help-19

[vale vortex]

thats the answer?

i thought

the goal

was to solve for n

[silver stump]

n choose 2 - 2(n-2 choose 2) = half of (n choose 2)

[silver stump]

yea like the marking scheme has some working and it was written that somewhere

but thats not the answer

you'd get method marks for that

[vale vortex]

$2\binom{n-2}{2} = \frac{\binom{n}{3}}{2}$

[clever fjord]

Diamond

[silver stump]

can a GDC solve that

[vale vortex]

$ simplify 4\binom{n-2}{2} = \binom{n}{3}$

[silver stump]

and how did you come to such an answer

[vale vortex]

ho

w

do i write words

in latex

[vale vortex]

my brain

[silver stump]

no clue

[vale vortex]

idk

[silver stump]

lmaoooo

i genuinely have no clue on the thought process

[vale vortex]

$4\binom{n-2}{2} = \binom{n}{3}$

[clever fjord]

Diamond

[thin kelp]

comes from this

[silver stump]

yea

[vale vortex]

$\binom{n}{3} = \frac{n(n-1)(n-2)}{6}$

[clever fjord]

Diamond

[vale vortex]

ok i dont wanna do this anymore

[silver stump]

wdym

[vale vortex]

have fun

[silver stump]

ok ty ty

[vale vortex]

my brain hurts now

[thin kelp]

so first pick one of the two that cant be in the same group i.e 2C1 , then since there are now n-2 remaining people we want to select 2 from those to fill up the group of 3

[vale vortex]

atfer that one tho

u would expand the other one too

[silver stump]

ohh its a case by case

[silver stump]

bet

so i pick one of the students to be in group A

and the other is in group B

so group A i'm choosing 2 students out of n-2

then switch the students around

and it's the same thing

?

[vale vortex]

well

they werent assigned a group yet

before they asked to be in diff groups

so

yea

1 sec

[silver stump]

ok

[vale vortex]

$\binom{n-2}{2} = \frac{(n-2)(n-3)}{2}$

[clever fjord]

Diamond

[thin kelp]

dont just hand out the solution btw

[silver stump]

what abt n choose 3

[vale vortex]

oh

[silver stump]

thats just

[vale vortex]

ok u can figure it out from this point

[silver stump]

yea

[vale vortex]

$4 \cdot \frac{(n-2)(n-3)}{2} = \frac{n(n-1)(n-2)}{6}$

[clever fjord]

Diamond

[vale vortex]

twas already typed

[silver stump]

yup ok

then from there i just

use my gdc

tysm

.solve

.solved

[odd edge]

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[distant umbra]

is my working right for the first part of this question?

[odd edge]

@distant umbra Has your question been resolved?

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[lilac skiff]

Hi hydraulics question here

[wild hull]

is this part of fluid mechanics?

[lilac skiff]

yeah

i guess

[lilac skiff]

Is that ok?

[wild hull]

ye its ok

but it may be bettter to ask in the physics server

[lilac skiff]

I see

Do you know how to do it?

[wild hull]

hmm

let me see

[wild hull]

sorry i can't

[lilac skiff]

Oh man

[wild hull]

#old-network

theres a physics server in here

[lilac skiff]

I joined it thanks

[odd edge]

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@lilac skiff Has your question been resolved?

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[abstract marsh]

Can someone help me with this

[crystal roost]

bro

did you not see me typing

[abstract marsh]

I was first

On my end

[crystal roost]

no you weren't..

[abstract marsh]

Yes I was

[crystal roost]

just go

im leaving

[abstract marsh]

You started typing after me

[crystal roost]

you dont need to lie

[abstract marsh]

I'm not

Ok but going back

[signal yacht]

!status

[odd edge]

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

[abstract marsh]

I'm typing it rn...

[signal yacht]

okay

[abstract marsh]

So, basically ik I have to start with f(x)' for something, and dunno what to do next

[signal yacht]

find f'(x), find zeroes, find sign f''(x), find values of f(x) for extrema, ensures it's a global extremum

[abstract marsh]

You mean f'(x) =0?

And what is sign f"

[signal yacht]

uh finding critical points gives you extrema or inflection points

you don't want inflection points

so you check f''(x) to ensure it's not an inflection point

[abstract marsh]

Inflection point is a point where it changes its direction ye?

And

How to do I calculate the f' of smthing like this? String rule orr ' of first x then from another ?

It's smthing this and it looks weird

[signal yacht]

no just flattens out for a second

oh graph flattens

derivative changes sign yes

[signal yacht]

sum rule and power rule

[abstract marsh]

What's sum rule?

[abstract marsh]

Just what I did here?

[signal yacht]

i honestly can't read it

[abstract marsh]

Treating them like 2 separated derivatives?

Read what

[signal yacht]

sum rule is just $\frac{d}{dx}(f(x)+g(x))=f'(x)+g'(x)$, nothing fancy

[clever fjord]

Percy

[signal yacht]

your writing

it's late i'm tired

[abstract marsh]

I didn't have the d/dx thing yet

[signal yacht]

uh what?

