help-36

[atomic spindle]

I think x is differentiable for all x in the interval (-infinity, 4) but im not sure
y = sqrt(4-x) btw

[winter sleet]

y

[atomic spindle]

bc of the domain

actually

its , 4) bc it cant be sqrt0

im pretty sure

[winter sleet]

y has derivative, and 0^2=0

[atomic spindle]

so its (-infinity, 4]?

[atomic spindle]

what does this mean

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[fervent oar]

differentiate

[worthy shale]

yeah?

[fervent oar]

ive finished the quotient rule and got y' = 2(x^2+6 / x^2+6)(-24x/(x^2+6)^2)

[worn barn]

can someone help

pelase

[worthy shale]

#❓how-to-get-help

[worn barn]

#help-33

[fervent oar]

huh

ping @ helpers

for help

@worn barn

[worn barn]

i did

[worthy shale]

$y'=2\frac{x^2+6}{x^2-6} ~\frac d{dx}(\frac{x^2+6}{x^2-6})$

bruh

[soft zealot]

chlamydia

[worthy shale]

and then

[fervent oar]

i did that im just stuck on the algebra part

after quotient rule

[worthy shale]

yeah i'm just working it out here

[fervent oar]

oh alright

[worthy shale]

what algebra part

[fervent oar]

after quotient rule, i got -24x over (x^2-6)^2

[worthy shale]

$\frac d{dx}(\frac{x^2+6}{x^2-6})=\frac{2x(x^2-6)-2x(x^2+6)}{(x^2-6)^2}$

[soft zealot]

chlamydia

[worthy shale]

which you got

so $y'=2\frac{x^2+6}{x^2-6} ~\frac{-24x}{(x^2-6)^2}$

[soft zealot]

chlamydia

[fervent oar]

yes so far thats where im at

[worthy shale]

$=-48\frac{x(x^2+6)}{(x^2-6)^3}$

[soft zealot]

chlamydia

[fervent oar]

how do i combine it though is the thing

its just the fractions that are confusing for me

[worthy shale]

combine what

[fervent oar]

this, like whats the process for combining them

[worthy shale]

they are all multiplied together

so 1/(x^2-6)* 1/(x^2-6)^2 becomes 3 of them

which is (x^2-6)^3 on the bottom

yeah?

[fervent oar]

alright

the assignment is saying its wrong though?

[worthy shale]

that's too many xs

[worthy shale]

you got this right?

[fervent oar]

oh alright i got it

[worthy shale]

ok

ok

[fervent oar]

its just the algebra towards the end thats confusing for me

like sometimes im not sure if i should distribute or not

thank you though

i appreciate it

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[sonic thistle]

Not sure what I am doing wrong the qoutient I got was 3x+1

[sonic thistle]

3x gave me 3x^2-9x for substraction which left me with x-2

[worthy shale]

it should be -x-2 right?

-10x-(-9x)=-x

[sonic thistle]

Oh yes -x-2

[worthy shale]

so quotient is 3x-1?

[sonic thistle]

The rest is fine?

[worthy shale]

you'd have to find the remainder again

[sonic thistle]

Oh yea

okay wait

So if I take the negative does that change it to -x+3

[worthy shale]

yes

[sonic thistle]

Or do I still subtract -x-3

ok

so remainder is 1

Nope I am dumb

grr

Cause with -1 I get (-x-2) - (-x+3)

Wait

[worthy shale]

yeah

[sonic thistle]

negative 5

Thank you!

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[daring sleet]

need help on this one

<@&286206848099549185>

[tranquil pine]

hi

[daring sleet]

hey

i need some help here

how do i prove this using trig. identites

[tranquil pine]

what's the overall question

[daring sleet]

its number 1

in the first pic

[tranquil pine]

what does it say?

It's a bit blurry

[daring sleet]

is it blurry?

okay

[tranquil pine]

plus my monitor is crap

use Latix syntax maybe

[daring sleet]

can u see?

[tranquil pine]

we need to find d/dx[tan(x)]?

[worthy shale]

,rotate

[daring sleet]

dang thats neat

i beleive thats what its asking

sinx/x=1. compute deriv. of tangent function using trig identities

[tranquil pine]

so d/dx[tan(x)] = lim{h -> 0 } (tan(x + h) - tan(x))/h

[daring sleet]

do what?

[tranquil pine]

turn tan(x) to sin/cos

in the limit

and try simplifying until you get something like lim{h ->0} sin(h)/h + ...

remember sin(a + b) = sin(a)cos(b) + cos(a)sin(b)

[daring sleet]

so was this work incorrect?

