help-17

[oblique lark]

156 wasn’t it

but still thank u so much bro

[warped relic]

it's how integration works 🌚

[fathom perch]

My 0 to 2

[warped relic]

considering COM was pointless

[oblique lark]

ITS OK LOL

[warped relic]

it's not like radius of gyration here..

[oblique lark]

chin chin if it’s okay can u explain ur work?

like how you set up your function and stuff

[warped relic]

yes

you take the chain, and divide it into segments of length dx

[oblique lark]

what does the dm/dx mean too?

[warped relic]

whats the mass of each segment?

[oblique lark]

ohh it’s 8

[warped relic]

mass per unit length

[warped relic]

yesyes

[oblique lark]

i gotchu

[fathom perch]

Ohhh i just realised my mistake

[warped relic]

for 1m length, mass is 8
for dx length, mass is 8dx

does that make sense?

[oblique lark]

yuh

[fathom perch]

We took m=8x where x was the segment of chain chosen

So x is the entire height raised

[warped relic]

now, work done to lift each dx segment up to x height

dW = 8dx * g * x

does that make sense?

mgh,
your m of each segment is 8dx, g is g, and x is the height you're taking it up to

[oblique lark]

is dW the work?

[warped relic]

yesyes

work done

to lift one small segment

[fathom perch]

Infitesimal work

[oblique lark]

ty 😤

[warped relic]

now you sum up all the small segments, which we call integration

[oblique lark]

yes it makes sense so far!

[warped relic]

lower limit 0 cause it starts from the ground,
upper limit 4 cause thats the maximum value of x

and then just integrade

[oblique lark]

ok bet this makes a bit more sense 🙏🏽

i just gotta study more

tysm for your help guys!!!

[warped relic]

nw

catenary version wouldve been more fun

[oblique lark]

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[fathom perch]

I am disappointed lmfao

I let my physics cloud my math

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[devout trellis]

is this just a(n) = n − 1 if n is prime, a(4) = 2, and 0 otherwise?
https://oeis.org/A061006

[devout trellis]

yes

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[vast shale]

Can someone explain this to me?

[vast shale]

The same question was solved correctly on the left but I got something different on the right

[civic otter]

What difference?

[vast shale]

On the right I wanted to cancel out the negative by multiplying them together because of the slope formula y2-y1/x2-x1

[civic otter]

And if you do you get 6/(-6) right?

I don't understand your doubt

[vast shale]

No I ended up making the 2 a positive and adding it to the -4 which gave me the wrong answer

Here’s the whole question and what I put in (-3)

I wanted to know why I couldn’t cancel out the negatives like I did with the top part of the slope formula

[civic otter]

I'm sorry I don't really get you 😬

[warped relic]

you're not subtracting -2 here

you're subtracting just two

there isn't a 2nd negative

-4-2 = -6
-4-(-2) = -4 + 2 = -2

[vast shale]

OH

[warped relic]

better to use your eyes sometimes

[vast shale]

thank you sorry I got confused

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[midnight scroll]

something is not clicking in the noggin

[midnight scroll]

what am i doing wrong exactly?

[flat whale]

,rotate

[midnight scroll]

like i am getting completely different numbers

[flat whale]

Show the original question

[proven bramble]

Did you square the b term properly?

[midnight scroll]

no

lol

oops

but i dont think it would still get that answer

right?

[proven bramble]

There seem to be a couple hurried errors

Take it step by step, start with the discriminant

[midnight scroll]

wait 2y^2 would be 4y^2?

[proven bramble]

(-2y)^2 = 4y^2 yes

You also have one more error in that square root

[midnight scroll]

this is where i am at right now

[proven bramble]

Are you sending a picture?

[midnight scroll]

yes sorry

bad internet

[proven bramble]

Oh ok no worries

[midnight scroll]

,rotate

[proven bramble]

You made the same mistake again

[midnight scroll]

ahhhhhhhhhhhhhhhhhhhhhhhhhh

[proven bramble]

The b term is good

4ac term has a mistake, check once more and I'll give you more of a hint

[midnight scroll]

4ac?

[proven bramble]

In the quadratic formula

b^2 - 4ac

Okay actually let's speed it up

How would you do "-24 * (1-2)" without solving the parenthesis

[midnight scroll]

distribute ( i think is the right term) like i would do -24(1) and -24(-2)

[proven bramble]

Yeah and what would you get?

-24 + 48 right?

[midnight scroll]

yes

[proven bramble]

The minus cancelled the that other minus

Now look again at what you wrote

In your square root

[midnight scroll]

okay

so it's -116y^2 + 96?