[abstract marsh]

The d/dx

Or is it just a fancy way to write derivatives

Is it better now?

[signal yacht]

it's the standard way to write derivatives lmao

[signal yacht]

yes

much better

okay we got the derivative

[abstract marsh]

We just started like using it let's say, and as far as I know, my college teacher never used it before with us, just now for new topics, and my friend told me the vertical wave + d/dx is someway a reversed derivative

[abstract marsh]

Ye now I do =0 and calculate critical points? (Critical points are the points suspected to be min and max right?)

And they have to contain in the [-2;2]

Yes?

[signal yacht]

or inflection points yes

[signal yacht]

a what?

reversed derivative?

[abstract marsh]

But infection point was the point where curve changes it's smthing

[abstract marsh]

The yy wait

[signal yacht]

inflection point is where the curve flattens out without changing direction

look at

,wolf graph x^3

[clever fjord]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by percykel

[abstract marsh]

This

[signal yacht]

x=0 is an inflection point

[signal yacht]

it flattens, but doesnt change directon

[signal yacht]

uh nonononno $\frac{d}{dx}f(x)$ is just how you write $f'(x)$ properly in most modern math

[clever fjord]

Percy

[signal yacht]

The first is Leibniz's notation

the second is lagrange's.

[abstract marsh]

So my math isn't modern

[signal yacht]

Bit weird you'd be taught anything calc without leibnz notation is all

[signal yacht]

also read this

[abstract marsh]

Okay ig

Ah ye

[signal yacht]

ping me if i disappear and you have a question

[abstract marsh]

But explain this

[signal yacht]

i'll prolly be around but chemistry work

[abstract marsh]

And u r gone

Gg

@signal yacht

[signal yacht]

it changes curvature

also i mistakenly told you the definition of a stationary point instead of inflection sorry

inflection is it changing curvature

concave to convex or viceversa

[abstract marsh]

Ye

I have this now

And D: x≠0 cuz idk

[signal yacht]

also ig you can just dm me instead if i do disappear

[abstract marsh]

Mhm

[signal yacht]

i super can't read it i'll just assume you did this right (Check with calc)

[abstract marsh]

Let's say my math is right and I did the f'=0

And I only took the nominative cuz =0 cuz if bottom is 0 it doesn't exists(?)

And I got x=2

So I assume that's my "critical point" or wtv

[signal yacht]

wha?

[abstract marsh]

Now I just put the 2 to my normal f(x)?

Okay wait

[signal yacht]

,wolf solve d/dx(-x^{5/3}+5x^{2/3})=0

nice

[clever fjord]

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Upgrade to WolframAlpha Pro!

Requested by percykel

[signal yacht]

yeah okay

[abstract marsh]

Wow I got it right

No way

[signal yacht]

woohoo

[abstract marsh]

Okay so now

This 2

Is my critical point(point suspected to be min or max)(?) Yes?

[signal yacht]

yes

[abstract marsh]

So now

I do x=2

And put it in my normal f(x)

To calculate my extremum or wtv it's called

But the question is

I have only one number, so do I don't care, or take the -2 from the [-2;2]

And do the same

[signal yacht]

no it's just 2

you check the double derivative though to make sure it's an extremum not inflection

also i'll prolly go now

that should be enough

extremum is if double derivative is either positive or negative

[abstract marsh]

So now I do the f"

If it's not 0 I'm good yes?

And if it's "-" it's min and if it's "+" it's max yes?

[signal yacht]

or undefined

[signal yacht]

the opposite i think

[abstract marsh]

Okay thanks for everything

Have a good night or wtv the time is for you

[signal yacht]

i have workkk so not night for ages actually

i sidetracked for 1 and a half hours

lmao

[abstract marsh]

Bruh

Not that bad

[signal yacht]

lmao idk

[odd edge]

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[crystal roost]

Hey, I could use some help with my Statistics homework.

The assignment starts with the question:

"Use the Exercise data to find p ̂ for the proportion of adults who exercise on a regular basis with a BMI less than 25. (Round 4 decimal places)."

Easy enough, right? But the actual dataset we've been provided doesn't include a variable for the frequency of exercise.

I'm just really frustrated and confused here.

The data set: https://www.statcrunch.com/app/index.html?dataid=4667560

[odd edge]

Please don't occupy multiple help channels.

[crystal roost]

I'm sorry but nobody responded to my original channel for an hour

[wraith shell]

Ping helpers

[crystal roost]

i already pinged once

i dont think you're allowed to ping again

especially since my first time was too early

[wraith shell]

How much have passed since then

Also close the old channel

[crystal roost]

closed it

[crystal roost]

<@&286206848099549185> Hello, sorry for ping again but i have waited an hour for @.kaithedoge to respond and it doesnt look like they're coming back, I could still use some help if that's okay?

