help-28

[glossy valve]

ExpertEsquieESQUIE

[brisk minnow]

Wait no, u said not to use that idea

[brisk minnow]

Then to prove that the cyclic subgroup is infinite

[queen gull]

you don't actually need that

but its good for you to understand why this is true, its implied by the definition of what it means for an element to have infinite order

[brisk minnow]

Well to prove that if the group is inf order then the cyclic subgroup is inf order is contradiction no?

I don’t really see the starting point in answering the question

Left it so I could think abt it better today but somehow even more confused

[queen gull]

I want to make something clear

you are looking for infinitly many subgroups of G

not infinitly sized subgroups

[brisk minnow]

Ohh

So the size of each subgroup doesn’t matter then

It’s just whether G being infinite means it’s subgroups can also be infinite

And the fact that one element is infinite order

[queen gull]

what you have here is <g> is infinite, which makes your life even easier

[brisk minnow]

And this is a subgroup of G right?

[queen gull]

by definition yeah

[brisk minnow]

Alright so how does this make it easier

[queen gull]

.

[brisk minnow]

And we have to show there’s infinitely many of say <g> where it’s subgroups are of the form <g^n>

[queen gull]

If G was some infinite group, you need to argue for the existence of an element of infinite order, or argue that the non-existence of one still gives you what you want

[queen gull]

yeah you essentially need to show you have infinitely many different subgroups of <g> (which are also subgroups of G) of the form <g^n>

[brisk minnow]

Alright lemme try and write this down

[queen gull]

ping me if you need me again

[brisk minnow]

@queen gull this is the right idea?

[queen gull]

yeah you want to show Hn are different subgroups of G

the different here is the main part

[brisk minnow]

would this mean a contradiction proof?

[queen gull]

just in terms of notation, since you fix n, its more accurate to write Hn={g^nk | k \in Z}

[brisk minnow]

oh alright don’t need the n in Z+ ?

@queen gull this valid?

Argument

I think it’s logical

Maybe I need to prove why m = nk

[queen gull]

you need it out of the set builder notation

since you are not running over all n in Z+, you are fixing such n and defining Hn for it

[brisk minnow]

But that I can do by showing that the group is infinite

[brisk minnow]

Ah Alr

I’ll change it

[queen gull]

can't read this

but otherwise it looks fine

[queen gull]

and this issue also

[brisk minnow]

Want to show that Hn ie H1 H2 H3 … are distinct

[queen gull]

yeah right

[brisk minnow]

Finally 😌😌

Alr I’ll tweak the rest

[queen gull]

fix this, and then the only thing you can add is more details

[brisk minnow]

Ty

[queen gull]

if you want to

np

[brisk minnow]

yea I can probably insert the lemma for why m = nk etc

And I’ll fix that issue now

❤️

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[lime rover]

I need help with solving the Quadratic equations below:
x² + 5x + 8 = 0
x² - 15x + 35 = 0

[queen gull]

quadratic formula
?

[lime rover]

I forgot to mention that I can not use the quadratic formula for this one.

[queen gull]

the complete the square

any other method is basically guesswork

[azure eagle]

Complete the square

[full forum]

@lime rover Has your question been resolved?

[lime rover]

x² + 5x + 8 = 0
(x² + 2 × x × 2,5 + 2,5²) + 1,75
(x + 2,5)² + 1,75 = 0
(x + 2,5)² = -1,75
x + 2,5 = √(-1,75)
No real solutions.

[queen gull]

yeah

[lime rover]

x² - 15x + 35 = 0
(x² - 2 × x × 7,5 + 7,5²) - 21,25
(x - 7,5)² - 21,25 = 0
(x - 7,5)² = 21,25
x - 7,5 = √(21,25)
x - 7,5 = ± 4,6097722286

I don't know If I did correctly.

[fast peak]

looks good

(x^2-15x+36 would have much nicer roots. maybe you accidentally copied the question wrong?)

[lime rover]

Thanks for telling! I'm kind of half asleep right now.

67

[proud gorge]

💀

[lime rover]

Lol.

[proud gorge]

You can change x^2 to x * x or x(x)

[fallen ivy]

SIXXX SEVENNN

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[warped bone]

Hi, my question is:

"If W = 600 N in the figure, what is the force exerted by the rope on the end of the joist A? What is the tension in rope B?"

[warped bone]

And i got "possible" answers.

Like:
tension on joist A = 299.87 N
tension in Rope B = 519.7 N

Also, with the question "what is the force exerted by the rope on the end of the joist A?".

Im stuck with that part.

I made the calcs and results in:

Fx = 259.85 N
Fy = 450 N

(speaking of the force on the end of the joist A, cuz the rope B is like "holding on")

<@&286206848099549185>

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[thick hedge]

Very confused here

$E[XY] = \int_{0}^{\infty} \int_{0}^{1-x}2xy dy dx$

[glossy valve]

wai

[thick hedge]

This is $\int_{0}^{\infty} 2x \frac{(1-x)^2}{2} dx$?

[glossy valve]

wai

[thick hedge]

which makes no sense, as it doesn't converge

[umbral dome]

where are the bounds on x coming from

[thick hedge]

x>0

oh would be 1-y?

