help-23

[safe radish]

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[lean otter]

Would there be any other way of solving this

or pretty much what i did would be right?

[fluid token]

find the max of that function?

[lean otter]

wym?

wait i got it

.close

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[daring forge]

couldnt fit the entire problem in 1 screenshot, my apologies

it seems correct to me?

[rapid igloo]

the interval is [0, 2pi]

[daring forge]

for sin

isnt it [-pi/2,pi/2]

[quasi bison]

"it"

[daring forge]

yes

[quasi bison]

the problem asks you to give solutions in [0, 2pi]

[daring forge]

pronoun bc referred to it in previous sentence

[quasi bison]

just because the problem involves the sine function does not mean you get to disregard this [0, 2pi] or transmogrify it into [-pi/2, pi/2]

[pseudo scroll]

transmogrify

New word unlocked

[daring forge]

i forgot it said that

[quasi bison]

you forgor 💀

[daring forge]

i am completely lost

[quasi bison]

the task is to give all solutions of the equation which lie between 0 and 2pi.

[daring forge]

yes

for sin(x)=-0.28

[thin bridge]

is -0.28 between 0 and 2pi?

[daring forge]

no

its the graph in the problem tho

[thin bridge]

wdym

[thin bridge]

we are well aware of the problem

which lie between 0 and 2pi.

is -0.28 between 0 and 2pi?

no

[daring forge]

yes but am i not supposed to use the equation

[thin bridge]

wdym

which equation

[thin bridge]

that's what you're being asked to solve

[daring forge]

ohh

[thin bridge]

...

[daring forge]

so arcsin(-0.28)

?

[thin bridge]

that could be used

[daring forge]

nice

[thin bridge]

if you know what to do with the result

most of the work is fine,
the issue is just that

-0.28
which happens to be an approximate solution to sin(x) = -0.28
isn't between 0 and 2pi
the desired interval for the solutions

[daring forge]

so thats the problem

[thin bridge]

as we've been saying

[daring forge]

so D

thanks

.close

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[sand ember]

So for p-adic integers

[sand ember]

I understand how to work with them, if I have one how to substract, add, divide, multiply etc

What I don't understand is how to get them, for instance, how do I get 7763 as a 3-adic integer

[icy linden]

what is a p-adic number

?

[sand ember]

This is university you're not going to be able to help

[obtuse jackal]

If you have to ask such questions to the helpee, you shouldn't be the helper

[final halo]

you need to perform "p-adic long division"

[obtuse jackal]

7763 = 7500 + 240 + 23
= 23 mod 3 = 21+2= 2 mod 3

[sand ember]

But I don't get what you mean, p-adic long division would be if I already had two numbers in p-adic form, the question is for non-obvious examples how to get it into p-adic form

[final halo]

eh maybe its no the right terminology

look on the wiki page for p-adic number

they give examples

[sand ember]

The same question I think is just going to be "how do I write a number in a particular base"

That isn't 10 obviously

[obtuse jackal]

Technically yes

You look at the last digit

But it's simpler since you don't need to find out the other ones

[sand ember]

Well obviously that's true but this is going to be the issue in that choosing a is going to be difficult

Especially for a number like 7783 you could just go all the way down it and then realise you picked the wrong starting a

[safe radish]

@sand ember Has your question been resolved?

[safe radish]

@sand ember Has your question been resolved?

[plucky elk]

Dark mode wiki

[final halo]

wikiwand

[plucky elk]

Oh I forgot about that

I uninstalled it when I started mathing more. But it kept borking math equations

[final halo]

it does do that yeah :/

[safe radish]

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[serene kraken]

what should ı do?

[dusty fiber]

figure out what x is

then do some algebra to find y

then use a calculator

[granite idol]

it seems like none of those pairs satisfy the 2nd equation, unless my algebra is wrong

[tiny wraith]

Aren't they intervals?

[jade magnet]

its an interval which is why you dont need calc

you just guesstimate

[granite idol]

oh, I see it's y in ?

[final halo]

first find a range of values x could be given that 2^x = 5

[serene kraken]

then?

[final halo]

have you done that?

[serene kraken]

if we put 2

will gave us 4

[final halo]

that indeed is true

[serene kraken]

2^x=5

how?

[final halo]

what?

[serene kraken]

in the q

2^x=5

[final halo]

because x need not be an integer

but find a range of integers that it must be between

[serene kraken]

like 2,5

wait i understand that x range of integers

.close

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[plush sky]

Can I integrate while it’s in fraction forum

[peak estuary]

you probably can in some convoluted way. it just will be much easier to split it into two fractions

[plush sky]

So I split into 2 can I integrate the denominator?

[peak estuary]

split into two fractions, simplify the first one, use power rule

[plush sky]

What about the second one I can’t simplify it?

[peak estuary]

well you dont really need to

[plush sky]

Our teacher told us we can’t integrate while it’s in fraction form

[peak estuary]

what

[plush sky]

He told us we can’t integrate the equation if it’s in fraction form….