[tranquil pine]

put the limit

[daring sleet]

okay i added it

[tranquil pine]

use

[daring sleet]

why am i trying to get it to look like that? to make it similar to a trig identity?

[tranquil pine]

make it similar to lim h -> 0 sin(h)/h

[daring sleet]

okay

simplify this down?

[daring sleet]

or use this?

i apolagize im really bad at this

Am I onto something here

[tranquil pine]

wait

I'm working on it

[daring sleet]

okay take ur time

i have no clue what im doing tbh

just learned all this friday and suppose to have this done by tmr

[tranquil pine]

no worries

[daring sleet]

gettin anywhere?

[tranquil pine]

yeah

got: https://www.mathcha.io/editor/DNl5vhgjiNJCPGX3oQs7EBZBviV98QWGFOyv1kw

but got stuck

sorry

[daring sleet]

whats the link?

no problem

can i go to another person?

<@&286206848099549185>

[final saddle]

@daring sleet Has your question been resolved?

[worthy shale]

$\lim_{h\to0}\frac{tan(x+h)-tanx}h=\lim_{h\to0}\frac{\frac{tanx+tanh}{1-tanx~tanh}-tanx}h$

$= \lim_{h\to0}\frac{tanx+tanh-tanx+tan^2xtanh}{h(1-tanxtanh)}$

[soft zealot]

chlamydia

chlamydia

[worthy shale]

$=\lim_{h\to0} \frac {tanh}h \frac {tan^2x+1}{1-tanxtanh}=sec^2x\lim_{h\to0} \frac {sinh}{hcosh} \frac 1{(1-tanxtanh)}$

[soft zealot]

chlamydia

[worthy shale]

using $\lim_{h\to0}\frac{sinh}h=1 , cos(0)=1, tan(0)=0:$

[soft zealot]

chlamydia

[worthy shale]

$=sec^2x\lim_{h\to0}\frac1{1-0}=sec^2x$

[soft zealot]

chlamydia

[daring sleet]

got a question

[worthy shale]

yup

[daring sleet]

what would be my next step?

[worthy shale]

shouldn't that y be h

you should common denominate

[daring sleet]

yes good catch

[worthy shale]

it will help cancel things

[daring sleet]

how would i do that?

[worthy shale]

you also need tanx/h instead of tanx if you're splitting the fraction (3rd line)

[worthy shale]

make tanx on the same fraction as the other term

[daring sleet]

Like this?

[worthy shale]

yes

and then bring them together over same denominator

[daring sleet]

?

would tanx on top then cancel

[worthy shale]

when you times by 1-tanxtanh on bottom, you have to do the same on top

otherwise it changes the expression

[daring sleet]

i see

gimme 1 sec

like that?

[worthy shale]

redo carefully from here

you've got some extra h's

[worthy shale]

this is the target

[daring sleet]

in the denom?

[worthy shale]

at the start of both top and bottom

[daring sleet]

am i good so far

[worthy shale]

yes

[daring sleet]

when i create common denom. wouldnt it be everything on left times h?

in the denominator

[worthy shale]

like h(1-tanxtanh)?

[daring sleet]

h(h(1-tanxtanh))

[worthy shale]

but you already have a h there

you don't need to multiply by another h

you just need the denoms the same

[daring sleet]

so would i subtract the h?

or just leave it

[worthy shale]

you leave it

$\frac a{bc}+\frac dc= \frac a{bc}+\frac{db}{bc}= \frac{a+db}{bc}$

can you understand this?

[soft zealot]

chlamydia

[daring sleet]

yes but i didnt know thats how it worked

actually im confused as to hpw the b got into num.

nvm i get it

hold up

damn that helped

Okay got it

[worthy shale]

what's with the tanh^2x

tanh is a different thing

[daring sleet]

got it fixed

[worthy shale]

so you've got $= \lim_{h\to0}\frac{tanx+tanh-tanx+tan^2xtanh}{h(1-tanxtanh)}$ right?

[soft zealot]

chlamydia

[worthy shale]

and there's a tanx and -tanx => 0

[daring sleet]

yes

so tanx would cancel?

[worthy shale]

yes

$= \lim_{h\to0}\frac{tanh+tan^2xtanh}{h(1-tanxtanh)}$

[soft zealot]

chlamydia

[worthy shale]

and then we have tanh on the top that we can factor out

[daring sleet]

ok lemme do that

i appreciat the help

okay got it

[worthy shale]

yup

[daring sleet]

can i take deriv now?

no

i see why now

[worthy shale]

huh

[daring sleet]

nvm

what should my next step be?

