help-0

[fresh parcel]

so x would just be 1

[alpine sable]

what answer did you get for 3 ?

[fresh parcel]

oh wat

sus

[amber sage]

60?

[alpine sable]

good, because for 3 it's just an equilateral triangle

then, what about k = 4

[scarlet shell]

So answer is e^3(cos1 + i sin1) ??

[fresh parcel]

im pretty sure

[amber sage]

90

[fresh parcel]

i dont know though maybe you should ask someone else as well

but im pretty sure thats right

[amber sage]

hmm

[scarlet shell]

But it says compute real and imaginary

[amber sage]

oh

[bronze loom]

guys i know its a dumb question but

[alpine sable]

right, cause here it's a square, then keep on going with k = 5 and so on

[bronze loom]

is the "?" = 90-25?

[fresh parcel]

oh

what if you distribute it though

[amber sage]

oh i think i might get it

[alpine sable]

good, then you'll see by rounding the number you'll be getting closer and closer to 180 and you know it cant get over that, so you'll stop there

[fresh parcel]

now the second one

[amber sage]

oh i just need to go up and count until its 180

i see now

[fresh parcel]

ah

my bad i dont know how to solve that one

[scarlet shell]

Dont have any idea about 2nd one

[amber sage]

wait

[fresh parcel]

the third one would be the same with some minor adjustments

[alpine sable]

i just compute it, it might be long, but at some point you'll see the increase one degree by one, there you can deduce all the following degrees until 180 will eventually be there

[amber sage]

ok i see

[grizzled pagoda]

Can someone help with these algebra problems I just need help getting started and finding the equations

[alpine sable]

if you dont tell us what these problems actually are, noone cant really help

[scarlet shell]

Maybe i should do multiplcation with 2nd one

[amber sage]

the answer is 26 right?

[scarlet shell]

Any idea in b? <@&286206848099549185>

[grizzled pagoda]

nvm thanks tho

[alpine sable]

a bit higher than that

[amber sage]

umm

[alpine sable]

not a native english speaker, rounded off means getting the closest integer or the one below it ?

[amber sage]

closest integer

[alpine sable]

then you get 14 different values first, then you're at 158 and it start increasing one by one (all the others will follow

so 159 is the 15th value of n, 160 is the 16th, (...) 170 is the 26th, (...), 180 is the 36th

[amber sage]

i got 16 different values then at 160 it increases one by one so i added 20 to it

oh

[alpine sable]

you mistyped then, you wrote 26 instead of 36, but you got the write answer 😉

[amber sage]

i made a stupid mistake lol

yea thanks for your help

[fresh parcel]

maybe try using trig identities

sum identity gets you sin(1)cos(i) + cos(1)sin(i)

wait no

[alpine sable]

you know that cos(t) = ( exp(it)+exp(-it) )/2, this can be used with t = 1+i

[fresh parcel]

but its sine

i have a question

if q (a positive integer) can be expressed as the sum of two squares, prove that 5q can also be expressed as the sum of two squares

[alpine sable]

no problem, sin(t) = ( exp(it)-exp(-it) )/2

do you know cosh and sinh or not?

[fresh parcel]

no

[alpine sable]

would have just made things easier, but still you can use the 2 formulas i just gave

correction after mistyping : sin(t) = ( exp(it)-exp(-it) )/2i

[fresh parcel]

the problem was from another guy

[alpine sable]

you can get them from exp(it) = cos(t) + i sin(t) btw

[fresh parcel]

okay

[alpine sable]

i guess i'm getting a bit to tired mixing questions asker and answerers lol

[fresh parcel]

lol

[fresh parcel]

still confused about this one though

i finished the first part which proved 2q is the sum of two squares

[alpine sable]

Question : Ok so I have a game I and I have a problem to calculate a thing. I have 25 stages and they are randomely generated and each stage has a number from 1-25 respectively. Now each game have 6 stage generated randomely. So how many stages can be generated randomely?

For example
{1,3,5,2,1,5}
{7,21,4,4,2}
Like this tables above how many tables can be formed?

[fresh parcel]

uh

25^6?

[alpine sable]

@alpine sable I know i can be an asshole sometimes on purpose, but i dont want to help someone who just spammed the 10 help topics

[alpine sable]

tonk for ur answet

[magic lodge]

hello, I have a qns. 4^x+2 = 32^x ------- why isn't it x = 1 ?

[magic geyser]

Read #help-6

@alpine sable

[buoyant kayak]

$4+2\neq 32$

[ocean seal]

a disappointing son

[dusk tiger]

Hey I’m having some trouble with 2 questions in my math homework.

It wants me to solve these
3/x + 6 = -45
x-2/5 = 10-x/8

But I’m not quite sure how to go about it

[buoyant kayak]

isolate x

[flint badger]

@dusk tiger What's the first step in isolating x

[buoyant kayak]

in the first one, what would you do first?

[dusk tiger]

If it’s = would I subtract the -45?

So -51

[buoyant kayak]

?

[flint badger]

You're not subtracting -45

[buoyant kayak]

you want x on one side by itself

[dusk tiger]

Would I subtract the 6 from the -45

[buoyant kayak]

yes

[flint badger]

Subtract 6 from both sides is what you should say

[buoyant kayak]

that would be the first step

[flint badger]

What is the equation now equal to

[dusk tiger]

3/x = -51

[flint badger]

Ok now

Let's try to get rid of the fraction

How can you do that?

[fresh parcel]

<@&286206848099549185>

[dusk tiger]

Would I have to divide since x is on bottom?

[flint badger]

Divide by what?

[dusk tiger]

3

[flint badger]

No you wouldn't want to do that

[blazing rose]

well if q can be represented as the sum of 2 squares, a^2 + b^2 = q

[flint badger]

In order to get rid of the fraction, you need to use an operation that's the inverse of a fraction (which is dividing)

[fresh parcel]

yes

[dusk tiger]

So would I have to divide by X?

