help-38

[slim mountain]

What’s wrong with this

[trim lichen]

well one thing is that it's all on one line with very little room to see where each step ends and the next begins

so there's that

and the actual mistake seems to be that you forgor the +C

[slim mountain]

No I added it

[trim lichen]

it is nowhere to be found in your photo

[trim lichen]

ah but you added it in the wrong place.

[real rose]

b) Q=(-15,-5/3)
R=(5,5)

[trim lichen]

your penultimate step should have been $$\tan^{-1}(y) = -\frac{4}{9}x^9 + C$$ and then taking tan of both sides gives you $$y = \tan\paren{-\frac49 x^9 + C}$$

[solid kiln]

ann.in.a.teacup

[trim lichen]

and the +C ends up inside the tan

not just tacked on like you did there

[slim mountain]

Bruh

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[quartz cloud]

turning this into a system of eqations is 12x+2y=249
3x+5y=123
right?

[clear cloud]

Seems good

[quartz cloud]

and then i remove x to get y by multiplying 3x+5y=123 by -4 turning it into -12x-20y=-492

and then 12x+2y=249
+ -12x-20y=-492

[limpid dawn]

Sportsfreund said seems good

[quartz cloud]

i know but idk how to plug in y correctly

[limpid dawn]

sorry

[quartz cloud]

np

pretty much y is 27/2 or 13.5

do i plug it into 12x+2y=249? or something else

to get x

[clear cloud]

No you can plug it back

Thats the method

[quartz cloud]

so x = 37?

ig?

[clear cloud]

Not the result i have with your values

For x

I have 18.5 for x

Rewatch calculation

[quartz cloud]

oh yeah it is 18.5

ok ig i got it

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[clear cloud]

Gut

[clear cloud]

Spezi

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[hasty idol]

Can someone give me a guide on which estimators I have to use for calculating confidence intervals and hypotheses? I know how to calculate these but can you give me some intuition on which estimators I need to use for each unknown, for each distribution

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[lime sphinx]

give an example and some more context

that would help I think

[hasty idol]

Why when I am calculating an confidence interval for the expected value for a distribution X with and unknown variance I use

$$ \dfrac{\overline{X} - \mu} {S/\sqrt{n}}$$

[solid kiln]

vascomarq

[hasty idol]

Why does this approaches the N(1,0) distribution for a random distribution X when n is large, but a t-Student distribution when X is normal

[lime sphinx]

The theorem that proves this is the central limit theorem

[hasty idol]

I get that for the random distibution

Why doesn't that work for the normal distribution

[lime sphinx]

and if I remember correctly the student distribution converge in some sense to a normal distribution when n is large, prehaps as a special case of the central limit theorem.

when X is normally distributed

[lime sphinx]

that does not hold as an approx when n is small

That’s why you need the student distribution in that case to make your CI more precise when n is small

[lime sphinx]

but for n big CLT says this variable is pretty much normal

even when X is normally distributed

[hasty idol]

Thanks

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[fervent fern]

yo

[west sleet]

Hallo

[fervent fern]

how to do number 3

this is graphs, relations

[hidden dew]

the relation is 10-x ?

[fervent fern]

yes

[hidden dew]

then yea just input your x-values into the equation
10-x

[fervent fern]

wym bruh

x

10-x(2) is this what u mean

[hidden dew]

nope
10-(2)
10-(4) so on

[fervent fern]

does (2) mean 2 by itself

so like 10-4

aight ty

so the y's would be

8,6 and 2?

ty

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[fervent fern]

i understand it

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[slim temple]

Knowing that the integrate of an infinite sum can only be evaluated as the sum of its integrated parts over a range, given that its absolutely convergent on said range:

[solid kiln]

zzz0nnn

[slim temple]

Does this rule also apply while differentiating?

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[slim temple]

<@&286206848099549185>

[burnt mulch]

https://www.dpmms.cam.ac.uk/~agk22/uniform.pdf

I think that you're looking for Theorem 2 here

@slim temple

[empty orchid]

There is no x term for the integral?

[slim temple]

ik i didnt write it, but just pretend, lmao

[empty orchid]

You could also apply Fubini for certain bounds

I don’t know about a generalized a and b term though

[slim temple]

thanks, ill check

[empty orchid]

Obviously the series is convergent, so you could probably apply DCT (Dominated Convergence Theorem) and Fubini, if I recall correctly

[slim temple]

thanks guys, ill have a read on those things

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[amber tulip]

(d) If a sequence of nonnegative numbers converges, its limit also is nonnegative.

[amber tulip]

I'm kind of stuck as to how to prove this

i know that if a sequence of nonnegative number converges, it is bounded

but im not sure how to show what its bounded by

if i can restrict the bound to like [0, L] that would be nice

[lament reef]

contradiction is the easiest way iirc

and use the limit definition

suppose the limit is negative. what problem does that pose?