[charred bough]

u should write to the person that provided you with the data set

[crystal roost]

my instructor is unfortunately not available

[charred bough]

only he could know. it looks like a faulty question

[crystal roost]

yeah normally i would assume so but i dont think it is, there are other questions in the section that also rely on the non-present variable of the exercise frequency

[viral ginkgo]

if there is no other information and the instructor is not available, i would just state the assumptions that i make and answer the question as best as possible (and any reasonable instructor would give you points for attempting the question)

like i would say, i assume that this dataset is for people who exercise regularly (so everyone in this dataset qualifies)

[crystal roost]

That's a good idea. My teacher is kind of a hardass but i guess it's worth trying

[viral ginkgo]

yeah just start the assignment with: "I couldn't find a variable that describes how often a person exercises, or a threshold that describes what is considered 'regular basis' exercise [every day? 4 times a week? once a week?] so I am going to work off of the assumption that if their data is included in this dataset, they are exercising on a regular basis".

[crystal roost]

Thank you! I'll try and proceed with this. As for the other sections i'll come back here if I need help

[mystic saffron]

whats ur pronouns

[crystal roost]

do you need them or want them

[mystic saffron]

i need them for my research

[crystal roost]

she/her

[mystic saffron]

thanks

[viral ginkgo]

wtf just happened here

xD

[mystic saffron]

.close

[wraith shell]

@crystal roost seems like you forgot to close

[mystic saffron]

!close

[mystic saffron]

i think shes doing her part time job

[crystal roost]

.close

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[odd edge]

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[graceful nacelle]

I’ve tried 5y = 4x - 20

I don’t know

[odd edge]

@graceful nacelle Has your question been resolved?

[odd edge]

@graceful nacelle Has your question been resolved?

[tacit wasp]

Yeah, go on... Write it in the explicit form y = mx + b

[graceful nacelle]

Uhh y=5/4 - 20?

[tacit wasp]

Nope 🤔

[graceful nacelle]

I don’t know

[tacit wasp]

Well, you should revise basic maths then

[graceful nacelle]

Wait no

[tacit wasp]

If you have 5y = ... how can you get y = ...?

[graceful nacelle]

y= 4/5 + 20?

[tacit wasp]

Much better, but still not the correct one

Also, why did the minus become a plus?

Plus, why did x disappear?

[graceful nacelle]

y = 4/5x - 20?

[tacit wasp]

Almost there

4/5x is right, but why did you keep -20 as it is?

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[warm horizon]

how do i do this if i dont know f(x)

[quasi sparrow]

you can answer all of the questions just knowing f'(x)

f is increasing when f' > 0 and decreasing when f' < 0

[warm horizon]

oh

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[glass mortar]

Limit exercise:

[glass mortar]

Anybody knows how to solve it?

.close

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[elder vault]

A quick fact check

[elder vault]

Given f(x) has coefficients of real numbers

If f(2+i)=0 then f(2-i)=0

Good?

[ashen cradle]

Yes

[narrow crypt]

F(x) being a polynomial, yes

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[exotic sonnet]

Can someone help me simplify the Variance formula as shown in the pictures, but for Sample?

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[short knoll]

so i did this question, I understood letter E but I honestly just guessed for the second answer, letter B

I'm not sure how they got there if some1 could pls explain it 🙏

[weary eagle]

Because when you go from 0 to make 2π rotation you reach back 0

[short knoll]

OHHHHHH ok got it, thanks

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[paper onyx]

@short knoll

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[paper onyx]

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[proper maple]

alright here's a really fun one

a) Let F: R3 -> R4 a non-null linear transformation, G: R4 -> R3 epimorphism/surjective and GoF=0. Find dim(Nu(F))

So since G(F) = 0 we know the image of F is the null space of G

which means the dimension of the null space of G is the dimension of the image of F

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[cloud elm]

How do I find the inflection points on this function

[crude skiff]

How do you usually find inflection points of a function

[cloud elm]

second derivative

I can't solve it

[vernal yacht]

Then do it

[thick shell]

product rule

[cloud elm]

Stucked*

[crude skiff]

Are you given an interval on which you are analyzing?

and are calculators allowed

[vernal yacht]

There are a lot

[crude skiff]

so unless you have access to a calculator and you have an interval which you are analyzing on you can’t really solve it that easily

[cloud elm]

yea sorry forgot to add

[paper onyx]

What's the interval?

[cloud elm]

0≤x≤2π

[cloud elm]

no i can't use calculator

can i solve it without calculator algebraically?

or i should said it will takes a long time to do it?

[paper onyx]

I would just say think about the graph

Like in x*cosx

It becomes 0 at 0, pi/2, 3pi/2.....