[proven bramble]

Yup that's the other thing

The rest is all correct

[midnight scroll]

but the answer on my program said it is different

is there a different step i am missing?

[proven bramble]

Yeah, you can simplify your final answer

Do 116 and 96 have a common factor?

[midnight scroll]

four?

[proven bramble]

Indeed

[midnight scroll]

oh my gosh

okay

yes

[proven bramble]

You take the 4 in front and you can take it out of the square root as a 2

Then everything simplifies

[midnight scroll]

ur a god 🙏

thank you!

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[wanton bloom]

Solve this equation.

(a-e)ln(a) - a + 1 = 0

[flat whale]

,w solve (a-e)ln(a) - a + 1 = 0

[twin meteor]

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[dry horizon]

how to get help from bot

?

[wanton bloom]

a neq = 1

Type ,w [your query]

[dry horizon]

hmm how?

[wanton bloom]

like this

[dry horizon]

ok lemme try

,w solve 1000000000+45489864

[twin meteor]

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[dry horizon]

te it works

ty

[drifting jackal]

#bots

[dry horizon]

what is this?

[drifting jackal]

Go there if you want to use the bot, don't spam/use it in someone else's channel

[wanton bloom]

this, or that?

I allow you to use bots in my channel.

[dry horizon]

uhhh i didnt understand what you said about spamming?

[drifting jackal]

If you are trying to use it to do calculations, do it in #bots not in someone else's channel as you would fill it with unrelated clutter to what they are asking

[dry horizon]

so where is my channel?

can you say

[stray sage]

#help-22

[dry horizon]

there isnt a channel help 24 broo

#help-30 how to create my own channel

[heavy yoke]

#help-3 please stick to your channel

[dry horizon]

i dont understand where is my chnnel??

atleast say how could i create

[heavy yoke]

your channel is #help-3 please stop talking in this one

[dry horizon]

ahh okay thanks

[vocal sleet]

@wanton bloom Has your question been resolved?

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[wanton bloom]

Solve this equation.
(a-e)ln(a) - a + 1 = 0

[wanton bloom]

I was gone somewhere.

a neq = 1

[paper depot]

i am just going to assume you came up with this yourself so im gonna tell you there's no better way than numerical methods

[vocal sleet]

@wanton bloom Has your question been resolved?

[dim quail]

$\ln a^{a-e} -a + 1 = 0$

[twin meteor]

Bettim

[dim quail]

thats all you can do

[heavy yoke]

,w solve (a-e)ln(a) - a + 1 = 0 to 32 decimal places

[twin meteor]

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[wanton bloom]

sad

thanks y'all

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[cedar kernel]

attempt

i thought i could get it into telescopic form

or something

in short i have no clue how to proceed

[scenic ravine]

I wonder if the equation has simple roots

,w 375x^2-35x-2=0

[twin meteor]

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[scenic ravine]

yea

[paper depot]

you are asked for the value of alpha/(1-alpha) + beta/(1-beta)

geometric series

[scenic ravine]

though finding these by hand would probably be a pain

[lucid bane]

then just apply vieta formulas :3

[cedar kernel]

ah fu i didnt even consider finding the roots

yeah that makes sense

[cedar kernel]

only choice i have 🙏

[scenic ravine]

do what moosey suggested

[cedar kernel]

im all ears

[scenic ravine]

use the relation b/w the roots and the sum and product of the roots

you basically want $\frac{ \alpha}{1- \alpha} + \frac{ \beta}{ 1 -\beta}$

[lucid bane]

combine these into one fraction and simplify

[twin meteor]

wai

[cedar kernel]

right

[cedar kernel]

oh damn

yeah

but

[lucid bane]

you'll get a bunch of things in terms of sum and product of the roots (then just apply vieta)

[cedar kernel]

like

dang that does simplify it

[desert hornet]

this probably works as well

[cedar kernel]

however i still need to know if they gp or not

[lucid bane]

gp?

[scenic ravine]

a^r and b^r are GPs by defn

[cedar kernel]

oh what if i had considered the middle term as tr?

[scenic ravine]

geometric prog

[cedar kernel]

oh wait yeah im triping

[desert hornet]

just sum up the relation 375 T_{r+2} - 25 T_{r+1} - 2 T_r = 0 from r=1 to infinity

[scenic ravine]

over complicated though

[paper depot]

that's exactly the same thing i said, but guess i wasn't listened to

[lucid bane]

I was listening i literally referenced you twice 😭

[desert hornet]

are you talking about my method?