[amber tulip]

at some point the terms has to approach this negative limit meaning that at some point the terms of the sequence will become negative

idk if thats "rigorous" to put in a proof thhough

[lament reef]

that's the correct logic, but yeah you would need to formalize that

[amber tulip]

hmm

do I use the definition of convergence

then use the fact that a < 0

as a contradiction

[lament reef]

that's the gist of it yes

you can use the fact that if an -> L, then for EVERY epsilon > 0, there is an N such that n > N implies |an - L| < epsilon

there is a contradiction to be had there

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[quartz cloud]

does -2x-y=-4
2x+y=4
have infinite solutions

[limpid dawn]

what do you think

[quartz cloud]

idk thats why i came here

ig infinite cus 0=0?

[lone basin]

Multiply the top equation by -1

[limpid dawn]

geometrically, both equations represent the same function basically

[quartz cloud]

alr

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[ionic pendant]

what have you tried so far?

[coarse meadow]

i tried to find the height of triangle

i drew a line down from r+2 to r+5 at 90 degrees and found it was 1/2r+1

@ionic pendant

[ionic pendant]

how did you get that length?

[coarse meadow]

30 60 90 triangles

[coarse meadow]

is it wrong or do i need to do something else

[ionic pendant]

you have the right idea, but i don't see how you got that specific length

[coarse meadow]

because when you draw the line down at 90 degrees

you can make the height x

so sin 30 = x/(r+2) so x=1/2x(r+2)

[ionic pendant]

ok i see now

[coarse meadow]

is it correct?

[ionic pendant]

yes, although over text i would write it as 1/2 r + 1 rather than 1/2r + 1, which reads more like 1/(2r) + 1

[coarse meadow]

o mb

[coarse meadow]

would the triangle be 1/2(1/2 r+1)(r+5)

[ionic pendant]

that's the area formula, yes

[coarse meadow]

so 1/4 r2+7/4r+5/2=r2+2r+1

and then 0.75r+1/4r-1.5=0

so 3x2+x-6=0

[ionic pendant]

this doesn't quite follow from the previous step

[coarse meadow]

wait oops

i think thats good

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[red mirage]

The relation at a) is this

At least some idea

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[lilac cloud]

For Q16, I'm having trouble thinking about / visualizing the vector space. In Q15 I proved it by assuming vectors $e_1,...,e_m$ which is linearly independent spanned the space. Then showing that $e_{m+1}$ is not in the span of the others, so it must be infinite dimensional. However, I'm not even sure what basis vectors for the vector space in Q16 would even look like

[solid kiln]

Luca M

[lilac cloud]

I thought maybe a series of functions $f_x$ where $f_x(x)=1$ and everywhere else $f_x$ evaluates to zero. But then they wouldn't be continuous and so wouldn't be elements of the space at all

[solid kiln]

Luca M

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@lilac cloud Has your question been resolved?

[split pulsar]

Use Taylor

$f_n(x) = x^n$

[solid kiln]

LooseEthics

[lilac cloud]

Wait so its just the same as the vector space of polynomials over the interval [0,1]

[austere cedar]

It does happen to be, yes. That's not a trivial fact.

[lilac cloud]

Ok thanks

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[shy acorn]

Can someone please tell me what I'm doing wrong? I'm doing Lhopital practice problems, and somehow I got - infinity instead of positive infinity

[exotic tundra]

what's the derivative of $\sqrt{x}$?

[solid kiln]

Sepdron

[shy acorn]

1/2x^(-1/2)

1/2sqrt(x)

[exotic tundra]

oh mb I thought it was negative that

looks correct to me

,w lim as x to 0+ of 1/x - 1/sqrt(x)

[solid kiln]

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[shy acorn]

but the correct answer on my textbook is different from my answer 🤷

yeah thats the problem

[exotic tundra]

oh wait, it isn't 0/0

it's 1/0

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[scarlet forge]

i did 3x - 95 = 1 so i can find x

<@&286206848099549185>

[gritty hollow]

You can solve this as a simultaneous equation

[scarlet forge]

how

there is no y

@gritty hollow ?

[gritty hollow]

Try doing the ratio equal to 48/1 to solve for x

[gritty hollow]

11x+95=48 divided by this and solve for x

[scarlet forge]

i did that buut i got -4. something

it was hela long

nvm, i just used gauth and it says i needed to cross mulitply, thank you anyway @gritty hollow

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[gritty hollow]

I got 35

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[sweet quest]

could anyone show me the step by step process I'm a bit stumped

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[real rose]

For part a)
You should add multiples of 360 to the angle. In this case, -840+3*360=1080-840=240 degrees.
For part b) On the left hand side, you have the half angle identity for cotangent(theta/2). Give me a second.