[umbral dome]

no, the outer integral bounds should be constants

but you should try drawing the region where f(x) is nonzero

[thick hedge]

oh

wow

such a stupid mistake

$\int_{0}^{2} \int_{0}^{1-y} 2xy dxdy$

[glossy valve]

wai

[thick hedge]

that's much better

[umbral dome]

that upper bound still

[thick hedge]

hmm?

the lower bound is 0, as y>0

[thick hedge]

I don't get what's wrong

[umbral dome]

,w plot x + y <= 1, x > 0, y > 0

[glossy valve]

Results provided by WolframAlpha

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

Requested by cloudedhorizons

[umbral dome]

your upper bound is implying that y can be 2 somewhere in there

[thick hedge]

right

should be from 0 to 1

now for $\sigma^2_X$

[glossy valve]

wai

[thick hedge]

$\sigma_{X}^2 = E[X^2]-(E[X])^2$

[glossy valve]

wai

[thick hedge]

X^2 wou;dn't be 4 here would it

right...

the mariginal is 2(1-x)

got it

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[misty flare]

I need some help with this task. (This is the original description, not translated, say so if i should translate it :) ).

The change in the height of the water *h * in the pool with respect to time (seconds) can be described by the equation 1.

the first task was to calculate the value of k, given that the outlet valve has a diameter of 20 cm. I did that with the help of equation 1.

[misty flare]

Now i would like help with task 2:

Now determine a formula for h as a function of time when the maximum water depth is 2 meters. In other words: Solve equation (2)

the values of f is calculated to 0.03141592654 m^2 and k is calculated to be -0.0009328147767 N/kg

[sonic stratus]

Separate as variables and solve the DE?

like:

$\int \frac 1{\sqrt h} dh = \int k dt$

[glossy valve]

∫ᴄ 𝐅·𝑑𝑟 = ∬ʀ ∇⨯𝐅 𝑑𝐴

[misty flare]

yeah did that, but don't know if it's correct

wait... i will send my calculation

[sonic stratus]

why did that end up as numbers?

i might be missing something of the problem anyways

[misty flare]

i tried to calculate the constant c 🤔

[sonic stratus]

oh yeah, right, mb

didnt read right

[misty flare]

Also, the differential equation of equation (1) can be simplified be written as equation (2)

[sonic stratus]

yeah, i was looking at that

[misty flare]

ah, ok.

If there's something i should translate, you can just tell me :)

[sonic stratus]

As far as the DE goes, yeah, thats the solution, the problem seems a bit strange on wording anyways

But yeah, the math is right

[misty flare]

So, for the formular of h, i did it like this:

Is this correct?

[full forum]

@misty flare Has your question been resolved?

[misty flare]

<@&286206848099549185>

[full forum]

@misty flare Has your question been resolved?

[misty flare]

<@&286206848099549185>

I need some help to know if the formula for h is correct before I can continue

[burnt cedar]

in which one?

where

pls send a pic

[misty flare]

this one

[burnt cedar]

what language is this?/

can't read

lemme try

[misty flare]

Danish.... don't worry about it, just explained what i did...

Tell me if I should translate it

[burnt cedar]

but like it is about what? what topic

[misty flare]

Okay, so the overall topic is differential equations, but there is a connection to the tasks...

so..

i will give you the description in english

[burnt cedar]

sure

i mean it seems right from the equations alone but to make it simple just make it ${(k.t + c)/2}^2 $ in step 2

[misty flare]

**The assignment is: **
The newly hired lifeguard has problems emptying the swimming pool before the last bus has left, so he turns to a student in the family and asks for advice. The family member has just learned about differential equations and therefore knows that the change in the height of the swimming pool water h per unit of time (second) can be described by:
$$\frac{dh}{dt} = -\mu \cdot f \cdot \sqrt{2 \cdot g \cdot h} \div A$$

[glossy valve]

TheWideDuckling

[misty flare]

where µ is an outlet constant determined by the design of the bottom outlet valve, whose cross-sectional area is denoted f and is given in m2. The surface area of ​​the basin is A and g is the acceleration due to gravity. The dimensions of the basin are 8 by 25 meters and µ can be set to 1.34.

Slightly simplified, the above differential equation can be written as: $$\frac{dh}{dt} = k\cdot\sqrt{h} (2) $$

Yes. i know, it's long, but this is the whole description

[burnt cedar]

ok but here is the 2 under the root or outside it?

[glossy valve]

TheWideDuckling

[misty flare]

no. it's not. it's just to show that it's equation 2

[burnt cedar]

oh ok

[burnt cedar]

could you please explain in english what you have said here in the 4th line?

[misty flare]

sure

"We can use the following equation, as this is the expanded form of the solution for h(t), i.e. the parentheses have been calculated, which results in":

[misty flare]

<@&286206848099549185> ^

[hearty wagon]

What is the actual question?

[misty flare]

I need help to conclude if my formular for h is correct here (see also the other messages if context is needed)

[burnt cedar]

yes it is correct

[misty flare]

Do you know if i'm done on this or am i missing something?

[misty flare]

Thanks for the help

.close

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[open basin]

Hey
Can someone please help me with this optimization problem?

[unreal wren]

Where is 'viewing angle o'?

[open basin]

sry, thats bad translation

its meant to be phi

[unreal wren]

Oh

!status

[full forum]

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

[unreal wren]

The first thing we need to do is solve for phi, as a value of h

Do you see how we can do this?

[open basin]

no

[unreal wren]

Let me send a picture, wait a moment

Solve for the red and orange angle first

Use the red angle to find the green angle

[open basin]

maybe
$redAngle = \arccos(\frac{standTillH}{hypotenuse})$

[glossy valve]

Lukas

[unreal wren]

Maybe use arctan instead

It's simpler

[open basin]

$redAngle = \arctan(\frac{h}{standTillH})$

[glossy valve]

Lukas

[open basin]

$orangleAncle = arctan(\frac{h}{110 + standsStillH})$

[glossy valve]

Lukas

[open basin]

but i dont know how to get the the green one with the red one 🫣

[full forum]

@open basin Has your question been resolved?

