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[magic rover]

if a-1<x can I say that a-1<=ceil(x)-1, if a and x are positive reals?

[smoky wing]

Try some numbers

[magic rover]

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[teal oriole]

how would i answer the 4th one here? im confused what to do with the +4

[umbral dome]

split it into two integrals you know: the integral of f(x) you know and the integral of 4 (which you should be able to find)

[teal oriole]

like getting 4x+C?

[umbral dome]

yes, then plug in the bounds

[teal oriole]

but the answer would be different depending on C

[umbral dome]

the c cancels out

the C's always cancel out when doing definite integrals

[teal oriole]

how do they cancel out?

[umbral dome]

if F is your indefinite integral, then the definite integral (with bounds) is F(upper bound) - F(lower bound)

[teal oriole]

thanks, that makes sense

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[dense nexus]

why is the 20.0 N here not negative?

[limber flicker]

W = 2 * 40 + (6-2)(-20)

W = 2 * 40 - (6-2)(20)

W = A_1 - A_2

it is, they just yoinked the negative

[dense nexus]

but i still got the wrong answer

[limber flicker]

u shouldnt

[dense nexus]

after all of this, i did 80 - -80 which gave me 160

[limber flicker]

can u show full working? I'm not sure why they have written it this way as it is confusing

[dense nexus]

i can't anymore, i moved on to another problem

[limber flicker]

the work is the sum of those areas you compute, and A_1 is positive, A_2 is 'negative' so the total work is A_1 + (-A_2) which is just A_1 - A_2

the negative comes from the force which has the negative sign slapped on it

so when you write it in the form A_1 - A_2 , the force in A_2 no longer has the negative in it

I don't really recommend doing it this way, as it is just confusing, just use the negative on the force, and know that the work is the sum of the area.

[dense nexus]

so this is -40 too?

[limber flicker]

yes

[dense nexus]

bruh

khan academy is stupid

im just practicing for an upcoming test

[limber flicker]

these ARE negative forces

the negative infront has been taken out to the front

-(4)(20) = (4)(-20)

[dense nexus]

oh, why?

oh wait, because the area is in the negatives right?

[limber flicker]

because , well I don't know why they would do that, it is just notation, and it makes it confusing

you'll get the correct answer if you just do W=A_1 + A_2 + ....

and have the force with the correct sign in each A term

maybe this makes it a little clearer

W = A_1 + A_2

A_1 = (4)(-20) = -80

A_2 = 1/2 (4) (-40-(-20)) = -40

@dense nexus stick to this, keep the negative attached to the force, it makes it much clearer

[dense nexus]

ok ok, highschool test would do this right?

[limber flicker]

It doesnt matter what they do, its notation choice , the answer is the same as you can see

One just makes sense, the other is the reason you are confused

[dense nexus]

ok

thx

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[vagrant tangle]

The question is to find a power series representation for the function and then determine the radius of convergence.

My question is if I'm on the right track for this? I am not a hundred percent certain where to go from here, but my guess is to derive again twice more so I end up with no arcan left, and then simplify, but it seems like that will be a nightmare so before I do it I want to confirm that is in fact how to solve this

[umbral dome]

it's probably possible to do it that way, but i think the easiest way would be to:

1. find a power series for arctan(x)
2. substitute x for x³
3. multiply by x²

[vagrant tangle]

Oh, I can do it that way?

That's a relief

I already know the power series for arctan I just wasn't sure I could jump straight there

Thanks for saving me probably 40 minutes of useless work lol

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[sleek quest]

what do i do in this problem? im stuck

[upbeat crag]

think about modifying sum of 1/2^n

changing just a tiny bit should be enough

[sleek quest]

wdym?

[true wraith]

@feral wren

[inland dagger]

Hi, is anyone there?

[true wraith]

@inland dagger

[upbeat crag]

you know how

1/2+1/4+1/8+1/16+1/16 or stuff like this = 1 right

but then you see there’s two 1/16s 1/16s

try modifying it a little bit

[upbeat crag]

hint: look at the example given here

[inland dagger]

?

[sleek quest]

yeah, but that wouldnt work for odd n

oh wait

its just n numbers

[upbeat crag]

why not?

example for n=5: ||1/2 + 1/4 + 1/8 + 1/12 + 1/24||

open spoiler at your ownc aution

[sleek quest]

interesting

[upbeat crag]

u get it or

[sleek quest]

1/8 is repeated in a way

[sleek quest]

=1/2+1/4+1/8+1/8
and same for n=5

[upbeat crag]

so you can just construct the rest of the cases

cuz this readily generalizes

[sleek quest]

it always adds to 1/8?

for the last 2?

