’m pretty dumb

[scarlet atlas]

cap

[alpine sable]

56 + 82 is 138

360 - 138 222

So each are 111

Wait can u help me with some questions more? @scarlet atlas

[scarlet atlas]

surea

sure

[alpine sable]

a,b,c,d,e,f

[scarlet atlas]

figures/

?

[alpine sable]

No

Shapes

[scarlet atlas]

e-square
a-rhombus
b-trapezium

try to imagine these

right now i have to go

bai bai

[alpine sable]

Bye

Sadly I don’t know them

[plain osprey]

How the hell did they go from top row to bottom one

What kind of algebra sorcery is this? It’s in induction

I need to prove 10^n+18n-28 always divides by 27 using induction

[alpine sable]

I’m sorry I don’t know

Have a good day

[elder glacier]

@plain osprey can you translate what the text on the bottom says

or just post the q

[lavish matrix]

the 10^n is being multiplied by 10 cause 10^n+1

then we subtract 9 of the other terms because they're also multiplied by 10

it should be noted that what's in the bracket divides 27, 9x8 obviously divides 27 and so does 9x28 + 18

[plain osprey]

im sorry I don’t understand can u maybe show me step by step

[lavish matrix]

Ok, sure well in induction we assume the statement is true for a certain positive integer n

[plain osprey]

Yupe

[lavish matrix]

and we try and prove it true for every subsequent value n+1

so lets sub in n+1 to give 10^(n+1) + 18(n+1) - 28

[plain osprey]

So far so good

[lavish matrix]

= 10 * 10^n + 18n + 18 - 28

= 10 * 10^n + (10-9) * 18n + (10-9)*18 - 28

[plain osprey]

Omg

[lavish matrix]

= 10 * 10^n + 1018n + 10 * 18 - 9 * 18n - 918 - 28

= 10*(10^n + 18n + 18) - (something on the right thats divisible by 27)

and remember the assumption is that (10^n + 18n + 18) is divisible by 27

meaning we have the sum of two integers divisible by 27 so the whole thing is divisible by 27

[plain osprey]

Yes thank you!

[lavish matrix]

now having proved it true for every n+1 assuming true for n, just prove it true for the base case of n=1 and you will show it works for every pos int

yeah no worries

[plain osprey]

This is where i got confused i would have never thought about doing this on my own

[lavish matrix]

ahh yeah just try and incorporate the assumption into the rearrangement

its really hard sometimes

[potent pebble]

hey could i get some help with this?

[alpine sable]

Wish I could help

But I’m to dumb

[lavish matrix]

use the binomial expansion formula

[potent pebble]

ah ye i have

[lavish matrix]

the terms should be C(n, 0) * b^0 * a^n, C(n, 1) * b^1 * a^n-1, C(n, 2) * b^2 * a^n-2

[potent pebble]

wait lemme show you what ive done so far

[lavish matrix]

ok

[potent pebble]

give me a sec i need my phone to charge because its kinda a lot to type

[lavish matrix]

sure

[visual dew]

can i ask

[potent pebble]

so i used bionomial expansion to find equations for p, q and r

and then tried to merge them together

[lavish matrix]

well i think you got the right values for p, q, r

[potent pebble]

aye

[lavish matrix]

so we just need to check the multiplication

pr = a^2n-2 * b^2 * (n^2-n) / 2

q^2 = b^2 * a^(2n-2) * n^2

so q^2 / pr = (b^2 * a^(2n-2) * n^2) / (a^2n-2 * b^2 * (n^2-n) / 2)

this looks really hard but lets proceed by cancelling the a and b terms

well the a and the b terms actually have the same power so they just go away

[lavish matrix]

giving us n^2 / ((n^2 - n)/2)

which when you evaluate should give 2n/(n-1)

@potent pebble

[potent pebble]

i see

thank you

[lavish matrix]

no worries

[neon snow]

@lavish matrix can you explain the prime number thereom pls?

[alpine sable]

Help

@lavish matrix

[lavish matrix]

Okay well you can translate up, down, left and right

[alpine sable]

Thx

[upbeat bloom]

if x+2y = z, is there a way to minimize the difference between x and y?