[worthy shale]

well there's a lot of parts to this fraction now
if you already know the derivative of tanx is sec^2x, then you could take the (1+tan^2x) out -- also because the limit with respect to h doesn't affect x

then the tanh/h, you could use lim(h->0)sinh/h=1

[daring sleet]

why could i take the (1+tan^2x) out?

[worthy shale]

because the limit h->0 doesn't affect x

[daring sleet]

what do you mean by take it out?

[worthy shale]

factorise it outside of the limit

$(1+tan^2x)\lim_{h\to0}...$

[soft zealot]

chlamydia

[daring sleet]

i coulnt do that to the bottom however because h is in it correct

thats a h not k sorry

[worthy shale]

in $\lim_{h\to0}\frac{tanh(1+tan^2x)}{h(1-tanxtanh)}$, tan^2x+1 is a separate multiplier

[soft zealot]

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

[worthy shale]

why is there sec^2h now

[daring sleet]

suppose to be tanh i thing

[worthy shale]

yes

[daring sleet]

okay fixed that

i honestly think im going to ask him about this one tmr

and no worry about it anymore tonight

i appreciate the help

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[tranquil pine]

What do I take on y axis?

Volume or pressure

Really confused

[dry light]

Pressure

It's whatever's not being manipulated

Pressure with increasing volume implies you're manipulating volume

Which is your independent variable

[tranquil pine]

Here too?

Volume on x axis right

[dry light]

Yeah

[tranquil pine]

Okay thank you so much

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[cyan adder]

hey i could i get some help with a question

[cyan adder]

i dont have a picture but i can type it out

i think it was

16^1/5 x 2^x = 8^3/4

so how would i figure out x?

[strange shore]

$16^{\frac{1}{5}} 2^x = 8^{\frac{3}{4}}$ ?

[soft zealot]

Herels

[cyan adder]

yes that was it

[charred chasm]

convert everything so that the exponents have the same base

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[abstract trellis]

for f and g i got 41.4

says i am incorrect can someone please correct me here

lower bound f and g i got 41.4

i did 49.15 - 7.75 = 41.4

upper bound f and g i got 41.4
i did 49.25 - 7.85 = 41.4

[onyx plank]

Smallest value of f-g is lower bro, so It should be 49.15-7.85=41.3.Same for upper you should get 41.5

[abstract trellis]

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[safe widget]

what should I do after I draw the 2 circles

[safe widget]

I am confused on the region of integration

is it the part where they both meet?

[frosty musk]

yea, we have two overlapping circles,
I'll split the region so our bounds look nice
if 0<=x<=1/2 then -(1-(x-1)^2)<=y<=(1-(x-1)^2)

can you see how to describe the overlap lying in 1/2<=x<=1

[safe widget]

sorry why are you doing 0 <= x <= 1/2?

This is what I have atm

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@safe widget Has your question been resolved?

[safe widget]

<@&286206848099549185>

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[copper grove]

Hi, I'm stuck with this problem, I have to find values of a, b and k, so that rolle's theorem can be verified

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@copper grove Has your question been resolved?

[copper grove]

<@&286206848099549185>

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@copper grove Has your question been resolved?

[round ocean]

can you write the question here because it's not clear

f(x) I can see

[copper grove]

F(x) ln(x) when x>1 and a x^2+b when x≤1

I have to find the values of a b and k, so the function verified rolle's theorem in [-1,k ]

[round ocean]

alright

sooo

you get a relation from demanding f is continuous at x = 1

and you get another from demanding f(-1) = f(k)

so a + b = k^2a + b?

what if you do k = 1

this would be so much easier if you wrote it cleanly

you said f = ax^2 + b, but your photo shows ax^2 + bx

@copper grove

[copper grove]

It's bx..

[round ocean]

consider a = 0.5, b = -0.5, k = e^2

f(-1) = f(e^2), function is differentiable in [-1,k], rolle's theorem applies

f'(x) = 0 at x = 0.5

[copper grove]

So, with that it's verified it's differentiable in that interval, so I guess I have to make each part equal to 1 and k?

[round ocean]

sorry my mistake

the triplet I gave is not correct

rather, k = e, instead of e^2

so f(e) = f(-1) = 1

[copper grove]

But how do you got to k?

[round ocean]

played in desmos with values

[copper grove]

Ah ok

[round ocean]

as you wrote, f must be continuous

and also the derivatives must agree on x = 1

then, find k such that f(k) = f(-1) = 1...