$\frac{1-\cot(\theta)-\csc(\theta)}{\csc(\theta)-\cot(\theta)-1}$

[solid kiln]

mathisfun

[real rose]

$\frac{\sin-\cos-1}{1-\cos-\sin}$

[solid kiln]

mathisfun

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[real rose]

@sweet quest

[real rose]

For part c)
Note that we have cos^2(x)csc(x)-sin(x)=1, which implies cot(x)cos(x)-sin(x)=1.

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[plain phoenix]

hi, im not sure how to start. i barely know how to (if i even remember) how to do this in just regular form

[plain phoenix]

and before anyone asks, yes, this is the ful question

[lyric hawk]

factored form is $a(x-r)(x-s)$ where $r$ and $s$ are roots and $a$ is a constant

[solid kiln]

lpieleanu

[plain phoenix]

wait a minute
are they the x intercepts?

also please excuse me if im slow to type, keyboard doesnt wana work right

[lyric hawk]

yeah

[plain phoenix]

oh, an then a is whatever makes it curve up and get the y intercept?

[lyric hawk]

yep, exactly

[plain phoenix]

oh okay! i gues its just filing in numbers from here on desmos 😭

bc i cant realy do it mathematicaly and to be honest, itd be mroe stresful to do that rn. when i have abreak i ned to learn that

also holy crap i hate this keyboard 😭

wel that one was realy easy to gues the numbers

1(x+6)(x+1)?

[lyric hawk]

yes

[plain phoenix]

yay! thank you for hlping me

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[plain phoenix]

i know my intercepts are -1 and 2 i just dont know how to write it

[last nebula]

You can factorise x^2 - x - 2 using the intercepts you found

(x+1)(x-2)

So the product will be negative when one of the factors is negative and the other one is positive

[plain phoenix]

is it 2, -1?

wait

no, i ned intervalnotation

thats al i ned

fuck i wish i could typeon this this

nevermind

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[sweet quest]

thank you!

[sweet quest]

I'm still a bit confused on part B though

thats where the main problems start

[real rose]

I know. I am trying to figure it out.

[twin storm]

you can multipy the 1+c/1-c term by 1+c/1+c

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[covert spindle]

f(x) = arctan(1/|x|)

[clear cloud]

Ok

[covert spindle]

determine all discontinuities

wait let me translate rq

[clear cloud]

Where is arctan defined ?

[covert spindle]

Determine and classify all possible discontinuities by calculating the left and right limits at these points.

[covert spindle]

R

1/|x| R \ {0}

[clear cloud]

Indeed

[covert spindle]

and left limit in 0 is equal to the right limit in 0 so it is defined everywhere?

[lethal valve]

not exactly still not defined for x=0 i assume

[clear cloud]

No cuz you can't defined f(0)

[safe loom]

f(0) doesnt exist

[covert spindle]

aah so lim x->0- = lim x->0+ = f(0) then it is defined?

[clear cloud]

If they all real numbers

Also

[covert spindle]

aah okay

and either one must just exists right?

so lim x->0- f(x) = f(0) would also exist?

[clear cloud]

Depends where you are on the interval

If you at a bound yes

The right bound

[safe loom]

all of them have to be equal

unless there's a scenario like
D = [0;inf) then 0+ = f(0)
D = (-inf;0] then 0- = f(0)

[covert spindle]

aaaah okay

alright so it is continuous everywhere expect 0?

x=0*

thank you very much guys

[covert spindle]

imma write this down real quick and then close it thanks 🙂

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[covert spindle]

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✅

[covert spindle]

Now i must answer on what intervals is the function differentiable

[clear cloud]

Where is arctan differentiable

[covert spindle]

anywhere?

since 1/(1+x²)

[clear cloud]

And where is 1/|x| differentiable ?

[covert spindle]

anywhere expect 0

[clear cloud]

No we have composite here

[clear cloud]

So its differentiable where ?

[covert spindle]

R \ {0}

[clear cloud]

Sounds good ?

[covert spindle]

yes

I did this tho:

So i figured for x<0 f'(x) = 1/(x²+1)
x>0 f'(x) = -1/(x²+1)
both are differentiable on their domain

so the entire function is differentiable on R \ {0} ?

is that also allowed?

[clear cloud]

How do you diffenrtiate it ?

[covert spindle]

ill show wait

I did this?