[lavish matrix]

If the function we translate is f(x), then f(x) + a denotes the function translated a units up. Conversley, f(x) - a denotes the function translated a units down. f(x+a) means translating it a units left and f(x-a) means translating it a units to the right

[distant hazel]

Task 1: The sum of its digits was subtracted from the four-digit number n and received a palindrome. Find the largest possible value for n.

[alpine sable]

Okay thx

❤️❤️❤️❤️❤️

[upbeat bloom]

?

[lavish matrix]

If there are no other bounds, we can just set x = 2y right?

[lavish matrix]

Thank you, KING

[upbeat bloom]

but that might not work all the time yeah?

like the minimum difference wont be 0 all the time

it could be 1 or 2 or more?

[alpine sable]

No thank you King

[lavish matrix]

Thank you

[lavish matrix]

are we assuming x, y are integers?

[upbeat bloom]

yeah

like 1.334 + 2.333 = 1000

where x = 334, y = 333 and z = 1000

[lavish matrix]

Well it depends on what z is then

if z is a multiple of 3 then x=y works

if z gives remainder 1 when divided by 3, x = y+1 works

if z gives remainder 2 when divided by 3, y = x+1 works

[lavish matrix]

n = ABCD or 1000A + 100B + 10C + D. Sum of digits = A+B+C+D.
Their difference is 999A + 99B+ 9C.

Now we have to maximize n such that 999A + 99B+ 9C is a palindrome. Remember, A, B, C, D are single digit integers. If A = 9, we have 9* 999 = 8991. I immediately notice that if A = 9, B = 0, C = 2 then we have a palindrome so the solution definetely has A=9.
999A + 99B+ 9C becomes 8991 + 9(11B + C). Now, it should be noted that each 4 digit palindrome is divisible by 11 (check the divisibility rule), meaning 8991 + 9(11B + C) divides 11. In mod 11, 11B has no bearing on the congruence mod 11 so we can reduce the expression to 4 + 9C divides 11. This is only satisfied when C = 2. So we now have 8991 + 9(11B + C) or 9009 + 99B. By checking for each value of B from 0 - 9, we can see that B = 0 is the only value that gives a palindrome (9009). Therefore, we have A = 9, B = 0, C = 2. Since there is no bound on D, we can maximize it giving D = 9. So our final number is 9029. Checking the answer, we ahve 9029 - 20 = 9009 which is a palindrome

[upbeat bloom]

ohh, how did you arrive at that? it makes sense

[lavish matrix]

i mean if z is a multiple of 3 then x can equal y cause x + 2y just equals x + 2x = 3x. We know 3x can always fit z as it is a multiple of 3

[daring schooner]

Help?

[upbeat bloom]

ah right, thanks a lot!

[lavish matrix]

@distant hazel

[lavish matrix]

Cool

[plain osprey]

Wait when did we assume that

[alpine sable]

hello uh

https://www.desmos.com/calculator/o3mnvf3rpp this is odd function?

the red one

[plain osprey]

We assumed 10^n+18-28 is divisible @lavish matrix

[lavish matrix]

mistyped

yeah meant to be 28

[small bear]

it is, sine is an odd function and it is easy to see after that

[alpine sable]

What does average m mean?
Average m of 2 complex numbers?

i see

thank you

[elder glacier]

Can someone explain why v2 doesn't have a solution? Thanks in advance and apologies if channel is in occupation

[elder glacier]

midpoint?, not entirely sure but

[humble pecan]

Hey y’all

[alpine sable]

Actually it was a variable lol.

The sentence kinda confused me.

[elder glacier]

whats the q

[alpine sable]

What is the average m of z1 = -10+2i and z2 = 2+3i?

[coral sedge]

Not sure this is the right place, but I'll try to explain in a few points what I'm looking for. (Please forgive the lack of accuracy in my terminology)

1. I'm not a STEM aficionado, I'm mostly interested in philosophy

2. I studied a little code, and lambda calculus, to have a better grasp of formalized systems. I understand how you can derive vertically a somehow complex systems from a few fundamental axioms

3. what I don't get is: how do you model a system that is not completely "vertical"? For example, if you want a physical model of a star, I guess you'll have to account for

• general relativity
• the dynamics of the gasses that compose the star
  -the way general relativity influences said gasses
  -the way the mass of the star influences the spacetime
• the nuclear reactions
• the way nuclear reaction alters the gasses
• the way general relativity affects the nuclear reaction
• the way the nuclear reactions affect the mass of the star, which affects the spacetime etc.