So in between becoming 0

It must have turned

[cloud elm]

the question reuiqred me to use the method to find the inflection points to find concavity though

[paper onyx]

Just use this to find inflection points

[crude skiff]

With advanced strategies but not really with basic algebra and trig

[cloud elm]

ok

this is high school calculus so i guess no advanced strategies

[ruby widget]

can anyone help me with this question

[crude skiff]

get a help channel

[ruby widget]

how to get help channel

[crude skiff]

#❓how-to-get-help

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[odd rain]

Someone help with #24

What I did so far

[tacit wasp]

This part is wrong

I don't actually understand how you got that

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[torn bloom]

is this invertible

[torn bloom]

?

rn i have this one

[forest sky]

assuming your row operations are correct, if you can find an inverse it's invertible

[torn bloom]

i would assume that it isnt invertible because how the last matrix looks

in the last matrix first line and third row theres a -i

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[forest sky]

so?

[brittle beacon]

(you can still clear that -i by an appropriate row operation)

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[abstract marsh]

Is it correct way to solve it?

[undone basin]

,rccw

[abstract marsh]

So?

[undone basin]

no, i don't think its the right way

1^infty is indeterminate

[abstract marsh]

Oh thx

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[winter pecan]

What's good can someone explain me this i don't know how to start

[winter pecan]

P and q* sorry guys trying to translate from IT to ENG

<@&286206848099549185>

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[wise zodiac]

Where'd the 8 come from in the common ratio

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[tired sleet]

How do I proceed? Any hints?

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@tired sleet Has your question been resolved?

[tired sleet]

<@&286206848099549185>

[river spindle]

Hi

[tired sleet]

hi

[river spindle]

You need to divide the interval (0,1) into multiple subintervals.

[tired sleet]

yeah but how do i deal with the floor(1/x)

wont there be an infinite number of sub intervals?

[river spindle]

Yes, there will be

For interval,
(1,1/2) -> [1/x] is replaced by 1.
(1/2,1/3) -> [1/x] is replaced by 2.
And so on...

Something like this.

[tired sleet]

Ohh

Thanks

.close

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[finite mulch]

why it wrong

[proven harbor]

that is true for tan when A+B+C = 180 deg

[mystic saffron]

What does that dot mean?

If it means product, why is it at the end of cot C too?

[fluid tundra]

this is not true

equality holds when the sum is 90, not 180

[fluid tundra]

better question is why intentionally interpret something wrong

[mystic saffron]

His question is incomplete

[odd edge]

@finite mulch Has your question been resolved?

[proven harbor]

is it?
i remember it being true when A, B, C are angles of a triangle

[fluid tundra]

a = b = c = pi/3
sqrt3 =? 1/3sqrt3

[proven harbor]

like root(3) + root(3) + root(3) = root(3) * root(3) * root(3)

[fluid tundra]

that would be a = b = c = pi/6

which indeed sums to pi/2, i.e., 90 degrees

[proven harbor]

im talking about tan

[fluid tundra]

ah ok i cannot read, perfect

[proven harbor]

lmao

[fluid tundra]

still why

w/e

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[frank coral]

Need to solve for theta. I know I need to factor but I don't know what.

[frank coral]

This is what I have so far

[proven harbor]

take 1/2 common on RHS

[frank coral]

Don't you have to move everything on one side

?

[proven harbor]

sure

but then take 1/2 common from - cos^2 x / 2 + 1/8

[frank coral]

And leave everything else the same?

[proven harbor]

yup

like what you did in blue is impressive but i dont think we can go anywhere from there

[frank coral]

Should I take out a -1/2?

[proven harbor]

yes that will be better

[frank coral]

And then just factor out a cos^2 x - 1/4?

[proven harbor]

exactly!

[frank coral]

Okay. I will try that and see if I get anymore hiccups

[frank coral]

I noticed that lol 😅

[proven harbor]

use brackets

on cos^2 - 1/4

and that is all equal to 0

[frank coral]

Okay. Should I convert the csc into sine or get a common denominator?

[proven harbor]

no need to convert

use $(x-a)(y-b) = 0$ then $x=a \text{and/or} y=b$

[clever fjord]

Wumpus Man

[frank coral]

I don't think I've learned that

[proven harbor]

idk how to fix it

[proven harbor]

hmm

if i give you the eqn $(x-2)(y-5)=0$

[clever fjord]

Wumpus Man

[proven harbor]

what will be the roots?

[frank coral]

X= 2 & 5

[proven harbor]

x=2 or y=5

[frank coral]

Oop. Right mb

Wait! I think I got it

[proven harbor]

what if if i give you the eqn $(\sin{\theta}-1)(\cos{\theta}-1/2)=0$

[clever fjord]

Wumpus Man

[frank coral]

Isolate for theta on both sides right?

[proven harbor]

that is correct

[frank coral]

Okay Okay let's see where this goes

For the equation with the sine, should I multiply by the reciprocal first to get rid of the fraction?

[proven harbor]

you mean multiply by 2 or sin?