[magic geyser]

Btw next time please don't help someone who posted in every channel, which would be unfair to the other people who are wiaitng to get helped.

[flint badger]

Ok @dusk tiger

3/x is dividing right?

It's the same as saying 3 divided by x

[dusk tiger]

So wait

[flint badger]

What's the opposite of division?

[fresh parcel]

Also, I proved before that 2q is the sum of (a-b)^2 + (a+b)^2

[dusk tiger]

Multiply

[flint badger]

Exactly, so we would multiply both sides of x

The reason is

$\frac{3}{x}\cdot :x$

[ocean seal]

eggdog

[flint badger]

Gives you 3x/x

Do you see that?

[blazing rose]

but how does that help u prove that 5q = a^2 + b^2

[fresh parcel]

when you distribute the sums cancel out and you end up with 2(a^2 + b^2)

i have no idea

thats the second part of the problem

[flint badger]

I should probably do it like this

$\frac{3}{x}\cdot \frac{x}{1}$

[ocean seal]

eggdog

[flint badger]

You see how it becomes 3x/x right

[dusk tiger]

So then if I divide that by 3 it’d isolate the x?

[flint badger]

No

We can isolate later

You want to get rid of the fraction first

[dusk tiger]

Ok

[flint badger]

Multiplying by x on both sides will do that

Because 3/x will become 3x/x

and x/x is just 1

So on the left side it'll be 1, but on the right side we multiplied -51 by x

[dusk tiger]

Oh

[flint badger]

$\frac{3}{x}\cdot \frac{x}{1}$ So here's what that step looks like again

Oops wrong one

$\frac{3}{x}\cdot \frac{x}{1}=-51x$

Bruh

[ocean seal]

eggdog

[flint badger]

There we go

If you simplify the left side what do you get

@dusk tiger

[dusk tiger]

3x/x

[flint badger]

Which is?

[dusk tiger]

1x

[flint badger]

Remember

x/x = 1

[dusk tiger]

3x

[flint badger]

x/x = 1 so it's just

3 * 1

$\frac{3x}{x}$

[ocean seal]

eggdog

[dusk tiger]

So then divide both sides by 3 to isolate it

[flint badger]

That won't isolate x though

And remember we want to get rid of the fraction before we isolate

Ok after we multiply both sides by x the x's will cancel out and it'll just be 3 = -51x

[dusk tiger]

Omg this is so confusing lol

[flint badger]

$\frac{3}{x}\cdot \frac{x}{1}$

[ocean seal]

eggdog

[flint badger]

do you see why this gets rid of x? @dusk tiger

[dusk tiger]

Uh

No

[flint badger]

After we multiply

It will look like this

$\frac{3x}{x}$

[ocean seal]

eggdog

[flint badger]

You know that right

[dusk tiger]

Yes

[flint badger]

What is x/x

[dusk tiger]

X

[flint badger]

x/x isn't x

When you divide a number by itself what do you get?

[dusk tiger]

Well when you multiply it’d be squared

[blazing rose]

paige

whats 2/2

[dusk tiger]

A whole

[flint badger]

You mean 1 right

2/2 = 1

The same applies for x/x lol

x/x = 1

[dusk tiger]

Yes

OH

[blazing rose]

LMAO

[dusk tiger]

OHHHHHH

[flint badger]

lmao

[blazing rose]

easy peasy lemon squeezy

[flint badger]

$\frac{3x}{x}$

[ocean seal]

eggdog

[flint badger]

this evaluates to 3 * 1

or just 3

[dusk tiger]

Ok tysm 😂

[flint badger]

do you see why now lol

[dusk tiger]

Yes

[flint badger]

Ok now the equation looks something like this

3 = -51x

what can you do to isolate x

Now that we got rid of the fraction

[dusk tiger]

Divide by -51

[flint badger]

Remember to say on both sides

But good

[dusk tiger]

Ok thank you so much

[flint badger]

$\frac{3}{-51}=\frac{-51}{-51}x$

Yeah, and then just simplify that

[dusk tiger]

Kk

[ocean seal]

eggdog

[flint badger]

Should probably do that so it makes more sense

[dusk tiger]

Got it

Thank you

[flint badger]

What'd you get

[dusk tiger]

-1/17

[flint badger]

Good

Ok now for the second problem

Now that you know it'll be easier lol

[dusk tiger]

Yes 🙏

[flint badger]

x-2/5 = 10-x/8

Ok just a question

[fresh parcel]

i tried splitting it up into 4q and q but that gets me nowhere

[flint badger]

$\frac{x-2}{5}=\frac{10-x}{8}$

[ocean seal]

eggdog

[flint badger]

Does it look like this?

$x-\frac{2}{5}=10-\frac{x}{8}$

Or is it this

[ocean seal]

eggdog

[dusk tiger]

Now time for the other assignment 😂

[flint badger]

Oh did you already complete it?

[dusk tiger]

Only had 3 things to do

[flint badger]

The question that I just posted

Ah ok

[dusk tiger]

Oh that

Yeah I did it

[flint badger]

What'd you get

[dusk tiger]

X = 66/13

[flint badger]

Great

[fresh parcel]

find the area of the current enclosure first

so 35 x 18

[pale tartan]

yeah

[fresh parcel]

then set up the equation: (35 + x)(18 + x) = 2(the area of your current enclosure)

then itll be easy

oh wait its a quadratic lmao

okay just use factoring or quadratic formula

if you can

[pale tartan]

okay imma try it

[fresh parcel]

it shouldnt be too hard

[frozen moon]

If it’s not too much trouble, can someone help me with this

[mossy lion]

First use the binomial theorem to find expressions for lambda_k and mu_k. Then use those expressions and the other givens to solve for a.