[lucid bane]

i just didn't wanna ping

[scenic ravine]

I didn't notice. Sorry 😭

[scenic ravine]

yea

[cedar kernel]

i got it ann ,

[desert hornet]

it's not bad

[cedar kernel]

i dont see it

[desert hornet]

375(L - T_2 - T_1) - 25(L - T_1) - 2L = 0

[cedar kernel]

i got the base method thanks a lot guys!!!!

[desert hornet]

you just need to find T_1 and T_2 and then solve for L

[cedar kernel]

i just wanna know the newton formulae aproach

[cedar kernel]

i wasnt able to catch you there what did you do there exactly-

[desert hornet]

we agree that with $T_r=\alpha^r+\beta^r$ we have the relation [ 375T_{r+2}-25T_{r+1}-2T_r=0? ]

[cedar kernel]

yes

[twin meteor]

kheer257

[desert hornet]

now sum this up from r=1 to infinity

[cedar kernel]

OHHH

YES

I GET WAT YOU MEAN NOW

Considering summation of r = 1 to infinity as L

[desert hornet]

correct

[cedar kernel]

wow thats neat

thanks a lot

[desert hornet]

yeah it's pretty nice now you only need to find T1 and T2

[cedar kernel]

lit

thanks wai moosey ann and Kheer!!!!!

!

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[cedar kernel]

without calculator this method(newton formula one) is a tad lenghty- , but good to know the aproach

[desert hornet]

I feel like it's still faster than converting it into a GP

[inner osprey]

I have not looked at the other method but gp takes maybe 30 seconds to do

since (a + b - 2ab)/(1 - a)(1 - b) is findable immediately

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[cedar kernel]

sending my aproach 1 sec

[cedar kernel]

,rcw

[cedar kernel]

i got wat i did wrong

when i sqrt(X) i think i limited the range for x>0

how can i got about finding this for x<0 ( is the only way to cross multiply and find the quadratic in y )

[cedar kernel]

*i think thats what i did wrong

[scenic ravine]

so you need the extrema of $\frac{2x}{x^2+x+1}$. Maybe a trig sub?

[twin meteor]

wai

[scenic ravine]

x= tan(t)

$\frac{2tan(t)}{sec^2(t)+tan(t)}$

[twin meteor]

wai

[scenic ravine]

can you work with this I wonder

[cedar kernel]

oh wow

wait can i

i thought of puting the tan t in the denominator (dividing)

2/(2cosec2x+1)

and then using cosec2x range ?

[scenic ravine]

I suppose so, yea

[cedar kernel]

damn

[fathom perch]

There's an easier method for quadratic by quadratic no?

Take the quadratic in the denominator to the other side in multiplication with y

Then make another quadratic by shifting everything to the LHS

And find range

[cedar kernel]

yeah but that calculation would take some time

i have that method in mind as a last resort yeah

[fathom perch]

Alrighty

[cedar kernel]

during exam if nothing clicks 🙏😭

[fathom perch]

I dont think it would take as much time as the above method in this qn btw

Should be quicker

[cedar kernel]

this does work

[cedar kernel]

yeah considering this has to click in me the moment i see this then only trig sub would be helpful

otherwise the quadratic/quadratic would be prol faster

fair fair

thanks

🙏🙏

[fathom perch]

Yw

[cedar kernel]

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[cedar kernel]

.reopen

[vocal sleet]

✅

[cedar kernel]

any variation i can make in my aproach to make it valid of x<0 too?

[fathom perch]

Ehhhhh nothing comes to mind, if you're gonna use AM-GM to find the range then that can only be found for positive numbers in the first place

And also by taking the square root in the very first step all x<0 is instantly rejected, a variation in the method would just mean a different method then

[cedar kernel]

yeahh lmfao

fair

[pearl wadi]

differentiate?

[cedar kernel]

yeah thats fair

[pearl wadi]

when we differentiate we get x= +-1
x=1: value of function = 1/3
x=-1: value of function = 3

[cedar kernel]

yeah i should have done that

brain fart

[pearl wadi]

lmao

[cedar kernel]

thanks!

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[finite hatch]

n

[finite hatch]

how do id od dis

[twin meteor]

Monkey•D•Luffy

[silk rampart]

,, a\log(b) = \log(b^{a})

[twin meteor]

fluX

Monkey•D•Luffy

[limpid monolith]

We mean just use the properties of log

[finite hatch]

wait im confused on the

3log10(2)

do i just put 2 to the power of 3

[silk rampart]

yes

[finite hatch]

and then use these properties

oh

ok thanks

[river kettle]

bum chicken

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[polar vine]

Hello

[polar vine]

May u explain how we got DQ here?

Btw the figure is exactly same as the diagram drawn on second pic

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[somber quiver]

Does anyone know how to apply ACO Metaheuristics algorithm?