[upbeat crag]

then make it add to another number you like

1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/32 = 1

but there are two 1/32s

try changing a 1/32 to something else

[upbeat crag]

(this is the case for n=7)

[sleek quest]

1/(16*2)?

[upbeat crag]

no like

change 1/32 to a sum of two reciprocals

[sleek quest]

oh

1/64+1/64

[upbeat crag]

such that you dont have two same reciprocaisl

[upbeat crag]

well then now you have two 1/64s

[sleek quest]

ohhhh

i see it now

[upbeat crag]

ggs

[sleek quest]

thanks!

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[proper grotto]

the asnwer is d right?

[empty sapphire]

well the curve is certainly concave up

so it can't be (d)

so that leaves (a) or (b)

[proper grotto]

u can see the arc is decreasing

soo it cant be a

[empty sapphire]

I would actually say the arc is increasing

remember what we're looking for is how much f(x) increases, not x

also I'm assuming that (b) is supposed to be ARC and IRC

[proper grotto]

so then its a

hmm

[empty sapphire]

I mean arc is a weird word to use here. But no it's not a

remember it's increasing as x goes onward

not decreasing

[proper grotto]

so then which one do you think isnt true

[empty sapphire]

oh

oh my bad

yeah it's a

lol

[proper grotto]

lmaooo

i was confused for a sec

[empty sapphire]

forgot we were looking for not true

[proper grotto]

i read the questin wrong to at first ur good

[empty sapphire]

sounds good, glad you gotit

[proper grotto]

thanks for the help g

[empty sapphire]

np

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Please don't occupy multiple help channels.

[arctic wedge]

What have you tried?

[fast verge]

I am not understanding the question properly

[wild sleet]

same

[fast verge]

What is comprime factors?

[wild sleet]

how do you count that

[fast verge]

Should i use euler phi function

Then factors again

[wild sleet]

google says they mean "pairs"

[arctic wedge]

I would take it to mean touples rather than just pairs

As long as all of your numbers are co prime

[wild sleet]

maybe

[fast verge]

How to solve it?

Should I have to use euler totient function twice?

[wild sleet]

they mean literally pairs of any 2 coprime factors

like (1,4)

i think

[fast verge]

So i got 192

And when i apply euler again i got 64

Anyone there?

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[weak iron]

@fast verge you can only have one ticket open at once

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[pliant grove]

How would I solve this?

[pliant grove]

I just need help starting I don’t need help for the whole thing

[tacit sapphire]

log

with the base of 3

[pliant grove]

Thankyou very much

[hot herald]

base e or 10 would be more convenient if you're going to use a calc later to get an approximated value

[tacit sapphire]

ye

[pliant grove]

So Log10(3) =x
And Log10(2) =x+1?

[hot herald]

no

[pliant grove]

x •Log3= x+1 • Log10(2)

[hot herald]

missing ()

[pliant grove]

Log10(3)

[hot herald]

$x\log(3) = \red{(}x+1\red{)}\log(2)$

[glossy valve]

ℝαμΩℕωⅤ

[pliant grove]

Oh yeah I forgot to put it in brackets but I new it was one term

[hot herald]

if you don't write stuff properly, you might forget one or two steps down the line

[pliant grove]

Yeah I will make sure

[hot herald]

also makes it a pain for others to read your work

and deduct marks depending on how strict they are

you now essentially have a linear equation
solve for x

[pliant grove]

Thankyou very much

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Please don't occupy multiple help channels.

[restive roost]

oh

oops i forgot to close.

.cose

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[twin wolf]

How do I proceed with this

[twin wolf]

I thought to bring it to base e and do a u-sub for e^x but it didn’t work because of the ln3 attatched

What do I do?

[wise wyvern]

what's your u?

[twin wolf]

u = e^x

[wise wyvern]

What why

[twin wolf]

why not?

[wise wyvern]

Well, I suppose there isn't a reason for not, but there certainly were better choices.

[twin wolf]

Like e^(x+2)?

[wise wyvern]

no.

(x+2)ln(3)

[twin wolf]

well what then?

[wise wyvern]

Entirely.

[twin wolf]

Oh

i didn’t think I could do that

[wise wyvern]

You can.

[twin wolf]

I guess it makes sense

[twin wolf]

if I do this then do I have to bring it back to its original form of e^(x+2) when I differentiate it or can I treat (x+2)ln3 as if they were multiplying

[wise wyvern]

latter.

Because I'm not sure what the former means.