[peak estuary]

you either misunderstood your teacher or he was telling bullshit

[hot thistle]

i think he meant more like, there's no general form that we teach for integrating a fraction like the one above

and instead you separate it and use power rule

[plush sky]

Ok I integrate it what do I do after

[hot thistle]

what did yyou get

[peak estuary]

dont forget about the constant of integration

and then you want to find that constant so that f(4)=5

because the curve passes through (4,5)

[plush sky]

Then we plug everything in and find c?

Is that it?

[hot thistle]

yes

[safe radish]

@plush sky Has your question been resolved?

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[lean otter]

The answer doesn't seem to be correct for me

[lean thorn]

what's the full problem?

[fast gazelle]

are those variables all "x", all "n", or a mixture? i can't tell

[lean otter]

Simplify

[lean otter]

The question is like that

Number 1

[worthy hemlock]

Your x's looks like n's, that's why bee asked if those were x's, n's, or both

[glass carbon]

I think 1 + x^2 + x^4 = (1+x+x^2)(1-x+x^2)

[median vigil]

$\frac{1}{1+x+x^2}-\frac{1}{1-x+x^2}-\frac{2x}{1+x^2+x^4}$

[lean otter]

Noo

Yes this

[flat frigate]

cloud

[lean otter]

Did from first and second exp

But incorrect

[worthy hemlock]

Did you attempt the problem?

[lean otter]

yes

[worthy hemlock]

Because if you did, show your work

[lean otter]

ok

I did it like this but my teacher told to do it by first and second

Is this also correct

[glass carbon]

yes

at least final result

but seems you overcomplicated this

[lean otter]

I guess yes lol

[glass carbon]

it's enough to see that

[flat frigate]

Modus

[glass carbon]

then it will take 2-3 lines

[flat frigate]

Modus

[lean otter]

Oh wow

Thanks 👍

.close

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[static yacht]

It's 2 AM, far past my bedtime, yet here is a last attempt for the night.
I have these 2 subspaces. I can see the solution, that a combo of b2 and b3 are the answer. However, how do I do this correctly / mathematically?

[static yacht]

This is my thought so far

Question is: Show U \cap V is a straight line through origo

and decide a direction vector.

Obviously, a must be 0. And if b = -c, it works, but this is pure guesswork, and doesnt seem very "correct"

[final halo]

b must be equal to -c, thats what your second equation says after deducing a=0

[static yacht]

but is it sufficient that I can just "see" that? No formula or otherwise formal work?

[final halo]

this is encoding 4 equations

you just solve the equations

b = -c comes from the second equation, you don't have to see it

[static yacht]

Fantastic, forgot to look at it like 4 equations damn

Thank you 😄

.close

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[safe radish]

Please don't occupy multiple help channels.

Channel closed

Closed due to the original message being deleted

[oak fog]

.close

[zealous mason]

.close

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[hushed minnow]

Hi

[hushed minnow]

Given a function

$$f(x, y) = -3x^4 -y^2 +4yx^2$$

[flat frigate]

szahu420

[hushed minnow]

Does it have a local maximum at (0,0)?

I calculated that it in fact has, however wolfram alpha disagrees with me

These are my calculations:

[crimson field]

How did you calculate that it does?

[hushed minnow]

Well the above calculation

[crimson field]

It does not conclude what you think it does.

[hushed minnow]

what does it conclude then

[crimson field]

Nothing.

[hushed minnow]

isn't it how you calculate local extrema?

[crimson field]

The test doesn't work for your particular point.

[hushed minnow]

you mean the test for negativity/positivity of the matrix?

also why not

[crimson field]

Your version of hypothesis three is not satisfied since it is zero.

I might have something though to help you. I'll just check the details for this problem.

[hushed minnow]

whta's f_11 and f_22 here? f is not a 2x2 matrix

[crimson field]

f_xx and f_yy respectively.

[hushed minnow]

ah

it seems that the function doesn't satisfy the conditions for the saddle point either, shouldn't it be a saddle point since it's neither a maximum or a minimum?

[crimson field]

I'm trying to apply something like this:

You'll need to consider two paths, say y = x^2 and y = -x^2.

[hushed minnow]

looks promising, since there is a suspicious parabola like shape that approaches 0

[crimson field]

Based on the function it doesn't look like a single path will show it's a saddle point.

f(x, x^2) = 0 so just modify the path slightly.

Try y = x^2/2 instead.

[hushed minnow]

hmm I'll try

[crimson field]

I'm just making up paths so you might have to be lucky to pick the perfect path first time.

[hushed minnow]

yeah I'm trying a few, none have worked so far

The green line represents the path I'm taking, and the red line is the function on that line

I would expect that to work, but still

Perhaps I can share to whole assignment and you could help me with that

The question was:
For any vector of length 1 v = (a,b),

$$h_v(t) = f(ta, tb)$$

[flat frigate]

szahu420

[hushed minnow]

Does h_v(t) have a local maximum at 0 regardless of v, and does that mean f has local maximum at 0.

I did prove that in fact h_v(t) has local max at 0, my intuition tells me that should me f has too, but it doesn't seem to be the case

Nevermind

I was graphing f(x^2, x) not the other way around

[crimson field]

It seems that the function is flat or negative in the neighbourhood of the origin which is the problem.