[slate violet]

if the height is h, then by trig the base length is (5 + h/tan(20))

so that allows you to find this angle here

and then similarly, you have a big triangle with base length (105 + 5 + h/tan(20)) and height h

find that other angle too at the top

[shy blade]

20 degrees is the incline from the start of the stand right? not from the goal

[slate violet]

yep

[open basin]

let me reconstruct, one moment

but whats even my main condition which has to be maximum for the angle phi

i cant use trigonometric function for none right triangles, right?

[shy blade]

south's idea got me theta as a function of h but i differentiated it to find a maximum and its absolutely horrible to solve for h

plotting on desmos though shows there is actually a maximum so thats nice at least

[shy blade]

basically as south said:
for triangle CDE tan(20)=h/CD so CD = h/tan(20)
x = CD = h/tan(20)

now for triangle BDE the base is x+5 and you can find angle BED using x+5 and h and tan

let y = angle BED, then use right angled triangle AED to find the angle AED and theta will be angle AED - y

you should then have theta as a function of h from which you can differentiate and set equal to 0 to find the value of h where theta is maximised

[slate violet]

I really don't see any other better way

sine rule is just awful

(I get around h = 8.02 if you want to check)

[shy blade]

yeah i just got the answer w pen and paper

kinda nasty question tbh

but cool method

[open basin]

im confused

whats e.g. angle AED

[slate violet]

this is a creative problem but it would absolutely be calculator-allowed on an exam

[slate violet]

here

[shy blade]

if you start from A, go to E, then down to D, the line you trace along will contain your angle

[shy blade]

tbf i did it with no calculator

idk how a calc would even help here

my exact value ans was || 5sqrt(22) * sin(pi/9) in radians ||

no clue how wolfram alpha is unable to simplify this lmaoo

[open basin]

so the angle in corner E?

[shy blade]

yes

[open basin]

thats where i am rn

[shy blade]

extended base is htan(beta)+5 not -5

unless im reading this wrong

[open basin]

wait isnt extendedbase just h * tan(beta)

[shy blade]

ah sorry i thought you had swapped alpha for beta for some reason

[open basin]

cuz base = h * tan(beta) - 5

[shy blade]

you want to solve extended base for beta though, not base

because once you have beta, you can find the angle of AED then subtract beta to get phi

[open basin]

:= ist just an assigning operator and the thick equals is an equation

[shy blade]

yes but you solved for base whereas you need to solve for beta

[open basin]

oh yeah

[shy blade]

yeah now you need to find the angle of AED

[open basin]

oh wait

but h is still unknown

[shy blade]

to make it easier though do 110+base instead of 105+extended base

[shy blade]

we will solve for h later

[open basin]

alr

[shy blade]

yep now we need to make the function of theta using h like this

sorry i keep forgetting to say phi instead of theta

theyre same thing my bad

[open basin]

no worries

[shy blade]

have you done calculus? because once we have phi(h) we need to find the maxima

[open basin]

why is phi + beta the same as aed? doesnt the angle get smaller like if it would be at the edge it would be very small?

[open basin]

yup

[shy blade]

ahhh we were meant to find the angle in the corner E for the triangle BED, but its fine thats just gonna be 90-beta

[open basin]

i did calculate the angle in corner E

[shy blade]

oh ok sorry i was confused by this

beta should be the corner E but of the triangle BED

not of the triangle AED

theyre different

[open basin]

no beta is corner c

[shy blade]

yeah thats not the angle we need let me show you what i mean

[shy blade]

see here

b is where beta needs to be

i think you might have to resolve for beta but after its fixed, then you can do AED - beta and it should give phi

[open basin]

so should i calculate the new beta?

[shy blade]

yes beta should be where b is drawn in south's image

[open basin]

so this is my current state

whats my next step?

[shy blade]

now you do AED-beta, then differentiate that with respect to h, set the derivative equal to 0 and solve for h

then you will get your answer of h

[open basin]

so is my main equation which has to be maximum
aed - beta

[shy blade]

aed-beta

you find the maxima of that function yes

[open basin]

alr i'll try

thanks i came to the correct answer
but i still dont know why aed - beta equals phi

[shy blade]

because in the diagram , beta is BED, if you do AED - BED you are left with phi

[open basin]

but like the angles phi and beta are more deep inside the triangle, do they still have the same values

[shy blade]

well phi + beta = AED

like if you imagine pushing phi more towards the corner to connect if with bed

you can see that it will just be the same as AED

[open basin]

but if i push phi more towards the corner, it gets to big to fit into this white little triangle

[shy blade]

the angle is the same no matter how far from the corner for example if you have a right angle, a small square is the same as a big square, both are 90 degrees

[open basin]

ohh alr

thanks for your time and helping me solve this task 🙂 i understand it now better

[shy blade]

no problem sorry it took so long haha

[open basin]

dont worry, my bad for not understanding it

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[proper pewter]

Hi

Anyone here

[azure onyx]

yes? which question, and what have you tried/understood about the question?

[proper pewter]

Number 3 i am confused of which line is line 3

[azure onyx]

what topic is this? what kind of angles have you learnt? because I don't particularly see any good name to call angle 3 (not line 3, by the way),,,

[proper pewter]

This lesson is called Angles and Congruence

[onyx glen]

you mean angle 3?

[proper pewter]

If u want i can send u the answer key file

[proper pewter]

Yes

[onyx glen]

do you see the number "3" on the diagram

[proper pewter]

Which angle is angle 3

yes

[onyx glen]

right

that digit is where angle 3 is

[proper pewter]

So another name is ADC?

