help-0

[thorn heath]

only thing i know so far is that a and b must be a factor of 256

[urban pine]

do you know pascals triangle?

[thorn heath]

yes

a bit

how would i use it

[urban pine]

or maybe i should say binomial theorem

related

[thorn heath]

yaya

this is kinda like working backward from it, and im confused

[urban pine]

https://1.bp.blogspot.com/-xLs3U72NE7E/WD0O8ngcE-I/AAAAAAAACb0/fU1jcuf2GtoQJbb17JK5Lbr_RxbPUOHPACLcB/s1600/The%2BBinomial%2BTheorem.jpg

so we can plug in and see which term

[thorn heath]

wait how

[urban pine]

we'll know the binoms for each since the args are in the exponent

[thorn heath]

args?

[urban pine]

arguments to the binomial function

[thorn heath]

yea idk any more lol

what would be plug in where

[urban pine]

sorry lemme write out what you have already it's really tiny on my screen lol

[thorn heath]

okok sry lol

[urban pine]

(a + b)^8
term 1: 256x^16
term 8: 34992 x^2 y^7

i'm gonna write binomial as C(n, k)

[thorn heath]

okay

[urban pine]

so for term one: that should look like C(8, 0) a^8 b^0 = 256 x^16

[thorn heath]

yes

[urban pine]

b goes away

and we can compute C(8, 0)

[thorn heath]

yes

oh

[urban pine]

so simplified we have?

[thorn heath]

so a would be 2x^2?

nono

[urban pine]

yep!

[thorn heath]

thxx

[urban pine]

now you can do the same for the other term but now we know a as well

[thorn heath]

how would we do be then

oh

ok so wait

8th term is

(2x^2)b

which is also equal to that big number

so do we just solve for b?

[urban pine]

how'd you get this?

[thorn heath]

ab

omg

what am i even doing

ignorrrr

[urban pine]

loool nw

[thorn heath]

8th term is

8C7

times

a x b^7

[urban pine]

yep!

oof that index switch hurts my brain

[thorn heath]

like the format?

[urban pine]

the sigma index starts at zero for the first term

[thorn heath]

oh yea yea

[urban pine]

i would usually say the zeroth term or something lol

[thorn heath]

lol i get it

[urban pine]

well anyways now we can just equate

[thorn heath]

yup

gimme 1 sec

ok so 34992x^2y^7 = ab^7

then 17496y^7=b^7

wait b is a decimal?

[urban pine]

check a again

[thorn heath]

2x^2

it is 2x^2 right

[urban pine]

i mean a is correct but make sure you're subbing correctly

[thorn heath]

oh myb

i divided by acc

wait what

hold on

34992x^2y^7=2x^2b^7

[urban pine]

don't forget the binom on the rhs

[thorn heath]

its just ab^7 right?

2x^2 b^7?

[urban pine]

C(8, 7) = 8

[thorn heath]

ohh

the coefficient right

[urban pine]

yee

[thorn heath]

okok

1 more time

34992x^2y^7=8 (2x^2b^7)

34992x^2y^7= 32x^2b^7

good so far?

[urban pine]

wait 8*2

[thorn heath]

omg

the exponenet looked like coefficient

cant catch a break

[urban pine]

100% understand lmao

[thorn heath]

34992x^2y^7= 16x^2b^7

[urban pine]

yiss

[thorn heath]

then 2187x^2y^7=x^2b^7

okok

cancel out x^2

2187y^7=b^7

b=7y

[urban pine]

niceeeee 🥳

WAIT

no

[thorn heath]

LET SGOO

[urban pine]

party canceled

[thorn heath]

oh damnit

[urban pine]

im so sorry

[thorn heath]

NOOOO

wait i get it

LMAO I TYPED THE WRONG THING

i meant 3y lolol

[urban pine]

YESS

FORE REAL

[thorn heath]

what a rollercoaster damn

[urban pine]

party's back on bb 🥳🥳

aight nj, dinner time for me lol

[thorn heath]

kk

bon appetit and tyty

can i add you?

@urban pine if yes please add me, if not that's okay

.close

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[harsh nimbus]

how would we do this

[tacit arch]

Heat flow isn't a math thing. Show the formula here

Once you look it up you can probably do it

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[open fjord]

so, im working on Statistics and i have to put these numbers into a bar graph but i dont know how to label the bar graph

[remote heron]

its basically asking you to label the axes

[open fjord]

would movie attendance go vertically?

[remote heron]

That's one way to do it, yea

[open fjord]

oh okay, thank you

[remote heron]

the question isnt clear

but one of the would be Attendance (%)

the other should be clear

[open fjord]

its basically label a bar graph, i was stuck on if the age group would be vertical but i guess its not but also this is stats and i dont expect much on this topic

that basically solves my question

thanks

[remote heron]

both styles are fine, i think

thats why its a weird question i think

you obviously see both

maybe the first is more conventional though

[open fjord]

yeah the left one is better

thanks

its the 1st week of school anyways lol

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[restive hearth]

Can someone assist me with the following problems?

[tawny condor]

Do you need to simplify these?