[clear cloud]

Id say thats a good way of thinking yeah

[covert spindle]

x<0 f'(x) = 1/(x²+1) is just not logic for me tho ;-;

since that should integrate to arctan(x) and not arctan(-1/x)

[clear cloud]

There is two derivatives to abs(x) depending the sign of x thats why

[covert spindle]

aaah okay

alright thank you 🙂

have a good day/night

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[clear cloud]

You too

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[shy valley]

how does this get factored

[real rose]

Should be $\qty(\frac{(x+10)^2}{2})^2+1+((x+10)^{-2})^2$

[solid kiln]

mathisfun

[real rose]

Try to work from there

Recall that $a^2+2ab+b^2=(a+b)^2$

[solid kiln]

mathisfun

[shy valley]

i saee how the side ones will work out

but how would the 1 workl

the equation is 2ab

[real rose]

$1=2\qty(\frac{(x+10)^2}{2})(x+10)^{-2}$

[solid kiln]

mathisfun

[real rose]

Ugly

But this is the way 🗣️

[shy valley]

oh.

so when thetres a 1 should try doiing 2ab
and see if its 1

or whatever taht number is

in the middle

@real rose

[real rose]

Yes

[shy valley]

i see

thanks

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[bright seal]

‎‎‎‎‎‎‎‎ ‎ ‎

[bright seal]

Is this correct ?

[wanton rune]

what?

[bright seal]

This

[wanton rune]

there's...nothing there

[pliant lava]

Bro's speaking the Empty Language

[sharp heart]

There's nothing there. Did you post a picture link that we don't have access to?

[bright seal]

Do you not see?

[bright seal]

I'm using the Latex

[lament locust]

theres nothing there for us

[ionic dove]

‎‎‎‎‎‎‎‎ ‎ ‎

[lament locust]

this is me highlighting empty text

[ionic dove]

Did you copy paste an empty character

[bright seal]

$\int \frac{1}{sin(x)^3} dx$

[solid kiln]

Task Bot

[bright seal]

Now do you read?

[ionic dove]

Yes

[bright seal]

I used the weierstrass sub

Is it right?

[lament reef]

that's overly complicated imo, you could treat it as csc^3(x) and then use a trig identity

ah that might not work actually. weierstrass is fine

but very painful

[soft pendant]

1/sin(x)^3 = csc(x)^3

then you can write is as csc(x) * csc(x)^2

csc(x)^2 = 1 + cot(x)^2

csc(x) * (1 + cot(x)^2)

so you have csc(x) + csc(x) cot(x)^2

$\int \csc(x) dx + \int \csc(x) \cot(x)^2 dx$

[solid kiln]

jandro0103

[bright seal]

Wow

[soft pendant]

the (1) is equal to -ln(|csc(x) + cot(x)|)

[bright seal]

(1)?

[soft pendant]

the csc(x) integral

so you have

$-\ln(|\csc(x) + \cot(x)|) + \int \csc(x) \cot(x)^2 dx$

[solid kiln]

jandro0103

[bright seal]

Ehi

[bright seal]

This is the question, I'm not what you are answering

[soft pendant]

now

you can do this

$\int (\csc(x) \cot(x)) \cot(x) dx$

[solid kiln]

jandro0103

[bright seal]

????

[soft pendant]

and you can do this by parts

indeed

the integral of csc(x) cot(x) is -csc(x)

[bright seal]

.close

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[soft pendant]

<@&268886789983436800>

this guy is trolling

[bright seal]

Why?

[soft pendant]

i was explaining a way

to evaluate the integral you sent

[bright seal]

He did not answer the question

[spiral kettle]

what is happening?

seems like miscommunication

oh well, the channel is locked anyways.

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[wraith hinge]

is this done by checking if all the combinations of points

has the same slope

is that it

i did do it and it came out 4 for all

is that enough to say they are colinear

[hallow spruce]

Pretty much

[wraith hinge]

i see because same slope would mean

same line

and it kinda makes a chain

if AB on same line BC on same AC on same

that would mean ABC

on same

[hallow spruce]

You could shorten it a little to (if B is the "middle" point) if AB and BC lie on the same line then ABC is one line

Saves a step checking AC

[wraith hinge]

i think AC is irrelavant because AB on same line and BC on same line would mean

YEAH

righttt

it does

cuz C would be on same line as B

and B is on same line as A

alright thanks for the help! have a good one

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[neon dirge]

those eyes haunt me

[wraith hinge]

lmao

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[brave wadi]

how do i start w this

[lament reef]

trig substitution

[brave wadi]

ah ok, i thought it would start differently like breaking it apart or something, thanks

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[honest cipher]

Hi, how would I go about solving this practice question?

I understand that its a conditional probability question, but the 0.99, 0.95 and especially the 0.02 are throwing me off. I'm unsure on how to approach the solution.