[onyx glen]

indeed

[proper pewter]

For questions 5,6 and 7 I don’t know what they mean

[onyx glen]

do you know what "opposite rays" and "bisect" mean

[proper pewter]

No i forgot it because we learnt this lesson/topic 1 month ago

[onyx glen]

opposite rays are two rays which together form a straight line

to bisect an angle or line segment is to divide it into two equal halves

[proper pewter]

Ok

So i do 14x+5=17x-1?

@onyx glen

[onyx glen]

yes

[proper pewter]

So the answer is 2

[onyx glen]

the value of x is 2

but note what they ask for

[proper pewter]

Find angle FLH

[onyx glen]

yeah so youre gonna need to do a bit more calculation with that

[proper pewter]

So the I multiply the smaller angle by 2

2(14(2)+5)=66

??

[onyx glen]

yeah working out either of the smaller angles and then doubling it works

[proper pewter]

So angle FLH=66

[onyx glen]

yes

[proper pewter]

ok can we move on to question 6

[onyx glen]

you're gonna need to scroll down so that we can see the diagram for questions from 6 onward

also learn how to take a proper screenshot on your laptop

[proper pewter]

Ok

Wait nvm my teacher said we do 7 not 6

[azure onyx]

this is not the correct diagram for Q7, I believe.

it should be the one under that.

[proper pewter]

Well this the only diagram so i think there is no diagram

[proper pewter]

Let me check

[azure onyx]

most likely that is the diagram for Q6+.

because the question statement for Q6+ implies the existence of points B, A, and C, none of which are in the diagram you just sent.

[onyx glen]

scroll down on your laptop

[proper pewter]

@onyx glen or @azure onyx

[onyx glen]

ok, so you want 7.

[proper pewter]

Yes

[onyx glen]

ray BH bisects angle EBC

the two halves of angle EBC thus are angles EBH and HBC

and this is the exact same question as #5, but with different numbers.

[proper pewter]

Ok

So same equation?

[onyx glen]

the idea is the same

the literal equation you write down will not look one-for-one the same

[proper pewter]

R=14
Then
Angle ADB=3(14)+5=47
m angle DBC=5(14)-27=43

@onyx glen

[onyx glen]

what is R

as in where did R come from in this question at all

...

did you do a completely different question with completely different numbers/letters or what

[azure onyx]

yeah, where did ADB/DBC come from?

[proper pewter]

Oh i did question 7 from the powerpoint not the textbook

[azure onyx]

so we're looking at completely different questions?

[proper pewter]

Yes mb

X=11
Angle EBH=6(11)+12=78
So angle EBH= 78 degrees

[proper pewter]

This is for 7 Mb for the mix up

@azure onyx or @onyx glen because i need to go study other subjects

Ok igtg study other subjects i think this is correct thx for your help have a good day

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[lean rock]

Is there easy way to see if this is ≠0 ?

[queen gull]

Gaussian elimination until you get to simpler matrix

But I don't think tou can do much better then just calculating

[lean rock]

Thank you @queen gull

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[dense charm]

In a lottery draw, six numbers are drawn from the numbers 1 to 45.
Calculate the probability that

c. the smallest number is greater than 5

I need the thought process behind this

[dense charm]

Sophomore year

[queen gull]

the smallest number is greater then 5 if and only if all of the numbers are greater then 5

[dense charm]

yes

but how do i like make the combination so it’s only greater than 5

[keen vector]

pick from numbers 6 to 45

[dense charm]

nvm i understand it

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[fluid prawn]

if i have vector divided by a regular number whats it become

[fluid prawn]

like <1,-2>/sqrt(5)

does that become (1/sqrt5, -2/sqrt5) or <1/sqrt5, -2/sqrt5>

[onyx glen]

what is the difference in your eyes between () and <>

[fluid prawn]

< is vector

[onyx glen]

btw dividing a vector by a scalar is just a different phrasing for multiplying it by the reciprocal of that scalar

$\frac{\bd{v}}{a} = \frac{1}{a} \bd{v}$

[glossy valve]

Ann

[onyx glen]

and ordinary brackets?

[fluid prawn]

idk

a point

[onyx glen]

so why did it occur to you that a scalar-vector product can sometimes produce a point

[fluid prawn]

so its parenthesis?

[onyx glen]

the result is a vector

how you notate it on paper is between you, your professor, and god.

if you notate vectors with <> then it's <>

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[silver pecan]

Correct answer

$180-(7x-5)=90-(2x+5)$ results in x=20deg, so k=20

[glossy valve]

UCYT5040

[onyx glen]

jee ahh question

[silver pecan]

Then 7(2)^2 -13 * 2 + 5$ = 7, 7^2=49

[onyx glen]

wait hold on tho are you sure that k=20

[silver pecan]

why wouldn't it be?

[onyx glen]

complement of A is 2*20+5 = 45

therefore A itself is 45°

k=45 not 20. k is not the same as x

[silver pecan]

oh

wait

thats so obvious

ok thank you!

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[silver pecan]

@silent rose look at this

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[silent rose]

I’m still confused why would the compliment be 2*20+5 can you explain?

[modest whale]

k

[forest trail]

Hi! Do you first understand why x = 20? If so, they just substitute it into the equation.

[silent rose]

Ohhhhhhhhhhhhhhh I get it now

That makes sense

I forgot to substitute in the equation

Bc x dosent equal angle

But 7(20)-5+A=180 does right?

[forest trail]

Yep.

[silent rose]

Got it! Thanks!

[forest trail]

No problem.