[restive hearth]

Correct

[tawny condor]

Okay, let's start with question 25

What you wrote there is a step in the right direction

Notice that:
$\left(\frac{\sin{x}}{\cos{x}}\right)^{2}=\frac{\sin^2{x}}{\cos^2{x}}$

[ocean seal]

RedstonePlayz09

[tawny condor]

Try using that and simplifying more

[restive hearth]

Yes.

[tawny condor]

also, what u wrote there is missing the x

instead of (sin/cos)

it needs to be

(sinx / cosx)

[restive hearth]

You’d be left with sin^2x and cos^2

Which simplifies to 1.

#24 is a bit more tricky.

How would I go about solving that?

[tawny condor]

Try factoring out the sin(x)

And see if there are any identities u can use afterwards

[restive hearth]

Like so?

[tawny condor]

No,

Remember how to factor:

ab + ac = a(b + c)

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

etc

there is a sin(x) in both terms of the expression

that's why you need to factor out sin(x)

[restive hearth]

Sin x (1-cos^2)

[tawny condor]

Good

Can you see how to continue from here?

[restive hearth]

Don’t think so.

(1-cos^2) can be turned into sin^2

Sin^3x as simplified.

[tawny condor]

yeah

that's it

sin^3(x)

This is the simplest form the expression can take

[restive hearth]

I may need help on a few others so I’ll keep this chat open for few minutes more.

[tawny condor]

Sure

Someone else might need to help you though

[restive hearth]

Sounds good. Thank you for the help. Much appreciated!

[restive hearth]

I don’t think I am doing this correctly.

[tawny condor]

u are almost right

you multiplied sin(k) by 1/sin(k)

and got 1

but then you multiplied sin(k) by - sin(k) and got - sin(k) which isn't right

[restive hearth]

1-sin^2

[tawny condor]

1-sin^2(x)

yes

now continue

[restive hearth]

Cos^2 = 1-sin^2k

[tawny condor]

cos^2**(x)**

yes

[restive hearth]

I see, that cannot be simplified any further?

[tawny condor]

nope

[restive hearth]

(Cos k + Sin K)^2 = 1?

[tawny condor]

open the parenthesis

wait

dont

take the square root

by the way, this is an equation. u have to solve for k here

[restive hearth]

It just states to simplify the expression using trigonometric identities

If you distribute the square root.

That’d be cos^2k + sin k^2.

[tawny condor]

You said = 1

So I thought it was an equation

if you're simplify (cos(k) + sin(k))^2

then you should open the parenthesis

[restive hearth]

Sorry, I was stating that simplified = 1?

[tawny condor]

nope

it doesn't simplify to a constant

[restive hearth]

I’m confused now.

[tawny condor]

(cos(k) + sin(k))^2

= sin^2(k) + cos^2(k) + 2sin(k)cos(k)

continue from here

[restive hearth]

How did you get that?

[tawny condor]

(a + b)^2 = a^2 + 2ab + b^2

(a+b)^2 = (a+b)(a+b) = (a+b)a + (a+b)b = a^2 + ba + ab + b^2 = a^2 + 2ab + b^2

[tawny condor]

you can use this straight away though

[restive hearth]

You lost me on the 2ab + b^2.

I don’t think I have ever seen that.

[tawny condor]

Can someone else help? I have to go

[tawny condor]

@restive hearth it's just a formula, and this is how u "prove" it

(a + b)^2 = a^2 + 2ab + b^2, square of a sum formula

[restive hearth]

Feel free to go!

Thank you for the help.

[lone heart]

@restive hearth Has your question been resolved?

[lone heart]

@restive hearth Has your question been resolved?

[lone heart]

@restive hearth Has your question been resolved?

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[stable night]

hi guys, in dijkstra’s algorithm do i ignore repeated vertices?

[sage violet]

repeated vertices, wdym?

[stable night]

like a - f - e -d - f

at d, i can choose a e f z

do i ignore those that are already chosen

[sage violet]

isn't djikstra's finding the shortest path

[stable night]

yeah

lets say im trying to find shortest path from a - z

[sage violet]

and

you don't repeat a verte when trying to get there in the shortest

possible path

unless there's special conditions such as it not being bidirectional

[stable night]

oh right

one more qn:

what if a-z is 20

wont the algorithm not work

[sage violet]

i mean if it is the hsortest

then it is the shortest

and the algo works

[marsh rapids]

It always works. I'd recommend reading on it a bit more because you look confused

[sage violet]

yep that too ^

[stable night]

but wont the algo go like this: a - f - ... instead of a - z?

[stable night]

ye lol

[sage violet]

no

djikstra's goes everywhere

it tries out everything

[marsh rapids]

Depends on the heuristic

[stable night]

oh wait now that makes more sense

so it tries everything until it reaches z

for every iteration

then it will compare and take the shortest

[sage violet]

im just basing it on my

[marsh rapids]

Not everything. Only the potentially useful things

[sage violet]

cs knowledge on djikstra's

[stable night]

ahh okay i see

wont the time complexity be

really bad tho

since it tries out almost everything

[stable night]

do u know the time complexity of this lol

[sage violet]

O(V^2)

where V is vertices

[stable night]

hm

okay, thx

.close

[lone heart]

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[marsh sonnet]

if f(x+y) = x+f(y) and f(0)=2, so f(2019) =...