[hushed minnow]

you were right, x^2 works perfectly sorry

[crimson field]

I can't seem to generate an example which shows it has positive numbers in the neighbourhood.

[hushed minnow]

red is f(x, x^2)

algebraically that's x^4

[crimson field]

The only other thing I could suggest is to try and find or determine your own test using higher order terms using Taylor's theorem.

[hushed minnow]

that's not enough?

[crimson field]

I get f(x, x^2) = 0.

[hushed minnow]

oh sorry that was 2x^2

then it works

[crimson field]

Oh yeah. f(x, 2x^2) = -3x^4 - 4x^4 + 8x^4 = x^4.

We have shown it has both positive and negative values in the neighbourhood so it's a saddle point.

[hushed minnow]

that concludes it, Thanks a lot for your time !

.close

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[lean otter]

what type of intergral is this?

[lean otter]

from https://github.com/msolides-2022/MU5MES01-2022/blob/main/01-Linear_Elasticity/cantilever_beam_given_to_class.ipynb

[safe radish]

@lean otter Has your question been resolved?

[safe radish]

@lean otter Has your question been resolved?

[safe radish]

@lean otter Has your question been resolved?

[safe radish]

@lean otter Has your question been resolved?

[safe radish]

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[olive sorrel]

how to solve this without using sec trigonometric identities

[quasi bison]

what qualifies as "sec trigonometric identities"?

as in you disallow yourself from using tan^2(x) = 1/cos^2(x) - 1?

[olive sorrel]

just identities including secant

[empty gyro]

Question is : why?

[olive sorrel]

because it is not included in my study content

anyways i solved it

.close

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[empty gyro]

[safe radish]

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[mossy ivy]

can someone please explain to me how to solve this problem

[mortal fern]

sum of angles is 180deg right?

and you have a right angle

which is 90deg

• you are given that the angle A is 80 deg

[mossy ivy]

yessir

[safe radish]

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.

[crimson jewel]

there's a property called exterior angle property in a triangle

sum of two angles is equal to opposite exterior angle

work it out

[mossy ivy]

so since half of 80 is 40 i use that for sides A to C

right or at i completely wrong

am*

[deep depot]

Why did you halved 80 into 40?

[mossy ivy]

A is the longest side right?

[deep depot]

A is a point

[crimson jewel]

Arnab Pal, I don't think he is understanding

[deep depot]

Yup me too

[mossy ivy]

i’m sorry i’m just confused a lil bit

do i use pythagorean theorem

[deep depot]

You need to find the find Angle "alpha"

[deep depot]

Pythagorean theorem is used to find the missin side in a right angle triangle

But you need to find angles here

Do you know sum of all interior angles in a triangle is 180°

[mossy ivy]

yessir

[crimson jewel]

it's related to length of sides. you are finding angle

[mossy ivy]

so i’m using 45 45 90

[deep depot]

What type of information do you have about this Triangle (ignore my drawing)

@mossy ivy ?

[mossy ivy]

ummmmm

explain

[deep depot]

Focus on ∆ACD what should be your approach to find the missing angle

You have given in the question that angle ADC = 90° and angle A = 80°

You need to find the missing angle ACD

You would use Angle sum property of the triangle right

[mossy ivy]

ohhhh you subtract and get 10

okayy damn i’m stupid

[deep depot]

Yupp

[mossy ivy]

i didn’t think of that i’m slow af

my bad lol

and thank you very much

[deep depot]

,w plot x^2 + {y -3/4(x^2)^(1/3)}^2 < 1×1

[flat frigate]

Results provided by WolframAlpha

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

Requested by 𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛#6985

[mossy ivy]

.close

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[subtle kernel]

i am attempting to find the remainder of (2x+3 - 4x + 5)/(x+3) using synth. div. but i got 35 and the answer is -37 HALP

[subtle kernel]

since the denominator is x+3 i used -3 as the root for the div

so it looked like
-3|2 -4 5

which gives you 2x - 10 r 35 if i did my arithmetic right

but it appears as though i did not

[peak estuary]

did you write down the polynomial correctly?

do you mean 2x^3 -4x+5 ?

[subtle kernel]

let me check

[peak estuary]

I am not familiar with that notation but I'm assuming you missed the 0 from the missing x^2 term

[subtle kernel]

oh shit thats it 💀

okay i remember that from class

thanks! i can do it now

you a g fr

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[crystal sparrow]

hello, im confused on how I should be setting up the system of equations for the matrix to have x1 to be 11.

[crystal sparrow]

Should I manipulating the system where x1-3x3 = 5 is eleven?

[thorn gulch]

does it want you to plug in 11 for x1 to get x3?

[crystal sparrow]

is it that simple?

[thorn gulch]

or does it want you to find x1, x2, x3, x4 when x1 is 11

[crystal sparrow]

I believe it wants me to find the full solution

so x1, x2, x3, x4, when x1 is 11

[thorn gulch]

i believe so

[crystal sparrow]

my professor gave me the values of what the solution should be and it isnt clear to me how to get there. the values are <11,2,-2,-4>

[flat frigate]

Broken

[thorn gulch]

yeah thats what i got\

so since x1 is given as 11, in the first equation you get:
11 + 3x3 = 5
3x3=-6
x3=-2

then you can start plugging in these values into row 3 to get
x2 - 2x3 = 6
x2 - 2(-2) = 6
x2 +4 = 6
x2 = 2

and the last row already gives you x4=-4

so your answer is <11,2,-2,-4>

[crystal sparrow]

I see, now thank you so much for your help!