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[rotund juniper]

I like 67 kid

[queen gull]

do you have a question?

and please don't troll in help channels

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[zenith haven]

hi

[zenith haven]

how we obtained the equation below 3-23 ?

[sturdy valve]

all that shit in the bracket is just the distance

E = kq/r^2

they have added electric field contribution due to +q and -q

and that r term is whats making it complicated

[zenith haven]

right

[sturdy valve]

if u want to go back to the original equation

then multiply the kq term inside

and then cancel the factors

[zenith haven]

I mean

[sturdy valve]

?

[zenith haven]

I dont understand the idea here what did we do here exactly?

[sturdy valve]

u asked how they got 3-23..

[zenith haven]

I dont understand how manipulated the equation

[sturdy valve]

but ok

[zenith haven]

below 3-23 xD.

[sturdy valve]

basically for a dipole we take the distance between the 2 charges as very small

much smaller compared to R

and then they just used binomial approximation

<@&268886789983436800>

(nvm sorry it got deleted)

[cyan aurora]

No problem!

[zenith haven]

what is bionomial approximation exactly?

[zenith haven]

Respect to the mods!

[sturdy valve]

(1+x)^n can be approximated to 1+nx if x is very small

[zenith haven]

oh I mean this

as a start

[sturdy valve]

they squared inside and took root outside

2 = 4^(1/2).

[zenith haven]

so we took this to numerator then we took root of what?

[sturdy valve]

.

[zenith haven]

oh I see now

it clicked

Thanks a million

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[snow mulch]

my sister needs help and idk what to do here

[snow mulch]

ChatGPT has been wrong everytime

[atomic hare]

at the x intercept, y is 0
at the y intercept, x is 0
solve for the intercepts by plugging in 0

[snow mulch]

Alr ty

I’ll lyk what I get

[sturdy valve]

now someones gonna put !nogpt

[snow mulch]

I got y=-5 and x=7

[atomic hare]

sounds right

[snow mulch]

It was

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[stuck fiber]

I dont understand the solution here, why is x also > 0 and < 0

Like we dont get rid of the x on the bottom, I multiplied both sides by x to get it from under the denominator

[queen crater]

Multiplying by x changes the inequality depending on the sign of x

[stuck fiber]

Yes thats how I got x >= 1 and x <= 1

x + 1 >= 2x and x + 1 <= 2x

x >= 1 and x <= 1

I still dont see where the x > 0 and x < 0 came from

[queen crater]

I don't get what you mean

[stuck fiber]

x + 1 >= 2x and x + 1 <= 2x
x >= 1 and x <= 1
This is what I did

But I dont see how multiplying by x on both sides adds x > 0 and x < 0

[queen crater]

,, \frac{x+1}{x} \geq 2 \land x > 0 \implies x+1 \geq 2x \
\frac{x+1}{x} \geq 2 \land x < 0 \implies x+1 \leq 2x

[glossy valve]

Nel

[queen crater]

That's all there is to it

[stuck fiber]

Can you explain where it comes from sry

[queen crater]

.

[stuck fiber]

changes it how

Like I can remember this but id rather understand it

[queen crater]

Multiplying an inequality by a positive number does not change the "direction"

Multiplying an inequality by a negative number does

[stuck fiber]

Of the sign?

[queen crater]

The "greater than" or "less than"

And of course multiplying by 0 makes it an equality, but that's not very interesting

[stuck fiber]

Yes thats what I did though right? I just dont see where the x > 0 and x < 0 comes from

Ohhh wait

I think I get it

okokokok

Thanks!

❤️

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[stuck fiber]

Better image with more important info:

But I understand up until the last blue line

'So we should choose delta not larger than 1'

Why not?

Why cant we pick 1?

[proud gorge]

1 isn’t larger than 1, it’s equal
You can’t pick a greater amount because the limit is 1

[stuck fiber]

But its just the normal limit right?

Its not limit from the left

So we can pick 1, no?

[proud gorge]

In the limit where x -> 1, 1/x=1

Wait so x is one

As x approaches one, the answer approaches one

[stuck fiber]

Look here in this example:

[proud gorge]

It’s only equal, not greater, so probably

[stuck fiber]

The limit approaches 1

But we picked 1

to sub in for x

[stuck fiber]

Idk the answer says we cant

Im just trying to understand why not

[proud gorge]

Maybe because limits are used for the sake of impossible equations
So like in 0/0 we use limits to say that y offshoots to infinity as x approaches 0

[wicked condor]

its hard to read with the color

[stuck fiber]

Sorry for some reason my screenshotting tool captures my blue light filter lol

Just one of those random things that works weird on linux 😅

[stuck fiber]

Better?

[wicked condor]

yea

[queen crater]

I'll be honest I don't quite understand the reasoning, but bounding delta is typical in these exercises

[wicked condor]

okay ur proof is correct

[stuck fiber]

Its not mine, im just trying to understand it

Why 1/2 instead of 1

[stuck fiber]

What does bounding delta mean sry

[queen crater]

Picking delta within some small interval

[stuck fiber]

Yes its always the hardest part of these questions for me

Like to me it seems obvious to pick 1 here

1/2 seems so random

[queen crater]

Think about what it would mean to pick 1 for delta here

x could range from 0 to 2

But 1/x is undefined at 0

[stuck fiber]

Ahhhh

[queen crater]

Also, 1/x as x approches 0+ is arbitrarily large

So it's kinda hard to match the epsilon

[stuck fiber]

So we cant pick a range that includes 0

So then we cant pick 1

Makes sense, but wait

[queen crater]

Well you probably can if you figure out a complicated formula for delta

But why bother

[stuck fiber]

What about here tho

We picked 1 here

And its still |x - 1|

So shouldnt we also pick 1/2?

