help-39

[rugged jewel]

oh ok thanks

[inland ivy]

(x+y)^3+(y+z)^3+(z+x)^3=-(x^3+y^3+z^3)=-3xyz

[rugged jewel]

yeah

thanks

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[rapid wagon]

what is wrong? mclaurin series of the function of order 4

[rapid wagon]

cos0=1..
-cos0=-1/3!..

[rough forge]

derivative of sin(x/3)?

[rapid wagon]

cosx/3*1

[rough forge]

nope

you didn't apply chain rule

or you tried but it did wrong

[rapid wagon]

oh, cosx/3*1/3

[rough forge]

cos(x/3) * 1/3 yes

you basically lucked out

you prob failed the other derivatives too, but still got half right because sine evaluates to 0 if x = 0 which makes everything 0 anyway

but the issue is you have to do them again

[rapid wagon]

yea true

its ok im doing it

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[valid vigil]

WTF is this ( ' and '' ) on the angle? I know about trigonometry, but i never see these symbols before (on math).

[plush bramble]

https://mathsathome.com/convert-degrees-minutes-seconds/

[valid vigil]

ty

[errant fable]

minutes and seconds

you read it as 34 degrees 52 minutes and 8 seconds

[valid vigil]

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[vestal pelican]

Write out the form of the partial fraction decomposition of
the function

[vestal pelican]

so i found x=2 and x=-3

then i did:
((x^2)/(x-2)(x+3))=(a/x-2)+b/x+3

i did x=-3 and got B=9/-5 and x=2 and got A=4/5

so ((x^2)/(x-2)(x+3)) should equal ((4/5)/(x-2))+(-9/5)/x+3 but it doesnt tho

[sudden pumice]

because the degree doesn't match

[vestal pelican]

what degree

[sudden pumice]

do you know the logic / actual steps behind this

[vestal pelican]

yes

we make A=0 so we can get B and vice versa

[sudden pumice]

first convert the fraction to a form in which it is linear eqn/ quadratic eqn and then do it

like 1-(6-x)/(x-2)(x+3)

now write it as 1-a/x-2 - b/x+3

[vestal pelican]

the main fraction?

[iron stream]

Polynomial long division.

[cobalt hinge]

do you know how to do long division

on polynomials

[vestal pelican]

maybe i do can u remind me

[cobalt hinge]

ok i like to think of it this way (at least for same degree in numerator and denominator)

what is the limit as x->infinity for the integrand

[vestal pelican]

oh wait i do know polynomial long division

[cobalt hinge]

👍

[pearl pond]

@vestal pelican Has your question been resolved?

[pearl pond]

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[acoustic tangle]

can someone teach group theory to me

[keen frost]

Yes: https://www.amazon.se/-/en/Steven-Roman/dp/0817683003

[summer imp]

Group theory is very broad... it is taught in whole courses. It's not really something one can really teach in a help channel...
There are lots of resources to learn about it, be it from YouTube playlists featuring classes or textbooks.

[keen frost]

(This is a joke not a book recomendation)

[acoustic tangle]

okay

i’ll give a specific question

[summer imp]

MIT has an open course available you can go through in lecture format, albeit it probably won't be super complete.

[acoustic tangle]

part d

[acoustic tangle]

i mean like i’m just trying to understand what i’m doing in school right now really

not teach myself everything

[summer imp]

You need to determine whether (x * y) * z = x * (y * z)

I think you've done good so far

[acoustic tangle]

(x * y) * z = x * (y * z)
x * y = xy + x + y

idk how to multiply it out

[summer imp]

(xy + x + y) * z = (xyz + xz + yz) + (xy + x + y) + z
x * (yz + y + z) = (xyz + xy + xz) + x + (yz+y+z)

[acoustic tangle]

ohhh

so whatever’s in the brackets gets replaced

ok

that makes sense

[acoustic tangle]

is this associative then

[pearl pond]

@acoustic tangle Has your question been resolved?

[pearl pond]

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[pearl pond]

Please don't occupy multiple help channels.

@keen lichen Has your question been resolved?

[keen lichen]

@helper

<@&286206848099549185>

[keen lichen]

close channel

.close

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.close

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[keen lichen]

this shit makes no fucking sense

[heady hearth]

Isnt this basic trig

[keen lichen]

i thought it was

until i look n shit

i can get all the angles for the 2 top triangles but

the bottom trnagle w 1 side

i cant use nth bro

no trig formula

no laws

nth

[heady hearth]

Ye idk just like use a photmath idk

[keen lichen]

<@&286206848099549185> its been 15 minutes bro

please somone help

[midnight minnow]

3 angles and a side determine a triangle completely, im thinking try calling romeos horizontal distance to juliet a, call Paris's to Juliet b, and relate them using pythagorean theorem, then do some magic

i cant fully solve this myself right right now but im curious what you're trying

[pearl pond]

@keen lichen Has your question been resolved?