[thorn gulch]

np

[crystal sparrow]

.close

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[normal crown]

help

[normal crown]

can someone explain how i would solve this please

[worthy hemlock]

Use the cofunction identities

[normal crown]

ive never even doen this

could i have an example

?

[weary lotus]

do you know what the cofunction identities are

[weary lotus]

yeah that ^

[normal crown]

thankyou.

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[earnest wagon]

in the function y=f(g(x)), why is the domain of this function a subset of g(x)? Shouldn't it be the other way? That g(x) is subset of the domain?

[hot thistle]

by subset of g(x), do you mean subset of the domain of g(x)?

[earnest wagon]

Teacher used th word subset of g(x) only

[hot thistle]

if so consider the functions
g : A -> B, f : B -> C, y : A -> C, defined as y = f o g

[earnest wagon]

I can assume that g(x) is range

[hot thistle]

g is a function

g(x) also represents that function

[earnest wagon]

Yeah

[hot thistle]

saying "subset of g(x)" is a bit weird

i'm assuming you're not treating functions as sets are you?

[earnest wagon]

So g(x) should be domain of g(x)?

[earnest wagon]

I'm not, I'm only refering to the exact words just heard in a lecture

[hot thistle]

g(x) is not a set then

[earnest wagon]

I see

[hot thistle]

at least not as far as your situation is concerned

[earnest wagon]

So it should be domain of g(x)

[hot thistle]

so saying g(x) is a domain doesn't really make sense

yes

[earnest wagon]

So domain of this function is subset of domain of g(x)?

[hot thistle]

yes

[hot thistle]

let's refer back to this

here the domain of y is still A

however, let's change it slightly

[earnest wagon]

Yes

[hot thistle]

to g: A -> B, f : C -> D, and y = f o g

where C is a subset of B

[earnest wagon]

However are you sure that domain of y is A?

[hot thistle]

in the earlier example yes

(assuming g is surjective)

[earnest wagon]

Oh

[hot thistle]

actually

we don't need surjectivity

the domain is still A

we have

[earnest wagon]

No

If it's not surjective the elements of A will miss out

[hot thistle]

no

so

g(A) is a subset of B

that is

[earnest wagon]

Ohh

[hot thistle]

ok

so f(g(x)) is well defined for all x in A

since g(x) is in B which is the domain of f

does all this make sense so far

[earnest wagon]

Give me a second, I need time to consume what you said..

[earnest wagon]

I just noticed that f is defined from C to D and not B to C..

[hot thistle]

that was for another example

[earnest wagon]

And C is a subset of B

[hot thistle]

we started with this

g : A -> B, f : B -> C, y : A -> C, defined as y = f o g

in which case, the domain of y is A

[earnest wagon]

Yeah

[hot thistle]

however in the other case, where f : C -> D

[earnest wagon]

Let me make a arrow diagram

[hot thistle]

ok

[earnest wagon]

I just noticed that for function y=fog(x) to be defined, g must be surjective..

So you were right

And domain of y is A here, ok

[hot thistle]

no

it musnt

take g : R -> R, g(x) = 0
f : R -> C, f(x) = sqrt(x)

f(g(x)) is defined for all x

but g is clearly not surjective

[earnest wagon]

There is a condition that domain must be the complete left set for a relation to be a function and in this case f(x) is not defined for x<0

[hot thistle]

f(x) is defined

we're going to the complex numbers

so it's well defined

[earnest wagon]

R->C

R is not complex number inclusive though

[hot thistle]

the domain isn't

but the codomain is

so every value in the domain maps to a single value in the codomain

it doesn't really matter though

[earnest wagon]

Ohh

[hot thistle]

make it f(x) = x^2

[earnest wagon]

You're right, it's defined for whole R. And in this case g is not even surjective...

[hot thistle]

yes

so that should give you an idea of how y : A -> B -> C, y = f o g still has domain A

[earnest wagon]

Now this example

[hot thistle]

ok

so

since the codomain of g is B

[earnest wagon]

Yes

[hot thistle]

and i will remphasize that C is a subset of B

there may be values in A that mapped under g go outside of C

i.e.

g(x) is in B but not in C

this is fine if we're just worried about g

but then we want to take g(x) and map it under f

so we want f(g(x))

if g(x) is not in C, then this is not well defined

does this make sense so far

[earnest wagon]

Okay let me make arrow diagram for this one as well to see if it goes according to what you said

[earnest wagon]

So for f(g(x)) to be defined g(x) must be in B as well as C?

[hot thistle]

g(x) is in B by the definition of g

[earnest wagon]

Yeah

[hot thistle]

but yes, for f(g(x)) to be defined we also need g(x) to be in C

[earnest wagon]

And that's how it's a subset of g(x)

I see

[hot thistle]

yes, we take by convention the largest subset of A such that g(x) is in C

so as to lose as little information as possible

[earnest wagon]

I see

Thank you

.close

[safe radish]

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[hot thistle]

no problem

[safe radish]

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[lean otter]

can 2( ) be considered a function in this image?