[twin wolf]

i dont know what either means

[wise wyvern]

Well let ln(3)(x+2) as u

Then differentiate and get du

Then sub

[twin wolf]

boooooo

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[upbeat wren]

hello, can someone help me prove that real numbers are a subset of complex numbers and explain it to me

[scarlet herald]

Because the real numbers can be viewed as complex numbers with the imaginary part being 0

[upbeat wren]

can you explain the first part

[scarlet herald]

When i learn the language

[upbeat wren]

i just mean ofr example,

its trying to prove that r is a set

why is it taking those actions

[scarlet herald]

What is a complex number @upbeat wren

How is it written

[upbeat wren]

a+bi

[scarlet herald]

What is a real number

[upbeat wren]

i understand that its expressed with real numbers but still

[scarlet herald]

How is it written

[upbeat wren]

what does the book say

is there something else i need to know?

[scarlet herald]

I don't know what the book says lol im asking you

[upbeat wren]

yes

[spice orchid]

They are showing that elements of the set of the form (something,0) are closed under the operations

[upbeat wren]

and what about

the square of )=(0,1) being

-1

[spice orchid]

Multiply (0,1) by itself using the rules of multiplication in this set

[upbeat wren]

isnt it

(-1,0)

oh and thats -1

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[torn jolt]

can anyone solve some complex number problems? might take some time to solve all of them
https://media.discordapp.net/attachments/1167734578648199219/1172927229798387722/IMG-20231111-WA0002.jpg?ex=6562189b&is=654fa39b&hm=976662066a2cc9f9953cc3392f08ffeed01124957fe05eee776379f2693e44f7&
https://media.discordapp.net/attachments/1167734578648199219/1172927229500596294/IMG-20231111-WA0003.jpg?ex=6562189b&is=654fa39b&hm=659ac64a32c454418d2bdf881ce978e4cd54d1458ab6d10e92d95c2c9a6cef34&

[torn jolt]

@raw aurora

[smoky wing]

Blud noones gonna do all these qs

[tight tinsel]

what is ur major @torn jolt

[torn jolt]

it's Asya's

she in 12th grade

[tight tinsel]

nope

[raw aurora]

Yup it's for me

High school student

[tight tinsel]

this is not suitable for 12th grade

[torn jolt]

I swear right

[tight tinsel]

which country do u live i

n

[raw aurora]

Idk bro I wanna cry

[smoky wing]

How old is that

[torn jolt]

like I am also in 12th but my complex number is a lot easier

[raw aurora]

I'm from Syria but I live in Lebanon

[tight tinsel]

your name sounds like Turkish

[torn jolt]

it's common everywhere

[raw aurora]

No I'm Syrian its an Arabic country

[raw aurora]

Yesss

[torn jolt]

so do u have difficulty in understanding all of these problems or just few

[raw aurora]

Not all of them

[torn jolt]

specify which ones you have difficulty in understanding, will make it a lot easier

oh shit another one

[raw aurora]

This one from the last year it comes in the final exams

[torn jolt]

you need this done as well?

[raw aurora]

We wanna solve it also

[torn jolt]

3 pages of problems..

[smoky wing]

Choose one question to start with

Noones gonna sit with you and do all of them

[tight tinsel]

pretty good idea to start

[torn jolt]

yeah

[raw aurora]

I want to solve the first 2 that u send them

[torn jolt]

choose one from there, the one you have the most difficulty in understanding

then we continue

[raw aurora]

I'll start by this one

[torn jolt]

I mean one single problem/question not the whole page hehe

😭

[raw aurora]

Okay I'll start solving it rn and I'll see

[torn jolt]

yeah

then ask specific questions so that it's easier for others to explain to u

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@torn jolt Has your question been resolved?

[raw aurora]

First part 1) i wanna transfer Z bare to Z
Then If I'll want to put a modulus | |
For |i|.|Z-1| ÷ |Z-1| = |-1| and simplify |Z-1| the answer ll be |i|=1 --->1 = 1

But how I'll do Z power 12 ?

[torn jolt]

anyone?

@tight tinsel @smoky wing

[smoky wing]

Which one?

[raw aurora]

Part 1

[smoky wing]

it would just mean z* = 1/(i-1)

[smoky wing]

I’m not sure what you did here

[raw aurora]

How did u calculate it ?

[smoky wing]

Setting z’ = 1 and you can solve for z* immediately

or z bar

[raw aurora]

But z'= -1

[smoky wing]

Whoops

Then z* is 2/(i+1)?

[raw aurora]

The problem is not z* we wanna solve z power 12

[smoky wing]

But we can solve for z by just conjugating it

[raw aurora]

Bro just forget I'll see tomorrow how to solve this

Thank u guys for ur time

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[lofty heath]

for the surface area

do I take the cube SA and subtract the cylinder SA?

I think I’m overthinking it

can someone just clarify

[proper hawk]

no

[lofty heath]

huh?