[keen lichen]

gotchu

so i pretty much got it almost

so lets name the angle under h: b

angle b is the top of the RP triangle

this is should be 90degrees

now i have an angle and a side length in that triangle

so now im doing pythag therum n diong rb^2 + bp^2=100m

but im stuck here

[stable dune]

well lets just start with pythagorean

$a^2 + b^2 = 100^2$

[jolly parrot]

hiidostuff

[stable dune]

we dont really want both a and b to be a thing

since we already have h

and its hard to trust that we would have enough equations to find all of them

so lets represent b in terms of a

rearranging, we get $b = \sqrt{100^2 - a^2}$

[jolly parrot]

hiidostuff

[stable dune]

so lets say that a is the side length under the 20 degree angle

and b is the side length under the 18 degree angle

what trig function should we use to represent the angle in terms of h and a/b?

[pearl pond]

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[ashen lance]

This table shows height of 50 sportswomen.

Find :
a) average
b) median

[ashen lance]

With average

It’s just

(160+164)/2

= 162

Do 162*5=810

And do that with every row

And plus it together

[quick star]

uhm yeah

[ashen lance]

And then divide by N number.

Yeah

I’ll do that first

Later I’ll need help with median.

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[bitter herald]

What language is this btw judt curious

[pearl pond]

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[sharp smelt]

Trying to switch the order of integration

[iron stream]

Did you draw ?

[sharp smelt]

I did graph it

yes

[iron stream]

Can you share !?

[sharp smelt]

If I were to switch the order of integraytion

the bounds would be 0 to 3

wrt x

[iron stream]

?

[sharp smelt]

$\int_{0}^{3} e^{y^3} dx$

[jolly parrot]

What a wonderful world!

[sharp smelt]

yeah

I now need to change the bounds for y

[iron stream]

Yeahh !

Initially we integrated this first

We need to make it vertical

So from , x = 0 to ?

[sharp smelt]

3

[iron stream]

Why ?

One min wth

[sharp smelt]

Yeah

[iron stream]

We need to integrate

From x = 0 to the curve

[sharp smelt]

so If I were to draw a horizontal line though the region it enters at y=0

[sharp smelt]

Yeah

so the horizontal lines enter at x=0

and leaves at x=3

[iron stream]

Nah

[sharp smelt]

oops

wait

[iron stream]

The horizontal line varies

[sharp smelt]

no

x = y^3

[iron stream]

Y³?

[sharp smelt]

and y varies between 0 and 1

$\int_{0}^{1} \int_{0}^{y^3} e^{3y^2} dx dy$

[iron stream]

You mean 3 y² right ?

[sharp smelt]

oops

yes

[jolly parrot]

What a wonderful world!

[iron stream]

$\int_{0}^{1} \int_{0}^{3y^2} e^{y^3} dx dy$

[jolly parrot]

XOR-11

[iron stream]

What are you doing bro 😭!

[sharp smelt]

No idea

Want to switch the order here

here, the bounds would be 0 to y^3

and 0 to 2

[iron stream]

Did you do this correctly?

[sharp smelt]

yea

I think

[sharp smelt]

so $\int_{0}^{2} \int_{0}^{y^3} \frac{dx dy}{ y^4+1}$

[jolly parrot]

What a wonderful world!

[iron stream]

This is correct

[sharp smelt]

Thanks!

[pearl pond]

@sharp smelt Has your question been resolved?

[pearl pond]

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[dire magnet]

Let $(u_n)$ be a sequence. If $u_{n+1} = u_n$ for all $n \geq 1$, then $(u_n)$ is a constant sequence.
Is this a formal definition of constant sequence?

[jolly parrot]

AN-602

[rose ibex]

yeah sure it works

alternatively u_n = u_1 for all n>1

[prime bramble]

yeah, this definition is okay

[cursive tree]

yes

[pearl pond]

@dire magnet Has your question been resolved?

[dusty rock]

hi guys i am new to this server

[toxic fractal]

Hi new to this server, please dont intrude in help channels

[pearl pond]

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[sharp smelt]

I'm getting 2(3t-5)+3(2t+1)=-7

so 2x+3y=-7 is a part of the curve?

[autumn trellis]

what

[sharp smelt]

I've been asked to elimnate the parameter

[autumn trellis]

6t + 6t =/= 0

[sharp smelt]

oops

not +

[autumn trellis]

okay that works

[south inlet]

Then it’s not -7

[hot canyon]

Yes 2(x + 5) = 3(y - 1) is the curve

[sharp smelt]

what

[autumn trellis]

the rhs

[sharp smelt]

oh, should be -14

*-13

x+2y=7 works?

[south inlet]

2x + y you mean?

[sharp smelt]

yes

wait

yes

Thanks!

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[barren owl]

Solve the equationsystem algebraicly

X/2=Y/5=Z/6
2x + y - z = 6

[barren owl]

I’m so lost

[iron stream]

x/2=y/5=z/6 = k

so express x,y,z in terms of k

[barren owl]

What

Why

[iron stream]

Plug in eqn 2

And find k

[iron stream]

For simplicity

[prime bramble]

since x/2 = y/5 = z/6, all three are equal to a constant k

that yields x = 2k, y = 5k, and z = 6k

now you can plug these expressions into the second equation and solve for k

afterwards, translate the value of k back to the values of x, y, z

[barren owl]

K as in kx+m?