[mellow tendon]

You identify first the random variables that you will use to solve this question

Like what Random variable would you assign for a product that is actually defective

[honest cipher]

uhm

[mellow tendon]

Or None Defective, it works the other ways
But no need to do both because the two are complements

[honest cipher]

not too sure on how to get a random variable

what should i look up to learn what that is sorry

[mellow tendon]

You don't get it, You assign them your self

[honest cipher]

oh oh

[mellow tendon]

Like you say let X be the random variable for the product being classified Defective

[honest cipher]

okayokay

[mellow tendon]

Then assign a random variable for the event of the quality control identifies an object that it is defective

Then write it in mathematical form

[honest cipher]

so i'll end up with a few random variables for the different cases

and i'll have to work through them

[gusty delta]

0.95 0.5
0.02 0.098

is the table

sum the first row and divide 0.02 by the sum

this gives the probability

[wraith hinge]

Ok its pretty easy

First make the tree

[mellow tendon]

Yeah like let's say that the random variable Y is the quality control identifying objects as defective

[honest cipher]

okay okay

[honest cipher]

wait im confused

[gusty delta]

,calc 0.02/(0.95+0.02)

[solid kiln]

Result:

0.020618556701031

[honest cipher]

do i make a tree of the possibilites or a table

[gusty delta]

table

[mellow tendon]

Then
Writing the question as mathematical form
P(Y|X) = 95%

[wraith hinge]

Make a tree

[gusty delta]

nuh uh

[honest cipher]

table for all events right

[gusty delta]

yes

[honest cipher]

oh okay okay

[wraith hinge]

I’d make a tree, then just calculate P(defective)

[honest cipher]

thats y on the condition of x

i understand that

[wraith hinge]

We have all the info we need in the text

[gusty delta]

table makes more sense

0.95 0.5
0.02 0.098
is the table
sum the first row and divide 0.95 by the sum
this gives the probability

[mellow tendon]

You understand why I wrote it like this though?

[honest cipher]

why would I sum the first row?

[wraith hinge]

I learnt to make trees

[honest cipher]

yes i get it now

[wraith hinge]

Ig we all have different solutions

[honest cipher]

but what would i do next

[gusty delta]

total outcomes of defective

[mellow tendon]

Ok it may make sense but in my opinion understanding how this work would be better than following instructions blindly

[gusty delta]

yes sir this is the fast method

[honest cipher]

yeah im a little confused with the table

[wraith hinge]

Making a tree helps to visualise better imo

[honest cipher]

what do i do with the random variables

[honest cipher]

im okay with a tree also im just practicing right now

[mellow tendon]

Then let's move to the rest like
You have
P(Y|X) = 95%
P(Y|X`) = 2%
P(X) = 1%
P(X`) = 99%

[wraith hinge]

Exactly

[gusty delta]

tree bad

table good

tree is heresy

[honest cipher]

just confirming, but Y is the event that the object is defective, and X is the event that the machine recognises it as defective?

[mellow tendon]

No Y is the event of it being classified as defective by the quality control
Whether it is defective or not
X is the event of the object being defective

[honest cipher]

oh okay okay okay

okay makes sense now

i get it

how do we get this exactly

[wraith hinge]

Wait gimme a sec

[honest cipher]

okay okay tysm

[mellow tendon]

So now you want P(X|Y) the probability of it being actually defective after being classified Defective

You should be able to get it via Bayes' therom

[honest cipher]

ah okayyy

let me work on this a litt

little*

thank you so much i understand it much better now

[mellow tendon]

You are welcome

anything else?

[wraith hinge]

@honest cipher

Here is the tree

[honest cipher]

yeah there are a few more questions ill get this one through then ill get to them

[wraith hinge]

Ignore the calculus above lol

[honest cipher]

i think ill open a new channel for them

[honest cipher]

woa

[honest cipher]

ofc haha

definite integrals are nice

[wraith hinge]

That’s the question right there

[honest cipher]

shouldnt D be non defective?

you've written P(D) as 0.99

[wraith hinge]

Oh yeah lol mb

[honest cipher]

yesyes

[wraith hinge]

Stupid mistake

[honest cipher]

issok issok

[wraith hinge]

Here is everything corrected

So yeah let’s evaluate P(R)

[honest cipher]

yesyes

how would i go about that

[wraith hinge]

It’s late at night lol sry if I make lil mistakes, that’s the final correct tree

[honest cipher]

is this P(Defective | Correct Test)

[honest cipher]

thats okay

[honest cipher]

@gusty delta

[gusty delta]

yes

i think

no

wait

maybe

[honest cipher]

yes uhhh

im also confused 😭

[wraith hinge]

So here is the final answer

@honest cipher

0,0097

Is everything clear ?

[honest cipher]

hi uhm

i also tried just now

i got a different answer im not too sure what i did wrong

[wraith hinge]

Show me your work

[honest cipher]

i got the total probability for P(R) by P(R|D)*P(D) + P(R|D')+P(D')

came out to be 0.9425

then i used bayes (i might have used it incorrectly)

like P(D|R) = (P(R|D)P(D)) / P(R)

and i got 0.997

<@&286206848099549185>

[wraith hinge]

I think P(R) = P(D ∩ R) + P(Opposite D ∩ R)

That’s the formula for conditional probabilities

[honest cipher]

ah

0.0457 is my answer. i made a mistake during the caluclations

[wraith hinge]

I believe what I found is correct

[honest cipher]

how did you get to 0.0097

after P (R intersection D) / P(R)

[wraith hinge]

Oh wait

I think I found what makes my result weird

Actually P(R) is 0.01 x 0.95 + 0.99 x0.02

So P(R) = 0.0293

And then when you use bayes you get 0.324

I misunderstood the text sry

I’m not used to resolve problems in English

@honest cipher

I heading to bed now

Hope I helped a lil bit lol

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[lunar sonnet]

doing continuous distributions and am on g). right now. the equation for expected formula is like E(x) = xf(x)dx , i want to make sure that i’m not suppose to plug it into the second x in f(x)?