[copper grove]

Ahh ok

[round ocean]

I still dont get the point of the exercise

[copper grove]

Idk, to make us think how to get to those values (? Maybe

[round ocean]

e.g. try a =2, b =1 , k = 0.5. now f has a discontinuity, but rolle's theorem still applies to the parabola part

[copper grove]

Thanks!

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[brazen nacelle]

Are these equal?

[bleak granite]

yep!

negative can go on top/bottom or out front of a fraction

[brazen nacelle]

Thanks!

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[bleak granite]

[grim badger]

🙅‍♂️

[bleak granite]

[grim badger]

[brazen nacelle]

For the record youre joking right

[grim badger]

Yes

Me and mrfancy are bffs

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[merry plaza]

convert 265 degrees to radians. it said the correct answer is 53pi/18 but i got 53pi/36?

[bleak granite]

,w 265/180

[soft zealot]

Results provided by WolframAlpha

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

Requested by XxMrFancyu2xX#6050

[bleak granite]

53pi/36 is correct

worked solution probably did a simplfication mistake :)

[merry plaza]

thank you!

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[median widget]

I have this list $A = {6, 4, 3, 2}$ and I want to find the probability that the 4 digit number does not contain all same number, and does not contain triple of same number. So the following numbers are not valid, eg, $3333$ and $3334$.

[soft zealot]

RockLEE

[median widget]

there will be $4^4$ total elements in the sample space and we remove $4$ because there is only 4 elements that have 4 same numbers

[soft zealot]

RockLEE

[median widget]

idk how to remove 3 digit same numbers from this, can i get some help

Out of the four places, 3 places will be equiped by the same digit x, we can choose the positions in (4 choose 3) ways. The remaining spot can have 3 numbers so we multiply (4 choose 3 ) * 3. However, since there exists 4 numbers, therefore this is just (4 * (4 choose 3) * 3) = (4 * 4 * 3) = 48 ways to have 3 same digit element in 4 digits

So the final answer is $4^4 - 4 - 48$ ?

[soft zealot]

RockLEE

[median widget]

or is it $4^4 - 64$ i dont get it

[soft zealot]

RockLEE

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@median widget Has your question been resolved?

[median widget]

<@&286206848099549185>

[novel terrace]

for each number there are 9 different ways it could be repeated three times, and one way it could be repeated 4 times. so that's 4 cases of 10 repeated numbers you want to avoid, in a sample space of 256 (4^4), hence the probability of you avoiding those numbers are:

1 - (40/256)
= 216/256
= 27/32

@median widget

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[uncut granite]

i dont know how to begin, pls help

[uncut granite]

pls

heeeeeeeelp

[outer yacht]

find the term containing x^5 and x^6 in the binomial 3x+1

[uncut granite]

why x^5

[outer yacht]

because x^5 times x = x^6

polynomial degree

[uncut granite]

ok

but how do i do that

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[swift thistle]

i don't know how to solve point b and c

[swift thistle]

<@&286206848099549185>

<@&286206848099549185>

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@swift thistle Has your question been resolved?

[swift thistle]

<@&286206848099549185>

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[celest coral]

Suggest me a book/video/playlist or anything else that actually explains why and how to use probability and statistics. Preferably, something even a dummy would understand.

I feel like I've learnt half-baked stuff and confused myself with a lot of concepts during classes, especially with the hypotheses testing concept. So, I wanna relearn from the beginning (and if possible, unlearn as well). Tag me for reply

[plush merlin]

#book-recommendations

this is a more suitable place for your request

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[slender estuary]

never seen a problem like this, confused as to how to solve

[slender estuary]

tried u sub with ln4x as u, gives me 9int(sin(u)/x)

[prime oar]

by parts

[cosmic warren]

huh ngl woulda taken me ages to see the by parts method

[slender estuary]

they dont have to be separate before using parts?

[cosmic warren]

you're not using parts on sin and ln

If you have a function f(x), you can always express it as a product of f(x) times something

Well if you have any number

You can do that

Just gotta think of the right something :p

[slender estuary]

im not following

[cosmic warren]

Let v = 1 and u = f(x)

[slender estuary]

ah

[prime oar]

evil question im ngl

[cosmic warren]

Yeah

[prime oar]

even if you do by parts once it isn't super obvious what to do 💀

[slender estuary]

this is where im at

not sure how to progress tho

by parts again would just complicate it

[cosmic warren]

u didn't derive u right

chain rule

[slender estuary]

ah

lmoa

[cosmic warren]

Still not super obvious when you do it correctly tbh but yeah should at least have that part right

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[slender estuary]

got to here, but stuck again

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[stark apex]

does it matter if u switch the f(x) and g(x)?