4. I have probably made some mistakes in my star example, but you get the gist of it: I'm talking about systems in which the various factors influence each other over time.
   What is the correct term to refer to such systems? And what kind of model is required for them?

(I'm not sure my question is clear, I'm not a native English speaker)

[alpine sable]

Hiya.

Actually, I don't think question-0 is an appropriate channel to introduce tho'.

[humble pecan]

How r u?

[alpine sable]

Superposition of many states.

[humble pecan]

Nice

[alpine sable]

whatsup yall

[vapid yew]

Hi

[proper socket]

i think a is the answer

[vapid yew]

how T^T

[proper socket]

firstly you want to find the ratio

given that it is a geometric sequence

[vapid yew]

It’s 0.1, right¿

[proper socket]

to find the ratio you just get a number and divide it by the number behind it

in this case i do 343/2401

[vapid yew]

then thenn

[proper socket]

then you just chuck it into the formula

[vapid yew]

0.1 = 1/10?

[proper socket]

i got

1/7

as the ratio

[vapid yew]

okay okay

then?

[proper socket]

you just chuck it into the formula

for the sum of a GP

[vapid yew]

i got 100,842…

how T^T

[proper socket]

are you sure youre using the one for geometric and not arithmetic

[vapid yew]

Sn= 16807
———
1-1/7

[coral sedge]

<@&286206848099549185>

[proper socket]

how did you get 100,842 lol

i did that exactly the same you did and it came with 19608.16667

[vapid yew]

idk the next step after thiss

[proper socket]

well thats pretty much it, alll you have to do is divide 168057 by (1 - 1/7)

if you dont get the answer or are still confused youre better off pinging an acutal helper

since im just an ordinary person

in this server

[vapid yew]

gets

thank u!!!

thanks for helping <33

[proper socket]

alg

[plain osprey]

A subset of a linear independent set is always linear independent right?

Can someone explain what im missing and how it’s still true in this case?

In my mind this set is linearly independent because u cant make u2 from u1 and u3 but the subset of u1 and u3 is linearly dependent

[alpine nacelle]

u1, u2, u3 is not linearly independent

Since u3 = 2u1

[plain osprey]

To be linearly dependent u don’t need to be able to make every vector out of the others?

It’s still dependent even if u can’t make u2?

[alpine nacelle]

No, you don't need to, you're mistaking it for a generating set

[alpine nacelle]

Yes

[plain osprey]

Ok, just making sure i get u - if even one vector is a combination of two others it’s a linear dependent set

[alpine nacelle]

Here the combination is u3 = 0u2 + 2u1

[plain osprey]

I understand that

[plain osprey]

The answer to this is yes?

Kk

Ty

[alpine nacelle]

Yes, in fact you can define linear independency of u1, u2, u3 like this: au1+bu2+cu3 = 0 implies a = b = c = 0

Which is not the case for your vectors

[plain osprey]

Thanks again!

[supple timber]

Bro 0.1 = 1/10

really?

this is very easy

[vapid yew]

thenn?

[quick prism]

Question

[woven dock]

Question?

[quick prism]

I was trying to put the pic😅

[woven dock]

Oh

[quick prism]

Can you help?

[woven dock]

Like draw two overlapping circles?

P(Prom)=0.85
P(Grad)=0.35

[quick prism]

Ya

[woven dock]

Good

Now it's your turn to draw

[quick prism]

Is it supposed to be a two circle Venn diagram or a three

[alpine nacelle]

Two

Prom and Grad are you two events

[woven dock]

Hello Mélo

[alpine nacelle]

Hello

[finite scroll]

help

[quick prism]

Ya I don’t know where to put the given information into the Venn

[quick prism]

Would prom be on the left side and head on the right and both in the middle

I’m not understanding the question at all

[opaque oxide]

10?

[finite scroll]

10?

the answer is 5472

but idk why

[opaque oxide]

i thought this was sets

[finite scroll]

oh is this channel already being used?

my bad

[opaque oxide]

i thought u were asking about sets

[finite scroll]

nah

the question is asking how many permutations in that word

so how many ways can you arrange the letter that make it up

[wary stream]

Are you sure this is correct answers?