[lean otter]

First u expand the brackets

Wasn't the question

What

I know the anser is 1

[wise blaze]

oh again this question

[lean otter]

I'm asking if 2 ( ) can be considered a function

[wise blaze]

thats why i hate sign of division

[lean otter]

why?

It's pretty obvious what the answer is

[earnest wagon]

Why would 2() be a function

[lean otter]

why not?

[earnest wagon]

Because function is something where your input are considered with outputs

Can you tell what is input and output for 2()

[lean otter]

2x

3( ) would be 3x

1( ) or ( ) would be x

[earnest wagon]

You're assuming () is x

[hot thistle]

the answer is "yes 2 could be a function, but that's confusing notation"

[obtuse plover]

Are u asking if u can use a traditionally numerical symbol as a symbol used to represent a function (which is traditionally represented by a letter)?

[lean otter]

I'm asking if 2( ) is a function similar to f( )

[earnest wagon]

y=2() is indeed a function whose domain and range is R?

[earnest wagon]

No it would be similar to f(())

Not f()

You're clearly substituting () notation for traditional x

[lean otter]

I see

[hot thistle]

brandon what is the goal of your question

do you want to know if you can use "2" as the name for a function?

[lean otter]

explain this

but anyways

I've spent enough time

[earnest wagon]

I don't know what's the difference between h(x)=3 and h(x)=1+2

[lean otter]

no difference. Just copied the numbers from here

I'll get back to studying. Thanks for your insight

.close

[safe radish]

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[toxic stratus]

that doesn't change the fact that the original image is a badly written expression

you're just imposing the order of evaluation by rewriting it

[safe radish]

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[earnest wagon]

Are all rational numbers not fractions? If so, please give me an example.

[marsh walrus]

rational usually means fraction

but consider like 2/1

[earnest wagon]

Wait

It says that it's not necessary that all rational numbers are fractions

[marsh walrus]

right

like 2 is a rational number

since it can be written as a fraction

(even though its usually not)

[earnest wagon]

2 is also fraction

[marsh walrus]

2 is not a fraction

[earnest wagon]

Denominator 1 is hidden

2/1=2

[marsh walrus]

this is the point being made in the image you posted

2 is not a fraction

but it is a rational number

[earnest wagon]

Isn't 2/1=2

[marsh walrus]

sure

but 2 isnt a fraction

[earnest wagon]

why?

[marsh walrus]

because it has no denominator or numerator

[earnest wagon]

2 is the numerator and denominator is 1 though

[marsh walrus]

i mean, its not written as the ratio of two numbers

[earnest wagon]

It's written as the ratio of 2 and 1 isn't it?

[marsh walrus]

do you see a 1?

[earnest wagon]

Isn't it hidden like we know 2 is 2 * 1 but 1 is hidden

[marsh walrus]

idk what to say

do you usually assume parts of math problems are invisible?

[earnest wagon]

Yeah

[marsh walrus]

well thats gonna cause issues

[earnest wagon]

2=2/1 so what's wrong with that

[marsh walrus]

2/1 is a fraction

2 isnt

be aware im not writing anything invisibly in the second line

the 1 really is just missing

it is not present

[earnest wagon]

You are saying 2 is equal to 2/1, 2 is not fraction but while 2/1 is a fraction even then

[earnest wagon]

Oh

[marsh walrus]

2 is equal to 6/3

or 10/5

[earnest wagon]

Ohh

I see now, what you mean

Thanks

.close

[safe radish]

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[safe radish]

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[coarse anvil]

how is lhs same as rhs of top row ?

[light shoal]

have you heard of telescoping?

[coarse anvil]

I dont think so

[light shoal]

try writing out an example for small n, say n=3

when r=1 the summand is 2^5 - 1^5, right?

[coarse anvil]

yeah

[light shoal]

and when r =2?

[coarse anvil]

3^5-2^5

[light shoal]

yep

and when r=3?

[coarse anvil]

4^5-3^5

[light shoal]

yep

now add those three together, what do you get?

notice that a bunch of stuff cancels

that's the "telescoping"

[coarse anvil]

Ahhhh

Ive done that before but it was called method of differences

[light shoal]

ah cool

[coarse anvil]

Thanks

[safe radish]

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[lean otter]

@lean otter why would you subtract tho?

29.4-14.7=m(9.8-4.9)

Doesn’t 9.8 and 4.9 go in the same direction because the 3kg is going upwards?

[safe radish]

@lean otter Has your question been resolved?