[somber quiver]

I need an example of how to apply the algorithm as I am a bit confused

If we apply the tsp problem to solve it with the ant colony metaheuristic, How could we initialize the pheromone matrix?

And how we start from which ant

🤔🤔

And to which Node

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[tidal osprey]

I've made this graph n so many others someone help fr

I can't figure out how to find the other angles n lengths

[tawny nacelle]

did you mean to draw the 55 degree angle like that?

is it supposed to be flipped around, so as it be wedged between the red and green lines?

[tidal osprey]

yeah wouldn't it be alternate angles...?

[tawny nacelle]

anyhow, what I’d suggest is looking at the 120 degree angle

[tidal osprey]

where the purple would be 145 -90 = 55

Or am I missing something...

[tawny nacelle]

55 is correct

you can use that to find the bottom right angle of the triangle

remember that a right angle has 90 degrees, and note that 55 + bottom right angle in triangle = right angle

[tidal osprey]

the black is also an angle my drawing is just bad, does that change anything?

😓

[tawny nacelle]

oh, I missed that angle

yeah you can find that too

let me get my laptop so I can draw

[tidal osprey]

i've been staring at this for so long i'm numb give me some direction please higher math being 😭 😭

[tawny nacelle]

hmm

this ended up being a bit harder than I anticipated

[tidal osprey]

Do u wanna see the original question maybe I just understood it wrong

[tawny nacelle]

you can post it just for clarity, sure

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[rotund basin]

solve for a (Alfa)

sin(a + 18) = 1,2 x sin(a)

[wanton bloom]

What is 1,2?
1 point 2?

What is alfa?

Alpha?

[rotund basin]

Yep, sorry I am from Slovakia

[flat whale]

is x multiplication?

[rotund basin]

Mhm

[flat whale]

try using sum angle formula and pythagorean theorem

,tex .sum diff trig/sin

[twin meteor]

riemann

[flat whale]

$\sin^2 a + \cos^2 a = 1$

[twin meteor]

riemann

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[lavish quarry]

guys does anyone know how to solve this as i think the path method will not work here as it gave me the same values in the limits

[lone linden]

Polar

[golden herald]

try converting to polar

almost always works with these problems really

[lavish quarry]

i did try it but i dont know if its right

[flat whale]

that looks fine unless you're expected to use epsilon delta proof

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[cunning yew]

\begin{align*}
&\underline{Exercice:} \
&47x - 43y = 1 \
&\text{after solving we get: } \
&S = {43k +11 , 47k+12} \
\end{align*}

[twin meteor]

<rajel />

[cunning yew]

anyways

here's the question im struggling with

[
x \in \mathbb{Z}, x^{41} \equiv 4 \pmod{43}
]

prove that x and 43 are coprime

[twin meteor]

<rajel />

[cunning yew]

#help-8 message @hard atlas i dont think thats enough

43 is prime but it doesnt mean that its coprime to x

[hard atlas]

the only problem would be if x is a multiple of 43

and it clearly isnt

how is the equation 47x-43y=1 in any way related

[cunning yew]

how its clearly not

[cunning yew]

hmmm , its probably not

[wanton bloom]

43 occurs in both the questions, but that doesn't mean they're related.

[hard atlas]

if x = 0 mod 43, then x^41 = 0 mod 43

[cunning yew]

they didnt say that the 2 parts are unrelated so

[cunning yew]

damn

how did i miss that

[hard atlas]

idk

[cunning yew]

lol

its so fucking annoying to spend alot of time on something that simple lmao

[wanton bloom]

With someone having to tell you.

[cunning yew]

exactly

[fathom perch]

i thought your parents were calling you

[wanton bloom]

I am back.

[fathom perch]

well, go to the channel, reopen it and tell us which chapter the question is from or I'll report you to modmail for trolling

[wanton bloom]

It was my own question.

[fathom perch]

so you made it yourself?

with your only intention being to waste helpers time?

what was your intention then?

[wanton bloom]

To solve it?

[cunning yew]

.close anyways

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[fathom perch]

why did you say it was from hall and knight then

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[storm sigil]

please help, i feel like its a dumb qn but i dont understand it

[storm sigil]

yup i did that i got

x^2+13x=168

so i decided to dvided 13

12.92

then i decided to sqre root it

[glass oak]

[hollow pendant]

Come back here, and solve it like a regular Quadratic.

[storm sigil]

okay

i would -168

x^2+13-168=0
then

[hidden turret]

how are you even typing a plus or minus in desmos bruh

[hollow pendant]

You didn't use the quadratic formula properly. Also, where did the 7 come from?