[gusty gorge]

f(2019 + 0) = ?

[marsh sonnet]

2019+2?

[gusty gorge]

does that answer your question

[marsh sonnet]

dont know

maybe

[tacit arch]

what are you unsure about

[marsh sonnet]

f(2019)

[tacit arch]

do you know how to simplify 2019 + 0?

[marsh sonnet]

uh

no

[gusty gorge]

,w 2019 + 0

[ocean seal]

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Requested by Saccharine#3780

[marsh sonnet]

so the answer is 2019+2?

[tacit arch]

Do you know how to simplify 2019+2?

[sage violet]

but what if

you do

nvm

it works

[naive valley]

you can get a closed form formula that works for all x by evaluating f(x) = f(x+0) = ...

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[marsh sonnet]

.close

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[supple storm]

Hi I have a very minor doubt regarding this question (I've attached my solution below). In the end, even though the Wavy Curve Method yields an answer [0,1], why is the actual answer to this question [0,1)? Why will we not include the 1?

[naive valley]

,rotate

[supple storm]

My solution:

[naive valley]

,rotate

[naive valley]

well if the range includes 1 that means there has to be an x such that $x^2 + 2x + 1 = x^2 + 2x + 7$

[ocean seal]

Bungo

[naive valley]

what do you get when you simplify that?

[supple storm]

Ah I see (3=9)

So you need to check the end terms?

[naive valley]

i looked at your work, note that you don't actually have a quadratic in x if y=1, because then 1-y = 0

so the rest of the work doesn't apply in that case

[supple storm]

Ohh that's right, I forgot to specify in the initial quadratic equation that y≠1

Thank you!

[naive valley]

so yeah, you can just handle that separately as a special case

[supple storm]

.close

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[gritty slate]

In https://arxiv.org/pdf/quant-ph/0507171.pdf#page=2 , could anyone explain a bit more on SO(4) ?

[tacit arch]

Do you know the definition?

[gritty slate]

nope

[tacit arch]

https://en.m.wikipedia.org/wiki/Rotations_in_4-dimensional_Euclidean_space

Group / Lie Algebra of rotations

https://en.wikipedia.org/wiki/Orthogonal_group#Special_orthogonal_group

Read that first

I don't know what your math background is, but if you're reading that paper without having taken a year of algebra, I don't think you'll have a good time

[lone heart]

@gritty slate Has your question been resolved?

[gritty slate]

you are right, my algebra knowledge is insufficient for these

@tacit arch but let me read these 2 articles first before I come back for more enquiries

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[spice cape]

!claim

[spice cape]

the answer:

my question is, shouldnt the angle of depression from the balloon to the park be like this:

?

[candid dagger]

Same thing

[gray isle]

the angle of dep from the balloon to the park is equal to the angle of elev from the park to the balloon,
they'll both be 60°

[spice cape]

but then according to my diagram, to find the height wouldnt the answer be 1.2/tan30?

[candid dagger]

Actually, same thing

[gray isle]

wait, misread that

yeh same thing

[spice cape]

wdym same thing

my diagram is the same?

[gray isle]

you diagram explicitly shows the angle of depression

[spice cape]

correct

[gray isle]

,W 1.2tan(60deg) = 1.2/tan(30deg)

[ocean seal]

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[spice cape]

oh so i was right?

but we just did it a different way

cheers

.close

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[unkempt wolf]

Help

[unkempt wolf]

Tysm

I found it

.close

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[alpine sable]

Hello, could you give me advice on how to solve it ? it is not graded this an excercise in an edexcel book

[alpine sable]

this is the information i have to work with

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

i found the soultion but the beginning doesn't make sense to me beacuse PS is (ae-ae) and (0 - y)

[fluid eagle]

i barely know anything about ellipses so i just googled what eccentricity is, but if you let PS = 2 and PS' = 4 without loss of generality then AS+AS'=PS+PS' allows you to calculate AS=AS' and furthermore you can calculate SM so also AM, so you can get both a and b by their geometric definition

i wasn't able to understand the solution you posted either sadly because i just don't know all the algebraic stuff about ellipses

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[alpine sable]

.close

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[silver walrus]

I’m trying to find a formula to find the possibility of winning the lottery (not for irl lol):

Thé only information I’ve gotten is that there are 45 different numbers and I can only choose 7.

[languid bolt]

ok so

what is the possibility that you get the first number right?

[silver walrus]

1 out of 45

[languid bolt]

so basically 1/45

so you have to do that seven times

so

1/45 * 1/45 * 1/45 ..... * 1/45

7 times

wait.. im giving the answer and not guiding

f

just realized

[sage violet]

f

[gray isle]

the wrong answer too

[sage violet]

fine

[languid bolt]

wait why

[sage violet]

LOL

[languid bolt]

wait why ramonov

[sage violet]

you can choose 7

numbers

right

[languid bolt]

ohhh

i thought it meant you need to choose 7 correct numbers

[silver walrus]

Yeah

[gray isle]

without replacement

[silver walrus]

7 correct numbers

[languid bolt]

wait what

so... is my answer correct?