[frank coral]

I want to say multiply by 1 x sin 2/3x

[proven harbor]

3/2 x

[frank coral]

Like that?

[proven harbor]

what?

$\frac{1}{\sin{\frac{x}{y}}} \neq \sin{\frac{y}{x}}$

[frank coral]

So it's 2/3x?

[clever fjord]

Wumpus Man

[proven harbor]

you can do that either

[frank coral]

?

[proven harbor]

nope

[frank coral]

I forgot to erase the bottom

[proven harbor]

$\frac{1}{\sin{x}} - 1/2 = 0 \newline\newline
\frac{1}{\sin{x}} = 1/2 \newline\newline
\sin{x} = 2$

umm

[clever fjord]

Wumpus Man

[proven harbor]

finallyyy

[frank coral]

But I don't understand what happened with the 3 theta/2

[proven harbor]

did you see how i did it?

now do it yourself with sin(3x/2)

[frank coral]

Just barely. But I have to go now. Let's see how I do on this test 🤐

[proven harbor]

ohh

good luckk

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[frank coral]

Yes

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[fresh stirrup]

can anyone teach me how to solve this? using T1y and T2y all went downhill since I can't factor them out since their angles are different

[forest sky]

you can use that in combination with a second equation from summing the forces in x

[fresh stirrup]

so the second equation would be

T1cos45 = T2cos30

right?

[forest sky]

yes

[fresh stirrup]

but what do I do next after that

cus theres still t1 and t2 in the equation

[forest sky]

yes, but now you have a system of two equations in two unknowns

[fresh stirrup]

can u explain in simpler terms?

[forest sky]

you have two equations (one from x and one from y) and T1 and T2 need to satisfy both at the same time. so you can use one to solve the other

[fresh stirrup]

how exactly?

[forest sky]

one way you could do it is to solve for T1 in terms of T2, then plug that in to your other equation

(you could also solve for T2 in terms of T1, it doesn't really matter which order you do it)

[fresh stirrup]

so in order to do that

using the x equation, do I divide both sides by cos45?

[forest sky]

yes

[fresh stirrup]

but there's still T2 in the numerator

[forest sky]

yes, but then you have T1 = ...
and in your other equation you can replace T1 with whatever you get. and you are left with an equation only involving T2

[fresh stirrup]

wait lemme write it down to get a better view

for the y equation, the formula is

T2sin30 + T1sin45 = 150N

right?

do I transpose the T1sin45 and then divide both sides by sin 30?

[forest sky]

you do replace the T1 with whatever you got in the previous step

[fresh stirrup]

whaat

i don't get it

[forest sky]

so what did you get from solving for T1 in terms of T2 in the x equation?

[fresh stirrup]

how am I supposed to get anything in T1 if there's T2 in the equation

[forest sky]

you can get T1 = (some expression involving T2)

[fresh stirrup]

what do I do next after this?

i can't continue the solve since there's T2 in the numerator, that's the part that's making me confused

and I can't substitute the T2 since it doesn't have a value

<@&286206848099549185>

[alpine hawk]

What's the value of cos 30? Substitute it and solve it further

[fresh stirrup]

do I divide 0.87 and 0.71?

[quartz trellis]

converting to fractions would be easier

[fresh stirrup]

what?

[fresh stirrup]

I think it would be better for me to use decimals since it was how I was taught in class and would be weird if I strayed off

[quartz trellis]

alright

[fresh stirrup]

so, can u help?

[quartz trellis]

use a calculator

0.87/0.71 = 1.22535211

[fresh stirrup]

But then what do I do with the T2

T1 = T2(1.23)

[quartz trellis]

wait

you need to form two equations

to solve T1 and T2

[fresh stirrup]

Wait do I solve them both at the same time?

[quartz trellis]

wait

[quartz trellis]

first equation

horizontal

now vertical

T1* sin(45) + T2(sin(3) = 150

solve both of those

to get T1 and T2

[fresh stirrup]

Vertical is

T2 = 150N/T1sin45

[quartz trellis]

Do you get this

horizontal is T1* cos(45) = T2* cos(30)

@fresh stirrup now solve

[fresh stirrup]

How?

@quartz trellis

[clever fjord]

Alaska

[fresh stirrup]

Am I missing something here

[quartz trellis]

wait

[clever fjord]

Alaska

[quartz trellis]

are these both equations correct

[fresh stirrup]

Yes

[quartz trellis]

first solve this

don't use decimals for now

solve for T1

[fresh stirrup]

Idk how to solve using that

[fresh stirrup]

How'd both become t2

[neat crown]

look at the first line i replaced t1

[fresh stirrup]

can't I just solve it with decimals? We weren't taught to solve it with fractions

[neat crown]

i mean i cannot solve this using decimals

[fresh stirrup]

[quartz trellis]

you can solve

using calculator

[fresh stirrup]

I hve an example from yesterday's class but the tension's angles have the same values