[lament reef]

yeah, just do x^2 f(x)

[lunar sonnet]

okay thank you thank you

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[silver wolf]

so there are 13 number prime ?

[zinc ginkgo]

,calc 2 + 3 + 7 + 9

[solid kiln]

Result:

21

[zinc ginkgo]

do you know divisibility by 3 rule

[silver wolf]

hmm idk ?

for sure all number divisible by 2 are not prime except 2 right

[silver wolf]

also for sure all number divisible by 3 are not prime except 3 right

[silver wolf]

owh ok i just know about this

how about what is the divisibility rule of 2 ?

[zinc ginkgo]

a whole number that ends in 0,2,4,6,8 is even

[silver wolf]

ahh i see so 2379 is divisible by 3 and not prime

i just take last two digit 79 and div by 3 but can't so i assume prime haha

[zinc ginkgo]

why are you looking at just the last two digits

[silver wolf]

i think the last two digits can represent the rest of the number is it divisbile by 3 or not let say

wait so all the number not prime ?

[zinc ginkgo]

no, don't make things up

[silver wolf]

yeah my bad

so 0 number are prime ?

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[brave wadi]

I don't understand why this isn't a division by du

[limpid dawn]

because chat gpt makes mistakes

[eternal nimbus]

This makes very little sense

[brave wadi]

ok thanks, so its really a u^3/du

although im still wondering how to continue from where

[eternal nimbus]

This also doesn’t make sense

[brave wadi]

ok what steps do i take for this integral

[limpid dawn]

du = sec^2(theta) d(theta)
du/sec^2(theta) = d(theta)

[limpid dawn]

sec²(theta) = tan²(theta)+1 = u²+1

use that

so your actual integral

u³/(u²+1)²

[brave wadi]

should the denom be squared?

[limpid dawn]

you could do here another substitution with v = u²+1

[limpid dawn]

yes

[brave wadi]

why?

[brave wadi]

ill try it

[limpid dawn]

that is a trig identity

but you have sec^4(theta)

so you square both sides

[brave wadi]

i actually didnt look too hard at this but why is it 1/sec^2 twice?

[limpid dawn]

because d(theta) = du * 1/sec²(theta)

it brings an additional factor 1/sec²(theta)

it comes from differentiation both sides of u = tan(theta)

and solving for d(theta)

[brave wadi]

why? also im not sure if the d theta should be there

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[fervent fern]

hi

[fervent fern]

The second number in each ordered pair is a multiple of the first number. If the range is given as 6, 12, 20 and 30 then list a suitable domain for the relation

that would be 3, 6, 10 and 15

but

heres the question

ordered pairs are 7,p, what is P?

[turbid leaf]

Is this what the original question asked

[fervent fern]

wym

[real rose]

!original

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Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[fervent fern]

that is the original

[tender hemlock]

is it word for word? because its sort of ambiguous. usually youd expect something like "[...] 7, p where p exists in the set P, describe the set P for which the previous relation holds for all p"

something to that effect

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[fervent fern]

yes

[tender hemlock]

then i guess id say something like

The range of the function $f : \mathbb{N}^+ \rightarrow \mathbb{N}^+$ where $f(x) = 7x$

[solid kiln]

Karma

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[celest hemlock]

This is a year 12 exercise on projectile motion. Any help would be greatly appreciated.

[celest hemlock]

This is my logic so far. I apologise for the messy writing.

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[silver wolf]

is this the right answer ?

[celest hemlock]

.reopen

<@&286206848099549185> Anyone have any suggestions?

[silver wolf]

i think this is kind of parabowling

[celest hemlock]

Sorry, my internet is apparently slow so I didn't see your post

I'll help you anyways

The question asks to solve the problem graphically, meaning that you have to plot two lines and find the coordinates of their intersection

What are the two equations that we can obtain from the question?

Hint: represent the number of juice and soda bottles with x and y, respectively

[silver wolf]

hello

yeah x = 4 and y = 2 ?

@fervent thorn

<@&286206848099549185>

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[opal egret]

Find each possible integer value of k so that 2x^2 +kx + 18=0 has integer solutions.
can someone help?

[frozen pumice]

what do you think u should do first?

[opal egret]

thats what im trying to figure out...

[frozen pumice]

ah

srry lemem try to rephrase it

what type of equation is this?

linear, quadratic, etc.