[lean otter]

<@&286206848099549185>

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[lean otter]

it is probably fair to assume that the liquid is incompressible

so take the difference between the in and out flow rates

[modern jolt]

oh okay that makes sense

I been overcomplicating things in my headf

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[lean otter]

i substract to calculate 'net force'

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[lean otter]

im stuck on last part

[safe radish]

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[potent osprey]

Hello, I have to do a cryptanalysis of a homomorphic scheme over the integers but am completely stuck on trying to break it. I am supposed to find the hidden key $p$ from ciphertexts $c_i = x_i y_i^{-1}$ mod $p$ where $x_i$ and $y_i$ are small integers (with bit length less than $\frac{\lambda}{2}$), the bit length of $p$ is $\alpha \lambda$ where $\alpha$ is an integer $\geq 2$. An evaluation key $x_0 = p\cdot p_2 \cdot p_3$ is also given where $p_2$ and $p_3$ are primes of bit length $\lambda$. So given a list of ciphertexts, $\alpha$, $\lambda$ and $x_0$ I am supposed to retrieve $p$. I am pretty sure that the attack should be based on lattices. Any suggestions?

[flat frigate]

DAILI

[potent osprey]

For some more context on how the small integers $x_i$ and $y_i$ are obtained for each ciphertext (may help to break the scheme): a number $e = CRT([m, r], [p2, p3])$ is calculated where $m$ is the message and $r$ is a uniformly random integer from $0$ to $p_3 - 1$, then $x$ and $y$ are calculated based on the shortest vector in the lattice consisting of the solutions of $x - ey = 0$ mod $p2 \cdot p3$ and the ciphertext for this message becomes $x \cdot y^{-1}$ mod $p$.

[flat frigate]

DAILI

[potent osprey]

<@&286206848099549185>

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[untold topaz]

Can anyone help me check the domain n range?

I feel kinda off when everything's the same

[obtuse plover]

don’t let them psych u out

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[obtuse plover]

But yea u should be good lol

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[jolly swan]

If someone help me i have test tomorrow explain to me each sentence with a very detailed drawing. It is called the tangent to a planar curve gamma in a regular point M0 of it belonging to a simple arc of the curve, the line located in the limit position of the point M0 and of a current point M of the arc when M tends to M0 on the arc considered.

[jolly swan]

I try to draw but i don t understand there are two tangents?

🙏🙏🙏🙏🙏😭😭😭😭

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@jolly swan Has your question been resolved?

[jolly swan]

How can i close a channel

?

[granite idol]

type .close

[jolly swan]

.close

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[narrow vault]

What operation was done for this simplification/ what property?

[narrow vault]

Sorry mistake

Never mind I meant

This

[obtuse plover]

Were u able to figure this one out?

[narrow vault]

Yessir

[obtuse plover]

Aight cool

[pseudo scroll]

Stephen helps stefan

Meet your German relative

[obtuse plover]

So we can make each factor into one fraction

[flat frigate]

Stephen

[obtuse plover]

Make that into 1 fraction

[narrow vault]

Im really not sure

[flat frigate]

Stephen

[obtuse plover]

Just get a common denominator

[narrow vault]

(X+1)/x?

[obtuse plover]

Yep

Now do that same process for the other ones

Lmk what u get

[narrow vault]

Is the common denominator of (1/x+1/y)=(x^2y+xy^2)/xy?

[obtuse plover]

It’s kinda unclear what’s being divided and stuff

Just let me know what u got for each of the other two factors and we can go from there

[obtuse plover]

Ok so the first two are correct

$\frac 1x + \frac 1y$

[flat frigate]

Stephen

[obtuse plover]

What’s the common denominator

[narrow vault]

I’m asking myself how many times does 1/x go into xy

And that is

X^2y

[obtuse plover]

No

If the common denominator is xy

$\frac 1x \cdot \frac yy = \frac {}{xy}$

[flat frigate]

Stephen

[narrow vault]

Is this wrong

[narrow vault]

I don’t do it like that And I’m not following

[obtuse plover]

U can’t just multiply by x^2 * y

It’s not equivalent

[narrow vault]

That how I find common denominator. Asking myself what to multiply 1/x to get xy

[obtuse plover]

to get xy where? U want xy in denominator, so ask urself how do u get from x to xy in denominator

[narrow vault]

Do you have a trick for computing common denominator faster

[obtuse plover]

Yes this

Common denominator of 1/x and 1/y is just the product of the denominators

xy

Thus we have to figure out what to multiply each fraction’s denominator by to get xy in the denominator

To get 1/x to having an “xy” in the denominator, u must multiply both the numerator and denominator by y

[safe radish]

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[safe radish]

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[gentle tapir]

hi i have a really simple question

[gentle tapir]

how do you solve an inequality?

[winter summit]

Post problem

[gentle tapir]

the question is literally "what are the steps to solving an inequality" there is no equation or expression

we did this a few years back but i forgot

[empty gyro]

Isolate the variable, and keep track of the direction of your inequality

[gentle tapir]

thank you!

[crimson jewel]

@gentle tapir close channel if done

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[hushed minnow]

Hi

[hushed minnow]

For

$$f(x,y) = e^{xy}-2xy$$

[flat frigate]

szahu420

[hushed minnow]

Show that it has local minima at points

$$P = (x, \frac{\ln 2}{x})$$

[flat frigate]

szahu420

[hushed minnow]

I already concluded that the first partial derivatives are zero there, but what nexty

I was given a hint to inspect the following function

$$g(t)=e^t - 2t$$

[flat frigate]

szahu420

[royal pivot]

for this

find the turning point

[hushed minnow]

.

oh the second one?