[prime bramble]

no

just a constant k

call it N if you want or something

[barren owl]

U just randomly chsoe it

[prime bramble]

the letter doesn’t matter

[barren owl]

Oh okay

Still don’t understand why it equals k

But let’s move on

[prime bramble]

well they have to equal something

x/2, y/5, and z/6 are all equal to some number

we don’t know what the number is, so we call it N

then we get x = 2N, y = 5N, and z = 6N

[vagrant briar]

as the quantities are equal we can just assume that they are all equal to some other new qunatity say k

[barren owl]

Ohh

[prime bramble]

it seems like the usage of the letter k is confusing for OP

but yeah, that’s the idea

[vagrant briar]

i prefer lamda hehe

[barren owl]

U multiplied then to remove the bottom thingy

[prime bramble]

yup!

[barren owl]

Okay

I understand

[prime bramble]

I personally prefer a :p

[barren owl]

Ok imma substitute them

[vagrant briar]

good luck!

[barren owl]

2*2k + 5k - 6k=6

And then

3k=6

Divide by 3

K=2

?

[vagrant trout]

x/2 = k -> x = 2k, y/5 = k -> y = 5k, z/6 = k -> z = 6k

4k + 5k - 6k = 6
9k - 6k = 6
3k = 6
k = 2

x = 4, y = 10, z = 12

[barren owl]

I see

Tysm

[vagrant trout]

Ofc

[barren owl]

Btw

What’s the difference between a variabel and a constant

[vagrant trout]

a variable is for example x, something you don't know the value of, sits there as a placeholder for a value

[barren owl]

Mhm

[vagrant trout]

meanwhile a constant is usually a value, that no matter how you manipulate, will always remain the same

for example:

e^x and e^2

e^x can be manipulated into faster growth

while the growth of e^2 stays the same

as 2 is a constant

and x is a variable

[barren owl]

Ahh

Ic

How do I solve these graphically

With a calc right?

[vagrant trout]

which ones?

[barren owl]

In general

Equation systems

[vagrant trout]

well

graphically i suppose on desmos

[barren owl]

Ah

Gotta learn how to use it

@vagrant trout on another question

I’ve tried myself but quite unsure if I’ve done right so far

Can u check

[pearl pond]

@barren owl Has your question been resolved?

[barren owl]

<@&286206848099549185> can anyone help

X-y+z=3
6x+9y+4z=9
12x+6y-z=4

[rigid valve]

have you tried substitution

[barren owl]

Yeah can I show what I’ve done so far

[rigid valve]

yes please

[barren owl]

Did I do something wrong

Or is it right

@rigid valve

[rigid valve]

you're y is equal to 13/15 correct?

[barren owl]

That’s 2z

Lol

[barren owl]

Ye

2z

Not 22

[unborn shuttle]

use replace

[barren owl]

.close

[pearl pond]

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[plucky carbon]

I don't know where to start : The length of the sides of a right triangle are consecutive even integers. Find the integers.

[plucky carbon]

the only thing I got is 3 x's cause I have to find 3 integers

[sharp vigil]

how might you write a formula that produces 3 consecutive even integers?

[plucky carbon]

not sure maybe like x+x+1+x+2 not sure though

[west sapphire]

if you want to cheese this, remember that 3,4,5 is a pythagorean triple

[sharp vigil]

that gives 3 consecutive integers, not 3 consecutive even integers

[plucky carbon]

so would it be x+x+2+x+4 ?

or does the first one have to be x+2 ?

[west sapphire]

is x+2 always even? what if x=1

[plucky carbon]

idk then tbh cause if I leave it as x then what if x is 1 and if I do x+3 then what if x is 2

[west sapphire]

so what can you do to x to make sure you always have an even number?

[plucky carbon]

I am inclined to say make it a constant but I feel like that isn't right

[west sapphire]

well you could multiply it by 2

[plucky carbon]

oh wait why did I think of that lmao

[west sapphire]

ig it's not really necessary, either way you're gonna get a quadratic equation

and if there's an even solution it will be one of the solutions of that equation

so x, x+2, x+4 are the sides

what should you do to solve for x?

[plucky carbon]

honestly i can't tell you my teacher kinda just threw this question in randomly do we have to use some sort of forumla

maybe multiply them ?

[west sapphire]

well they're supposed to be the sides of a right triangle

so how are the sides related?

[pliant vessel]

its a right triangle

try hypotenuse

[plucky carbon]

do I have to do x^2+x+2^2=x+4^2 ?

cause a^2+b^2=c^2

[pliant vessel]

yes

also since they are consecutive even numbers their sum would be an even number too

say 2n

[plucky carbon]

dude I have to take calc in like a year i'm fucking cooked if I can't even get this shit right

[pliant vessel]

you have 2 variables 2 equations

i think this could work

[plucky carbon]

so x^2+(x+2)=(x+4)^2 is x^2+x^2+2x+2x+4=x^2+4x+4x+16 which is 2x^2+4x+4=x^2+8x+16

[pliant vessel]

try solving it

only take the positive value since a triangle cannot have negative sides

seems like you dont need to add the sides afterall

[plucky carbon]

I really don't even know what that means can you simplify it ?

[pliant vessel]

you got an equation in quadratic here right

get all the material in just one side

[plucky carbon]

ohhhh

2x^2+4x+4+x^2+8x+16 like this ?