[alpine sable]

If x_1,...,x_n are n distinct numbers, find a polynomial fuction f_i of degree n-1 which is 1 at x_i and 0 at x_j for j not equal to i.

[cold sky]

Can i ask my question here?

[glass lichen]

No

It's clearly in use

[alpine sable]

I been stuck on this, the problem gave a hint. The product of all $\prod_{j=1}^{n} (x-x_j)$ is 0 when x = x_j. Which of course is true, but I am not sure how I could use that to solve the problem.

[ocean seal]

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

[alpine sable]

That close enough, any tips on how to handle this?

[naive bobcat]

Read and analyze the following problems. Tell whether the problem is a routine or non-routine problem then
solve. Use RGESA steps in solving routine problems and use the UPER steps in solving non routine
problems.

____________1. Rica’s allowance everyday is 200 pesos. She spends 1/2 of it for her recess and lunch and
1/4 of it for transportation fare. The rest is her savings. How much is her saving everyday?

____________2.The teacher gave 3/4 full box of pizza to be shared equally to his 4 students. How many
pizza will each of them receive?

[glass lichen]

Cause one of the factors will be 0...

Or is that not the problem?

[ocean seal]

xie

[alpine sable]

FIFY

[naive bobcat]

can someone please help me?

its 28 days overdue

and

if i dont pass it tommorow

[stone minnow]

Ok so there are two types of animals, which are dogs and birds

[naive bobcat]

i am doomed

[finite scroll]

yeah

[stone minnow]

Dogs accounts for 1/3

So how many birds

[naive bobcat]

2?

[stone minnow]

Correct, 2/3 of the animals are birds

Sp plug in the value 18

There are 6 dogs and 12 birds

[alpine sable]

🐶 🐶 🐶 🐶 🐶 🐶 <- Each has 4 legs.
🐦 🐦 🐦 🐦 🐦 🐦 < - Each has 2 legs.
🐦 🐦 🐦 🐦 🐦 🐦

[naive bobcat]

soo the answer is? this?

for the 3rd question?

But it said use the rgesa steps?

[stone minnow]

Refer the mr.xie, 4x6+2x12 = 48

[naive bobcat]

i am confused

[supple timber]

what is the 3rd question

[naive bobcat]

and i need to show work...

that i didd it...

this is too stressfull

[supple timber]

36 legs for dogs and birds

[alpine sable]

You just got the number of DOGS and BIRDS.

Now you need to count the number of legs for all and that would be your answer.

Read the question slowly and carefully, again, if you are still puzzled.

[wary stream]

Don’t give answers

[alpine sable]

It’s problem 6a.

That is the problem I was talking about.

[naive bobcat]

nvm

i'll just do it yself

there

are too many people

saying it

makes me confused a bit

Required
Given
Equation
Solution
Answer

[supple timber]

no

[naive bobcat]

Rgesa?

[stone minnow]

Eh did you calculate wrong

[supple timber]

is directly proportional

[stone minnow]

.

[supple timber]

6/4 6/2

[naive bobcat]

ummm

[wary stream]

What?

[supple timber]

LMAO

opps

[alpine sable]

The given condition i is not equal to j does it mean for any given pair of distnict number x_i, and x_j the polynomial function must be 1 for x_i and 0 for x_j. The hint showed a way given for x_j but I am confused.

[naive bobcat]

sooo

i saw the example

and i have to do it like this

Allysa gave 3/4 of a pizza to her friends, Kyla and Marie. Kyla ate 1/4 of the pizza. Marie also ate 1/4 of the pizza. How much pizza was left?
R- How much pizza was left?
G- 3/4 , 1/4 ( Kyla) , 1/4 ( Marie)
E- 3/4 - ( 1/4 + 1/4 ) = n
S- 3/4 - 2/4 = 1/4 A- 1/4 pizza was left.

.......

[wary stream]

That’s just showing your work in a step by step process

[alpine sable]

How would I answer this

[potent pebble]

do you know power rules?

[alpine sable]

If you do not know law of exponents

then try expanding the powers

[velvet condor]

given that $(x,y)=1;xy|x^2+y^2+1$
prove that xy-1 is a square number

[ocean seal]

Minh Baka

[velvet condor]

bruh ty for pinging for me

[stone minnow]

You need to know a rule that n^a * n^b = n^(a+b)

And this is one of the power rules they are talking about

So basically the answer is 3 ^ (4+6-2-5) = 27

[jovial sky]

What do i do next to simplfy further

Do i mutiply everything by 2?