[gray isle]

there are only 44 options left after the first number

[silver walrus]

You need to find a combination of 7 right numbers to win

[languid bolt]

why

doesnt say without replacement

[gray isle]

it's a lottery

do you know how standard lottos work

[languid bolt]

of course

not

never tried one

[supple storm]

There will be 2⁴⁵ possibilities if math serves me right

[gray isle]

it does not

[supple storm]

no wait that's the formula for all subsets...

[silver walrus]

You guys are starting to confuse me

[languid bolt]

Me too

I thought lottos were just guessing numbers

[supple storm]

So there are 7 digits in the lotto, correct?

[languid bolt]

no

[supple storm]

therefore each digit can range from 0-9

then what

[languid bolt]

45 different numbers bro

[supple storm]

one or two digit?

[gray isle]

45C7 will get you the number of combinations

[supple storm]

permutations and combinations

yeah that'll do it

[gray isle]

if you need all 7 numbers to win,
it'll be 1 over that

[languid bolt]

does the arrangement matter in a standard lotto btw

[silver walrus]

What does the C stand for

[supple storm]

combination

[gray isle]

combination, choose

[candid dagger]

Not choose?

Oh k

[gray isle]

choose more common and what's said when reading allowed

[silver walrus]

Alright thx everyone

.close

[lone heart]

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[hazy violet]

Derivative of y= [x+root of (x^2-a^2)]^n

[hazy violet]

wrt x

[desert tendon]

chain rule

[sage violet]

in other words, you want

$\frac{dy}{dx}((x + \sqrt{x^2 - a^2})^n)$

[ocean seal]

Not Trout -_-

[sage violet]

chain rule

[hazy violet]

yess

[hazy violet]

use tht twice right ?

[desert tendon]

yes

[hazy violet]

im stuck at the part of finding derivative of root of x^2- a^2

[sage violet]

factor it i guess

[hazy violet]

sqrt{x^2 - a^2}

[sage violet]

then chain rule again

[hazy violet]

can you jus do tht part alone

plz

[sage violet]

i think a^2 is a constant

or at least treat it was one

[hazy violet]

OK.

[lone heart]

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[gray falcon]

Tax on income is paid as follows: 23% on the first €100 earned and 42% on the remainder.
Calculate what the person’s gross pay and their net-pay and total tax deducted.
What steps do I have to do to do this?

[alpine sable]

I think we need more info, like their pay

unless you are being asked to create a piecewise function what works for anyone

[gray falcon]

€1,043

unless you are being asked to create a piecewise function what works for anyone
yeah, that is what i was asked to do but i'd rather figure out that part myself the €1,043 number should be fine for this I think

[alpine sable]

first, split 1043 into two parts. The part taxable at 23%, and the part taxable at 42%. Then calculate the tax deducted for both brackets. Then find the net pay by subtracting

once you work out a few examples, the piecewise function should become more intuitive

[lone heart]

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[vale wigeon]

there are three possibilities for which vertex is opposite to the missing vertex

depending on your choice of which vector plays which role, this should give you all three values.

[lone heart]

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[alpine sable]

\

[alpine sable]

racking up my brain , not able to get anywhere with this

what are you trying to do?

[alpine sable]

well the relation between 1993 and 84601 is same as 2017 and the number which is in the options . we have to use the relation between 2016 and 927 as the reference and solve it

so the double colon doesnt mean anything special?

https://www.desmos.com/calculator/irvugxqmou

I get -2711

[lone heart]

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[true skiff]

I am not sure about what the question is asking
what i understand so far is that it's asking me to divide the given polynomial by the given quadratic and give the quotient and remainder
now i tried a particular example and i can obtain the coefficients by matching coefficient on both sides it gives me a triangular system in that case
but what does it mean by deriving a method that uses nested multiplication
i know that it has something to do with Horner's method but that's all

[true skiff]

Btw this is a question from an Oxford course( available on the website i am just doing this to improve my understanding)

[tacit arch]

is this real analysis?

[true skiff]

this is constructive math

[tacit arch]

https://plato.stanford.edu/entries/mathematics-constructive/ ?

a little bit of real analysis

[true skiff]

This is the link where i got it from https://courses-archive.maths.ox.ac.uk/node/37565

[tacit arch]

oh more numerical analysis

[true skiff]

yeah just numerical analysis

[lone heart]

@true skiff Has your question been resolved?

[true skiff]

@lone heart No

[lone heart]

@true skiff Has your question been resolved?

[lone heart]

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[mortal acorn]

.help

[lone heart]

Commands:
clopen: .close, .reopen
factoids: .tag
help: .help

Type .help <command name> for more info on a command.

[mortal acorn]

Oh

[mortal acorn]

Me so

Mk so

[lone heart]

No command called ".tag" found.