[storm sigil]

i copied it

my bad 13

right

[storm sigil]

sorry, i didnt sleep yesterday and i just came back from practice, im little hazed

8

YAY

[storm sigil]

may i ask if u have any more of these

[storm sigil]

thank you. mr.ஆற்றல்

[hollow pendant]

!done

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[storm sigil]

.close

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[hidden turret]

I just googled the name

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[desert estuary]

I am pretty sure my derivative is correct

However

The answer key says differently

[fathom perch]

lemme check

[desert estuary]

Alr ty

[fathom perch]

uh i dont see a square on (x^2-y^2) in the first step

did you forget to write it down

[desert estuary]

Yeah i forgot

But i did square it

None the less

[fathom perch]

yeah i saw

[desert estuary]

Nonetheless*

[desert estuary]

Yeah mb on that part

[fathom perch]

seems good

idk what values u put at the end but the differentiation part is correct

[desert estuary]

Alright

Thanks

Also I just realized

That the 25(x^2-y^2) isn't squared on the question idk why my brain filtered that out

[fathom perch]

lol

redo time

[desert estuary]

Thank you for checking the other derivative

It was good practice for me nonetheless lol

[desert estuary]

Ty

Have a great day

[fathom perch]

same

[desert estuary]

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[keen igloo]

Help

[keen igloo]

I don’t know if i did them correctly cause i dont know what they mean by by how much

For question 5 and 6

[glass oak]

there are two things "by how much" could mean, and theyre not the same

actualyl let me think

[keen igloo]

Ok

[whole shard]

the work looks right

[glass oak]

they probably mean compare the unit price

either as a difference or as a relative percent

[keen igloo]

Like the percent difference or how much less you pay for the better deal?

[fathom perch]

probably a difference

[glass oak]

those are my two guesses

how much less you pay (bigger)-(smaller), or

(smaller-bigger)/bigger * 100%

changed it

[keen igloo]

Since it doesnt specify should i do both?

[whole shard]

yeah

[keen igloo]

K

[glass oak]

depends on your teacher's personality lol

basically one is saying how much better a deal is by subtraction, and one is saying how much better a deal is as a relative size

[keen igloo]

Can i add a picture that might determine which one is more likely correct?

[glass oak]

it's not against the law

in my state

to do so

[keen igloo]

This is what I did before those questions

The example was in the book

[glass oak]

yeah theyre using a formula like the percent difference

[keen igloo]

Thanks

[vocal sleet]

@keen igloo Has your question been resolved?

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[vast shale]

163 ques

Is it 120

[main meadow]

i think 90

[vast shale]

Ok ty

.close

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[runic valve]

can someone explain how you would do question c)

[thorn flax]

A

By that way you get the interest you paid

Wait

[sly sierra]

by that way you get the principal you paid

[thorn flax]

Uhh

[runic valve]

wait what

[thorn flax]

It is a bit harder

You need to calculate how much you pay each month

[runic valve]

bc for b) you have to calculate for like 20 years right

[thorn flax]

Yes

So instalment+ interest x 60
That is the amount you paid

[river kettle]

bungoooo

[thorn flax]

Then you get 425k- answer B

[sly sierra]

hey wb!

[thorn flax]

And then you do
Amountpaid-theothercalculation
That should be it, I think

[runic valve]

ohhh okay

thanks

[sly sierra]

fun fact, before the 2008 crash they were giving out "interest only" mortgages, where you would make payments every month and your balance never went down

[river kettle]

bungo fact of the day!

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@runic valve Has your question been resolved?

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[runic valve]

can someone help pls idk what the diagram is supposed to look like

[fathom perch]

how do you think we should start?

[runic valve]

um so i drew like

the bearing thing

thats it 😭

[fathom perch]

ok so let's take a coordinate system to make this easier

assume yolanda starts at (0,0)

[runic valve]

okay

[fathom perch]

now what's given in the question?

[runic valve]

100km east

is that like a straight line

[fathom perch]

(btw in the coordinate system we're assuming +x is east and +y is north)

[fathom perch]

yes

in the +x dirn

[runic valve]

ok but like i dont get the turning thing

[fathom perch]

ok do you know what bearing means?

[runic valve]

uhhh not rlly

i just know its like

[fathom perch]

bearings are measured clockwise from the north

[runic valve]

okok

[fathom perch]

so now can you tell what 220 degree bearing means?

[runic valve]

uhh

clockwise 220 degrees

[fathom perch]

yes

from?

[runic valve]

okay i know its in like the third quadrant

north

[fathom perch]

correct

just draw a rough diagram no need to measure it accurately

now, do you know what 'second leg' means in the q?