Why would I do that, I want the second derivative to be positive, thus showing that there is a local minimum

[royal pivot]

oh yeah

my bad

first derivative

[mortal fern]

i got the answer from using the first derivative, but I'm sure I've done something illegal

[royal pivot]

no

[mortal fern]

isnt it just implicit differentiation and then searching the zero point of the derivative or am I doing something illegal here

[hushed minnow]

I already found the zero point of the first derivative

[mortal fern]

and i got x,ln2/x

doing that

[hushed minnow]

.

that's not a proof

could be a saddle point

[mortal fern]

ah right

[hushed minnow]

<@&286206848099549185>

[narrow vault]

.close

[hushed minnow]

bruh

[misty leaf]

@hushed minnow so you have that the partial derivatives are 0 at $\left(0, \frac{\ln2}{x}\right)$
And you're looking to prove that it's a saddle point?

[flat frigate]

MKing625

[hushed minnow]

No and no

I have partial derivatives are 0 at P

[hushed minnow]

.

I am to show that it's a local minimum

which is quite intuitive when you look at the graph of the function

[misty leaf]

Ok, so that's where you would use the determinant of the second derivative matrix (a mouthful, I know 😅)
$M=f_{xx}\times f_{yy}-(f_{xy})^{2}$

[flat frigate]

MKing625

[hushed minnow]

That's 0

so it doesn't prove anything just yet

[misty leaf]

Oh

.

Then nvm, past that idk
Sry

[hushed minnow]

thanks anyway

<@&286206848099549185>

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[safe radish]

@hushed minnow Has your question been resolved?

[hushed minnow]

.close

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[lean otter]

Hi

[lean otter]

I need help with this one

Those are the formulas needed normally

<@&286206848099549185>

Can i get help with any of these ?

[deep depot]

I think the solution of first one should be 4cos²((a-b)/2)+4 assuming a=alpha and b = beta

[lean otter]

Wasn’t that oubvious?

I need to prove it

Like this

<@&286206848099549185>

[deep depot]

I mean you don't have +4 in the question

That's why I m asking that you wrote your question right ?

First expand the Squares if you need to solve the first question

@lean otter

[lean otter]

Hi

[lean otter]

Ye thats why i said

[deep depot]

For solving this question expand the Squares first

[deep depot]

Are you a doctor

[lean otter]

So like (a+b^2

[lean otter]

U can write the first part like cos^a online u will get it

[deep depot]

Expand (cos a+ cos b)² and (sin a + sin b)² assuming a and b are alpha and beta respectively

[lean otter]

Ye so how?

[deep depot]

(a+b)²=a²+2ab+b²

Got it

[lean otter]

Ok wait

[deep depot]

Yupp

[lean otter]

Can i do it like this

[deep depot]

?

[deep depot]

Fuck no

[lean otter]

So writing cos in each part?

[deep depot]

Yupp

Cos² a + cos ² b + 2cos a.cos b

Smth like this

[lean otter]

Isn’t it? Cos^2 a + 2cos a cos b + cos^2b

[deep depot]

It's the same thing the order doesn't matter in addition

[lean otter]

Ye but u put cos^2 a + cos^2 b isnt that wrong?

Okay but now what?

[deep depot]

I didn't write cos^b anywhere

[deep depot]

2 common

[lean otter]

I just mean the first part

[deep depot]

And you would see that you got
$\sin{\alpha}\sin{\beta}+\cos{\alpha}\cos{\beta}$

[flat frigate]

𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛

[deep depot]

Which is ultimately equal to

$\sin{\alpha}\sin{\beta}+\cos{\alpha}\cos{\beta}=\cos{(\alpha-\beta)}$

[flat frigate]

𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛

[lean otter]

Okay so what now?

How do i delete the pic

[deep depot]

Try to simplify that equation into this

[deep depot]

Tap on the pic

[lean otter]

<@&268886789983436800> delete this pic

Can’t

[warped roost]

you should be able to

but whatever

i did it for you

[lean otter]

Thnx

[lean otter]

Like?

[lean otter]

Couldn’t somehow

[deep depot]

$2(2+\sin{\alpha}\sin{\beta}+\cos{\alpha}\cos{\beta})$

[flat frigate]

𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛

[deep depot]

You have this right

Notice that

$\sin{\alpha}\sin{\beta}+\cos{\alpha}\cos{\beta}=\cos{(\alpha-\beta)}$

[flat frigate]

𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛

[lean otter]

How do u get the second 2 in 2(2….

[deep depot]

$2(1+\sin{\alpha}\sin{\beta}+\cos{\alpha}\cos{\beta})$

[flat frigate]

𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛

[deep depot]

My bad

Now alright ?

That's why I was gettin that +4 at last anyways small mistake

[lean otter]

I just dont get how little sin and cos we have how did u remove most of em?

[deep depot]

Sin²a+cos²a = 1

sin²b+cos²b=1

1+1=2

That's why I took 2 common

[lean otter]

Give me a min

[deep depot]

Ok

[lean otter]

So u took those and turned them into ones?

[deep depot]

Yupp sin²a + cos²a=1

That's an identity

[lean otter]

So this?