[stuck fiber]

for this reasoning

[queen crater]

Doesn't really matter

[stuck fiber]

So I could also pick 1 for the original question?

[queen crater]

f(0) is defined here

[stuck fiber]

Ohhhhhhhh

And its not in the original

[stuck fiber]

So the reasoning still tracks for both

Okokokok

I think I get it

Thank you!

❤️

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[digital void]

So I have gotten this far, and i wonder first of all if i am right up to here, and also if i can go on from where i stopped using some basic combinatorics knowledge. I am being general because i cant really think of how to implement combinatorics here

,rccw

[digital void]

(btw P(n) is the mathematical statement)

[latent surge]

please help me

[digital void]

you gotta ask it in an available help channel

[latent surge]

which one is available ?

[digital void]

the ones on the list "Math Help (Available)"

[latent surge]

OHHH

okk thanks

[brittle sun]

Good going so far

Now given a subset of A, how do you make a subset of B

[digital void]

uhm

B\cap (sub of A) - {b} ?

the minus is ""

yeah cant write it lol

/ this reversed

[brittle sun]

You're overthinking it

[digital void]

oh

[brittle sun]

It's exactly the same idea as the base case

Let's start with some guesswork

What's the size of P(A)

[digital void]

2^(|A|)

[brittle sun]

Numbers pls

2^n

[digital void]

ye

[brittle sun]

And now what's the size of P(B)

[digital void]

thats what were tryna find tho

but 2^(n+1)

[brittle sun]

Well yes what do you want it to be

[brittle sun]

Good

So it's double the size of P(A)

[digital void]

mhm

[brittle sun]

So given a subset of A, you wanna generate two subsets of B

At least ideally

Now can you do this

[digital void]

lemme think a bit

yes

just unionize with b

not for work inequalities

[brittle sun]

That's one

[digital void]

yeah and the other without b

[brittle sun]

Yup

Just leave it alone

So for every subset of A, you get two subsets of B

[digital void]

hmmmm

is that all i need?

[brittle sun]

A small argument to make sure that the generated subsets of B have no repears

But that shouldn't be too hard

[digital void]

what does repears mean?

[brittle sun]

Repeats z

[digital void]

ohh

[brittle sun]

Man I can't type

[digital void]

hmm idk if i can prove there are no repeats tho

not objectively, like i suck at proving basic things

[brittle sun]

No worries

Well good for us we have an induction hypothesis

P(A) has 2^n elements with no repeats

Now what happens if two elements generated are the same in P(B)

Two subsets*

[digital void]

uhm

they count as one

[brittle sun]

No no

[digital void]

(?)

[brittle sun]

We wanna show it can't happen

[digital void]

oh lol

[brittle sun]

Cuz if it happens that's bad for us

Cuz that will reduce the number

[digital void]

very true

[brittle sun]

In this case some case work is helpful

A subset of B is of two possible forms

[digital void]

if two subsets of P(B) are the same, then theres two cases

[brittle sun]

Four cases actually

[digital void]

oh

[brittle sun]

Well three cuz symmetry

[digital void]

yeah i think i know

[brittle sun]

Good luck

[digital void]

1. its {b}

[brittle sun]

Uh no that's too specific

[digital void]

lol

[brittle sun]

Here's a hint

[digital void]

1. its some subset of A plus {b}

[brittle sun]

A subset of B is of the following forms:

1. A subset of A
2. A subset of A union {b}

Now take two different subsets of B and equate the possible forms

[digital void]

i dont get ya man im sorry

A subset of B
AU{b} subset of B?

im kinda fried

[brittle sun]

No worriee

Let's take two subsets of B, S_1 and S_2

Case 1: S_1 and S_2 are both subsets of A

What happens now

Recall that we want to show S_1 and S_2 aren't equal

[digital void]

then they are either equal to each other or not equal lol

[digital void]

yes

[brittle sun]

Well thankfully we already know that they're not equal in A

So we just use that and we are done

[digital void]

sure

[brittle sun]

Now case2: both are of the form subset of A union {b}

How do we do this now

[digital void]

well S_1 U{b} , S_2 U{b}

[brittle sun]

I need to leave but hopefully you can continue from here

Bai

[digital void]

bye bye

.solved

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[snow dew]

sup

[vagrant grotto]

hey

[snow dew]

waiting for someone else

[tender nacelle]

Im here

[snow dew]

will see if he arrives else im leaving

[tender nacelle]

I reacted

[snow dew]

oih sup

so is that poissons ratio in my class notes wrong or what?

cause every website that i looked it was showing something different

[tender nacelle]

No it's fine

[snow dew]

how so

[tender nacelle]

What else have you seen? cause I think I can guess your mistake/misunderstanding

[snow dew]

even the symbols my class notes were using were different

they were using the "u" symbol instead of the "v"

and why are they using abs values

[tender nacelle]

Yeah i normally use the weird v

Symbol isn't that important though

They use abs values to say "poisson's ratio must always be + ve"

[snow dew]

but other poisson ratios that i've seen doesnt ues abs

[tender nacelle]

Other sources might omit the abs value for a "-" sign to say "poisson's ratio is typically +ve"

The latter approach adresses the edge case of Auxetic materials, which do have a negative pr

but in an intro eng class, this isnt important

[snow dew]

is that when the material is stretched but also grows larger on the sides?

[tender nacelle]

yeah\

[snow dew]

ok so you seem to know this stuff

can i ask you something else

why are there two Et formulas

[tender nacelle]

Not my field of expertiese but I can try

[snow dew]

https://i.imgur.com/jK5kzte.png

you seee there are two Et formulas

how are they different

[tender nacelle]

You're aware you posted the same photo twice?