2x^2+4x+4=x^2+8x+16 = 0

[pliant vessel]

subtract when you take those from rhs to lhs

and =0

[plucky carbon]

2x^2+4x+4-x^2+8x+16 = 0 ?

[pliant vessel]

yup

what are you getting now

[plucky carbon]

can you tell me what rhs and lhs is ?

[pliant vessel]

right hand side and left hand side

[plucky carbon]

oh

lmao

[pliant vessel]

of the = sign

lol

[plucky carbon]

kinda stuck here x^2-4x-12

do it turn this into a factors ?

like (x+x)(x+x) ?

cause thats the only thing I think of when I see that

[pliant vessel]

use the quadratic formula

it will give a clean integer answer

[plucky carbon]

this ?

[pliant vessel]

yup

[plucky carbon]

do I include my variables btw like for the first b

do i do -(-4x)

[pliant vessel]

yes

take them with their signs

and without the x

[plucky carbon]

what does that mean do you mean ? like if I had 20x I would just put 20x for b or would it be -20x since the negative is there

[main oriole]

let's say you have a quadratic like

5x² - 20x - 6

you take the coefficients

so the numbers with their signs

so for b you put -20

for c you put - 6

and for a you put 5

this is just an example

[plucky carbon]

got it

[main oriole]

so in that case you put
a = 1
b = -4
c = -12

[plucky carbon]

I don't know what to do with the -4 on the outside

but for the right side i got -4^2+48/2

oh wait

do I actually have to square that so instead of -4^2 it would be 16

[plucky carbon]

?

[pliant vessel]

damn

i cannot send photos on laptop

[plucky carbon]

my new one is 64/2 btw

[pliant vessel]

thats wrong

[plucky carbon]

cause I just squared -4

[pliant vessel]

wait i'll try sending a photo to my laptop

[plucky carbon]

is this good ?

[plucky carbon]

what is that forumla in the middle that is different from the one I have

b^2-4ac

[pliant vessel]

ah

the descriminant

b^2 - 4ac

it is the same thing you use in the formula

when you solve more types of questions you dont need to calculate the whole root a lot of times but just the D to find out about the function

anyways

its the same thing as the formula youre using just the part inside the root is written as D

[plucky carbon]

so what is the third integer cause there is 3

did we do something wrong ?

oh wait never mind

if x=6 then we just use what we had earlier

6,6+2,6+4

[pliant vessel]

yes

you got it

proud of you

[plucky carbon]

thank you btw do you have an tips so I can get better at math I am an undergrad and currently 5 lessons behind the class

I feel like we are moving so fast its hard to catch up

[pliant vessel]

just solve more questions

its also better to see the teachers solving it

[plucky carbon]

I just haven't been joining cause there is no point of joining if I don't understand what they are talking about so I think what I might do is catch up over this weekend cause I am on 1.2 rn and I think they are around 1.7 so if I do 1 or 2 lessons a day until monday I should be able to catch up

[plucky carbon]

thanks

[pliant vessel]

if youre done then .close

[plucky carbon]

.close

[pearl pond]

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[winged acorn]

Could anyone explain how it is transitive?

[winged acorn]

The relation R

[plush bramble]

why do you think it's transitive

[winged acorn]

Oops, sorry

How is it non-transitive?

[plush bramble]

come up with numbers (x, y) in R that are close to the boundary

repeat (y, z)

and see if (x, z) is still in R

[supple roost]

I was trying to do with random numbers

[winged acorn]

The only problem is it's R

I mean the set R

[plush bramble]

why is that a problem

what numbers are you picking

[winged acorn]

Just integers

[plush bramble]

uh huh

which ones exactly

also i said "close to the boundary"

you can get closer with rationals

[winged acorn]

It's true, but it's a university practice book

[plush bramble]

i don't see what that has to do with my suggestion?

[winged acorn]

You've got to use a calc

[plush bramble]

R = set of real numbers. it contains more than just integers.

[winged acorn]

But you're right, there's no excuse

[winged acorn]

Okay, for example I pick 0.9, 3

0.9 + 3*3 = 9.9

Then 3 + 3*2.3 = 9.9

And 0.9 + 3*2.3 = 7.8

It's smaller

[plush bramble]

uh huh

you picked x < y. do the reverse

[winged acorn]

Oh, yeah

It worked

3 + 2.4 * 3 = 10.2

Thank you, much obliged

[pearl pond]

@winged acorn Has your question been resolved?

[winged acorn]

.close

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[jade solar]

You would need to use Rolle's Theorem.

[plush bramble]

https://www.youtube.com/watch?v=LHym1ARc2cE

what does your problem have to do with stationary roots

[cursive tree]

there's also a song about this theorem if you struggle to remember it

for some reason

[jade solar]

Hm wait Rolle's theorem ain't applicable here, it's a normal continuity/algebra thing I believe,

What have you tried so far?

[analog forge]

well f(x) will have a root wherever g(x) is zero

[jade solar]

Well, consider $f(x)=x^2-9$, at x = -4 and x = 4 f(x)>0, but it still has two roots between -4 and 4.