[runic valve]

nope

[fathom perch]

ok so you know what laps are?

like in the races

so a lap is of fixed distance

[runic valve]

uhhh

[fathom perch]

a 'leg' here would also mean the fixed distance given

so yolanda travels 100km again, with a 220 degree bearing

[runic valve]

ohhhhh

[fathom perch]

understand?

[runic valve]

okay kinda

[fathom perch]

cool

[runic valve]

but like

how does it all like connect

into like a triangle or whatever

[fathom perch]

can you show me your diagram so far?

[runic valve]

okok

ok idk if this is right 😭

[fathom perch]

could you recheck the 330?

[runic valve]

okay

wait

where would 330 be

[fathom perch]

also you don't have to draw all the arrows from yolanda's starting location, but it's fine- you can make her travel path parallel to those

[fathom perch]

ok so around a graph how many degrees in total are covered?

[runic valve]

360 right

[fathom perch]

yes

so which quadrant would 330 be?

[runic valve]

would it be like here instead

[fathom perch]

no

[runic valve]

oh 😭

[fathom perch]

the top thing is 360

[runic valve]

ohhh

[fathom perch]

on laptop, so trash drawing lol

so 330 where?

[runic valve]

uhhh

like between

270 and 360

[fathom perch]

yes approximately

more toward the side of 360

[runic valve]

ohh ok

[fathom perch]

can you incorporate that into your diagram

[fathom perch]

yes sure

[runic valve]

okay

[fathom perch]

ok now mark a point (100,0) on the x axis

since that is where yolanda travelled to

[runic valve]

okay

[fathom perch]

ok now draw a line parallel to the 220 degrees line from yolanda's current posn at (100,0)

[runic valve]

ok wait would i be solving for these lines

[fathom perch]

no

[runic valve]

HELP

OKAY

[fathom perch]

i said parallel to the 220 deg bearing

[runic valve]

ok let me try

like this??

[fathom perch]

yes

now extend the 330 degree bearing line to join yolanda's second position

[runic valve]

uhhhh

wait what

[fathom perch]

you see your 330 degree line?

[runic valve]

yeah

[fathom perch]

extend that line to join the line you just made, at its tip

btw this is just a rough diagram for now

[runic valve]

like downwards?

[fathom perch]

youre gonna have to take accurate measurements to get the answers

[fathom perch]

yes

[fathom perch]

yep

thats your triangle

now draw it with measurements

[runic valve]

ohhhh

so like

wait

[fathom perch]

mhm

[runic valve]

but theres like

no other measurements im given

[fathom perch]

you don't need any more measurements

[runic valve]

oh

[fathom perch]

you have two sides of the triangle

and you have all the 3 angles

what more do you need

[runic valve]

okay wait

so i just like calculate

the triangle

[fathom perch]

the area of the triangle

yes

[runic valve]

wait u mean perimeter

[fathom perch]

wait nm

area not asked

yeah perimeter

you dont even need accurate measurements for that

[runic valve]

uhhhh

[fathom perch]

just use law of sines

[runic valve]

wait

but like

how did u get the measurements for the other angles

[fathom perch]

from the bearins

bearings

do you understand?

[runic valve]

ummmm

ok hold on

[fathom perch]

the lines we drew for the sides of the triangle are parallel to our bearing lines

[runic valve]

yeah

[fathom perch]

so their angles with the axes would be the same

[runic valve]

omg

ok yeah i get it now

[fathom perch]

good

now find the 3rd unknown side

and you're good

[runic valve]

wait would the last angle be 110

[fathom perch]

why do you need it

but yes the angle where yolandas second posn is is 110

[runic valve]

OMG

I READ THAT WRONG

[fathom perch]

you are allowed a calculator right?

[runic valve]

ok so i just use like sine law

yeah

[fathom perch]

yeah phew

[fathom perch]

yes

[runic valve]

ok thanks i get it now

[fathom perch]

np

[runic valve]

.close

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[severe stone]

proof:

Let v0, a1,v1, .... , ak,v0 a closed directed walk.
if this walk has no loops, in other words. We dont encouter the same vertex twice. It is already a path. If not let vi be the first time we arrive at such a vertex, let vj be the second time we arrive at that vertex. Remove everything between vi and vj. If this new shorter directed closed walk is has no loop it is a closed cycle. If this is not the case repeat the step.

[paper depot]

why should that process of removing multiply-visited vertices ever come to an end?

[severe stone]

because it is a closed walk

it is finite

[paper depot]

it is finite, and?

