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[heady badger]

Product of complex number z = a + ib,
a, b ∈ Z, and the complex number w = 5 − 6i is
real number x. find and all values of z.
The result. 5k + 6ki, k ∈ Z.

apparently the result is "all numbers" but I cant find out how that is possible , am I even on the right tracks ?

[ornate bone]

how many permutations are there of the letters in the word RELATIONS, if the vowels must be in alphabetical order

[odd edge]

@heady badger Has your question been resolved?

[heady badger]

I will think about that , rn I got to go tnx

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[soft sand]

What’s the difference between explicit and recursive in pre calc? I searched it up but I think I just need someone to dumb it down for me in a clearer way

[low locust]

explicit: you can calculate the 1000th term directly by plugging 1000 into some formula

recursive: you have to calculate all terms until then step by step

[open onyx]

small technicality, explicit is when you can calculate a_1000 without knowing any of a_0 to a_999

[soft sand]

Hmm ok so So an = a1 + (n - 1)d and an = a1 • r n - 1 are explicit right?

Sorry idk how to do the thing where it shows up correctly formatted😭

[soft sand]

R u familiar with these equations?

[open onyx]

yes, since you can replace a_1 with its value

[soft sand]

What would be an example of recursive?

[open onyx]

here it’s a_n = a_{n-1} + d

if asked for a_1000 you need a_999 which needs a_998 which is why it’s recursive

[soft sand]

Isn’t this explicit? The arithmetic sequence explicit formula I believe

[open onyx]

you can easily construct an explicit formula from it
but in that form it’s recursive

[soft sand]

So recursive u find a term by plugging in the previous term right?

[open onyx]

some previous term, not necessarily the term before

a_n = a_{n-2} + d is also a valid recursive formula

[soft sand]

Ohhh I see

Alr tysm!

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[cyan axle]

I don't understand how II and III are the answer

[cyan axle]

is 9x-12 the equation for f'(x)?

but plugging in 2 gives 6 which is answer for II

[gleaming wharf]

(9x-12)´= 9

9*2-12 = 6

f(0)=-12 is not guaranteed true because we do not know the equation for the line tangent at that point.

[cyan axle]

ohhh

that makes sense, thanks

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[wet forge]

https://media.discordapp.net/attachments/1164318344254590986/1164326054685577256/image.png?ex=6542ce23&is=65305923&hm=61ec7ee08a14a77f94a4626382d10d2ba28b832fcbadc1344d6df037e136e13d&=&width=1059&height=676

[wet forge]

im confused how you could answer this?

isnt it contradictory

and none of these is never the answer for some reason

[static totem]

Q: f' = 0

so not q

P has f' > 0, but f'' < 0

so none of the above

[wet forge]

so f is postion, f' is slope and f'' and conacivity? (position again ig)

[static totem]

f'' is rate of change for slope, you can tell the slope decreases in P

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[lapis helm]

Is this right? and if not, what do i do?

[desert marlin]

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[blissful jolt]

yo @signal halo

[blissful jolt]

ok so this is what froth said

a^(n + m) a^n TIMES a^m

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

but this is telling me otherwise

[void yew]

huh

[blissful jolt]

huh

[void yew]

This is right

[blissful jolt]

so why it doesn't apply here

their adding

[void yew]

For starters do u really mean 2^2(x+1)? Cus that equals 4(x + 1)

[blissful jolt]

2^2^(x+1)

[void yew]

that equals 2^(2(x + 1))

[blissful jolt]

slightly different

[void yew]

Or also, 4^x*4^1

Ur not breaking a^(x +y) = a^x * a^y

U just discovered a new rule

(a^b)^c = a^(bc)

Congrats

[blissful jolt]

ur making me hate math

So much shit

so u got

2^(2x + 2)

now its

2^2x * 2^2

is that RIGHT

[void yew]

2^(2x)*2^2 ye

[blissful jolt]

how do you go there

[void yew]

.

2^(2x) = (2^2)^x = 4^x

and 2^2 = 4 = 4^1

[blissful jolt]

2^(2x)

why isn't this 4x mannn

[void yew]

why would it be

[blissful jolt]

is this a new rule

👼

[void yew]

no

[void yew]

.

[blissful jolt]

damn ok

so products in the power

each are powers of the base

[void yew]

OK so like at least for natural number powers u can reason out this rule

Say m is a natural number like 1,2,3,....