[raw river]

Yes f(g(x)) would be $\sin\sqrt{x}$

[soft zealot]

homme

[raw river]

Imagine that is cube root instead of square root

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[novel terrace]

need a proof that all positive even integers greater than 4 can be expressed as the sum of two primes, for homework.

[royal gust]

Me too. For, uh, work work.

[novel terrace]

somebody help quick! my class starts soon, i don't wanna be the only kid in class who hasn't done the homework.

[vestal frigate]

We're not here to do homework for you boss

[novel terrace]

maybe just point me in the right direction then please, i don't need the answer necessarily, but any help would be appreciated.

[fathom walrus]

yea me three

[mild portal]

Seems like it could be done by induction. Have you gotten to that topic yet?

Oh

Never mind

Ping me if you figure it out lol

[novel terrace]

will do!

[novel terrace]

yeah, no luck there.

[mild portal]

We could also try a proof by exhaustion

[novel terrace]

don't think so - the set in question is infinite.

[mild portal]

Just iterate through it ping me once you’re done

[novel terrace]

sounds like quite an extensive iteration at hand.

[mild portal]

That’s true

You just need time

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@novel terrace Has your question been resolved?

[novel terrace]

not yet!

[mild portal]

Keep going!

[novel terrace]

my class starts soon and i’ve still got 100% of the processing time to go!

[mild portal]

can you make it o(log n)

[novel terrace]

best i can do is O(inf).

[mild portal]

i see

this problem is a little difficult

maybe we can build up to it by solving a few similar problems

[novel terrace]

good idea.

[mild portal]

something like an odd number is the sum of three prime numbers?

[novel terrace]

i’ll have a think, thank you!

that's tough too, dang.

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@novel terrace Has your question been resolved?

[novel terrace]

any help?

maybe i should ping the Helpers.

need some advanced mathematicians on this.

[verbal basalt]

@goldbach

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@novel terrace Has your question been resolved?

[novel terrace]

hopefully my question is resolved soon.

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@novel terrace Has your question been resolved?

[mild portal]

https://arxiv.org/pdf/1312.7748.pdf

[zenith sierra]

Ah yes, Goldbach's conjecture for homework

[trail mango]

huh never seen ♥ used as a symbol

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@novel terrace Has your question been resolved?

[stiff belfry]

@novel terrace do not occupy help channels with jokes

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[wild reef]

hi

[wild reef]

i neeed help

i dont understand number 7,8, and 9

my homework was due at 11:59 but i dont get it 😦

can someone please help me

anyone?

someone

pwease

[tight void]

<@&286206848099549185>

[wild reef]

hi

thanks

<@&286206848099549185>

[onyx flax]

just ask Mr. Morin i think he would know

[wild reef]

lmao thanks

<@&286206848099549185>

nobdy came

[astral finch]

tough maybe try pinging again?

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[shell axle]

What is the level of que??

[vital crag]

don't open a help channel to just talk to people. go to #discussion

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[tranquil pine]

a few questions on this page just because it's a lot of new notation. first, when it says it maps into R (1.56), does this mean it maps into a scalar or it maps into a set a vectors in R

So if you act a tensor on a set of vectors and dual vectors, what is the result

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[worthy crescent]

not sure if my work is correct for this

ok i messed up and plugged in 16 instead of 8

my new answer is 1/4 pi

[unreal anvil]

looks good until the second last line, and the unit is incorrect

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[slender bramble]

how does this end up as

[slender bramble]

I keep getting 1/2 * arcsin(2/7*X) +C

[unique aspen]

show your working

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@slender bramble Has your question been resolved?

[slender bramble]

ignore right side

[worthy shale]

$u=4x \implies \frac1{\sqrt{49-4x^2}}=\frac1{\sqrt{49-u^2/4}}$

[soft zealot]

chlamydia

[slender bramble]

is it suppose to be u = 4x^2?

[unique aspen]

oh

you have u = 4x

but it should be u = 2x

then u^2 = 4x^2

which is what's in the square root

[slender bramble]

oh, noted, thank you for the help everyone!

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[glass heart]

For these, D is a d-system right and C is a pi-system contained by D? only way it make sense

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@glass heart Has your question been resolved?