[keen pasture]

.help tag

[lone heart]

Usage: .tag ...
Manage factoids.
Sub-commands:
.tag add <name>
.tag alias <name> <newname>
.tag delete <name>
.tag edit <name>
.tag info <name>
.tag top
.tag unalias <name>

Type .help tag <sub-command name> for more info on a sub-command.

[trim wagon]

What’s that 👀

[mortal acorn]

Say there are 20 strings and one of the strings are connected to a hidden piece of candy. You have a 1/20 chance of pulling the right string. Every time you pull the wrong string however, you have less options for the right string, leading for a higher chance of pulling the candy (1/20 -> 1/19). What are the chances of pulling the string with the candy in 5 tries

I hope that made sense

[lone heart]

@mortal acorn Has your question been resolved?

[slow hound]

is it within 5 tries

or exactly 5 tries

[mortal acorn]

Exactly 5

[slow hound]

right, then we cannot get on the first try

the probability of that is 19/20

we cant get it on the 2nd try either, the probability is 18/19 from there

and so on till the fifth try, where we have a 1/16 chance of getting it

[mortal acorn]

Do you just multiply the probabilities?

[slow hound]

im 95% sure, gimme a minute to make it 100%

[mortal acorn]

Aight

[slow hound]

yeah it makes sense

i just wanted to make sure i wasnt screwing anything up

multiplication principle of counting applies here

[mortal acorn]

Alr Ty

[lone heart]

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[minor wraith]

A line which passes through the point (3,4) intersects the coordinate axes in different points forming a right triangle. Find the area of the smallest triangle ?

[tacit arch]

do you know pythagorean triples?

[minor wraith]

yes ı know

I need to solve it as an optimization problem.

[tacit arch]

so you can't use pythagorean triples information?

[marsh rapids]

Why would information about integers be useful for this ?

[weary wyvern]

What triangle is being talked about exactly

[tacit arch]

(3, 4) and drop perpendicular line to x-axis

[marsh rapids]

No

[weary wyvern]

Just make the line go through (3,0)?

[marsh rapids]

But it doesn't make a triangle

[tacit arch]

oh damn i assumed it went through the origin

[minor wraith]

this problem calculus 1 maximum-minimum problema

[weary wyvern]

Yea we know

[marsh rapids]

Yes

[minor wraith]

🙂

[marsh rapids]

Just find the coordinates of the intercepts, find the area as b*h/2 and minimize

[minor wraith]

ı have answer but ı cant solve

[marsh rapids]

Should be a quadratic I think

[tacit arch]

ah yea okay i didn't understand the problem at all

[marsh rapids]

Which is very easy to minimize

[tacit arch]

so you have something like y = mx + b and goes through (3,4) and b > 0 ?

[weary wyvern]

Genuinely can't see how the area can't be arbitrarily small, assuming it can't be zero

[marsh rapids]

Yeah b <= 0 would be weird

[tacit arch]

the x and y intercepts have to be > 0

or m < 0 probably

[weary wyvern]

Ah yes m<0

[marsh rapids]

It contains the square of area 12

[minor wraith]

Does (3,4) have to be a vertex or a point on the edge?

[weary wyvern]

Origin and intercepts form the the triangle presumably

[tacit arch]

definitely not a vertex

[weary wyvern]

Should be mentioned in the question, we can't tell you

[minor wraith]

yes ı think so , but answer is 24 (?)

[marsh rapids]

Like this

[tacit arch]

thank you i was too lazy to do this

[tacit arch]

@minor wraith find the x and y intercepts as a function of one variable using this

[minor wraith]

so is this triangle (0,8), (0,0) , (6,0)

[minor wraith]

maybe

[tacit arch]

show your work

[minor wraith]

sure just a second

[marsh rapids]

12 + 3h/2 + 4(3*h/4)/2 I think

,w minimize 12+3h/2 + 4(3h/4)/2

[ocean seal]

Results provided by WolframAlpha

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

Requested by themateo713#5303

[marsh rapids]

Ok nvm

,w minimize 12+3h/2 + 4(12/h)/2

[ocean seal]

Results provided by WolframAlpha

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

Requested by themateo713#5303

[marsh rapids]

Haha

[tacit arch]

look at this cheater

[marsh rapids]

Just checking

[tacit arch]

24 / 3 / 4 /2 = 1

quick maffs

[worn fox]

No global min? Eh

[marsh rapids]

Probably for h < 0

[worn fox]

Aha

[true skiff]

<@&286206848099549185>

[tacit arch]

your channel got reset. gotta open a new channel and reset your timer

[worn fox]

.

[marsh rapids]

Because h < 0

[tacit arch]

what even is h in the triangle

[worn fox]

Your h must be bigger than 0 if you want a local min

[marsh rapids]

This

[tacit arch]

oh that makes sense

[worn fox]

Ah I would have parameterised by gradient of line

[tacit arch]

h< 0 makes m > 0 so triangle gets giant

[marsh rapids]

Was checking my answer before explaining it

[marsh rapids]

The sum is square + upper triangle + triangle on the right

[tacit arch]

i do this by default haha

[minor wraith]

xd

[minor wraith]

why ?