[glacial pasture]

it would be the SA of the cube, subtract the area of the two faces of the cyclinder
add the SA of length of the cylinder/curved face

[lofty heath]

so i subtract the cube SA with cylinder Sa and find the area of the two circles of the cylinder?

[glacial pasture]

no

you dont subtract the cylinder SA from the cube SA

[lofty heath]

okk

[glacial pasture]

imagine it

you have a hole where the cylinder would have been

that hole a wall that has area

which is the same as the circumference * the length of the cyclinder

SA of cube - 2(circular face area) + (area of side of cylinder)

[lofty heath]

why are we adding the side of the cylinder?

[glacial pasture]

because the hole has a wall of that area

its like a circular tunnel

the walls have area

[lofty heath]

oh ok

so area of a rectangle is w*l

do l is 15

*so

whats w?

6?

im confsued

[glacial pasture]

are you finding the cube SA?

[lofty heath]

no the area of the side cylinder thing

the curved reectangle

or square

cuz its a cube

[glacial pasture]

curved rectangle.....

anyway

its just the circumference of the circles * the depth/length

[lofty heath]

wait cant i just find area of the cylinder?

then the surface area

and then remove the two area of circle

s

[glacial pasture]

thats what i said

[lofty heath]

ohh ok

[glacial pasture]

actually, its that if you did it exactly how youre saying, youd have to remove the circle area 4 times, which is just unnecessary

2 is enough

[lofty heath]

ok so cube SA - area of two circles

and then what

[glacial pasture]

add the curved part of the cylinder

[lofty heath]

how

[glacial pasture]

.

[lofty heath]

lenght is 15?

[glacial pasture]

mhm

[lofty heath]

can u help me agian

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[true dagger]

Is the answer 6?

[royal hare]

No

[primal stag]

!show

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

[true dagger]

Each domain can have 3 maps

3 + 3 = 6

[primal stag]

ok is that all?

[royal hare]

Why 3 + 3 ?

[royal hare]

Also, you mean, each elements in the domain

[true dagger]

yh sry

[primal stag]

can you name em?

[true dagger]

(1, 1), (1, 2), (1, 3) (2, 1) (2, 2), (2, 3)

[primal stag]

ye true its 6

3x2 = 6

|A| x |B|
2x3 = 6

[royal hare]

No, it's not 6

[silk vine]

The Cartesian product is indeed 6

[silk vine]

And that’s what this is, the Cartesian product

[royal hare]

None of these are a map

[true dagger]

oh

[royal hare]

I will give you an example of one map between A and B

1-->1
2-->1

To every elements in A, you need to assign it an element in B

Here:

A = {1,2}
B = {1,2,3}

[silk vine]

For each map, 1 could be mapped to one of the 3 and 2 could be mapped to one of the 3

[primal stag]

so 6?

[royal hare]

No

[true dagger]

2 elements in domain can map to the same output?

[silk vine]

Yes

[royal hare]

Yes

[true dagger]

ah

[silk vine]

Not every map is one to one

[true dagger]

so 3x3 = 9?

[royal hare]

Yes

[true dagger]

ahh ok

thx

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[desert steppe]

How do I find the value of a here?

[torn jolt]

Use properties of log

Log base 9 a can be written as lna/ln9

Where the base of ln is e, but you can keep anything

@desert steppe

[desert steppe]

yeah but there are two unknown variables here

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[true wraith]

@feral wren

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[light lantern]

how does the example use the corollary to imply span(s) is subspace of R^3, i dont really get it

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[rustic pasture]

It's more clear by rewritting a₃=0 as 0a₁+0a₂+1a₃=0

The coefficient in the corollary is real number so it can be zero

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[runic spruce]

What formula is he using at the end to find the determinant

[red blade]

He?

[red blade]

They’re just doing the laplace expansion

[runic spruce]

Oh i get it just catching up

Thanks

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[left moon]

how do i do the very last box

[smoky wing]

What are the areas of the squares when n=1,2,3 etc

[left moon]

4, 8, 12, 16

wait

oops

mb

wait

idk

how i got that

hehhehehe

OOPS

[smoky wing]

okay chill

[left moon]

idk why i got that or how i got that 💀

[smoky wing]

neither

[left moon]

1, 4, 9, 16

[smoky wing]

Yeah do you see the pattern

Think about the formula for the area of a square with side n

[left moon]

i jus know that the second difference is 2

[smoky wing]

It’s really simple

[smoky wing]

Sure if we want to do it that way then 2nd difference is 2 means we have n^2

(Since you need to divide it by 2)

And plugging in n = 1,2,3 checks out so indeed n^2 is the answer

But you can see this from just looking at the area of a square with side length n

[left moon]

o

icic

how do i write the function from there

[smoky wing]

Just n^2?