[quartz trellis]

its a pain in the ass to deal with decimals

[neat crown]

yeah but i cannot take this into my examination hall

[quartz trellis]

yea

[fresh stirrup]

@neat crown btw what that tablet thingy called? I wanna buy one

[neat crown]

u do know the trigo value

of cosine and sin

[neat crown]

thats a writing pad

[fresh stirrup]

Nop

[neat crown]

tf

how will u solve this then

[fresh stirrup]

Idk

[neat crown]

i mean this is simple mechanics but u need to know trigo

[fresh stirrup]

Alr thanks, I still don't get it

[quartz trellis]

atleast you formed the equations

[neat crown]

i mean is that even possible without trigo great job

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[fresh stirrup]

.close

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[proper maple]

So a) requires that we find dimensions of the image and null of a linear transformation T

T is non null, not injective and not surjective

i've found dim(Im(T)) = 1 and dim(Nu(T)) = 2

now b) requires that we "make up" a linear transformation T: P2 -> P1 which verifies the given conditions

[proper maple]

so this must hold true as well as it must not be injective, surjective or null

.close

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[tawdry vault]

isnt there a mistake at (3)?

right before the hence statement above three we do | +lim inf y_n, but it seems like the lim inf y_n got swapped to a lim sup y_n is that correct? i dont think it is

why did the sup and inf swap already? we just conclude that in the next step that they are interchangeable for y_n so is it a mistake or am i gaslighting myself xd?

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[vague basin]

Hi, I have ANOTHER question in sequences. Based on something that’s in French. It’s on exercice 2.

[vague basin]

Wait

@weary pelican

J’ai ça

En fait jsp si j’ai le droit de le faire

Et donc je détermine que ça raison est r = 0,97

Et je mets divisé pas par Q(n) par ce que ça peut être égal à 0 vu que c’est définie sur N

Hoping for other frenchies :)

<@&286206848099549185>

I need a fellow Frenchman

[scenic pasture]

Hopefully French helper comes

[vague basin]

Only one?

..

@weary pelican

Pwease

:(

Aw man

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[wide drift]

Im stuck halway through

u = x^2 - 2

du = 2x

Oh wait

💀

nevermindddddddddd

.close

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[ember oak]

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[eternal glade]

Does anyone know what to do here? I have no idea how to approach the third task.

[dapper canyon]

what u do i

[eternal glade]

?

Wdym, im sorry

<@&286206848099549185>

[eternal glade]

Do you have an idea?

[dapper canyon]

idk i don't really understand the q

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[glacial sable]

I need help on how do I calculate tensions in particle equilibrium?
I’m struggling a bit to fully understand getting from the start expressions to the final solutions when trying to calculate the tension of Toa, Tob and Tob

I can get up to the Uoa,Uob and Uoc but the expression below just confuses me, how do I substitute to work out the tension forces?

Zfx 0 = 0.352 Toa – 0.491 Tob + 0Toc
Zfy 0 = -0.704 Toa – 0.655Tob + 0.658Toc
Zfz 0 = 0.616 Toa + 0.573Tob + 0.752Toc – 735.75W

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[mystic saffron]

g

[mystic saffron]

FRom just the information that

The sum of opposite angles of a quad is 180 degreesh

how can I prove that the quad is cyclic?

[ashen cradle]

it is a property of cyclic quad

[mystic saffron]

proof?

I mean

[ashen cradle]

wait a min then

[mystic saffron]

All cyclic quads

have opposite angles sum t0 180

but how does that imply

that all quads with opp summing to 180

are cyclic?

[ashen cradle]

Ignore the blue part

Ok this is the proof of quad having sum of opposite angles =180
Now I will give you proof of converse

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@mystic saffron Has your question been resolved?

[ashen cradle]

@mystic saffron

[mystic saffron]

ooo

Thats also a way to prove it

wow

hmm

Thx

+close

[ashen cradle]

It's .close ig

[mystic saffron]

.close

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<@&286206848099549185>

[remote drum]

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[near swan]

i get that we are using squeeze theorem here but, shouldn't it be 1-1/x <= [x]/x for the concept to be valid?

[latent scaffold]

Strict inequalities work as well

[near swan]

but why? 1<1 is not valid, right?

[stone vector]

we know for a fact x-1 is strictly less than x so we can use a strict inequality

[near swan]

got it, thank you

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[latent scaffold]

As you take limits, it doesn't really matter whether the things you're limiting are bounded by strict or normal inequalities.
The limits can still be equal despite one limiting value being strictly less than the other.

Consider like a_n = 1/n and b_n = 2/n as n -> infinity. These two sequences clearly have a_n < b_n for all n, and yet their limit it equal.
In general, if you have a_n < b_n for all N, then the limits actually obey a <= b, not a < b, as per the last example.
The same goes for limits over real numbers, just like sequences.

[near swan]

makes sense! thank you 🌸

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[reef cypress]

Good day, could somebody help me with the detailed answer of this question please? Much appreciated.