[frozen moon]

im not so sure but im going to assume lambda_k and mu_k are the weird symbols

[mossy lion]

$\lambda_k,\quad \mu_k$

[ocean seal]

nix (@ me for the love of euler)

[frozen moon]

ah i see

ayt gimme a min

so is this enough or to i need to express more of the 2 equations

oh wait

i think im starting to see smth

thx nix!

[late parcel]

Is this channel open

[frozen moon]

i think so

[late parcel]

29 where am I going wrong

This question is driving me crazy

[frozen moon]

wait what chaper is this

chapter*

[lapis sluice]

what is an extreme value?

[late parcel]

Chapter 5

@lapis sluice yes

[frozen moon]

i mean like

what is it teaching

[late parcel]

Extrema

Values

[frozen moon]

is quadratic formula?

hmmmm

[late parcel]

No

What

This is Calc AB

[frozen moon]

ah i see

[late parcel]

Application of derivatives

[lapis sluice]

extreme value is the functions greatest value?

im not studying math in english

[late parcel]

Yes I know that

[frozen moon]

in that case i cant help ya yet, we just started module 2 maths so i dont now much myself

sorry :/

[late parcel]

Np

[frozen moon]

gl with ur question tho!

[late parcel]

I’m going something wrong I think

[lapis sluice]

so where the derivative is 0 and the graph is increasing ok

i get it

i will have a look at it

[late parcel]

Thx

[sudden crater]

Will this channel be free soon?

I doubt people look at that channel though

idk

[lapis sluice]

ok, in our country we just say evaluete the monotonic properties of the function "lambda", we dont say extreme values xD

[late parcel]

Ok

So any idea where I messed up

[lapis sluice]

dont write the exponent as (-1) it makes it harder, write it as a fraction

then derivate with chain rule

[late parcel]

I checked my derivative and it is correct

That’s not where I messed up

[lapis sluice]

then the derivative should be something like $\frac{-x^2+1}{x^4+2x^2+1}$

[ocean seal]

Danajax

[lapis sluice]

it that what you got?

[late parcel]

Yes

[lapis sluice]

good

so figure out when the rate of change is 0

[late parcel]

-1, 1

[lapis sluice]

yes, seems correct

+-1

[late parcel]

Yep

[lapis sluice]

$\pm1$

[ocean seal]

Danajax

[lapis sluice]

so what's your problem then?

[late parcel]

Finding the Y value

That is the answer

And idk how to get it

[lapis sluice]

you dont know how to get the y value?

you have the x values though, so what is the issue?

[late parcel]

The answer has the Y value

I need to be able to find them

[lapis sluice]

you need to plot the x values into the function f

[late parcel]

Yes and I don’t know how to tell which is a max and which is a min

[lapis sluice]

for x = 1 $\frac{1}{1+1} = \frac{1}{2}$

[ocean seal]

Danajax

[late parcel]

Yes

Got it

[lapis sluice]

the maximum is the one with the greates x value, and min with the smaller value

[late parcel]

How do you tell that

[lapis sluice]

or you could derivate for x = 1/2, x = 3/2, x = -1/2 and x=-3/2, which will also tell if something is a top or bottom on a function

[lapis sluice]

how i tell that something is a top-point?

[late parcel]

Ya

[lapis sluice]

derivate for x = 1/2, x = 3/2, x = -1/2 and x=-3/2, which will also tell if something is a top or bottom on a function

or look at the y values

the function has to have an "extreme" point if the derivate is 0, for which we already found corresponding x values

[late parcel]

Thx

Got it

[earnest solar]

If 36 and 48 are the two smaller numbers in a Pythagorean Triple, what is the third
number?

answer it

urgent

[wary stream]

Just use pythagorean theorem

[upper bone]

Hi, can anyone help me?

[slate mesa]

60

[upper bone]

|x+2|+|x+1| = E(x)

[lapis sluice]

sure #help-1

[upper bone]

Ok

[glass lichen]

Don't give answers

[wary stream]

Don't give answers

[slate mesa]

oh sorry

i havent memorised the formulas and i have no idea how to do this

this is the ans

[wary stream]

Draw a triangle

[earnest solar]

how @slate mesa

[wary stream]

Like I said, pythagorean theorem

[earnest solar]

explain and write it

pls

urgent

[wary stream]

Do you know what pythagorean theorem is?

[warm brook]

is this for an exam

[earnest solar]

ya

[earnest solar]

obvio

[wary stream]

You know that cos = adj/hyp

[wary stream]

Then use that concept

[warm brook]

yeah no, that’s not allowed here

[earnest solar]

can't

[warm brook]

if you meant exam

[wary stream]

Also, you can't get help on exams

[earnest solar]

apply t

help

[slate mesa]

how do i know if its in 2nd or 3rd quadrant?

[wary stream]

ASTC

[slate mesa]

but both 2 and 3 have negative cosine

[earnest solar]

guys pls

[slate mesa]

so is it in 2 or 3?

[wary stream]

If this is an exam, you cannot get help for it

[earnest solar]

pls me

it's tom

bruh help now my exam tom

[wary stream]

I told you, pythagorean theorem

[earnest solar]

true

[wary stream]

Figure it out from there

You have two values, use them

[earnest solar]

write the answer

[wary stream]

No

[lapis sluice]

no!

[wary stream]

Not my job

[earnest solar]

pls

my exam tom

i am tensed

[lapis sluice]

stop begging for answers, figure it out yourself

[wary stream]

This is not the place to be getting answers

[slate mesa]

c = sqrt (a^2 + b^2)
sub in 36 = a and 48 = b

[lapis sluice]

spend 5 mins on your own and you will figure it out

[wary stream]

You figure it out yourself, using the info given

[late parcel]

Is this channel open?