That gives you the area of a rectangle of side length n

[left moon]

oh mb 😔 😔 😔 😔 😔 😔 😔 😔 😔

thank you for your helppp

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[marsh prairie]

How is it not 36? I get how they got 31, but can’t you just get 6 in the outside and multiply by the 6 inside

[static bramble]

What do you mean "get 6 in the outside?"

[craggy tapir]

he probably meant doing 1+5 on the outside first then multiply with the 77-71 on the inside

[static bramble]

Perhaps but I'd like to hear it from him

[marsh prairie]

Five plus one

[marsh prairie]

Yeah that’s what I did

Or is it just a matter of pemdas

[craggy tapir]

it's PEMDAS

you are supposed to do calculations in the parentheses first, then the multiplication then addition

[marsh prairie]

Ok thanks

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[terse hearth]

Hi, for num 47, whats a quick way to tell that you cannot write a linear combination?

[terse hearth]

This is what i worked out. Plugging back my C values, eqn 3 and 4 do not work

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[somber eagle]

at the 2nd step here, can i just sub in 1-2cos(4x)+(1-sin^2(4x)) instead?

and just do substituion for sin(4x)?

i get a wildly different asnwer though

i get du/2 = 2cos(4x) dx in the sub

oh i guess i cant right

i get 1 + ( 1 + u^2 ) - du/2

doesnt make sense

am i right on this

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[light lantern]

thanks bro

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[hushed agate]

Hi, could anyone help me with the second question?

[torn jolt]

you'd have add t_36 + t_35 + t_34 + ... + t_16, where t_n means number of seats in nth row

as it's an AP,
t_n = a + (n - 1)d
t_36 = 17 + (35) * 3 = 122
t_35 = 17 + (34)*3 = 119

it's basically sum of an AP whose first term is 122 and common difference is -3

use sum of AP formula \ \
$S_n = \frac{n}{2} (2a + (n-1)d)$

[glossy valve]

notamy

[torn jolt]

in this case, a = t_36 = 122, d = -3, n = 20

[hushed agate]

!thx

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[torn jolt]

you're welcome

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[elfin citrus]

Could someoon helo?

[lapis yarrow]

$\frac{1}{a^{b}} = a^{-b}$

[glossy valve]

Tangerine

[craggy tapir]

a^-x = 1/a^x

^

[elfin citrus]

what

[lapis yarrow]

which part do you not understand

its a rule

[elfin citrus]

im 14

no way thats the awnser

[lapis yarrow]

in this case a is 14, b is 9

[craggy tapir]

yes way thats the answer

[lapis yarrow]

$\frac{1}{14^9} = 14^{-9}$ if you still don't understand

[glossy valve]

Tangerine

[elfin citrus]

thats whaat the awnsers look like

[vestal bridge]

yeah

and it says what goes in the box

[lapis yarrow]

so you put -9 in the box

[elfin citrus]

no offence but i dont see like [pax] a^ whatever

[lapis yarrow]

whats so hard to understand

[elfin citrus]

okayy

[lapis yarrow]

??? a and b are unknowns

[vestal bridge]

yo

this is your problem

it says what goes in the box

[elfin citrus]

Ty

[lapis yarrow]

youre not supposed to literally use a and b to answer the questions

[elfin citrus]

No i understood

[lapis yarrow]

ok

[spiral hearth]

the answer should be -9 if i am correct

[lapis yarrow]

he already got it

[spiral hearth]

then why didnt he close the channel?

[lapis yarrow]

no idea

[spiral hearth]

💀

@elfin citrus please close the channel if there are no further questions

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[digital turret]

What's the awnser to this i been stuck here for an hour

[elfin compass]

No. Shaded Squares / Total Squares

[blazing nest]

Number of shaded squares / total number of squares

[digital turret]

Ik but the hard part is trying to simplify it

[blazing nest]

is there a common factor for both the numerator and denominator thats not 1?

[torn jolt]

Can anyone help me expand this log

[elfin compass]

use different channel not here

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[stark folio]

where can I find the exact forms of trigonometric functions of an acute angle or how can I calc it?

[fast peak]

what exactly do you mean with "exact form"

[stark folio]

like in the sin(45°) = (sqrt(2))/2 and not the approximate value which is ~0.7071

[torn jolt]

you cant for most angles

infact most angles will give you trancedental numbers

[queen crater]

Might be worth a read https://en.wikipedia.org/wiki/Exact_trigonometric_values

[stark folio]

but if there was a way to get approximate values then there should be the exact values somewhere

[stark folio]

that will work, thx

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[torn jolt]

trig functions are mostly approximated with their taylor series

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[fathom cairn]

Is this correct

[strong compass]

Remeber to subtract f(2) = 5 for your numerator

[fathom cairn]

Omggggggggg then it'll work

forgottt

tankkk youuuuu

[strong compass]

Glad to help!