[marsh rapids]

The last term comes from the triangles being similar

[marsh rapids]

That formula is wrong because I had h the wrong way in the proportionality

[tacit arch]

this doesn't show how you got your answer

[marsh rapids]

It's my h=4 value

But yes unexplained

Basically because WA said it's the min

But hey finding the min shouldn't be that hard

[tacit arch]

it's a few steps. find intercepts as a function of a variable, get area of triangle, differentiate and set to zero, solve

i'm exhausted just typing it

[minor wraith]

ı cant solve :/

[marsh rapids]

My idea of using h skips step 1

Though I think it makes the minimization part harder

[marsh rapids]

Because this

[plucky geyser]

We only have one point. Is this enough for us to find the function?

[marsh rapids]

Yes. We already solved the problem don't worry

[plucky geyser]

I was very worried. this put me at ease

[marsh rapids]

Such a gentlemen

[plucky geyser]

I just wanna say thank you, it's me you know

[marsh rapids]

A very cool ppl yes

[plucky geyser]

I was afraid you wouldn't notice that

but you did!

[minor wraith]

thx guys ı solve

.close

[lone heart]

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[agile skiff]

So i found this in a server discord and i want to know what this fuction mean

[mortal trellis]

do we get context?

that shit could mean a lot

[agile skiff]

Unfortunately not

But if i have to guess

Thé man who post it is a Minecraft modder that develop a mod that Can Do thing liké this

[worn fox]

There's next to no way to figure out what exactly this is for

[zealous crane]

it's a bunch of undefined symbols, so we have no clue since we have no starting point

[agile skiff]

Oh

I see

[tacit arch]

go ask the modder

[zealous crane]

regardless i don't think such a complex equation would be used for the much simpler things in the video

it's probably something else

[agile skiff]

Its not simple at all

[zealous crane]

what's being shown

the lever? the spinning windmill?

[agile skiff]

No

Its moving

Everything you sée is in a contraption that move

[zealous crane]

Oh, the whole island/house thing is moving?

[agile skiff]

Yes

It add physic to minecraft

Thé mod hé develop

[zealous crane]

yeah, you should ask him if you want to know more

[agile skiff]

Thé problem is

Hé keep it secret

But hé give this

[tacit arch]

i guarantee no helper is gonna read all that to help you just for a minecraft game

[worn fox]

He gave you some random desmos graphs lol?

[agile skiff]

No its in a conversation with a otjer user

[zealous crane]

it's like saying solve x, y, and z for x + y - z = 3

can you do that?

[worn fox]

Okay well if that conversation doesn't shed any light then you're all out of luck

What's your end goal here?

[tacit arch]

LOL

[agile skiff]

Thé user one Said "you are thé incarnation of 100 Bad déveloper" and hé répond "did you think that 100 Bad dev Can Do this ?"

[zealous crane]

tldr: we can't help you because we have no clue

[tacit arch]

yea this is an absolute waste of time

[agile skiff]

And hé post it

[zealous crane]

like i said, we have no clue

[agile skiff]

Yes i Can understand

[zealous crane]

say .close if you understand

[agile skiff]

.close

[lone heart]

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[alpine sable]

lim x->((1 x^(2) - 4x + 3))/(x-1)

[violet bear]

factor the numerator and cancel the like terms

[marsh rapids]

Notice that 1 is a root of the numerator

[alpine sable]

lol i meant x-> 1

lim x -> 1 (x * x - 4x + 3 ) / x - 1 = lim x-> 1 (-5x + 3 )/-1 = lim x->1 = -2

[lone heart]

@alpine sable Has your question been resolved?

[marsh rapids]

Obviously. That's the only limit that isn't trivial (all the other ones are found by continuity, i.e. plugging in)

[marsh rapids]

3 is the other root 3, not 5/3

[alpine sable]

ok i found it (-3x + 3) / - 1 and this evaluate 0/-1

[marsh rapids]

It is -2

[marsh rapids]

By factoring like you did, or by l'hospital's rule

Although the factorization was wrong lmao

[alpine sable]

yes sir i was suppose to wright x^2 -4x + 3 in the form of (x-3)(x-1)

[marsh rapids]

Don't know how you get (-5x+3) yeah

[alpine sable]

a mistake in the calculation it's suppose to be -3x+3

but it's also wrong

[marsh rapids]

Yeah because it should be (x-3)

Because 3 is a root

[marsh rapids]

Are you trying to do polynomial division ? That you made a mistake twice ?

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

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[alpine sable]

use the substitution u=x^2y^2

[hexed pond]

does this suffice or am i thinking about the partial wrong

[mortal trellis]

don't forget that you could also add g(y) to the function for some function g

[hexed pond]

so +g(y)+C?