[lapis sluice]

yah

[late parcel]

Just need help taking that derivative

Where am I wrong

On 24

x^1/3 (x+8)

Product rule

[wary stream]

If you know that cos = adj/hyp and hyp = sqrt(x^2 + y^2), that means hyp is going to most likely be positive meaning that the negative sign goes with value in numerator. So that means (-1)/3

[lapis sluice]

do you have knowlegde about chain rule

[late parcel]

Yes

[slate mesa]

like this? I dont have a very good grasp of ASTC

[earnest solar]

thanks i got it

[slate mesa]

wait omg calc err

[slate mesa]

ok i get it now, tysm!

[lapis sluice]

did your answer look something like $g'(x) = \frac{2x+8}{3\sqrt[3]{x^2}}$

[ocean seal]

Danajax

[lapis sluice]

@late parcel

[slate mesa]

whats the formula of decomposition of improper fraction into partial farctions? i cant find it on google

is it just long division

[lapis sluice]

is there a formula, i just do it in my head xD

[jade frigate]

hi

[slate mesa]

i mean like improper fractions of polynomials

[lapis sluice]

such as?

[jade frigate]

guys is dis da answer u need

[slate mesa]

ax^3 + bx^2 + cx + d/ax^2 +bx +c

or the denominator can be factorised too

[jade frigate]

im only in grade 6 but i almost mastered deriatives

ok so

[lapis sluice]

have you learned about complex numbers

[slate mesa]

nope

[lapis sluice]

oh ok, pretty much lets you factorize anything

[slate mesa]

i was wondering if there was a version of this for improper fractions

[lapis sluice]

that didn't answer your question at all though sorry

oh ok

i never learnt that

you just need to attempt to factorize i suppose

[slate mesa]

its ok, i think i can manage with long division and factorisation. Thanks though!

[lapis sluice]

good luck

[ocean seal]

Chai T. Rex

[oak chasm]

See this ^

[slate mesa]

ohh so the formula is just the same but adding another factor D behind?

[oak chasm]

Sorry, three variables.

A, B, and C.

[late parcel]

Is this channel open?

[lapis sluice]

no try #help-2

[oak chasm]

You'll get three simultaneous equations and A, B, and C to solve for.

[slate mesa]

ohh alright thanks alot!

[oak chasm]

No problem.

[glass estuary]

Hello I need help with question 8 am I understanding the question correctly?

So the question is invalid

[alpine sable]

d=-3

[oak chasm]

@glass estuary I'd take it to mean that the total decrease is 3 per row.

Oh, never mind.

On each end.

[glass estuary]

I thought it was 3 per row too and then I saw that part

And the answer on the back page is 3549 for some reason

[oak chasm]

It appears they're adding 3 instead of subtracting 3 each row.

@glass estuary ^

[glass estuary]

Damn

Thanks

[oak chasm]

Sorry, instead of subtracting 6.

No problem.

[glass estuary]

I'm losing faith on my text book each day

[late parcel]

Is this channel open

[alpine sable]

Hi, I'm wondering why (8x - 2)(3x - 1) is
8x * 3x + 8x * (-1) - 2 * 3x -2 * (-1)?

[oak chasm]

@alpine sable The distributive property.

(a + b)(c + d)
(a + b)c + (a + b)d
ac + bc + ad + bd

[alpine sable]

(a + b)(c + d) = ac + ad + bc + bd

[oak chasm]

See how I used the distributive property three times?

[alpine sable]

nvm

hold up

[alpine sable]

I see, but why does this happen

[oak chasm]

Well, let's go over the distributive property.

x(y + z)

[alpine sable]

ye

[oak chasm]

You take what the parentheses are being multiplied by and you multiply it by the terms in the parentheses.

x(y + z) = xy + xz.

[alpine sable]

yes

[oak chasm]

So, (a + b)(c + d) = (a + b)c + (a + b)d.

This is because (a + b) is just a number that's multiplied by the (c + d) parentheses.

Just like x was before.

Does that part make sense?

x(y + z) = xy + xz, so whatever is in front of the parentheses is what you multiply y by and what you multiply z by.

[alpine sable]

I get this

[oak chasm]

OK, so (a + b) is some number just like x is.

[alpine sable]

Why (a + b)c + a + b)d tho

[oak chasm]

Because you have this:

x(y + z) = xy + xz

And you do the same thing here:
(a + b)(c + d) = **(a + b)**c + **(a + b)**d

Whatever is multiplied by the parentheses, no matter how complicated, gets multiplied by each term in the parentheses.

[alpine sable]

ohh

[oak chasm]

Does that part make sense so far?

[alpine sable]

Sort of

nvm i got it

[oak chasm]

OK, now we do the same thing.

We have (a + b)c + (a + b)d.

(a + b)c = ac + bc.

Whatever's multiplied by the parentheses gets multiplied by each term in the parentheses.

Does that make sense?

[rapid coral]

help, i need create a equation

[oak chasm]

@rapid coral Sorry, this channel is busy.

[alpine sable]

Yeah

[oak chasm]

Step 1:
(a + b)(c + d)
**(a + b)**c + **(a + b)**d

Step 2:
(a + b)c + (a + b)d
ac + bc + ad + bd

[alpine sable]

I got it

[oak chasm]

OK 🙂

[alpine sable]

It looked really messy at first

But now i understand it, thank you.

[oak chasm]

You're welcome.

[alpine sable]

24^2 - 14x + 2 right?