[glass heart]

yea i just assume it is, so everything follows immediately

.cloose

.coose

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[dapper oriole]

https://gyazo.com/8952ff52961e6ee0fe0ffe393eb457e8?token=53f266f3082160f630b10ac0f4dfd6a3

[dapper oriole]

Can anyone help me on this

I’m thinking it’s B

I just multiplied the top by itself and bottom by itself

[compact breach]

Can you show your work

[dapper oriole]

Oh nvm I got it

Thanks though

[compact breach]

Great

[wet warren]

@dapper oriole
Don't forget to close the channel using
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[sonic crystal]

$\int x^{2}\sin\left(x^{3}\right)\cos^{3}\left(x^{3}\right)dx$ hmm using u-sub im not sure what to let u equal

[soft zealot]

water beam

[tired walrus]

i'd begin by combining sin(x^3)cos(x^3) into 1/2 sin(2x^3)

[sonic crystal]

how does that work

[tired walrus]

$2\sin(t)\cos(t) = \sin(2t)$

[soft zealot]

Ann

[sonic crystal]

huh

is that an identity or something

never seen that one

[tired walrus]

that's the double angle identity for sin

[sonic crystal]

ive never looked at that those kinds of identities lol

[tired walrus]

bruh what

[sonic crystal]

yeop

[tired walrus]

[sonic crystal]

im gonna let u = x^3

[desert mantle]

does trig stuff
doesn't know trig identities
there are better ways to torture yourself, you know

[sonic crystal]

and see where that takes me

[sonic crystal]

well i know how to like prove trig identities n stuff

like

i just havent been taught/learnt double angle identites

i know the other ones

i hope

i think

[sonic crystal]

a pdf

[tired walrus]

i made it myself

and it is only 2 pages long

[desert mantle]

I usually just check the wikipedia article

[sonic crystal]

can i apply it brainlessly or do I gotta actually properly understand it

[tired walrus]

nothing in math is brainless

[sonic crystal]

formula application is where i can go autopilot and plug in stuff

hold on

im gonna big brain this

thinking cap on

dont need double angle identity

@tired walrus is it legal for me to do 3 substitutions

if needed

is that like a normal thing that happens in integration

i dont even know how I will do 3 subs btw

[tired walrus]

it's legal for you to do up to 17 substitutions on an integral. only the 18th and up require notarized approval.

[sonic crystal]

nice

i hit a brick wall

[desert mantle]

you can apply for a lifetime pass for the 18th sub. costs only 299

[sonic crystal]

because dv = cos(u) but i have cos^3(u)

and i cant do

[tired walrus]

wait what

[sonic crystal]

d^3(v)

[tired walrus]

since when was the cos(x^3) also cubed

[sonic crystal]

since the beginning

[sonic crystal]

how do I do this im assuming i need a 3rd sub but i dont know how that works here

[sonic crystal]

@tired walrus does ur double angle identity still hold even for cos^3(x^3) because im guessing you missed that part

[tired walrus]

oh yes i did fuck

the double angle identity is no less true but it is less helpful

[sonic crystal]

hm ok then

so how would I proceed with a third sub here?

[tired walrus]

i'd let v = cos(u) rather than sin(u) here.

[sonic crystal]

mk ill try that and see what i get

okay so I may or may not have fucked up my signs

Really bad

Like really bad

but I think I got the right answer

@tired walrus can you help me like fix the signs and show me what I should’ve actually written because I tripped over my own foot multiple times there but still arrived at the right answer with the wrong working

[tired walrus]

weeeh

tired

[sonic crystal]

its 1.50am for me

[tired walrus]

and?

[sonic crystal]

nothing

I DIDD ITTT

I SOLVED IT MYSELFFFF

RAAA

.cloae

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[lucid dock]

AOB=120 R=2

[lucid dock]

i have to find area of the square

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@lucid dock Has your question been resolved?

[lucid dock]

<@&286206848099549185>

[lucid dock]

<@&286206848099549185>

someone help me

Ok I'll just give up.

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[cerulean tide]

Hi, can someone tell me how can I solve the matrix ^-1 ?

[mental roost]

you would start by calculating the inner stuff

so first multiply the two matrices

then add the third

and only then we get the inverse, if it exists

[cerulean tide]

ok, thank you

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[bronze vector]

If i have like cos(210)=cos(180+30) would that be -sqrt(3)/2 because its in second quadrant and cos is negative there ? Because i know cos is even function and it confuses me wheter it should be negative or postiive

[dry light]

Yeah

Think of the x axis as cos and sin being y axis

Where the x axis is negative is where cosine is gonna be negative

[bronze vector]

Okay thank u, it just confuses me as like if i have cos(-750) it would be cos(2*360+30) = cos 30 = sqrt(3)/2 right?