[jolly parrot]

RadMeerkat62445

[plush bramble]

f(x) is a rational function

f(x) has the same zeros as g(x)

[jade solar]

It can have any number of roots, but since we know that on both ends of the interval f(x) has the same sign, then the number of roots must be even

[analog forge]

oh right because if it dips down below the x axis it has to come up again for f(2)>0

yeah that makes sense

and then part b would be because of the asymptote right

ty

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[cunning pulsar]

hi can someone double check my work?

[pearl pond]

@cunning pulsar Has your question been resolved?

[pearl pond]

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[neon mortar]

trying to turn this: 23.4m * (0.155+x) = -4.3x into: x = bla

[neon mortar]

but I'm stuck

[elfin stirrup]

what is m?

first expand the bracket

[neon mortar]

m is basically x and x is y

[rough stream]

• Multiply everything out
• Put every term with an x onto one side, every term without an x onto the other.
• Factor x.
• Divide off whatever's multiplying x.

[neon mortar]

I haven't been able to isolate x

I could isolate m though

I mean, I could turn that into m = bla(x)

but not x = bla(m)

any hint?

thanks anyway

.close

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[dawn folio]

!status

[pearl pond]

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

[dawn folio]

2

[pulsar lark]

,rotate

[dawn folio]

i multiplied the sides and got 20x^2+13x-84=135

so then i subtracted 135 from both sides and got20x^2+13x-219 now im stuck

[cobalt hinge]

wait, nevermind

[dawn folio]

i tried factoring but it didint work

[cobalt hinge]

you can solve this equation, but it may not have a nice output.

[dawn folio]

couldent find the 2 numbers

ah

was tryna find multiples of 2190 not 4380

[cobalt hinge]

👍

[dawn folio]

got it

ty

.close

[pearl pond]

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[dawn folio]

.reopen

[pearl pond]

✅

[dawn folio]

wait

i got 73 and 60

so do i got put 20 under it so its 3 and 73 over 20?

[cobalt hinge]

yes.

[dawn folio]

k tyt

.clos

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[sterile coral]

.open

Wiat

[sterile coral]

How do I answer this

Its trigonometry

[edgy wren]

Sine rule

[spiral copper]

so he need to use cos right??

[edgy wren]

Nah just sines

[fallow sage]

No, still sin rule

[spiral copper]

oh yep my bad

[pearl pond]

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[grand juniper]

dumb question but can someone explain to me how x³ = 8 equals to x = 2

[drowsy adder]

you dont understand why x=2 is a solution?

[edgy wren]

Cube root

[grand juniper]

i said dumb question since i forgot but yeah

[drowsy adder]

oh well plug in 2 instead of x and see if it satisfies

[grand juniper]

oh yeah because 2 cubed is 8 right

ok ty

[drowsy adder]

yes

it actually has 2 more solutions but thats another story

[grand juniper]

it does? isnt 3 uneven

[drowsy adder]

it has one real solution and two imaginary solutions

but x = 2 should do for now

[pearl pond]

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[woven umbra]

hey

[floral ember]

helo helo what is your doubt just ask right away

[woven umbra]

I forgot most of my division

and wait let me just go to my online class real quick to see what I am learning

polar graphs

so can you help

[edgy wren]

Send a specific question to see about it

[woven umbra]

how do I do that because I am very confused

[midnight haven]

send a specific problem/question

if you dont tell/show us what you need help with we cant help

[pearl pond]

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[autumn anchor]

A^3 - 27 = ( ….-….) (…..+…..+….)

[autumn anchor]

analyzing

[plush bramble]

https://andymath.com/wp-content/uploads/2018/12/v61.jpg

[pearl pond]

@autumn anchor Has your question been resolved?

[shrewd forge]

27=3³ btw

[pearl pond]

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[lucid hazel]

nahh cuz can someone try this

[lucid hazel]

am losing my rain

brain

[hot canyon]

12, 12 + 1, 12 + 1 + 8, 12 + 1 + 8 + 27, 12 + 1 + 8 + 27 + 64, ... + 125

[lucid hazel]

hmm

i dont get it

[naive orbit]

1 = 1^3

[hot canyon]

each consecutive term has a difference of a successive cube number

[lucid hazel]

istg i dont get it

[hot canyon]

13 - 12 is?

[lucid hazel]

1

[versed mica]

he just told you

[hot canyon]

21 - 13 is ?

[lucid hazel]

8

[hot canyon]

what is the cube of 1?

[lucid hazel]

1

[hot canyon]

what is the cube of 2?

[lucid hazel]

8

[hot canyon]

what is 48 - 21?

[lucid hazel]

27

3^3

[hot canyon]

what is 4^3?

[lucid hazel]

112- 48 = 64

237 - 112 = 125

[hot canyon]

HUH WHAT

,calc 237 - 112

[jolly parrot]

Result:

125

[lucid hazel]

so it will be 125 + 216

[naive orbit]

yes

[lucid hazel]

the answer key says otherwise

[hot canyon]

dude, had you not been so impatient, you would not be getting 125 + 216 as your takeaway

what is 1^3?

you only really had to type numbers smh

[lucid hazel]

1

[hot canyon]

what is 13 - 12?

[lucid hazel]

sorry

[lucid hazel]

1

[hot canyon]

what is 2^3?

[lucid hazel]

8

[hot canyon]

what is 21 - 13?

[lucid hazel]

8

[hot canyon]

what is 3^3?