[severe stone]

well if it is finite and we keep shortening the walk

[paper depot]

maybe there's a way to like, remove one edge at a time from it forever and ever

[severe stone]

it will eventuallyt stop

[severe stone]

Hm?

[paper depot]

why will it eventually stop just because it's finite?

[severe stone]

because everytime we remove a small loop

the walk will get smaller

[paper depot]

ok but what if the sequence of lengths of intermediate walks is a strictly decreasing infinite sequence

can it be that

[severe stone]

intermediate walks?

[paper depot]

the cut-down walks you obtain at each step of your algorithm

[severe stone]

how can that be a strictly decreasing infinite sequence ;-;

[paper depot]

tell me why it can't

[severe stone]

idk cuz the closed walk is finite ;-:

[paper depot]

do you not have anything like "well-order of natural numbers" on hand

a principle for which one of the formulations is: "there are no infinite strictly decreasing sequences of natural numbers"

[hard atlas]

I assume its obvious enough for this course

[severe stone]

never heard of this before I think

I hope so ;-;

We only use simple graphs

[paper depot]

is it?

[hard atlas]

its obvious in any course that doesnt define N, Z etc from the ground up

I would say

[paper depot]

i think it pays to know how to rigorously prove that an algorithm terminates

[severe stone]

we only have 3 weeks of graph theory

6 lectures

[hard atlas]

this isnt about graph theory

[severe stone]

mb

[hard atlas]

this is about the general principle of a decreasing sequence of natural numbers having to stop at some point

[severe stone]

Aaah

is the proof correct tho?>

<@&286206848099549185>

.close

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[cunning yew]

2,2)

[cunning yew]

cant find 10^-1

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@cunning yew Has your question been resolved?

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[severe stone]

what do I want to do now?

I suppose x4 must enter since we use the smallest index rule

but how do we know who leaves?

.close

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[errant raven]

a guy on this server tried to send me a phishing scheme game

[errant raven]

his username was Jraw

[bronze osprey]

these are the maths help channels bud

you should DM @drowsy igloo

[errant raven]

ah thx

he dmed me through this server tho thats why i asked

[hard atlas]

yes and modmail will let you talk to the mods of this server

[errant raven]

k thx

hes been banned, thx for the help

[bronze osprey]

.close

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[arctic patio]

Need help with mechanics

[arctic patio]

Here’s the answer but I don’t understand

[bronze osprey]

impulse is a vector, not a scalar

[arctic patio]

?

I know

[bronze osprey]

yeah what don't you understand about the solution?

[arctic patio]

Any of it

I=mv-mu

So the mod is it’s components squared and rooted

But where is the 9root2 coming from

[west badge]

is this server also for school child struggling with maths?

[bronze osprey]

okay the diagram goes like this

[bronze osprey]

yes, it's for any level of maths

[west badge]

i am in 10th

[arctic patio]

Icl I don’t get the diagram

I’m also in 10th but I’m so dumb

[bronze osprey]

the resultant vector is in blue

[arctic patio]

That’s the final velocity

[west badge]

how much you got in 9th

[arctic patio]

Then the black is initial?

[bronze osprey]

yep

[arctic patio]

So initial velocity is 9i +0j

[arctic patio]

Can’t remember

[west badge]

are you guys doing maths above 10th

[bronze osprey]

no! the initial velocity is 3

[arctic patio]

Oh yeah my bad

[bronze osprey]

yeah then first find the velocity first, or actually it's better to work with impulses directly as vectors

[arctic patio]

So where does the 9root2 come from

[bronze osprey]

cause you can just do impulse/mass = velocity

[arctic patio]

Mark scheme didn’t do that did it?

Looks like it’s just one step for them

[bronze osprey]

well the horizontal and vertical components of the 9 m/s are 9/sqrt(2) to the right and 9/sqrt(2) up

[arctic patio]

Where’s the root 2 coming from lol

[bronze osprey]

9/sqrt(2) * 2 then

2 is the mass

[bronze osprey]

Pythagoras

you're solving for x^2 + x^2 = 9

[arctic patio]

I thought it was just I=m(v-u)=2(9-3)=2(6)=12

[bronze osprey]

no, because you're completely neglecting the direction of the vectors

[bronze osprey]

this is for when the vectors are on the same straight line, so you can just add and subtract them

[arctic patio]

Ok

[bronze osprey]

this is what I meant when I said this

[arctic patio]

So does u = 3i+0j or not?