Oh well one is just in terms of poisson's ratio and the axial strain

[snow dew]

and the other?

[tender nacelle]

Like typically you would calculate the axial strain using the second formula, stretch the material a bit and measure how much it narrows

If you magically happen to know poisson's ratio and the axial strain, you can apply the first formula

The first formula is more of a definition- rearranging the equation for poissons ratio you mentioned earlier

It's like saying stress = E * strain

As it follows from E = stress/strain

[snow dew]

so the first Et formula is more of a general formula you would use to calculate then sub into the poissons ratio?

[tender nacelle]

you mean Et = delb/b?

[snow dew]

the Et = ue

[tender nacelle]

I mean you would need Poisson's ratio to use it, right?

The first Et formula is literally just rearranging the poissons ratio formula

[snow dew]

oh its just a rewritten version of poissons law

so poissons law is actuall both?

[tender nacelle]

What you would typically do in an engineering context wouold use the two formulae on the right (for Et and Ea), to calculate the poissons ratio for that material (Ie. 1060 aluminum or something), and then moving forward "predict" transverse strain with axial strain using the first formula.

[snow dew]

Et = - ue and u = Et/Ea?

[tender nacelle]

Yeah

There's some sign shenanigans, but if you take u = -Et/Ea, it would make more sense

[snow dew]

what is the symbol u though?

[tender nacelle]

Poissons ratio

[snow dew]

what value is it supposed to represent

no i get that

https://i.imgur.com/jK5kzte.png

so i dont need to scroll up

[tender nacelle]

Unitless quantity representing how much a material contracts in the transeverse direction when stretched

[snow dew]

ok so a question gives 2 of the 3 values in poissons law the we can just solve for the missing variable

I have a question where we have to use like 4 different formulas to solve the question

[tender nacelle]

Think rubber, super ductile, it has a high u since it will contract a lot laterally when stretched. Cork would contract very little, and thus has a low u.

[snow dew]

so just to be clear.. the symbol used for poissons law is not relevant whether its a "u" as shown in notes or a "v"

and the abs is correct alsoi?

yea i know the rubber example

[tender nacelle]

Abs is correct in 99% of cases, but you can replace it with a "-" sign WLOG

[snow dew]

cork also...it can compress without shrinking along its transvers side?

[tender nacelle]

Yup goes both ways

[snow dew]

and in rare cases when a material is elongated, the perpendicular sides also grow larger such as engineered material

dude thanks for explaining

[tender nacelle]

np

[snow dew]

so thats why we have the neg sign?

for the rare caess?

[tender nacelle]

yeah, neg sign accounts for those edge cases

[snow dew]

but in most cases poissons law should be a positive value?

[tender nacelle]

yes

[snow dew]

ok got it

appreciate it...i just wished my class notes had better explanations

thanks

.exit

[tender nacelle]

happy to help

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[snow dew]

take care

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[urban oak]

I have no idea to do this statistics question,how should I transform the proportion into standard scores?Thank you for your help

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[waxen pecan]

39 is kind of confusing to me, does anyone have any idea?

[lime ether]

do you know anything about parallel lines

or perpendicular lines

[waxen pecan]

Yeah I get that completely, it’s just the solving that’s giving me trouble

[lime ether]

🤔

ok what do you get

formally

what can we say if two lines are parallel

please don’t tell me they never touch

[waxen pecan]

That’s what I was gonna say, sorry man😭

[lime ether]

💀💀💀

read you like a book dawg

anyways

[waxen pecan]

Though I do know it’s Also opposite reciprocles so -4 x 5 + 4 x -5 would be perpendicular or parralel?

Kinda forgot being completely honest, haha

[lime ether]

what is written here?

-4 x 5 + 4 x -5

what does this mean

[waxen pecan]

I’d assume they are opposite reciprocals

[lime ether]

what?

[lime ether]

this to me reads like -4 times 5 + 4x - 5

[waxen pecan]

Oh sorry, they’re both multiplication

Hold on

[wise hornet]

It is right to say, parallel lines are ones that never touch, but when we have a line expressed algebraically there is a neat way to instantly see that they never touch

[waxen pecan]

4 • -5

Would the the opposite of

-4 • 5

[lime ether]

maybe for lines in R^2

[onyx glen]

those two products both equal -20 dawg

[lime ether]

🤣

[wise hornet]

We are in R^2? Why would I be referring to another space

[lime ether]

i mean i think it’s just bad practice to rely on these ways of defining things

parallel has a precise meaning

and saying oh they never touch accomplishes nothing

[wise hornet]

It actually does. If you talk about the gradients being equal this is equivalent

[lime ether]

it’s like saying yea bro the derivative is just the slope and never actually learning it

or

yea dude integral is area

[lime ether]

you’ve missed my point

[wise hornet]

This is incorrect though and the derivative thing is imprecise

[waxen pecan]

My fault LOL, Matt has never been my strong suit so that’s why I’m here right now

[lime ether]

my whole point was that this wasn’t precise

😭

[onyx glen]

so what are we trying to do exactly anymore

[wise hornet]

One can define precisely what it means for things to intersect in this context. The intersection of their graphs is no empty

(This might not be immediately useful but it is still true)

[frigid carbon]

Guys stay on que

Lol

[onyx glen]

@waxen pecan what question or problem are you solving rn

[lime ether]

39

but he doesn’t have a working definition of parallel

[waxen pecan]

I get parallel kind of, my issue is just solving the problem

[onyx glen]

"two lines are parallel <=> they have the same slope"

did you know this before i said it yes or no

[waxen pecan]

Kind of? I was a little murky on it to begin with but had a vague idea parallel means the same

[frigid carbon]

Find slope if they same parallel if their product =-1 they perpendicular

[onyx glen]

there is no kind of

you either did know it or you didn't know it

[waxen pecan]

Yes I knew it

[onyx glen]

ok so

[waxen pecan]

I see, what equation would I need for this?