[lucid hazel]

27

[hot canyon]

what is 48 - 21

[lucid hazel]

27

[versed mica]

lmao

[hot canyon]

what?

=_=

what is 4^3?

[lucid hazel]

64

[hot canyon]

what is 112 - 48

[lucid hazel]

64

[hot canyon]

what is 5^3?

[lucid hazel]

125

[versed mica]

brother do you still not see it?

[hot canyon]

what is 237 - 112?

[lucid hazel]

125

[hot canyon]

what is 6^3?

[lucid hazel]

i do but am asking how do we find the last term

[lucid hazel]

216

[hot canyon]

what is x - 237?

[lucid hazel]

x-237 = 216

oh

ok

[hot canyon]

^^"

[lucid hazel]

tysm

but i have a question that is more important

[hot canyon]

!done

[pearl pond]

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

[lucid hazel]

how did you figure that sequence

that fast

[hot canyon]

wha

[lucid hazel]

it took me 5m and i still didnt know

[hot canyon]

differences

[versed mica]

you just go through subtracting each term in your head

first trick

[lucid hazel]

can you give me a bunch of tricks pls

ill write them down

cuz i got around 7 mistakes

[hot canyon]

check first difference for a pattern

[lucid hazel]

i got this wrong too

[hot canyon]

if not then second difference

[lucid hazel]

so first i check between the first 2 consecutive numbers

if not , then the 1 and 3

3 and 5?

[hot canyon]

no lol

first differences => make a new sequence by taking differences of each consecutive term

for example, here: first differences are: 7, 6, -1, 19, -14

[lucid hazel]

yes they dont make sense

[hot canyon]

hmm indeed they do not make much sense

[dusty jungle]

yeah nothing in the OEIS either

[lucid hazel]

no way you got the harder questions first 😭

[lucid hazel]

this question is easier

than the one i showed u first

[hot canyon]

it is?

[hot canyon]

yeah the alternative +, - were telling tales

[lucid hazel]

how do you think i should prepare fro these questons

[hot canyon]

study your book ._. i

[lucid hazel]

so basically i think you know me now, i got an exam 6h, with 6 different sections ( you have seen most of them). Idk how to practice to solve them or figure the patern within a mintute and 20s

[hot canyon]

I think it amounts to practice

and the best suggestion I can give is to time yourself

[lucid hazel]

i got limited practice sets too :<

only 70 questions

anyways thanks for your help

see you soon :>

.close

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[sour sluice]

if someone only had the equation for Fahrenheit, how could they know to preform non-standard operations to achieve the formula for Celsius?

[hot canyon]

you're royally cooked

[sour sluice]

WHAT

[hot canyon]

Yes lol

[sour sluice]

the 5/9 is disconnected from celsius entirely though

I mean 32**

[hot canyon]

explain how did you remove the 5/9 from Celsius

[sour sluice]

you divide the entire side then?

[hot canyon]

wow, the answer for a question is another question

I'll ask again. How'd you remove the 5/9 from Celsius

[sour sluice]

I removed the 9/5 from celsius by dividing 9/5 from it and the other side, giving F 5/9

[hot canyon]

so you divide the whole equation by 9/5 right?

cause if you divided left side by 9/5 to give F the 5/9, you ought to do the same to the right side too

and 32 is, unfortunately and unintentionally, a part of the right side

[sour sluice]

I see now

hold on just one follow up question

@hot canyon so when you have +32(9/5) on that side, how/why exactly can you shove it into the parenthesis with 5/9(F)? it seems like you would divide it from the right side of the equation, but it doesn’t seem like something i’ve had to do in algebra before

[hot canyon]

Huh?

[hot canyon]

Multiplying 5/9 both sides:

[sour sluice]

thank you. been awhile since I applied algebraic concepts, just trig shit

.close

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[hard hinge]

If f is a real function continuous in x0 and invertible in some neighborhood of x0, is the inverse of f continuous in f(x0)?

[hot canyon]

!show

[pearl pond]

Show your work, and if possible, explain where you are stuck.

[hot canyon]

Try using epsilon delta

[hard hinge]

Ok, I tried constructing a counterexample function by cases (one function for rational x and one for irrational x) and that didnt work out

I tried proving it using series but my proof requires continuity in a neighborhood of x0, which I don't have
With some epsilon delta I got that f being continuous in 0 (i'm setting x0=0 and f(0)=0 for convenience) means that for every positive epsilon, there's some positive delta such that if |y|>=epsilon => |f-1(y)| >= delta. (edit: corrected inequalities)
but for some reason that doesn't make sense to me

intuitively that means f-1 can't be arbitarily close to 0 outside any epsilon neighborhood of 0

[hard hinge]

@hot canyon do you know if that's true?

I mean the image of f-1 has to be some neighborhood of 0, so for x_n satisfying f-1(x_n) = 1/n (i'm skipping some steps) we get that x_n has to have some subsequence that goes to 0, i think

But I think that's just going in logical circles

[pearl pond]

@hard hinge Has your question been resolved?

[pearl pond]

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[hard hinge]

.reopen

[pearl pond]

✅

[hard hinge]

<@&286206848099549185>

[pearl pond]

@hard hinge Has your question been resolved?