[west merlin]

well where are you stuck?

[reef cypress]

What do you do after you get derivative of every individual element?

To be honest, i forgot how to do the whole equation, could you give me pointers on how you solve this?

Just a vague rundown is fine

[west merlin]

it's not really an equation. for the partial derivative of A with respect to x, you just do the derivation for each element in the matrix with respect to x and then put it back where you found it

do that for x, y, and z

[reef cypress]

So for the first question, there will be 3 matrixes correct?

[west merlin]

correct.

[reef cypress]

Now for the second question, i don't really understand the question.. should i find the derivative of A through z and fill each variables with (-2, 1, 4) respectively?

[west merlin]

i'm rusty on this, so i'm not as sure here, but I believe you're correct. using the partial derivative of A with respect to z, plug in (-2, 1, 4) and then find the determinant of that matrix

[reef cypress]

Aa.. yes i forgot the determinant lol, thank you so much.

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[livid kayak]

Help please

Someone please help me

And I would greatly appreciate it

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@livid kayak Has your question been resolved?

[runic swift]

square roots are 1/2 in power form

cube roots are 1/3

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[sly topaz]

Can anyone check where I’ve done wrong?

[feral scaffold]

you integrated u^-4 wrong in I2

[sly topaz]

Is the method alright though

[ruby girder]

can someone help me with this

[odd edge]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[sly topaz]

.close

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[feral scaffold]

ye I think so

also that simplification to cot^2 x in I3 is wrong

[odd edge]

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[wide drift]

I think I know how to solve this but im wondering something

In this question I have a choice between if I want to take sin(x) as my u or cos(x) as my u

For questions like this where I can pick, which one do you think is better to pick? Is one easier to work with that the other? Which would you personally do?

[keen geode]

Try converting it into sin (2x)
Using this 2Sin(x)Cos(x) = Sin(2x)

Then go from there

It will be much much easier imo

[wide drift]

Yeye I know how to solve it I think, I was asking more generally

If theres a question where I can pick whether I want sin or cos as my u, which is easier

In your opinion

[iron grotto]

with youll eventually know

but yeah

[keen geode]

In ny experience if you can pick b/w the two like there's no virtual difference then there's probably a 3rd solution that's simpler like here converting it into sin (2x) or converting the terms into tan x and sec x

[wide drift]

Okkkkkkk but if you guys had to chose 😂

[keen geode]

If it doesn't matter then yeah sinx = u

[rose grail]

id pick sin cuz differentiation has no sign change

[keen geode]

Just saying look for better solutions

[rose grail]

this

[wide drift]

Awesome, thanks guys!

❤️

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[ruby girder]

can you guys help

[odd edge]

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[opal tapir]

Can anyone solve this but also explain the steps and why thank you in advance

[warped glacier]

you need the angle bisector theorem

DE/EB = 12/8 = 3/2

hence DE/DB = what?

now since DFE and DCB are similar triangles, DE/DB = DF/DC

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@opal tapir Has your question been resolved?

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[mystic saffron]

How to find sin 18?

[mystic saffron]

Like we can find sin 15 with sin ( 45-30 ), but when to do when difference or sum of standard angles is not equal to our desired angle, like sin 18

[valid lava]

u cannot find exact value of sin 18, it is irrational

[serene axle]

sin(90) = sin(5 x 18)

[south plume]

it is irrational but you can find the value

[mystic saffron]

In form of root? Like sin 15 = ( √3 - 1 )/2√2

[valid lava]

yes but not exact

[serene axle]

Yeah you'll probably get something like this

[mystic saffron]

After that? 🥲

[south plume]

yes you can

[valid lava]

u can approximate by using taylor expansion

[south plume]

you can also do sin(36) = sin(2 * 18)

https://www.cut-the-knot.org/pythagoras/cos36.shtml

[serene axle]

Double angles and triple angles maybe

[mystic saffron]

Okay, lemme give it a try

[valid lava]

yes sin 18 could be found out with a relative easy way

[south plume]

this is the answer btw

[mystic saffron]

What is it?

[mystic saffron]

🙏❤️

[valid lava]

well, it is up to you to use any method to find it out, but as sin(90-x)=cos x, and 18 is 90/5, i believe double angle and triple angle formulae might help

[warped glacier]

$\sin 18 = \cos 72 = 2 \cos^2 36 - 1$

so $(2x \sqrt{1 - x^2})^2 + ((x + 1)/2) = 1$

given that x = sin(18 deg)

[clever fjord]

south

[warped glacier]

ah there should be a similar trick to get a quadratic equation instead

[mystic saffron]

:00000000

[warped glacier]

definitely it's online

[mystic saffron]

That's so ezy 😭

On Google it shows so big

[mystic saffron]

@warped glacier

[warped glacier]

https://www.youtube.com/watch?v=p2k756gbwik

ah yeah it's that

sin(2x) = cos(3x)

[mystic saffron]

Oh lemme check

.close

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[junior ether]

guys

[junior ether]

is the force from the pivot at the same angle as the tension

[serene axle]

Nope

A pivot always applies 2 normal reactions

One horizontally and one vertically

Sometimes some of these normals may be zero

But you should always take 2

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[crisp wadi]

You can show that A^TA and A have the same kernel and the equality follows

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[heady plover]

how to analyze the solution cases of A^TAx=Ab?