[fringe socket]

11

does anyone know why does bkj = Ajk

[jovial sky]

I need to simplfy it till this format

I got to this step

Dont know what next

[velvet condor]

try to create the form a^2-b^2

by multiplying something to the denominator

[distant gate]

Minh

Can u help me or busy?

[alpine sable]

You can post your question in any of the questions channel or topic channels and get help.
Feel free to ping @ helpers after 15 minutes if you get no replies.

[jovial sky]

Oh

Ty

[sonic wyvern]

im trying to solve this

i completed the square and made all my substitutions

and i end up with 9 * integral(sec(x)tan^2(x) dx)

how do i solve that integral

[velvet condor]

watch it

hmm

sinh-1 involved

[royal meadow]

let s = sec(x), t = tan(x)

[sonic wyvern]

wolfram says so, but it isnt

at least not the way im supposed to do it

[velvet condor]

oh-

[royal meadow]

it's because you can sub in u = cosh(x) or whatever

[sonic wyvern]

yeah

[royal meadow]

cosh^2(x) - 1 = sinh^2(x)

but anyway

watch this

[sonic wyvern]

we dont use hyperbolic functions in my class

[velvet condor]

i mean

you can simplify it

what does wolfram say

,w integrate (x^2+6x)^(1/2)

[ocean seal]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Minh Baka#9435

[sonic wyvern]

idk my wolfram is broken. it only shows me the first step of the step-by-step

even tho i bought the subscription

[royal meadow]

integral st^2 = integral s(s^2 - 1) = integral s^3 - s

integral s is something you should know

[sonic wyvern]

yes

[royal meadow]

integral s^3

[velvet condor]

,w simplify sinh^(-1)((x/6)^(1/2))

[royal meadow]

ffs

[ocean seal]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Minh Baka#9435

[sonic wyvern]

its the s^3 that im stuck on

[velvet condor]

easy game

[royal meadow]

ok well s^3 is classic

[velvet condor]

i suppose they are referring to ln

[royal meadow]

integral s^3 = integral s(s^2) = st - integral st^2 again

so basically integral st^2 = integral s^3 - integral s = st - integral st^2 - integral s

so integral st^2 = 0.5(st - integral s)

probs shoulda latexed it but you got that right

[sick ledge]

another dumb question why is displacement equals to (vf-vi)/2*t?
isnt it more appropiate to remove the /2?
like vf = vi + at
and you gain extra x amount of m/s within one t
isnt that you get like in 2t time,
you get vi + vi + of displacement which is vi + vf in one t?

ping me if you are willing to help!
anyone who sees this message will get blessed

[sonic wyvern]

yes thank u

[desert moon]

not sure how to do this after subbing the identity in

[analog delta]

@ionic jewel peut tu maider?

[ruby ether]

is this channel free?

if it's free, hi i just wanted to ask about this question, i may have forgotten about maths for few months but could some1 teach me about this

[sand geode]

hi @ruby ether

[ruby ether]

hi :3

[sand geode]

so Ø is symbol for empty set

a set within another set is called a subset

and curly braces {} are used to enclose contents of a set (also known as elements)

[leaden ocean]

The empty set is the set {}

You can think of it as an object of the form a if that helps and rewrite all these equations. that should add more clarity

[sand geode]

thank you @leaden ocean

[leaden ocean]

so like for the first and second line
a = {a}
$a \in {a}$

I think this is a more clear question. and the same to my understanding follows for the other lines

[ocean seal]

matthew

[ruby ether]

let me process ......

so uh.....

[ruby ether]

if you would've given me a hint, the first line is true and second line is also true?

correct me if im wrong, bcs i could have just processed it by how u interpret it to me xDD

[sand geode]

Let's make it simple.
Let F be a set of fruits
F = {banana, orange, apple, lemon, mango}
Now banana is an element of the set F. This is denoted banana∈F

And let A be a set of acidic fruits
A={orange, lemon}

We know that set A is also an element of set F [denoted A∈F] because all of the elements in A are in F.
OR
A is a subset of set F [denoted A ⊆F] because the whole set A can be found in F

In other words, we can rewrite set F as
F={banana, apple, mango, {A}}