[mortal trellis]

yeah. or combine the g(y) and the +C into one function

you could think of it as C=C(y) a constant depending on y

[hexed pond]

right, do i do the same direct integral with respect to y for the general solution or do i leave it as that

oh nvm i read the question wrong thanks

appreciate the help

.close

[lone heart]

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[frosty lark]

Hello can someone help me with proving this I see it’s correct but don’t know how to prove

[heady pollen]

if $A-(B \cup C)=\emptyset$

[ocean seal]

~Martin

[heady pollen]

then $A=B \cup C$

[ocean seal]

~Martin

[frosty lark]

Interesting

[heady pollen]

im just thinking out loud btw

[naive valley]

that's not true, you can only conclude that $A \subseteq B \cup C$, the right hand side could be strictly larger

[ocean seal]

Bungo

[frosty lark]

Oh yes no equal

[heady pollen]

what do you mean with strictly larger?
i cant think of an example where A is not equal to the union of B and C

[frosty lark]

A{1} B{1,}C{2}

A!=BUC

[copper stone]

yeah bungo is right

[frosty lark]

Is this good?

,rotate

[copper stone]

thats the idea but its not very formal

[frosty lark]

Okay what should I adjust I know I missed all the assumptions I just wanted to write down what I was thinking could work

I’d still have to start with assume that a b c are sets and whatever and assume a-buc =empty set and say we want to prove a-b is a subset of c

And I’d have to say since a-buc is a subset of the empty set than a is a subset of buc

Anything else

[copper stone]

yeah

okay i'll write down something for u

you see if you're fine with it

Suppose A-(BuC) = ø.
Let x ∈ A-B. Then x ∈ AnB'.
x∈A so x∈BuC (by assumption, since A is a subset of BuC) and x∈B'.
So x∈(BuC)nB' = BnB' u CnB' ⊆ C
so x ∈ C @frosty lark

i noted B' for B with a bar on top of it

[lone heart]

@frosty lark Has your question been resolved?

[frosty lark]

Sorry for late reply the ‘ means compliment right?

We haven’t had that in this class I know what it means but we have formally been taught it

[copper stone]

so you havent seen the notation x ∉ A => x ∈ Ā ?

[frosty lark]

No unfortunately

[copper stone]

Suppose A-(BuC) = ø.
Then A ⊆ BuC so A-B ⊆ BuC - B ⊆ C

[frosty lark]

Okay I see I see

[alpine sable]

have you solved it yet?

you can use contradiction easily

[lone heart]

@frosty lark Has your question been resolved?

[frosty lark]

I did one way I think worked how would you do contradiction?

[alpine sable]

suppose $x\notin C$ then $x\notin B\cup C$ but then $A\setminus (B\cup C)\neq\emptyset$

[ocean seal]

jswatj

[frosty lark]

A bit confused with this sorry

Could you expand on it a tad

[alpine sable]

So

the goal is to show a subset

so we assume $x\in A\setminus B$ right?

[ocean seal]

jswatj

[alpine sable]

that means $x\in A$ and $x\notin B$

[ocean seal]

jswatj

[alpine sable]

following?

[frosty lark]

Yup

[alpine sable]

okay

for contradiction we suppose the opposite, that $x\notin C$ (which is what we want to show)

[ocean seal]

jswatj

[alpine sable]

notice that $x\notin B$ and $x\notin C$ thus $x\notin B\cup C$ by demorgans law

[ocean seal]

jswatj

[alpine sable]

since $x\in A$ then $x\in A\setminus B\cup C$ which we assumed to be impossible

[ocean seal]

jswatj

[frosty lark]

Okay so that would mean there are elements of a for a-buc

So it wouldn’t be empty

And that contradicts our assumption

[lone heart]

@frosty lark Has your question been resolved?

[lone heart]

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[solid island]

what expression a 5/2 is equal to as long as A > 0

[wary stream]

Use that

[solid island]

so its either 1 or 2

but A is > to 0

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@solid island Has your question been resolved?

[lone heart]

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[alpine sable]

This is confusing me. How does 10 go into 1 0.1 times when 10 is way bigger

[wary stream]

Because it's one divided by ten

[last ether]

1/10 := 0.1

Lol

[wary stream]

It's parts out of a whole

For example, you cut something into 10 parts, you just take 1. That one piece you took, is smaller

[alpine sable]

But why is it 1 when you flip it around

[last ether]

Because you're taking 1 whole part out of 10

[alpine sable]

I mean 10

[last ether]

1 whole of 10 is 10

[wary stream]

Because you have ten divided by 1 vs 1 divided by ten

[last ether]

It's basically division

[alpine sable]

So 1/10 is 1 pizza 10 parts

1 piece out of 10

[wary stream]

Sure

[alpine sable]

Ffs why do I keep thinking it other way round

[last ether]

Top/Bottom = Top divided by Bottom

[alpine sable]

When you use modulo it’s other way round

[fierce prairie]

wdym other way round

[wary stream]

Hold up, you get confused with division, but you know modulo?

[last ether]

Modulo is finding the remainder

1mod10 is 1

10mod1 is 0

[alpine sable]

6%2 how many times 2 go into 6 = 0

[fierce prairie]

I recommend learning division before modulo

[last ether]

Yeah because

Modulo is simply just finding the remainder

As a result of division

[alpine sable]

Ok thanks I forgot!