Then a^(nm) = a^(n + n +... + n)

You sum n m times

Which is a^n*a^n*... *a^n, m times

Which by definition

Is (a^n)^m

[blissful jolt]

ok...

what about a^(mnq)

[void yew]

(a^m)^(nq)

or

(a^n)^(mq)

Or even (a^(nm))^q.... hope u get the idea :p

From there I guess u could do

((a^n)^m)^q

[blissful jolt]

So bc the exponents multiply together

it doesn't matter the order u have them

[void yew]

yeah

[blissful jolt]

could you do (a^q)^(nm) though?

[void yew]

Yeah

[blissful jolt]

Ok, I have a separate question

How would you go about getting the cube root of 4096

without a calculator

[void yew]

I guess I'd statt off by finding it's prime factorization

it's 2^12 which I know cus

[void yew]

When I was like 6 my mom kept asking me to do powers of 2 in my head for fun

[blissful jolt]

lol

ok so I didn't show all the powers of 2

but

for cube root you find three numbers that are the same

then you take them out right

but do they have to be prime factors

[void yew]

yeah

nah

[blissful jolt]

ok let's say I take out the first three 4

what happens

[void yew]

Then you have 2*cbrt(512)

[blissful jolt]

but didn't u just find the cube root

[void yew]

oh

I interpreted ur question as "take out the first three two's of the 4 groups of three two's"

[blissful jolt]

no I mean just the first four

ok so

square root 16, find 2 same numbers
4 4

I found 4

why is my answer 4

[void yew]

cus 4^2 = 16

[blissful jolt]

ok

[void yew]

and also it's defined to be the positive solution of x^2 = 16

cus otherwise (-4)^2 works also

[blissful jolt]

for 4096

I take out the first three 4's there

4^3

bu thats not 4096

so that logic doesn't work

[void yew]

yeah

What u have left inside the cube root is 4096/(4^3)

so like

by factoring out 3 4's

You have cbrt(4^3*n)

then

Here is another exponent rule u discovered

$(ab)^c =a^c *b^c$

[clever fjord]

992qqoloy

[void yew]

so $(4^3*n)^{1/3} = (4^3)^{1/3} *n^{1/3}$

[clever fjord]

992qqoloy

[void yew]

And $(4^3)^{1/3} = 4^{3 \cdot 1/3} = 4^1 =4$

[clever fjord]

992qqoloy

[blissful jolt]

now I hate math even more

so what does it even mean to find triplets

[void yew]

[blissful jolt]

in a cube root

you can take it out

like those first three 4's

[void yew]

Cube root of $k$ means to find the real number $x$ such that $x^3 = k$

[clever fjord]

992qqoloy

[void yew]

In general n-th roots of $x$ means to find the (positive if n is even) real number $x$ such that $x^n = k$

[clever fjord]

992qqoloy

[void yew]

For ur purposes, in other words if $n$ is odd just find a number that when raised to the power of $n$ (multiplied by itself n times) equals k

[clever fjord]

992qqoloy

[void yew]

If n is even find the positive number

[blissful jolt]

alright I'll just do that

How long did it take for u to understand this square root and various complex shit?

[void yew]

ider when I learned this anymore tbh

but with me in particular, ngl I've always been good at math 🙃, so I was ahead in math by a few years as a kid. Like my 4 years older sis got jealous once cus I wrote the Roman numerals on her workbook up to 2000, so she erased all my work

She literally went up to my mom like "he shouldn't be learnikng this yet" lmao

[blissful jolt]

lol, nice

mathematicans are a degree smarter than average people ngl

I don't how I'll ever be anywhere as good

[void yew]

honestly math as like a job requires a lot of diff skills from grade school/early college math

Compared to

I mean

Different frkm

like the shit mathematicians do is a lot more like writing English essays

whereas grades school and early college is like learn to apply rules and it helps a lot to be able to do them well in ur head

[blissful jolt]

gotcha

theres just so much fucking rules

[void yew]

So like u might be a lot better at logic and reasoning than doing calculations in ur head and memorizing rules u never prove

at some point u do get around to proving them tho, or at least being able to prove them with enough reading

And that can make it a lot easier to understand

But there is some shit you gotta p much take by faith if you wanna go anywhere in ur lifetime at any level 🙃, I don't really like that part but it is what it is

like for instance there's this theorem called "Fermat's Last Theorem" that's super easy to state, anybody can read it

But it took 300 years to prove

And the proof requires a loooooot of math

So it's better to just believe in it lol

[blissful jolt]

gadamn

humans can be amazing sometimes

its hard to believe someone like a normie can do shit like that

[void yew]

yeah the guy who finally proved it is an unusual example cus he kinda did it in secret in his own time lol