[fathom cairn]

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[fiery vigil]

how would i solve for me?
f = 1/2pi sqrt(k/m)

[fiery vigil]

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[fiery vigil]

what is (1/2*pi)^2

[worn matrix]

pi^2/4?

what do u mean

[fiery vigil]

well for this equation

f = 1/2pi sqrt(k/m)

i would have to square the f

so f^2

[spice orchid]

you presumably mean 1/(2pi)

[fiery vigil]

and i would have to square the 1/2pi right? along with removing the sqrt(k/m)

yes

[spice orchid]

then just square the top and bottom of the fraction

[fiery vigil]

1^2 is 1

and 2pi squared

is 4 pi^2

[spice orchid]

yes

[fiery vigil]

so my mass would be

m= 1/4pi^2 * k / f^2

[fiery vigil]

?

[spice orchid]

sure

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[nova basin]

solve for n ?

[smoky wing]

Are you not given more info? Show the whole question.

[sage harbor]

it series sum

i think this is proof think

it series sum if it 1+3+5+7+9......

so first 8 term is 8a1 + 28d

n/2 ( -30.5 + 4.5n) < 200

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[sage harbor]

i gonna say n = 9

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[waxen panther]

Hi guys could anyone spare some time to help me
Participants in the descriptive statistics lecture in the 2014/2015 winter semester were asked at the start of the semester
of the semester about stays abroad, among other things. The following (partial) results were obtained
for the 44 survey participants who answered this question:
27.27 percent of respondents were female and stated that they would like to spend a semester abroad during their studies.
semester abroad during their studies. 63.64 percent of male respondents do not plan to spend a semester abroad during their studies.
semester abroad during their studies. Overall, 45.45 percent of respondents want to spend a semester abroad.
given this text
i should fill out the kontingenztable
I have 2 events:

M = Male
A = Semester abroad
44 Participants
So 27,27 are female and like to spend a semester abroad

F(not M and A) = 27,27
If i want to get the absolute frequency
it would be 0,2727 * 44 = 11,9988
But somehow my kontingenztable doesnt make any sense if i do it like this

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[tight tinsel]

can someone prove these two

[red blade]

ofc

[tight tinsel]

i need well explained answers please

[red blade]

nvm then

!nosols

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

[quaint prawn]

We have a new better factoid for this situation

!noans

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The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[red blade]

ty austin

[quaint prawn]

Melih I’d be willing to work with you on the second question

Have you ever seen a proof for why the square root of 2 is irrational?

[tight tinsel]

ik that

[quaint prawn]

Likely you can do something using that fact here

Maybe an argument by contradiction

If this is rational, then => sqrt2 is rational

And then you’d be done

Or something similar

Just a thought

[red blade]

mhm

or you could do the standard way

of sps. that root 3(200) = a/b

for some a, b \in Z+ or sm

[tight tinsel]

gcd(a,b)=1

so?

[jaunty mountain]

hm

[red blade]

ye ye

maybe you can use 4 or sm in ther

eidk

[quaint prawn]

And likely all you need for your first question is to write out all of your definitions (but in the future, try to stick to asking one question at a time)

[red blade]

^^

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[spark vapor]

i dont get this example

[spark vapor]

in my head you can jsut calculate -5 mod 12 and 19 mod 12

and see that they are the same

i dont know what property this is because if it were n | b - a, then that would be -5 - 19 = -24 / 12 = -2

idk

i think there is a gap here

[obsidian agate]

Umm

I haven’t seen this before sorry

[dense vector]

yes correct..what's the query exactly?

[spark vapor]

i dont know how does it show that like

the congruence is true

[dense vector]

what you did is absolutely fine

the one with the image

[spark vapor]

why does it work

[dense vector]

if you have to prove a = b mod c where = refers to modulo then just show that b - a is an integer multiple of c

[dense vector]

it's the definition

if take a number x and divide with d you get a quotient q and remainder r..in this case we define x = r mod d where = again means congruence modulo

[spark vapor]

ohhh because there is no remainder

[dense vector]

remainder r can be anything ranging from 0 to d - 1 both inclusive

[spark vapor]

i hate this part

this congruence baby number theory stuff

[smoky wing]

It’s fun

You’ll learn to love mod

[dense vector]

I think it makes life a lot easier tbh

[spark vapor]

im trying to learn how to like this math and it is so hard

because my next class is basically this class on steroids

like stuff with autonoma

and other cs shit

[smoky wing]

Oh btw I saw this guy post a really nice mod question last night and stole from him

[dense vector]

which course is this?