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[bronze vector]

<@&286206848099549185>

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@bronze vector Has your question been resolved?

[rich rock]

<@&286206848099549185>

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[hollow warren]

I am completely stumped here

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[sage rapids]

Need help with these geometry 1 proofs, not sure if im doing anything wrong on purple but i might have an idea of what to do on blue

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@sage rapids Has your question been resolved?

[sage rapids]

<@&286206848099549185>

[sage rapids]

<@&286206848099549185> sorry if im being impatient or anything

[plush loom]

i think ur quite impatient

[sage rapids]

can you help me?

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[twilit trout]

hi

[twilit trout]

im@struggling on this can anyone@check over it

[cosmic warren]

no offense but it's kinda hard to read

1st one is right

[twilit trout]

sorry

bad handwriting

i can type answers if you want

and you can check em

[cosmic warren]

So is 2nd one

[twilit trout]

nice

i think 5 is wrong

[cosmic warren]

Yeah it is

U wrote the wrong thing for the area

[twilit trout]

oooh

how so

OH

BRUY

ITS SIPPOSED TO BE 276-2y(y)

[cosmic warren]

parentheses but ye

[twilit trout]

yeah

got it

9522

rest is good?

[cosmic warren]

Nice

Uh 3rd one is wrong also

U got 166/2 = 88

It's 83

[twilit trout]

☠️

mental math on bottom

[cosmic warren]

haha

4 is right I just dk if ur teacher or whoever will accept that format or not

[twilit trout]

i got 6889

yeah

[cosmic warren]

yup

Last one is good also

[twilit trout]

perfect

so all good

do you know second differences and shit

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[elder girder]

um

channel occupied

[acoustic flume]

Oops

[elder girder]

can someone help me find ab and perimeter of triangle 1

I don't have any lengths or coordinates for it that's why I'm confused

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[sand basalt]

I need help solving C for this problem, I'm pretty sure g(n) = n^2 lg n. But I'm pretty lost on how to solve/prove it

[sand basalt]

not sure if I'm on the right track or not but this is what I have written down so far

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[sonic crystal]

I thought I knew how to do this then im stuck

[sonic crystal]

what do I do from here

Can I change the sqrt(x) on the numerator in the last line to u?

so it becomes u^2 on the numerator?

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[tranquil pine]

Hello

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[vale python]

Show that the integers have infinite index in the additive group of rational
numbers

[vale python]

I'm not really sure what the angle is to this proof? so i want to show that there is an infinite number of distinct cosets

but what even is an example of the cosets for the group being the rationals and the subgroup being the integers?

I was thinking I don't need to show that it is of infinite index in general, just if an infinite subset of the rationals are all cosets?

[grizzled tusk]

a way to do it is to check that |Q/Z| is infinite

[tired walrus]

all these cosets are of the form q+Z where q is a fixed rational

for example 1/2 + Z

[cosmic warren]

isn't that p much what you're trying to prove

[tired walrus]

or 1/3 + Z

[grizzled tusk]

yes, but the point is that it's easy to prove like that, since Ann is currently doing it

it's true just from the fact that there are inf many rationals in [0, 1]

[vale python]

sooo just point out that 1/n + Z for an integer n is an infinite set of cosets ?

[cosmic warren]

It's just diff wording that doesn't illuminate anything but w/e Ann had the right idea so 🙃

[grizzled tusk]

it's not just a different wording, it's saying that we consider x-y is in Z as relation of equivalence

but then there are obv inf many cosets just in [0, 1]

or whatever interval you choose with length < 1 will be trivial example

[vale python]

whoa, wait, do you think we could go into greater detail on that? why consider x-y in Z as relation of equivalence, and why does the interval need to be of length less than 1?

[grizzled tusk]

looking at Q/Z is saying that we consider the cosets for the relation of equivalence where the difference between two elements of a same coset will be an element of Z
like 1/2 and 1/2 + 1 are of the same coset

another natural way to say it is that for this relation, x and y in same coset means x-y in Z

but then, take any interval [a, b] of length < 1

there are infinitely many rationals

pick 2 of them, they can't be in the same coset

because their difference is less than 1

so even without actually choosing them, we prove that there are infinitely many cosets

[vale python]

ohhhh okay okay i see this makes so much sense

damn, thank you so much for that explanation!

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[left echo]

$\int_{-\pi/4}^{\pi/4} \frac{2x^7 - 3x^5 + 8x + 1}{1 + \cos 2x} dx$

[soft zealot]

jewels!