[pearl pond]

@hard hinge Has your question been resolved?

[torpid harness]

the inverse function f^-1 is continuous at f(x_0)

why? if f is continuos at x_0 and invertible in a neighborhood of x_0, the invertibility ensures there's a one-to-one correspondence near to f^-1 being "controlled" near f(x_0)

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[upper comet]

what is it asking for

[torpid harness]

d is incorrect

and in e susbtitute g(x) into f(x) replace every x in f(x) with the entire g(x), then simplify

[pearl pond]

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[pearl pond]

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[midnight haven]

This is quite minor and I should know this but I'm second guessing myself here, just looking to clarify terminology:

As shown here and in general, what does "with respect to x" actually mean? Like I think I know but I just want to confirm because I can't really describe it..... sounds weird but any advice would help.

[midnight haven]

I see things like "in terms of x" and as with the above image "with respect to x" like if someone could give me simple examples of each phrase it'd help a lot please 🙏

[cobalt hinge]

$f(x)$ is a function in $x$, $f(y)$ is a function in $y$ (meaning that the input is either $x$ or $y$)

[jolly parrot]

;(

[midnight haven]

Yeah so I understand that but the "with respect to ..." and "in terms of ..." specifically is what I don't understand.

Like with that screenshot, what does it mean specifically just to have a reference to work with, "with respect to x" as written in the green at the bottom there?

[cobalt hinge]

like, x is the variable you are considering

you get more in depth for this in multivariable calculus

search up "partial derivatives"

[midnight haven]

I see, will give it a shot, I meant in general though like how do I interpret those phrases.

Thanks for the point in the direction though 👍

.close

[pearl pond]

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[cobalt hinge]

multivariable

i as a mere human cannot explain it to you well

you just intuitively learn it

[midnight haven]

Lol yeah that's what I feel too, I know what it means intuitively but. Iwas trying to get it in writing so I can make sure I'm not mistaken since it's starting to get to the point where I need to accurately understand descriptions of things

[pearl pond]

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[sharp smelt]

Trying to plot this

[sharp smelt]

I was thinking of converting to polar

$x=r\cos(\theta); y=r\sin(\theta)$.

[jolly parrot]

What a wonderful world!

[sharp smelt]

so $r^2= (2 \sin(\theta) \cos(\theta))^2 \implies r = \sin(2\theta)$

[jolly parrot]

What a wonderful world!

[hybrid basin]

Does level curve not work?

[sharp smelt]

Isn't this a curve in R^2

[hot canyon]

Yes it is ._.

[sharp vigil]

did you forget the cube?

[hot canyon]

No they simplified everything and wrote only the last step

[sharp vigil]

oh they divided out

[hot canyon]

Note that the curve is mirrored on ±x, ±y, so you can just draw on theta [0, π/2] and mirror it about x, y axes and 0

[sharp smelt]

Yea

[hot canyon]

To draw in [0, π/2] tho, it'd be best to plug values

[sharp smelt]

Thanks

[hot canyon]

Oh if it helps, it is also symmetric about y = x

[sharp smelt]

Yeah, it's a flower, right

[hot canyon]

It is

4 petal

[sharp smelt]

yup

tq

[pearl pond]

@sharp smelt Has your question been resolved?

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[visual canyon]

Can someone help me with this problem?

[shy patrol]

You need to be more specific we aren’t just going to do your entire assignment for you. Is there something in particular you don’t understand?

[visual canyon]

sorry, I'm just trying to make my working doc a bit more organized before I post it here

Here is what I have so far, I'm not 100% sure I'm headed in the right direction

There is also a strange bit of wording on the next section of the instructions that I don't understand. "Determine for how many minutes each plan is the best option for two customers."

I think I am supposed to figure out which plan best suits the needs of the two customers, but its basically the same sentence without "for how many minutes each plan is the", which leads me to think that maybe there is something more to it that I'm just not getting

<@&286206848099549185>

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[pearl pond]

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[pearl pond]

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[sharp smelt]

trying to find a way to relate $a_n$ to $a_{n+1}$ here

[jolly parrot]

What a wonderful world!

[sharp smelt]

if the seqence started with 2

then $a_{n}= 2a_{n-1}+1$ would work

[jolly parrot]

What a wonderful world!

[sharp smelt]

the best I can do is define $a_0=0$

[jolly parrot]

What a wonderful world!

[fierce totem]

Hint: find b such that
$a_n + b = 2(a_{n-1} + b)$

[jolly parrot]

TargetVN

[sharp smelt]

Can't I just define a_0=0

[glacial sequoia]

why do you even want to define a_0

[fierce totem]

Technically you can, but its pointless

[glacial sequoia]

you should not add terms to the sequence

[obsidian wing]

But why 1 is here? If we ignore that, it would be a perfect a{n+1} = 2a{n} + 1

But life is hard .-.

[sharp smelt]

yeah]

[sharp smelt]

hmm, okay

[hot canyon]

you want to write the general term?