[spark vapor]

something like discrete math

its like, the fundamentals of discrete math

thats i guess what its called

[dense vector]

Ohh... Idk whether it involves heavy stuff revolving congruence modulo

anyways I do love this topic and as I mentioned earlier you will realize that things do get easier if you use this

also most of the properties are very similar to equality and easier to understand

[spark vapor]

I wan to love this stuff

like functional programming is like

only induction

and functional programming sounds interestign

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[twin wolf]

Why and how does completing the square work in integration

[twin wolf]

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[nova crater]

my work so far. I'm having trouble doing this trig sub. I don't think this looks right

[gritty rose]

Looks fine. Just substitute back in for x

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@nova crater Has your question been resolved?

[nova crater]

Would this be the final answer?

[gritty rose]

,w int 1/(9-x^2)

[glossy valve]

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Requested by rie.mann

[gritty rose]

could be? mess around with the algebra and see if that's the same as what wolfie says

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@nova crater Has your question been resolved?

[nova crater]

<@&286206848099549185> The question and my attempt at the answer is above. Is my answer correct? Or did I do something wrong?

[royal oar]

Looks correct to me

[nova crater]

Nice. thanks for verifying

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[red blade]

maybe

maybe not

[red blade]

what is 100/605 * 500

and

2.4 / 4.5 * 500

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[barren iris]

can someone explain this step?

It looks like dy / y - r/b ?

he factored out a b

didn't he

[glacial pasture]

you can think of it like that yeah

[barren iris]

why did he do that

[glacial pasture]

they factored out 1/(-b) from the fraction, then multiplied by -b

[barren iris]

why?

[glacial pasture]

hm one mo

[barren iris]

I imagine it's to make the integral easier

but I don't see it yet

[glacial pasture]

if they did the integral as is, they would have to factor out a (-b) anyway so its in the form f'(y)/f(y) for ease

so they just multiplied by -b to get it into that form

[barren iris]

dang

that wasn't easy for me to see

sheesh

okay ty very much

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[nova crater]

Abs/Cond conv. or diverges

It passed the Alternating series test, but I'm not sure what to do from here

[smoky wing]

Didn’t need derivative tbh, we know ln(n) < ln(n+1) so 1/ln(n) > 1/ln(n+1)

What you do mean you don’t know what to do from here?

It converges by alternating series test

[nova crater]

It asks if it converges absolutely or conditionally

The ratio test was inconclusive so I tried this test

[smoky wing]

Does 1/ln(n) converge?

[nova crater]

yes

[smoky wing]

No

Compare it to harmonic series

[barren iris]

Harmonic series diverge !

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[nova crater]

Got it. Just had to review what was considered a harmonic series

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[barren iris]

Could I get a hint on this step?

OH! so I think the way they got k = 0 was by using the facts given.
n = 1 , making n odd. So, n = 2k + 1.
We startting with n = 1 so I think I can rewrite n as 1.
1 = 2k + 1 -> 0 = 2k -> k = 0 ?

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[blazing tusk]

im not sure if i can ask boolean algebra here. i was wondering if someone can help with simplifying an expression: A'B'C + AB'C + BC'

so far, I got B'C(A'+A) + BC'
where (A'+A) simplifies to 1

and then I'm left with B'C+ BC'
but im wondering if there are ways I can simplify that expression

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@blazing tusk Has your question been resolved?

[grim skiff]

I think that's all you can do

[blazing tusk]

there's no inverse rule?

[grim skiff]

No

Because you can't factor out anything

[blazing tusk]

ahhh okay

thank you

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[astral wyvern]

How do I go about this?

[sick karma]

and obtain θ and α by using inverse trig

or you can use pythagorean theorem too I guess

[astral wyvern]

i know, but

[red blade]

but what?

[astral wyvern]

how would i get the y value of theta and the other angle?

or rather

[red blade]

you don't know that $sin^2(x) + cos^2(x) = 1$

[sick karma]

.

[glossy valve]

nosqldb

[red blade]

so that $cos^2(x) = 1 - sin^2(x)$

[glossy valve]

nosqldb

[red blade]

and $sin^2(x) = 1 - cos^2(x)$

[glossy valve]

nosqldb

[red blade]

and you can take the correct sign based on the quadrant

[astral wyvern]

ill check this out

but inverse has to be on a special angle if you dont use a calculator

[sick karma]

I'd probably go with pythagorean theorem in your case then

[astral wyvern]

i forgot about these

[red blade]

why did you do so

[astral wyvern]

and i relearnt them like twice

[red blade]

never do so again

[astral wyvern]

ok

thanks for the help

[red blade]

jsut don't forget the pythogorean identity

and ".close"

[astral wyvern]

wait

i got cos^2(theta) = 8/13

so do sqroot now right?