[left echo]

I think I'm missing something simple because this looks very intimidating

[charred chasm]

try plotting it

ok fine if you don't want to do that, what can you tell me about the properties of each term?

[left echo]

what do you mean by that?

properties?

[charred chasm]

Think even vs odd

[left echo]

oh wait

[charred chasm]

you get it now?

[left echo]

all the x stuff is 0

Yeah

[charred chasm]

Great!

except

not all of them

[left echo]

Except 1 yes

[charred chasm]

👍

[left echo]

$\int_0^{\pi/4} \sec^2 x dx = 1$

[soft zealot]

jewels!

[left echo]

Lol that was easy

Thanks for the help

[charred chasm]

well twice that

but yeah

[left echo]

uh why

[charred chasm]

it's from -pi/4 to pi/4

you evaluated from 0

[left echo]

yeah but 1 + cos 2x is 2cos^2 x

So it cancels

[charred chasm]

oh i see what you mean

ok yeah

[left echo]

Thanks again!

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[inner jay]

(i apologize if my mathmatical english is not accurate
I tried translating as good as i could)

i am unsure how to solve this
i tried showing that they deliver the same results, by showing that they are the "same" equation via transfering them into each other with stokes' theorem, but that is not applicable here
Can someone help me?
I basically tried proving |φu × φv | = √det((Dφ)T Dφ)

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[inner jay]

<@&286206848099549185>

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@inner jay Has your question been resolved?

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[tranquil pine]

@inner jay

do you still need help with this matter

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[prisma berry]

is this correct?

[tired walrus]

yes looks like it

[prisma berry]

okay thank you very much!

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[hard stratus]

yep

[tranquil pine]

what's the question

like, to find dimensions?

[hard stratus]

okay so lets tackle the guy in the brackets first

[tranquil pine]

that's v² right

[hard stratus]

(m/2kT )^3/2

[tranquil pine]

substitute kT by PV/N

[hard stratus]

kT is dimension energy (= mass × speed squared) m is obv mass, so m/kT is dimension (inverse speed squared)

raise to 3/2 power goves u (inverse speed cubed), and then multiply by v² so the right hand side is dimension inverse speed

dose that make sense

or have i gone too quick

yea

2 is just a dimensionless number

everything else make sense?

ive also ignored the 4/√π, and the exp, for the same reason btw

is anything unclear

use index rules

(m² s^(-2))^3/2
= m^(2 x 3/2) s^(-2 x 3/2)

= m³ / s³

haha it happens

👍

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@rapid helm Has your question been resolved?

[rapid helm]

<@&286206848099549185>

[eternal lichen]

What have you done so far?

[tranquil pine]

whathat's to say

[rapid helm]

I tried using king property but it doesn't help

[eternal lichen]

Tried to find any trig identies that might help?

Any u-subs

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[rapid helm]

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[rapid helm]

Can i interchange sigma and d/dx If i have d/dx ( sigma(f(x))) then is it same as sigma(f'(x))

[rapid helm]

This is the question

[desert mantle]

the derivative is linear. so yes

[rapid helm]

I have d/dx sigma(log(x^2+r^2)) then is it same as sigma(2x/x^2+r^2)

[urban sky]

if you open up the summation and multiplication a bit and multiply 2 in numerator and denominator, you'll see the whole thing inside the integral is just the derivative of Π(x^2 + r^2)

[rapid helm]

Ok

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[tranquil pine]

DON'T GIVE ME THE ANSWER, isn't this no solution?

[urban sky]

it's an obtuse angled triangle

[tranquil pine]

it could be

[urban sky]

there is a solution

i think

yep, realising that its an obtuse triangle is the only thing, its pretty straight forward from there

[tranquil pine]

i got it

thx

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[mellow vale]

hi

[mellow vale]

so there is the unit circle and the eqation for it

thats one of the questons

thats easy, the slope was - sqrt(3)

and i got the equation and stuff

i dont get what to do here

[merry quartz]

it seems like OP is perpendicular to P line tangent

[mellow vale]

is it the inverse?

[merry quartz]

reciprocal

do -1/m with the slope of p

thats the slope of OP

m = slope

[mellow vale]

what would be the inverse of - swrt 3

[merry quartz]

do you mean

?

[mellow vale]

whats the inverse of the function f(x) = -sqrt (3)

i watned to see the difference between

the inverse and

the perpendicular

[merry quartz]

is this -squart3??

sorry im not pro at englisj

[mellow vale]

yes