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[clever fjord]

sotiris

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@mild sable Has your question been resolved?

[raven ermine]

sup

hru girl

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[compact steppe]

i need to make a guess what happens when x and y approach 0

so id say the numerator is of degree 3 and the denominator is of degree 4 so it’s blowing up to infinity as x,y approach 0

since denominator shrinks faster and small number divided by smaller number is a big number

i am aware that this reasoning is flawed, i hoped for someone to tell me how/where exactly it’s wrong

[brittle beacon]

Partly correct, but there is a path you can choose for which you won't get it blowing up to either infinity

[compact steppe]

thanks. i don’t understand this “path” thing, chatgpt told me similar stuff but it made bunch of other mistakes so i gave up on it

apparently for y=kx^2 we get something else, but i never saw this done

like this “path analysis”

like when u see the og function, whats ur thought process

why did you even consider to think about these paths

or id be grateful if u point me in the general direction where i can learn more about this kind of thinking

in my mind x and y are variables on equal terms, but somehow with this “path” mindset y^2 can grow faster than x^4

im sharing what im thinking to hopefully make it clearer where my confusion lies

i feel like it’s maybe a very obvious thing, too obvious for someone even to help me, if that makes sense

like we can just put y=g(x) where g is any function of x and consider that as a path ?

[brittle beacon]

(if it passes through the point you're taking the limit to, in this case, if it passes through (0, 0) then it's fine)

Basically the idea is that if the limit exists, then you can approach the point you're taking the limit to "however you want" and you should find the same answer (so you could e.g. approach (0, 0) along a straight line, along a spiral, whatever, and if the limit does exist, then you must find the same thing whatever way you choose)

[worldly zephyr]

do y = x^2 and then you get 1/2 and then do x = y^2 and you get y^3/2Y^2 = 0 so dne

i thikn

[brittle beacon]

So if you found two different paths and happen to find they give you different things, the limit doesn't exist

[compact steppe]

yeah usually we do this with sequences formally

but to do that i needed first to make the guess that indeed the function doesn’t approach 0

but i think i understand it a bit more

[compact steppe]

this helped

thanks a lot @brittle beacon

.close

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[pale trench]

learning about this stuff and i'm pretty bad at it lmao

[lost crane]

how did you calculate the first answer

@pale trench

[pale trench]

i used chatgpt tbh, i had no idea where to start with this one

[lost crane]

what is the decimal equivalent of 5.5%

[pale trench]

0.055 right

[lost crane]

yes

so how do you calculate 5.5% of a number

[pale trench]

erm

multiply?

[lost crane]

yes, do that, tell me what you get

[pale trench]

multiply 64,835 x 0.055?

[lost crane]

yes

[pale trench]

okay

3565.925 ?

[lost crane]

yes

now to calculate the total including sales tax what do you do

[pale trench]

um

i'm not even sure

uh

[lost crane]

it's one simple operation

[pale trench]

adding?

[lost crane]

yes

the sales tax is an extra cost on top of the purchase price, usually calculated by a percentage

so you add

[pale trench]

OH so add 3565.925 and 0.055?

[lost crane]

No?

[pale trench]

oh

[lost crane]

Add it to the original total

[lost crane]

.

[pale trench]

so add 0.055 to 64,835?

[lost crane]

You already calculated the cost of the sales tax

Just add it to the purchase price

What you could also do is realize that the purchase price is 100%, and sales tax is 5.5%, so total with tax is 105.5%, so you can multiply the purchase price by 1.055

[pale trench]

so 64,835 x 1.055?

[lost crane]

Yes

[pale trench]

looks like 68400.925

[lost crane]

Or calculate the sales tax separately which you already did and then 64835 + 3565.925

[pale trench]

oh okay

[lost crane]

That is the correct answer

[pale trench]

how do i round to the nearest cent

[lost crane]

2 decimal places

[pale trench]

do i move it forward or backward

[lost crane]

Have you not been taught rounding?

[pale trench]

i'm gonna be truthful

i have a hard time remembering things like this

[lost crane]

Okay

If the next digit is 5 or greater round up

[pale trench]

ty

68,400.93 ?

[lost crane]

Yes

[pale trench]

ty

okay i wrote that down

uhhhh down payment of 20% i have to find the down payment

so does that mean 20% of 68,400.93

[lost crane]

Yes

[pale trench]

okay okay

is 20% as a decimal 0.020 or 0.20?