[opal egret]

the topic is on factoring

[frozen pumice]

ye

[opal egret]

quadratic

polynomial

[frozen pumice]

ye

so typically they can be split apart right?

[opal egret]

wdym by split apart

[frozen pumice]

simplified

for example

[opal egret]

ya sure ig

[frozen pumice]

x^2-1=(x-1)(x+1)

srry if my explaining is kinda bad

but like this

[opal egret]

yaya

[frozen pumice]

yeah so try to do that to the equation u sent

[opal egret]

okok

gimme a sec

[frozen pumice]

2x^2 +kx + 18=0

find k

[opal egret]

(2x+c)(x+d) c and d are factored pairs of 18

[frozen pumice]

yes

try taking out the 2 first

it'll make it easier

[opal egret]

wdym take out the 2

srry if im a little bit braindead lol

[frozen pumice]

like factor out the 2 first

[opal egret]

isn't this completely factored tho?

[frozen pumice]

well

we dont know what k is

[opal egret]

k can be multiple answers ya

[frozen pumice]

bruh how do i even explain this

lemme work this out real quick

one sec

[opal egret]

sorry am i braindead 😭

[frozen pumice]

no

ok yeah

so you can divide by two

because right know we are assuming k can be anything

[opal egret]

so x^2 +kx/2 +9 = 0

[frozen pumice]

it reduce the other varibles to a smaller for to make it easier

yeah

[opal egret]

okk i got thatt

[frozen pumice]

what do u think comes next?

[opal egret]

do we bring over the nine?

to the other side

idk

[frozen pumice]

nope

it'll make the equation more complicated

[opal egret]

idk

[frozen pumice]

we can start simplifying the equation

so we need to find the

lcms of 9

lmk what numbers u get for the lcm of 9

[opal egret]

isn't it just 9

[frozen pumice]

i mean gcf 💀

[opal egret]

oh

then 3

[frozen pumice]

theres more

2 more

if im going too slow lmk

i dont wanna waste your time either

[opal egret]

uhm

i have to go in 5 minutes

😭

[frozen pumice]

ight

ok so gcm is 1,3,9

[opal egret]

ya

[frozen pumice]

so we can create 2 types of equations for this case

(x+3)(x+3)

[opal egret]

yes

[frozen pumice]

and (x+1)(x+9)

because we know it'll be equal to x^2+kx/2+9

and because of this we can also find the inside

so find k for both types

[opal egret]

im sorry i don't have time to show my work right nowww

im a slow typer 😭

[frozen pumice]

nw

so combining them

x^2+10x+9

x^2+6x+9

[opal egret]

yup

[frozen pumice]

and we know x^2+kx/2+9

[opal egret]

yup

[frozen pumice]

so we just need to find the ks that are equal to it

which are

20 and

12

so it'll look like this

2x^2 +kx + 18=0

[opal egret]

2 mins btw

1

[frozen pumice]

2x^2+20k+18=0

2x^2+12k+18=0

[opal egret]

ooo oky

i got it now

thx

[frozen pumice]

both of these

aight nw

[opal egret]

.close

[frozen pumice]

srry i took long

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[ruby robin]

Does anyone know how 11pi/6 goes into this

How does 11pi/6 go into pi(6n+11/12)

I know it’s something to do with general solution of tan function

But I forgot

How to progress further

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[ruby robin]

.close

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[echo jasper]

what is this do i just eyeball it

[ionic pendant]

use the equation

[echo jasper]

uh

[ionic pendant]

https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Introductory_Quantum_Mechanics_(Fitzpatrick)/08%3A_Central_Potentials/8.04%3A_Rydberg_Formula

[vapid frost]

not needed i think

longer wavelength just means weaker energy

so u just gotta choose the enegy level jump that is the smallest

so what is a smaller difference in energy?
2p->1s or 3p->1s

[echo jasper]

Oh

3p to 1s then?

[vapid frost]

higher jump = higher energy

higher energy = shorter wavelength

u are looking for the longest wavelength

so the weakest energy

so the smallest jump

[echo jasper]

oh

smallest jump 2p to 1 s

[vapid frost]

yep

do you know why longer wavelengths of light mean lower energy?

[echo jasper]

Uh no

[vapid frost]

nw

[echo jasper]

No jumps?

[vapid frost]

don't guess! >:I

grr

[echo jasper]

gpt time😔

[vapid frost]

(its ok to say idk, also guessin inphysics will get u nowhere)

not knowing things is ok

[echo jasper]

True

[vapid frost]

ok so

draw a high frequency wave rn

like legit rn

on ur paper

[echo jasper]

Ok

[vapid frost]

and then draw another one that is of lower frequency

and show me in chat

make the size of the waves the same btw, so if u drew one to be 1 inch the other one is 1 inch

[echo jasper]

Oh ok

There we go

[vapid frost]

perfect

ok which one has higher frequency

[echo jasper]

Top

[vapid frost]

correct

which one has the smallest wavelength

(distance between peak and peak)

[echo jasper]

Top

[vapid frost]

there ya go

[echo jasper]

OH

[vapid frost]

ba,

ba,

bam

fuck

bam

[echo jasper]

That made it easier 😂😂

[vapid frost]

yep

concepts go brrrr

[echo jasper]

Thnx so much

[vapid frost]

yee npnp

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[sharp reef]

I need dy/dx

[sharp reef]

What the Derivative of sec y? Would y prime sec(y) tan (y) be right?