[fierce totem]

Oh

Literally didnt see that 1 coming

[sharp smelt]

in terms of the previous term

yes

[fierce totem]

So its not a{n+1} = 2a{n}+1

[sharp smelt]

yea

unless we can add a_0 to the seqeunce

[fierce totem]

[hot canyon]

Imagine writing 47 as the next term and 95 for the term after that

[obsidian wing]

Maybe…
a1 = 1
an = floor(2.1a{n-1} + 0.8)

[sharp smelt]

That's quite a formula

[fierce totem]

Wolfram still understand the sequence as 2a_n+1 even though a_1=1

[fierce totem]

including floor

[obsidian wing]

It’s perfectly valid :)

[sharp smelt]

It is yeah

but it's ugly 😭

[obsidian wing]

Damn… this is hard :)

[hot canyon]

it does not give the term after 8328253

[sharp smelt]

hmm'

[hot canyon]

So do you want to get the sequence to OEIS'? or just define a_0 = 1, a_1 = 2, a_{n + 1} = 2a_n + 1 for n ≥ 1

[sharp smelt]

That 's how I would define it , yes

[hot canyon]

Do you want how to find a general sol to that?

[sharp smelt]

As in an explict formula

[hot canyon]

=> b_{n+1} = 2^n b_1 = 3* 2^n```

=> a_n = b_n - 1 = 3*2^{n-1} - 1 for n ≥ 1

[sharp smelt]

hmm

okay

thanks

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[torpid schooner]

Am I doing this right so far

[bitter lodge]

Sin + cos = 1
tan + 1 = sec
tan = sec - 1

[torpid schooner]

isnt that what i did

[bitter lodge]

[that](#help-39 message) was just me thinking

[torpid schooner]

oh

ic

[fierce totem]

didn't you ask this before

[torpid schooner]

yeah

didnt show my work yet though

i was doing it

[bitter lodge]

Nah she just asked if the u-sub is right

[fierce totem]

ah okay

[torpid schooner]

ok i erased it fully

[bitter lodge]

You wrote $\dd{u} = \sqrt 2 \tan(u) \sec(u) \dd{u}$

[jolly parrot]

King Leo

[torpid schooner]

isnt du suppose to be tanusecu since i made x sec u?

pretty sure thats teh derivative

[bitter lodge]

$$x = \sqrt 2 \sec(u)$$
$$\dv{x}{u} = \sqrt 2 \sec(u) \tan(u)$$
$$\dd{x} = \sqrt 2 \sec(u) \tan(u) \dd{u}$$

[jolly parrot]

King Leo

[fierce totem]

ye its true

[bitter lodge]

But this is du = ...

Im assuming the confusion stemmed from there

[torpid schooner]

yeah

soo sqrt2sec

not sqrt2tan

[bitter lodge]

No all you did was flip the order of multiplication

This is just standard commutative property

[torpid schooner]

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[pearl pond]

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[torpid schooner]

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[pearl pond]

✅

[torpid schooner]

sorry if this is really dumb question because it is but why is it that sometimes i see u substitution being on top? like usually its du/part you found the derivative of but sometimes it can remain on top where du = derivative of whatever and dx

does that makes sense

[bitter lodge]

Wdym u-sub being on the top

[torpid schooner]

like

[bitter lodge]

Do you mean the difference between
$$\dd{x} = \dots \dd{u}$$
$$\dd{u} = \dots \dd{x}$$

[jolly parrot]

King Leo

[torpid schooner]

uhh maybe like

here for example, du is on top or whatever idk im not good at math

[bitter lodge]

$$\int \frac{\dd{x}}{x^4 \sqrt{x^2 -2}} = \int \frac 1{x^4 \sqrt{x^2 - 2}} \dd{x}$$

[jolly parrot]

King Leo

[torpid schooner]

yes

[bitter lodge]

And youre asking why the dx is on the top?

[torpid schooner]

but then it should be (derivative) dx = du

then u divide

dx = du/derivative

because im making a substitution here shouldnt it be

du/derivative

[fierce totem]

that is u = f(x)

the original problem is x = f(u)

it's different

[bitter lodge]

$$u = x^2 + 5 \to x = \sqrt{u - 5} \to \dd{x} = \frac 1{2\sqrt{u - 5}} \dd{u}$$
$$\int 4x \qty(x^2 + 5)^3 \dd{x} = \int 4\sqrt{u - 5} \qty(u - 5 + 5) \cdot \frac 1{2\sqrt{u - 5}} \dd{u}$$

Wait

[jolly parrot]

King Leo

[bitter lodge]

@torpid schooner basically all you change is what equation you use to relate dx and du but eventually, all that matters is: if you make a u-sub, there must also be a du

[torpid schooner]

yes and du things are always 1/deriv right?

[bitter lodge]

Since $\dd{x} = \frac 1{2\sqrt{u - 5}} \dd{u}$, you can express that as $\dd{u} = \frac{\dd{x}}{\frac 1{2\sqrt{u - 5}}}$

[jolly parrot]

King Leo

[torpid schooner]

so

they are basically interchangable

[bitter lodge]

Yes

[torpid schooner]

ok

[bitter lodge]

Its just that, $x = \sin(u)$ is a lot easier to work with than $u = \arcsin(x)$

[jolly parrot]

King Leo

[torpid schooner]

yeah i understand

thank you

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[visual canyon]

am I correct?

true for all x is basically all real nums phrased differently

[verbal whale]

Yep

It's 5x - 11 on both sides

[visual canyon]

nice, thanks

.close