[oak chasm]

Yes, except with an x² in the first term:

(8x - 2)(3x - 1)
**(8x - 2)**3x - **(8x - 2)**1

(8x - 2)3x - (8x - 2)1
24x² - 6x - 8x + 2

24x² - 14x + 2

[alpine sable]

yeah

24^2

[formal fossil]

solve the equation f′(x) = 3 if f(x) = x^3.

hi guys, can anyone help me with this

[mortal palm]

Im pretty sure you just plot your points but add 3 eg 1 is 1+3, 2 is 8+3, 3 is 27+3 etc

[brave forge]

Or differentiate f(x) and solve for f'(x) = 3

[mortal palm]

Also could anyone help explain how to find the area of the outer blue circle

[slim fog]

Can someone help me derive that a•b=length(a)length(b)cosθ, knowing that a•b=a_x b_x+a_y+b_y?

[tight locust]

think about it from a physical perspective

W = F.d

the maximum work is done when the force is entirely in the direction of the displacement

[void anvil]

Please help explain how it got the answers on the right.The symbol is supposed to be Pi

[tight locust]

and the minimum work is done when it is perpendicular

so it must be proportional to cos(theta)

[slim fog]

Thanks for the intuiton but I am interested how to derive this from the other definition of the dot product

[glass lichen]

https://math.stackexchange.com/questions/509719/proof-of-equivalence-of-algebraic-and-geometric-dot-product

[tight locust]

express the components in terms of the magnitudes of the vectors

basic trig

[slim fog]

Oh so a_x=acosθ

And so on?

[glass lichen]

The Stack post I gave you does the derivation in R^2, going to R^3 just uses spherical co-ordinates, but follows the exact same process.

in R^4 and further the geometric formula starts to lose it's grounding, cause we then define the "angle b/w 2 vectors" as arccos(stuff)

[tight locust]

(a_x, a_y) = (acos(theta_a), asin(theta_a))
(b_x, b_y) = (bcos(theta_b), bsin(theta_b))
a.b = abcos(theta_a)cos(theta_b) + absin(theta_a)sin(theta_b)
a.b = ab(cos(theta_a - theta_b))

you just have to use the identity:

cos(x-y) = cos(x)cos(y) + sin(x)sin(y)

i'm pretty sure that you can derive this on the spot with euler's formula

exp(i(x-y)) = exp(ix) * exp(-iy)

cis(i(x-y)) = cis(x) * cis(-y)

cos(x-y) + isin(x-y) = (cos(x) + isin(x))(cos(y) - isin(y))

cos(x-y) + isin(x-y) = cos(x)cos(y) - icos(x)sin(y) + isin(x)cos(y) + sin(x)sin(y)

compare real and imaginary parts

cos(x-y) = cos(x)cos(y) + sin(x)sin(y)

[steady fern]

bruh

[short night]

i need help?

[tight locust]

exp(iz) = cosz + isin(z)
exp(-iz) = cos(z) - isin(z)

exp(iz) + exp(-iz) = 2cos(z)
(exp(iz) + exp(-iz))/2 = cos(z)

exp(iz)-exp(-iz) = 2isin(z)
(exp(iz)-exp(-iz))/2i = sin(z)

cos(x)cos(y) = (exp(ix)+exp(-ix))/2 * (exp(iy)+exp(-iy))/2 = 1/4(exp(i(x+y)) + exp(i(x-y)) + exp(i(y-x)) + exp(-i(x+y)))

sin(x)sin(y) = -1/4(exp(i(x+y)-exp(i(x-y)-exp(i(y-x))_exp(-i(x+y))

cos(x)cos(y) + sin(x)sin(y) = 1/4 ((exp(i(x+y)) + exp(i(x-y)) + exp(i(y-x)) + exp(-i(x+y)) - (exp(i(x+y)-exp(i(x-y)-exp(i(y-x))_exp(-i(x+y))) = 1/2(exp(i(x-y)) + exp(-i(x-y)) = cos(x-y)

[short night]

bruh

[still violet]

Hello

In terms of probability and machine learning, may I ask what is the difference/meaning of:

P(C1 | x)

and

p(x | C1)

C1 is just a class to classify in ML context

So, what is the difference between the capital P and p?

[vocal olive]

help factorizing
2x^2 - 2x - 9 =0

i think i can use psf

with product being 18

and sum being -2

but idk how to get a number that satisfies those criteria

is there a trick or something?

sorri fo dumb question, i just really wanna pass the upcoming exams :(

[wary stream]

Quadratic formula could be used

[vocal olive]

ik

but can it be factorized?

because thats also coming in the exams

[wary stream]

No

[vocal olive]

how do u know?

[wary stream]

Because I just did it

It's not factorable by hand

[vocal olive]

yea ok, but how would u know

[wary stream]

So quadratic formula

I just did it

[vocal olive]

i need to be able to tell if it is factorizable or no

[wary stream]

It's not

[vocal olive]

how would i know though

[wary stream]

AC method

[vocal olive]

ac?

[wary stream]

Take A times C

[vocal olive]

yea

[wary stream]

Find the factors that add up to B

And in that problem, it's not possible

[vocal olive]

thats what i call psf

[wary stream]

Because A times C equals -18

And no factors of 18 can sum up to -2

[vocal olive]

ahhhhh

[wary stream]

Therefore not factorable by hand

[vocal olive]

so u look at the factors and what they add up to

[wary stream]

So quadratic formula

[vocal olive]

understood

[wary stream]

Yes

[vocal olive]

thx

[wary stream]

Factors of 18 are 1, 2, 3, 6, 9, and 18

1 and 18 doesn't equal 2, neither does 2 and 9 or 3 and 6

[vocal olive]

yea got it

thx buddy

[lapis sluice]

....................................................................................................................................................................................

Ok so we all know that Abel proved that there are no general formula of finding a solution for n > 5, therefore there should exist a general formula for 5th degree polonomials! I, mean why use complex numbers when you could use the general formula 😎 . Anyone care to share it? So it would be the ABCDEF formula?

[bold monolith]

If this channel isn’t taken, does anyone mind telling me what I'd do next with this formula as I'm unfamiliar what to do next after moving over the constant

[lapis sluice]

what is your problem?