?

I tried can someone tell me if it's right

.closs

.close

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[visual shoal]

I am having some problems with the notation here and my method of proving |A|_M is a matrix norm.

[granite cove]

What have you tried?

[visual shoal]

well I think the right side is some kind of matrix decomposition, I think I am failing to understand what the m norm of a matrix really means

the only reference I have for the m-norm of a matrix is |A|_M = max x/=0 (|Ax| / |x|), which I don't think is going to be useful for trying to prove the right side is a matrix norm

what do you think about this?

are you there @granite cove ? sorry, just checking

<@&286206848099549185>

[granite cove]

It's not really necessary to know how exactly the matrix norm looks like. You can just show that the M norm satisfies the norm conditions using that ||•|| is any norm

[visual shoal]

so in this case the M in the left is arbitrary?

[granite cove]

It is an arbitrary invertible matrix

[visual shoal]

okay, so what you are saying is I just have to prove that ||M^-1AM|| is a matrix norm

alright I think that makes things a lot simpler, thank you. can I post a second problem here?

[granite cove]

Of course

[granite cove]

Yes, just go through each requirement. This should be straight forward

[visual shoal]

so for this one I got how to prove that ||E||_F = ||u||_2||v||_2, but I am not sure how to prove = ||E||_2

[wintry stag]

It doesn't really help you solve the problem but I would think of that norm as taking the norm of A after a change of basis

[visual shoal]

It makes sense when you put it like that. I believe I got confused with the notation I was given and couldn't get past thinking about it like a formula vs a transformation.

[wooden plover]

well you can just compute ||E||_2 and find that it's also ||u||_2||v||_2

use your favorite definition of the 2 norm and go at it

[willow mortar]

What is norm F

[visual shoal]

it's the sqrt of the sums of squares of the entries in the matrix

so the definition I have is ||A||_2= sqrt(lambda(A^TA)) which just means the sqrt(largest eigenvalue of A^TA). Now I need to prove that it = sqrt(sum |u|^2 * sum |v|^2).

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[gusty plank]

Need some hints for this. No idea how to begin this

[left oriole]

start with the definition of direct sum, what does it mean to say

(it's several statements in one, basically)

[gusty plank]

Well they're both subspaces and their intersection is {0} right?

[left oriole]

yea

and one more thing

[gusty plank]

Uhh i'd also have to show that just a regular sum would be equal to R^R in the first place

and then show that the intersection is {0}

can't think of anything else

[left oriole]

well what it means is that every function f : R -> R can be written as the sum of an even function and an odd function

[gusty plank]

ah yes ofc

[left oriole]

so you have to show several things here

(1) that U_e and U_o are subspaces

(2) their intersection only contains the zero function

and (3) every f can be written as an even function plus an odd function

so try tackling it piece by piece like this

[gusty plank]

so 0 is in U_e and U_o because 0(x)=0(-x) and 0(-x)=-0(x)

for U_e we have that (f+g)(x) is even because f(x)=f(-x) and g(x)=g(-x) therefore (f+g)(-x)=(f+g)(x)

and for x in R we also have that x*f(x)=x*f(-x) in U_e so it's a subspace

same process to show that U_o is a subspace... this seems to be the easiest part

so if we have f(x) in U_e and U_o then f(x)=-f(x)

then f(x) can only be 0 so their intersection is {0}

am i right so far?

<@&286206848099549185>

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[south siren]

I think that's right

[gusty plank]

so now i'm thinking how i can show that any real valued function can be written as the sum of even and odd functions

kinda stumped

[south siren]

For the third point, you should copy cosh(x) + sinh(x) = exp(x)

[gusty plank]

well that's just a specific case isn't it

i need to make a generalization

[south siren]

Yes but how are cosh and sinh defined?

[gusty plank]

(e^x+e^(-x))/2 and (e^x-e^(-x))/2

[south siren]

You should see something

Do you think this is limited to exp(x) ?

Just replace exp(x) by f(x) and you got your solution

[gusty plank]

f(x)=(f(x)+f(-x))/2+(f(x)-f(-x))/2 ?

[south siren]

Of course it is

Plus there's one odd function and one even function

[gusty plank]

hmmmm

i'm failing to get this through my head

i feel like i don't understand it completely

[south siren]

You can easily prove that (f(x) + f(-x))/2 is even