[bronze osprey]

it does, the initial velocity is

[arctic patio]

I don’t study physics at all so mechanics is so difficult for me

[bronze osprey]

ah

[arctic patio]

Ok so we don’t know v yet

Lemme draw a diagram real quick

So this is v so I need to work out horizontal and vertical components

[bronze osprey]

no, there is no vertical line

[arctic patio]

9sin45 and 9cos45

[bronze osprey]

but yes

[arctic patio]

So what’s wrong

[bronze osprey]

if you evaluate you get 9 sqrt(2)/2 i + 9 sqrt(2)/2 j

[bronze osprey]

should look like this

[arctic patio]

Mine doesn’t include impulse

Mine is just showing the direction after the impulse with the 45 degree turn

That’s how I’m working out v

[bronze osprey]

okay but you have to be clear that this triangle is not right-angled

[arctic patio]

No it is

[bronze osprey]

oh wait okay I see what you're doing

[bronze osprey]

okay and then the resultant vector of 3i + 0j and another vector is this

[arctic patio]

V=9root2/2i +9root2/2j

Then use the formula ok thanks

I’m so screwed for my exam tomorrow

[bronze osprey]

what formula do you mean? just checking up on you

[arctic patio]

I=mv-mu

[bronze osprey]

no!

again the vectors aren't pointing in the same direction

[arctic patio]

But it still works with directions

You just subtract the matching components

[bronze osprey]

so the red velocity vector must be (9 sqrt(2)/2 - 3) i + 9 sqrt(2)/2 j

[arctic patio]

Then square each component and add

[bronze osprey]

yep

so find the magnitude of the velocity vector

then multiply by the mass = 2 for the impulse

[arctic patio]

So what did I do wrong

[bronze osprey]

what did you do?

[arctic patio]

This and then I square and add no?

[bronze osprey]

ah okay then I see

yeah writing out on paper really helps

[bronze osprey]

yes

[arctic patio]

I didn’t get 14 lol

I got 12.9

[bronze osprey]

it's probably just calculator error then

,calc sqrt((-6 + 9 sqrt(2))^2 + (9 sqrt(2))^2)

[arctic patio]

Ok now I got 14.39…

Is that correct

[twin meteor]

Result:

14.396698762692

[arctic patio]

Ok nice

[bronze osprey]

yep!

[arctic patio]

Thanks for the help bro

Have a good day!

[bronze osprey]

no worries!

[arctic patio]

.close

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[wanton bloom]

This goes on forever.

Find the limit as n->inf
Find a decent approximation of this in terms of n and k.

n is a natural number and so is k.

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[arctic patio]

I think I’ve seen this before, is that answer 0?

Nvm

[edgy kayak]

what is the operation between the terms

- or product?

[edgy kayak]

are u even sure the series converges?

[wanton bloom]

yes, it's given

[edgy kayak]

how did u show that?

!xy

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[wanton bloom]

'tis my own question

[edgy kayak]

😭 then how do u know it converges

[wanton bloom]

Wait

I didn't say it converged

[edgy kayak]

.

[wanton bloom]

My bad.

[edgy kayak]

have u tried writing it in summation notation

[wanton bloom]

By "Find a decent approximation of this in terms of n and k." I mean something like Stirling's approximation.

[edgy kayak]

as in n/k - ∑(sequence)

[wanton bloom]

?

[edgy kayak]

i should start from 1

separate it from n/k because n/k is the only positive term

anyways once u do that, try telescoping it

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[hazy marlin]

how do i describe the lines?

[hazy marlin]

for example, how do i find intercepts based on the vector equation?

[wicked shard]

what are t and s

[hazy marlin]

scalars

?

[wicked shard]

alright

so for a

its just the vector [-2+3] + [t,0]

where t is any number

so what would that represent

[hazy marlin]

uhh

idk

[vast shale]

pls help

[flat whale]

#❓how-to-get-help

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[clear slate]

is this correct

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[dreamy raven]

how come the horizontal compressed is by a factor of 3/pi?

i thought pi/3 was the b value

[flat whale]

,tex .transformation rules

[twin meteor]

riemann

[flat whale]

b = 3/π

[dreamy raven]

this might be the most stupid ass question

but

are all fractions divided by pi under 1

like pi/6

[flat whale]

No

,calc pi/2

[twin meteor]

Result:

1.5707963267949

[flat whale]

Oh no I read that wrong

It is a stretch

[dreamy raven]

ooo okayy

thank you so much!

[flat whale]

I don't know how your teacher defines "stretch factor" or "compression factor"

[dreamy raven]

stretch is anything over 1 while compression is smaller than 1

is how he defines it

i probably worded it wrong tho

sorry 😭

.close

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[jolly obsidian]

hello

[jolly obsidian]

how do i solve this

this is what i got

(1.31233)

which is not exactly 4/3