[wary stream]

I think you have to solve for t

[lapis sluice]

yes use the general ABC formula

[bold monolith]

Where do I go next with the equation/formula in this case is the question after moving over the constant.

[wary stream]

You moved it the wrong way

[lapis sluice]

have you learned ABC-formula???

[wary stream]

It should be equal to 0

[bold monolith]

H(x) = 147, but do I really just set T to 0 in this case?

[lapis sluice]

we dont know

if t = 0

[wary stream]

You're solving for t

Like a regular quadratic

[ashen plaza]

when looking to see when a ball will be at a certain height using an equation, you can set the equation equal to that canstant then solve for that new zero

[lapis sluice]

i suppose he means that you are supposed to find $$-16t^2+100t-144 = 0$$

[ocean seal]

Danajax

[wary stream]

[lapis sluice]

then it is easier to proceed straight forward with abc-formula or divide by (-16) @bold monolith

[bold monolith]

I see, I'll try it from there on my own if thats the case since I get what you mean.

Thanks guys

[lapis sluice]

sure, let us know if you need more help

[wary stream]

I think dividing by 4 is the best, not 16

[rugged sphinx]

how do i find the range

[wary stream]

Because you'll end up with decimals

[wary stream]

If you can use a graphing calculator, use that

Plot it

[rugged sphinx]

i can´t, my teacher requests process

[lapis sluice]

yeh, makes sense as 100/16 $\in \mathbb{Q}$

[ocean seal]

Danajax

[mossy lion]

well you can use the fact that the highest degree is even and has a positive coefficient to get the upper bound

[lapis sluice]

^

[void anvil]

Help explain how it go those answers please

[mossy lion]

but tbh idk how youd get the lower bound without calculus

[lapis sluice]

inf(f(x))

[mossy lion]

unless this is a calc class in which case you should be able to find it

it might be kinda tedious since it means solving a cubic but theoretically its possible

[final karma]

if you create a new state with a density of 22,35 what could be the cuantity of homes in that state?

can somebosy help me?

or somebody that speaks spanish?

[wary stream]

Not enough info

[final karma]

here's a table

[lapis sluice]

privet, me llamo Ecuador

[final karma]

i'ts in spanish but i don't think it's important

[iron shuttle]

u looked asian

can u speak any other langs?

[wary stream]

If you're basing it off the avatar, that's probably not what the person looks like, the avatar just exists and doesn't have to represent the actual person

[lapis sluice]

haha yes, i'm european, if i would base it off your avatar then you would be a discord application

[iron shuttle]

u know

it feels different

talking to a asian about maths problems

its kind of racist

but asians are smarter i feel

[lapis sluice]

depends how you define smart, however this is a text channel for questions not discussions, so we should probably call it quits

[tardy plank]

after you factor how do you solve this to get 1?

[lapis sluice]

bad quality

my eyes are burning

[lapis sluice]

\upscale

ty thats better

[lapis sluice]

how do you get 1

and not 0

[tardy plank]

my bad It's actually 0

but how do you solve it to get 0 then?

[lapis sluice]

factoize

[tardy plank]

after I factored I got (x-y)/1

[lapis sluice]

yes

[tardy plank]

than when I plug in x I get 1 and when I plug in y I get -1

[lapis sluice]

1-1/1 = 0

[tardy plank]

omg thanks Idk what's wrong with me

but what does x not equal to y have to do with solving this prob

[lapis sluice]

np nothing is wrong with you, tbh i have never worked with limes that have mulitple variables, which is sort of wierd, because I have studied a lot of math

[tardy plank]

thanks @lapis sluice

[night geode]

How do I solve this? Do I have to use the Gaussian cofefficient binomial?

[lyric lily]

you can check where it's derivative=0 if the derivative has 3 roots check for the one for which there exist least minima and at that point gives the lower limit and upper limit is +infinity you can say by seeing its degree

[harsh ocean]

Any ideas?

Maybe summing bot h?

ok thx

[exotic dagger]

Can someone check if this is right?

woops instead of 6 x 10^9 and 7 x 10^9 its supposed to be 10^7

[harsh ocean]

i) 6·10^2, ii)(2/3)·10^8 ?

[exotic dagger]

Yes thats what I got at first but we also have this

[harsh ocean]

oh

looks ok to me

[exotic dagger]

phew

thanks :)

[tired drum]

If the y value was substituted as 75 how would you calculate x?

[quartz osprey]

what am i doing wrong hwere

[harsh ocean]

isnt it x^(-n-3)

2n-2-5n-7=-3n-9

then (1/3)(-3n-9)=-n-3

@quartz osprey

[vernal wind]

Hi can someone explain me what does the R2 value tells me in a polynomial trend line?

[alpine sable]

how do i make fraction binary

[karmic wraith]

like normal binary but you have a decimal place and each value is 2^-n

convert the fraction to a decimal first @alpine sable

[vague coral]

5/16 = 0,3125 = 3·10^{-1} + 1.10^-2 + 2.10^-3 + 5.10^-5

and then 10 = 2x5

[wary stream]

Convert the fraction to decimal and do the multiply by 2 trick I demonstrated before

[alpine sable]

ok

[wary stream]

This is decimal notation, not binary

[vague coral]

I know

[wary stream]

They asked for binary

[vague coral]

I know, read what I tried to do after that line

[wary stream]

That line after makes no sense since that's still a decimal value

[vague coral]

11001 = 1x2^4 + 1x2^3 + 1
I want to find a form like this

maybe that wont work

[celest flower]

;-;

:((

D:

0wo

UwU

[wary stream]

That's if you can see it, there is a mathematical way of do it instead of guessing powers of 2

[vernal wind]

<@&286206848099549185>

[wary stream]

The method for converting a base 10 decimal value to binary is just multiply by 2
$$7/16 = 0.4375$$
$$0.4375 \cdot 2 = 0.875$$
$$0.875 \cdot 2 = 1.75$$
$$0.75 \cdot 2 = 1.5$$
$$0.5 \cdot 2 = 1$$
Therefore $$0.4375_{10} = 0.0111_{2}$$
Because you read the value before the decimal point from top to bottom

[ocean seal]

dldh06

[alpine sable]

V

do i just add them

[wary stream]

Do you know what 0 + 0, 0 + 1, 1 + 0, and 1 + 1 results in binary?