I used modulo when making. Chess board

That’s only reason I know it l o l

[last ether]

Why would there be a modulo when making a chess board hmm

Hmmmm

Maybe the tiles

[alpine sable]

Yeah

[fallen verge]

what

is it to check for bishops or smthn

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[zenith birch]

how should i do b?
I think it's 0 but i dont know the right steps

[pure bolt]

you want to prove it or just use properties of limits?

if its just properties you can split the limit of a product into the product of two limits

limit of x times the limit of f(x)

[zenith birch]

just using the properties

[pure bolt]

yeah so then we get 4 times 0 which is 0

[zenith birch]

woah where did the 4 come from

[pure bolt]

oh cuz x is approaching 4

limit of x as x is approaching 4

is just 4

[zenith birch]

what about c, i got 3g for that

[pure bolt]

the answer should be a number not a function

this might help

[zenith birch]

what rule was used to get limit of x approaching 4

=4

[pure bolt]

its a technique called direct substitution

we just substitute the number x is approaching into the limit

[zenith birch]

hmm

so 4 would go into the function?

ohh nvm i get it

@pure bolt thank you

[pure bolt]

yea so we could substitute 4 into every x we see

[pure bolt]

we already know the function limits which are given in the question

[zenith birch]

what i just worked out in my head is on the equation y=x, at 4 the limit is 4

is that basically what is happening

so c would be 12

[pure bolt]

i get whats confusing you

$g^2(x)=(g(x))^2$

[ocean seal]

versbtm

[zenith birch]

9

[pure bolt]

yep

[zenith birch]

so just stupid algebra that i forgot

lol

[pure bolt]

yeah its just notation

[zenith birch]

thank you so much
have a good day

.close

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[earnest holly]

i gpt the first step

but how do u get to the next?

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[gritty verge]

Hi

[gritty verge]

I got a quick question

Okay so basically I need to solve this

Part a

I’m not sure how to exactly start it off

[real gazelle]

,rotate

[real gazelle]

by first principles do they mean using a limit?

or by using product rule

[gritty verge]

Limit is the and 7

I kind solved it but not sure if it the right way

[real gazelle]

okay can you show your work

and I can look through it!

[gritty verge]

Alright one second

Sorry for the bad handwriting

[real gazelle]

whattt your handwriting is so neat lol

yeah that's correct

[gritty verge]

Haha legit thanks lol

Ooh okay ty!

[real gazelle]

yep, good job :D

[gritty verge]

Haha ty

How do u simplify square root t plus h whole thing - square root t

My Math has died

[tacit arch]

Multiply by conjugate?

[gritty verge]

What’s conjugate o.0

Riemann sums lol nice name

[real gazelle]

Haha

Conjugate just means you switch the + to a - or the - to a +

like for example

$$\sqrt{t+h} - \sqrt{t}$$

[ocean seal]

Eric Tao (he/him)

[real gazelle]

the conjugate would be $$\sqrt{t+h} + \sqrt{t}$$

[ocean seal]

Eric Tao (he/him)

[real gazelle]

and then you can use the nice difference of squares identity :)

[gritty verge]

Ooh

I see

Lemme try that

[tacit arch]

Multiply top and bottom I should have said

You don't want to go changing the problem

[lone heart]

@gritty verge Has your question been resolved?

[gritty verge]

I got stuck at the end lol any tips?

My brain is literally fried atm

<@&286206848099549185>

[lone heart]

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[gritty verge]

.reopen

[lone heart]

✅

[gritty verge]

Help pls oof??

Oops I realised last line

Is wrong

But how to solve lol

<@&286206848099549185>

I’m sorry I’m a little bad with math atm haha

[oak perch]

$\frac{\sqrt{t+h}-\sqrt{t}}{h}=\frac{1}{\sqrt{t+h}+\sqrt{t}}$

[ocean seal]

Cogwheels of the mind

[gritty verge]

Oh i solved that

Try tho! Wait i need help with this lemmesend again

The last line is wrong tho

[subtle mango]

$\frac{s}{s^2-1}=\frac{1}{2}(\frac{1}{s-1}+\frac{1}{s+1})$

[ocean seal]

JellyShark

[subtle mango]

It’s easier to differentiate 1/s-1 and 1/s+1 respectively

[gritty verge]

Hmm but then i have to use limits?

To solve it

I keep getting stuck lol

<@&286206848099549185>

Guys help please I stuck

I’m stuck at this for a while

[subtle mango]

Calculate 2 fractions respectively

[gritty verge]

Oh wow

May I ask how u got that 0.5 out

[subtle mango]

$\frac{1}{s-1}+\frac{1}{s+1}=\frac{s+1+s-1}{s^2-1}=\frac{2s}{s^2-1}$

[ocean seal]

JellyShark

[gritty verge]

Oooo Kok

Ok!

Im stuck at the calculate 2 fractions lol

My math is damn bad

<@&286206848099549185>

Btw its at s = 4

Sorry s=2 i mean

[iron mulch]

Do you need to use first principals?

[gritty verge]

Yep!

[iron mulch]

Also shouldn’t you be factoring out a 2? Not 1/2?