[gray spruce]

ye

[astral wyvern]

ok

ill close soon, just finishing it up

Is this correct?

i dont feel like its correct, but

i dont see how its incorrect either

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[torn jolt]

i need help with expanding and simplifying. i do understand i just dont understand in one example

[torn jolt]

like the middle answer is not what i expected

(x-7)(x+2)

answer: x^2 - 5x - 14

so my understanding is

[marsh tusk]

you multiply eac

[torn jolt]

listen bruh

how i worked it out referencing the answer is

i get x^2

i get the last one whicih is 14

but whered 5x come from

[marsh tusk]

-7 multiplied by x is -7x

x multiplied by 2 is 2x

2x+-7x = -5x

[torn jolt]

ok thx

why would 5x be in the answer tho

originally i thought itd be x^2 + 14

@marsh tusk

[marsh tusk]

try factorising x^2 + 14 then

it wont be able to turn into the double brackets you had originally

[forest widget]

you can also substitute x for random numbers to perform quick checks

[marsh tusk]

its just how it works multiply each term in one bracket by everyterm in the other bracket and simplify the equation

[torn jolt]

bro im expanding and simplifiying not factorising 💀. i tryed factorising topic yesterday and i was struggling

[forest widget]

geometric intuition is this basically (also grid method above)

[torn jolt]

bro 💀 thats the next thing i have to do but i dont wanna

idk why it feels off

[marsh tusk]

i recommend khan academy algebra 1 unit 13

to practice all of this

[torn jolt]

alr

[marsh tusk]

https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring

this

[torn jolt]

bro the website is so complicated

[torn jolt]

asking for why theres an addition here tho

@marsh tusk

[marsh tusk]

because you add the terms you get together

u dont need it

it doesnt nothing because the subtraction connected to 7x cancels it out

[torn jolt]

so -7x +2x ?

[marsh tusk]

yeh

eah

yeah

no difference

[torn jolt]

wait no

like terms get added so that means there an addition?

correct?

@marsh tusk

[marsh tusk]

idk what ur talking about now lol

do you not know that $2+-2$ and $-2+2$ is the same thing

[glossy valve]

`

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[tidal aspen]

Wanted to make sure that I understand how to do this problem, do I simply insert the x and y from the point into the graph, or graph the equation?

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[tidal aspen]

.close

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[unreal hull]

am i supposed to distribute the ^4 first or something?

[unreal hull]

how do i start this problem?

[umbral dome]

use the fundamental theorem of calculus

[unreal hull]

only need to know the first steps to slve

[unreal hull]

💀

getting trolled already

[shrewd hamlet]

If antiderivative of A is equal to B, how do u get from B to A

@unreal hull

[unreal hull]

take derivative

[torn jolt]

well, that's what the question is asking you. use chain rule to differentiate

[shrewd hamlet]

Ye so take derivative

[torn jolt]

are you facing problem while differentiating the function? @unreal hull

[unreal hull]

wait what

its just asking me to take the derivative?

[torn jolt]

ye, derivative of (5x^2 + 3)^4

[torn jolt]

^^

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@unreal hull Has your question been resolved?

[unreal hull]

wait i had to do something

let me solve now

[unreal hull]

no?

[sharp thorn]

the derivative of (ax^2+b)^n is n[(ax^2+b)^(n-1)]2ax

where did the n-1 go

[unreal hull]

oh ye

i got it right

[unreal hull]

but why is the integral sign there if the question only requires me to take the derivative?

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[haughty flower]

i need help with like short answers in math's ( in 8-9 grade). could someone give me like a quick run down?

[undone vector]

Post a question and we can help

[haughty flower]

8p + 2= 1 - 3p

[naive kite]

add 3p to both sides

to get 11p + 2 = 1

then subtract 2 from both sides to get

11p = -1

then divide both sides by 11

p = -1/11

[haughty flower]

thank you so much!

[naive kite]

dm me if you need any help with questions alike

:)

or @ me

[haughty flower]

ty 😄

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[haughty flower]

🙂

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[rose parcel]

Hi everyone!! I have this problem -> Given the system AX=b, where A and b are the matrices shown below, rationally determine the value or values of the parameter "m" so that the system is determined compatible

[rose parcel]

I don't know how to deal with the variable 'm' inside the array. I don't know how it would be found. If anyone can help me? Thanks!

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[rose parcel]

<@&286206848099549185>

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