[onyx glen]

what's the slope of y=-6x+3

[waxen pecan]

6x?

[onyx glen]

no, your slope does not contain the x. it's attached to the x but the x itself isn't part of it.

what does slope intercept form look like generally?

[frigid carbon]

ts y = mx +c so slope is coefficient of x

[onyx glen]

no

don't even bring up derivatives

[waxen pecan]

Y= mxb?

[onyx glen]

missing a symbol

[frigid carbon]

K

[waxen pecan]

I don’t think we’ve used that yet actually, I really do appreciate it though 🙏

[waxen pecan]

Y = mx + b

[onyx glen]

y=mx+b

lowercase y

now

which letter stands for slope

[waxen pecan]

M

[onyx glen]

lowercase m

but yes

[waxen pecan]

Right

[onyx glen]

in y = -6x + 3...

what's the slope

[waxen pecan]

-6?

[onyx glen]

yes

and for y = -6x - 4?

[waxen pecan]

Still -6?

[onyx glen]

yes

therefore these lines are...?

[waxen pecan]

Parallel?

[onyx glen]

yes

though you could use a bit more confidence

rather than making every single one of your answers sound like a guess

[waxen pecan]

Haha sorry, most are, I’m really awful at this

[onyx glen]

you should not be guessing!

you should be

(a) listening to and understanding what ppl are telling you
(b) pattern-matching when told

[waxen pecan]

Yeah your right, I’ll definitely try to understand better from now on 🙏thank you for the help!

[frigid carbon]

.close

[onyx glen]

you cannot close channels that aren't your own.

[frigid carbon]

Oh k

[onyx glen]

only helpfuls and up can do that

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[fast spear]

nvm

.close

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[hearty plinth]

Hi how can i understand word problem more and or comprehensive it easily?

So i figured the question and 6 side die would be 1+2+3+4+5+6 = 21

But I have little bit difficulty to understand why they do q mark ? + 42 = 63 or 63 - 42 = ?

uh I just need way to understand it sorry if its too basic

[hot herald]

top row are the sides of a 6sided die

and there are 6 * 7 spots in the bottom row (which is given to be 42)

they did it that way since it uses the given info

so knowing those values,
one line of subtraction gives you what you want
compared to summing 6 numbers

[hearty plinth]

ohh so thats why so it can be 42+21 =63? so they do 63-42 = 21

thanks

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[plush heart]

I've been taught that in dominance of function, n^n is over a^n where a is a number greater than 1.
I've been given to solve the limit n^n/e^(n^2), which I thought was infinity since n^n dominates over a^n, but the answer is zero.
Does the rule I was taught works only when the power is first order? How do I solve the question? Gemini told me to ln both sides and uses Lhopitals rule, which are things that I'm familiar with but the course I am taking hasn't taught them yet so I am not supposed to use it

[astral sinew]

All you need is to rewrite n^n

e^(n log n)

Then this becomes e^(n log n) / e^(n^2) = e^[n log n - n^2] which should be obvious now

[forest trail]

Hi! It's important to understand why the function dominates.
a^n is just a times itself, n times.
However, for a large enough n, n^n with be n times itself n times, which means that inside will eventually be much bigger than a. In particular, a^n/n^n = (a/n)^n, which is 0 since a/n will eventually be less than 1.

The problem here is that e^(n^2) now has a squared exponent, which completely changes how you interpret the functions. It is no longer viable to compare n^n and e^(n^2) with the same logic, because you are essentially doing something different with the latter term. To therefore solve the question, do the thing that Mr Gamer is recommending or as you said, use another method.

[forest trail]

You could technically use an edited version of the same logic, that is (n/e^n)^n, and you can see that e^n dominates n. In general though, we'd like a little more nicer reasoning when proving these results rigorously, but they give you an idea of how the limit might behave.

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[tropic jolt]

can someone help me figure out eulerian figures?

[tropic jolt]

aka there's a random path and a bunch of intersections/vertice

i just watched a video, they said there were 2 rules,
. It cannot have more than 2 odd vertices
. It must have an even number of vertice
but I haven't yet seen an example where the second rule matters?

i've been able to trace a path with 17 vertice in one line granted there were 2 odd vertice

when exactly is the second rule in play?

[atomic hare]

can u link video

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[tropic jolt]

i got it

it was bsed on the fact that the number of vertices can only be 0 and 2, 1 isnt possible

so technically it has to be even to be an euler figure, not the total vertices

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[vapid canopy]

x^3+y^3=3xy
Find all integer solutions
how to even start solving this? something along the lines of expressing the left side differently?

[queen gull]

You can factor x^3+y^3-3xy

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[onyx glen]

you can and should use a calculator for that.

<@&268886789983436800> suspected troll

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[vivid berry]

why is it R2 - r2

[woeful pasture]

Washer method

Its volume of solid A - volume of solid B

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[hard wasp]

help me with this quuestion

[hard wasp]

pleaseeee

[unreal wren]

!status

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

[hard wasp]

1

these type of questions are very difficult, i dont even understand them

[unreal wren]

Do you know what row% and column% are?

[hard wasp]

yeah

i dont know how can i proceed after seeing the table

[unreal wren]

I see

Let's try to solve for acoustic broken string first

[hard wasp]

okay