[alpine sable]

1+1 is 10

0+0 is 0

1+0 is 1

but

does the first equation have a carrybit

[vague coral]

oh i forgot about this method

[wary stream]

So if 1 + 1 = 10, then the 1 is the carry bit

[alpine sable]

its over 6 digits

[wary stream]

It's like addition in base 10

[alpine sable]

see this is what I got for the first one

Is it right

Or is it not a carry it

Carrybit

[wary stream]

That's right

You did it correctly

[alpine sable]

Also u see the 2s

The bad e

Base

I keep the base right

So I put a 2 under it

[wary stream]

Yes

Put the subscript 2 to denote what base you're in

[alpine sable]

Is this right

Idk what 1+1+1 is

[wary stream]

To answer this, same concept applies with
1
+1

10
Both values were one bit but added created a 2 bit number

What's 1 + 1 + 1 in binary?

[alpine sable]

110?

Idk

[wary stream]

1 + 1 + 1 = 3

What's 3 in binary?

[alpine sable]

11

[wary stream]

So do you know how to take it from there?

[alpine sable]

So it’s c:1 110?

[wary stream]

Are you saying $111_{2} + 111_{2} = 1110_{2}$?

[ocean seal]

dldh06

[alpine sable]

Yea

[wary stream]

Then yes

[alpine sable]

But the 1 is a carry it

Bit

The first 1

To the left

Right

[rose cargo]

Could someone help me with a proof?

[wary stream]

Yes

[rose cargo]

Number 8

[alpine sable]

Bruh what’s wrong with me

I can’t answer 11011+10110

[wary stream]

What did you do?

[tight locust]

21121

[wary stream]

That makes it even more confusing since you didn't carry the bits

[tight locust]

haha

[wary stream]

That's not even right

1 + 0 = 1

Not 0

[alpine sable]

Idk

[wary stream]

Post the work

Let me see it

[alpine sable]

It’s 11011+10110

[wary stream]

Right to left, what's 1 + 0?

[alpine sable]

Wait

U do it right to left

[wary stream]

That's how math works

[alpine sable]

So I solve it from left to right but put the answer right to left

Oh

Wait nvm

I forgot what right was

[wary stream]

If you had
45
+55
You still do right to left

[alpine sable]

1+0 is 1

1+1 is 10 so I carried

[gaunt mulch]

Hi guys I’m looking to get really good at math and I’m in 9th grade what should I use?

[alpine sable]

1+0+1 is 10 again

[wary stream]

Yeah

[alpine sable]

So then what did I do wrong

[wary stream]

Khan Academy

[gaunt mulch]

Ok

Thx

[rose cargo]

Are you guys good with proofs in geometry H?

[wary stream]

That far left column, it's 1 + 1 + 1?

[rose cargo]

😦

[alpine sable]

Idk I’ll reqrite it better

Somehow got a different answer

[wary stream]

This is the answer

[alpine sable]

Really

[wary stream]

Yes

[wary stream]

,w 11011_2 + 10110_2

[ocean seal]

Results provided by WolframAlpha

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

Requested by dldh06#2659

[wary stream]

See 110001

[alpine sable]

Dam

,w 1010_2 + 110_2

[ocean seal]

Results provided by WolframAlpha

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

Requested by s8n#9333

[alpine sable]

Is the 1 always a carry bit

[wary stream]

If it's at the far left

Because it overflows

Like 6 + 9 = 15, technically the one is the overflow

[alpine sable]

Oh

,w 11100_2 + 10111_2

[wary stream]

Also only use this to check your work after you make an attempt

[ocean seal]

Results provided by WolframAlpha

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

Requested by s8n#9333

[alpine sable]

Yeah I am

So far I’ve done it all right

I got 1 more

[wary stream]

Wolfram is a powerful software

[alpine sable]

,w 100011_2 + 11110_2

[ocean seal]

Results provided by WolframAlpha

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

Requested by s8n#9333

[wary stream]

And I do suggest if you check your work, use #bots

So you don't blow up this channel with the bot

[inner sage]

Can someone help with how to solve B ?

[glass lichen]

how'd you solve a?

[wary stream]

http://www.sosmath.com/algebra/factor/fac12/fac12.html
Not sure if this is useful

[inner sage]

nvm, i think i got it. I was confused as how to solve it cause there were 5 terms instead of 4, but seems like its the same thing ? But ill just have 4 roots instead of 3 ?

[wary stream]

Yeah, the highest power normally denotes up to how many roots you have

[inner sage]

also, ive been using rational zero theorem, but it takes quite long

is it supposed to be ? Or is there a quicker way ?

ive been following the steps of organic chem tutor in https://www.youtube.com/watch?v=Iaq7z7reznM

[wary stream]

Finding the roots of any function that has a power greater than 2 is normally tedious

[inner sage]

ah ok

actually I do have a question lol. So is this correct so far ?

Do i have to do rational zero theorem again with this new equation ?

[inner sentinel]

how is this not 16

[wary stream]

What's the derivative of h(x)

[inner sentinel]

f'(g(x))g'(x)

[wary stream]

How are you getting 16?