[deep depot]

Yupp now take two common and use this

[lean otter]

Now what?

[deep depot]

$\sin{\alpha}\sin{\beta}+\cos{\alpha}\cos{\beta}=\cos{(\alpha-\beta)}$

[flat frigate]

𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛

[lean otter]

Is same as = cos a cos B +sin a sin B

[deep depot]

Yupp that's also and identity

[lean otter]

U get this?

[deep depot]

2+2cos(a-b)

[lean otter]

How this part is cos(a-b)

[lean otter]

Where the 2+2?

[deep depot]

Well now we know that $cos{(2\theta)}=\cos²{\theta}-1$

[flat frigate]

𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛

[lean otter]

I dont even know that 0 symbol

[deep depot]

$2(1+\sin{\alpha}\sin{\beta}+\cos{\alpha}\cos{\beta})=2(1+\cos{\alpha-\beta})$

[flat frigate]

𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛

[lean otter]

Y

[deep depot]

Theta is just a notation to show any angle or something ,treat it like a variable. It's an identity

[deep depot]

I already told you $\sin{\alpha}\sin{\beta}+\cos{\alpha}\cos{\beta}=\cos{(\alpha-\beta)}$

[flat frigate]

𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛

[deep depot]

Both are the same

[lean otter]

Ay man i get math in dutch can’t even understand these words

This correft?

[deep depot]

I don't know how to speak duch

[deep depot]

It's correct

[lean otter]

Okay so what now?

[deep depot]

Use this

Well now we know that $cos{(2\theta)}=\cos²{\theta}-1$

[flat frigate]

𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛

[lean otter]

My guy I didn’t learn that

So u think my teacher will accept that

[deep depot]

It's an identity

Mathematics is something which can be done by any method

[lean otter]

Even then i gave u what i have to use norhing else

Ye but idc about that if my teacher wants it that way i cant ignore. I only want to pass

Got another method?

<@&286206848099549185>

Can someone help me with any of these?

[deep depot]

I got another method where you have to use your identity but again it would not work if I don't use that cos (2 theta) = cos²(theta)-1

[lean otter]

Formulas sin2a cos2a tan2a sin^2a cos^2a can be used

[lean otter]

Can u solve the other ones without crazy methods?

[deep depot]

Bro I can't use 4 limited identities to solve these types of problems. It's already complex and you're makin it more complex by usin' some limited methods, mathematics can be done with various methods there are no limitations

[lean otter]

Okay wait

[lean otter]

All these can be used can it be done?

Simpson formulas method are the above ones

[deep depot]

Bro see my battery percentage 🥲

[lean otter]

Just charge it pls man i need to pass

Look just help me with 8) 7) and 5)

[lean otter]

.

[deep depot]

Is this a test?

[lean otter]

No

Exercice to help me for the test

?

[lean otter]

U helping?

[deep depot]

Check the time in my phone brother

,ti

[flat frigate]

The current time for 𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛 is 02:33 AM (IST) on Tue, 23/05/2023.

[lean otter]

<@&286206848099549185>

Anybody helpe me ?

[safe radish]

@lean otter Has your question been resolved?

[safe radish]

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[safe radish]

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[weary iron]

Why does the angle of the two tensions acting upon each other come out to 50 instead of 130? And why are the forces 800 N and 1500 N reversed from the left to right and vice versa?

[safe radish]

@weary iron Has your question been resolved?

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• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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[ashen rose]

How would i do number 2. I need to find the total number of ways you can get all the possible outcomes

[ashen rose]

.close

[safe radish]

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

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[tranquil mango]

hi

[tranquil mango]

find the value of the perimeter and the area of an external (regular) octagon from the value of Apotem= 4 of the internal polygon

thats the exercise

[tropic halo]

an octagon has 8 sides

which means that the angle between the two lines that cross in the center is 360/8 which is 45

so you can find the length of each side by noticing that there's a 22.5 angle in that triangle over there

i think this is all that you need

keep up

[tranquil mango]

ok yes, thats true

but I have a problem

[tranquil mango]

here there is 1 octagon

but in the problem I need an inner octagon

Can I show you?

[tropic halo]

sure

[tranquil mango]

its like this

[tropic halo]

any more information ?

[tranquil mango]

yep wait

sooo

the black mline

in the mid

is the apotem

that is 5

srry

4

and only with that info

[tropic halo]

man i'm not talking about that i mean is there any relations between the big oct and the small one ?

[tranquil mango]

no sir

or wait

like

maybe

cause the exercise says that I have to find the area and perimeter of the exterior octagon

[tropic halo]

just looking at the shape you can evaluate the quality of this exercise

the only info that i can get is the by looking at the shape you can notice that the big oct is just a zoomed version of the smaller one, that means if we have some kind of a value like R "ration" between the big oct and the small oct then :
Area(big oct) = R * area(small oct)

not sure about the perm though

[tranquil mango]

ok

sooo

[tropic halo]

yep

lack of information

[tranquil mango]

fuck my school, I am in 8th grade and seeing this

[tropic halo]

naah it's fine don't hate math cuz you're school suck, math is good, education is not

[tranquil mango]

I know but

its not putting presion rn

but