[buoyant kayak]

are you by chance looking at the value for f(x) instead of f'(x)

[buoyant kayak]

f'(3) is not -2

that's f(3)

[inner sentinel]

im dumb thanks

[pliant beacon]

why is the slope 1/3 and not 3?

i got y = 3x+4

[buoyant kayak]

how are you calculating your slope?

[pliant beacon]

y2-y1

and

x2-x1

[buoyant kayak]

so what exactly did you do?

[pliant beacon]

i did 4-5 over 0-3

[buoyant kayak]

and you got 3?

what is 4-5 and what is 0-3?

[wary stream]

$\frac{4 - 5}{0 - 3}$

[ocean seal]

dldh06

[pliant beacon]

bruh nvm

my bad

i thought the 4 was negative

thanks for the help

[tight locust]

haha

[inner sage]

can someone still help me with this ? 😅 I've gotten up to here, and I'm wondering if I'd need to use rational zero theorem again

[willow mirage]

Write an expression for the sequence of operations described below.
subtract the quotient of 9 and 5 from 10
Do not simplify any part of the expression.

help

[tawdry beacon]

someone help pls

[wary stream]

Rise/run

Gradient also means slope

[quartz osprey]

how do you od this

i dont understnd

[tawdry beacon]

idk what that means i have no idea what to do

[quartz osprey]

what i have so far is x-x^2=4^-3x

[wary stream]

Do you know what slope is?

[tawdry beacon]

something that has a higher level at one end

[wary stream]

Mathematical slope

[tawdry beacon]

im not sure

[alpine nacelle]

the trick is to write 64^(-x) as 4^(-3x)

[wary stream]

https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:linear-equations-graphs/x2f8bb11595b61c86:slope/v/slope-of-a-line

[quartz osprey]

yes i have that

[wary stream]

What happened to the 4 on the left side?

[quartz osprey]

x-x^2=4^-3x

oh

uh

4x-x^2=4^-3x

x-x^2=-3x

becomes this

and im kinda suck on solving it

[wary stream]

So move all the terms to one side, aka setting equal to 0

[quartz osprey]

ok

sec

x-x^2+3x=0

[wary stream]

Then solve for x

[quartz osprey]

alright

uhh

divide by x

[wary stream]

No

[quartz osprey]

well factor out x

x(1-x+3)

x(-x+4)=0

x=0,4

oh

thank you

[alpine sable]

can someone help me with this please f(x)= 2x+6 g(x)=√x+10

Find (g(f(x))

[quartz osprey]

:rolf

🤣 why was i stuck on this

g of f

[wary stream]

Take the f(x) plug it into g(x)

[quartz osprey]

so you plug in sqrt 2x+6 +10

was i right

i read it g of f so g is inside f?

nah f is inside g im so sad

[alpine sable]

so i start with the f?

wait would i be √2x+16

[wary stream]

If you had f(3), do you know what that means?

[wary stream]

Also is it $$g(x) = \sqrt{x + 10}$$ or $$g(x) = \sqrt{x} + 1$$?

[ocean seal]

dldh06

[alpine sable]

ok thank ya

[warped basalt]

could i pls get help w this, how do i find x?

<@&286206848099549185>

[wary stream]

You have to wait at least 15 minutes before pinging helpers

[warped basalt]

oh mb, i’m sorry

[wary stream]

Also that's an isosceles triangle

Determine from there

[bright reef]

Can someone verify this?
sin(x) = 1 / csc(x)
Likewise,
sin^5(x) = 1 / csc^5(x)
Right?

I’m having one of those moments of uncertainty in math

[glass lichen]

yes... csc(x):=1/sin(x)

[bright reef]

But raised to any power would be the same right?

[glass lichen]

yes.

[agile furnace]

Can someone help me solve this please

[bright reef]

Oh ok

[inner sentinel]

is this right

[alpine sable]

can i get help on my trig work

[kindred warren]

ok

[wary stream]

Don't ask to ask

[alpine sable]

what

[kindred warren]

just send the question you dont need to ask to ask

[alpine sable]

It wont let me send the photo

[kindred warren]

oh

[alpine sable]

file too big

[kindred warren]

its a picture?

[alpine sable]

yes

[kindred warren]

a picture larger than 8mb

damn

[alpine sable]

I think i got it

[buoyant edge]

Yep we can see the pic @alpine sable

So what have you tried so far

[wary stream]

Was asked in different channel

[alpine sable]

I tried it ealier and just couldnt get it

[buoyant edge]

Oh, alright then. Go back to that channel and someone will help you 🙂

[alpine sable]

can you help me

[buoyant kayak]

since you won't respond in the other channel, what have you tried?

aaand of course now you respond

[edgy sand]

what am I doing wrong?

i found the derivative and then replaced x with 0

and used that as my m

plugged it into y-y1=m(x-x1)

[buoyant kayak]

what is your derivative?

[edgy sand]

ln(5) x 5^x

[buoyant kayak]

and 5^0 is?

...?

[edgy sand]

1

sry

and then

[buoyant kayak]

so your slope is...?

[edgy sand]

1.6

and some decimals

[buoyant kayak]

a more accurate slope would be just ln(5)

[edgy sand]

ah

let me try that

[glass lichen]

yeah the slope is ln(5), not 1.6

[edgy sand]

okay cool that makes sense

didnt think id be able to use it like that

thanks

[vagrant flax]

how do i do question 5 part b?

do i work out the circle formula and change y to k and find k?

k=2?

[indigo jetty]

If you know what y=k looks like and then try drawing it as a tangent to the circle, the answer would follow immediately

[vagrant flax]

yep okay

i understand now

k is a constant so its a number w gradient of 0

[indigo jetty]

yup, basically a horizontal line

[vagrant flax]

Mind if you can hep me with another question lool

Im just confused on part C

[indigo jetty]

what can you tell about the line segment (which is part of the x-axis) that cuts across the circle?

[vagrant flax]

i can use its gradient to find perpendicular