These days mathematicians usually collaborate

but he basically just published enough shit quickly enough to satisfy his job requirements

Then spent the rest of his time working on the proof

For many many years

[blissful jolt]

lmao

I could never

thats what a passion gets you ig

[void yew]

yeeeah

You can probably get ogod enough for almost any job tho

Including any engineering job imo

I think anybody that isn't like, outright impaired can do any engineering thing they want with a reasonable amount of effort . Definitely any undergrad degree in any field incl math, and probably even grad degrees

[blissful jolt]

true, I'm at least better than 75% of students so If I can't do something with my life, then we're all fucked.. LOL
Hopefully AI does not steal jobs when I graduate ...

[void yew]

haha AI is noooooooooot replacing math anytime soon

It sucks so many balls

[blissful jolt]

im in computer science

programming can't be applied anywhere so it would suck

[void yew]

even the math and reasoning required for CS, that's not getting replaced

Like for instance at best chatgpt can build a quick template for code

[blissful jolt]

its honestly very great. People say it just copies what people have said in the internet based on frequency of words or whatever

but it writes shit as if it knows it itself

Hopefully it only being able to copy others is what prevents it from being good though, at least until we get intelligent AI

[void yew]

hmm well at least in math I have only ever seen it be right for like easy numerical calculations

It does write solutions very confidently tho

like I do see people sometimes come here having trouble in trying to understand an answer

Only for me to find out fairly quickly upon skimming it that it's either from chat gpt or some troll used a chat gpt answer to give the answer on some Q&A website

Like it's at least good enough to bamboozle those people tho, ig >. >

But bamboozling people into thinking something wrong is right is not helpful at all lol

The one thing I'll say it's very good at is writing coherent looking text

That's still impressive

[blissful jolt]

Its very good for english I'll give it that

[void yew]

I sux at English so idk what that's it, but I'd imagine professors wouldn't get bamboozled by it

I could totally see it bamboozling gradeschool teachers tho

[blissful jolt]

I like to use it for giving me ideas, comprehend a text, etc

[void yew]

ah kool

[blissful jolt]

writing an essay.. I found its essays to be bad so I haven't bothered

[void yew]

haha

I guess chat gpt is also good as a search engine

well depending on how you want the result to be put

Like if you don't want to see links, just text copied from others. And also if you want it to interpret a query written in natural language, like "what's the best pizza place in Antarctica yo?"

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[fast ivy]

Hello

So i see that the vertex is -2,3

So i have to pick to X number from the left and right

So i chose -3 and -1

When i plug in -1 into the equation

nvm i made a silly mistak

e.close

.clsoe

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[night dagger]

Need some help on this derivative question.

[night dagger]

I have this so far

[mystic saffron]

for f(5) just plug the 5 into the equation

the orginal equation

[night dagger]

I tried doing that and said I got in wrong

[mystic saffron]

Did you plug it in correctly?

[night dagger]

replace the x values with 5 correct?

[mystic saffron]

Correct

I plugged this in my calculator and got 3.524

[night dagger]

I must have entered it in incorrectly

you are right

[mystic saffron]

yeah, it happens sometimes

always the small mistakes

[night dagger]

what about part c?

[mystic saffron]

I was just watching that video lol

[mint mirage]

You already know all the terms, just put it altogether

Using the image I sent

[mystic saffron]

once you find the equation for c

Use 4.95 as the x value

and solve

[night dagger]

I got 3.524−0.449(x−5)

it said correct, I dont think I need to simplify cuz I didnt replace the x

[mystic saffron]

Now you plug in the 4.95

for part d

is what i meant

[night dagger]

yea I got them right

thx sm for the help

[mystic saffron]

np

[night dagger]

I have one question left if you mind helping with that

[mystic saffron]

Sure, send it

[mystic saffron]

ngl I haven't even done this yet

for part a you can use the a.r.c formula?

f(b)-f(a)/b-a maybe

oh you dont have a function

ig u could find the slope first

by using the points (1,120) and (2,198)

[night dagger]

these are the quesitons I submit to online

[mystic saffron]

find the slope first

y2-y1/x2-x1

and plug in (0.6)

[night dagger]

where wold I plug 0.6 into and how do i know the values of y2 and y1 and x2 and x1

[mystic saffron]

use the two points

I gave you

so
(198-120)/(2-1)

= 78

78(0.6)=46.8

try that and see if its correct

[night dagger]

nope

[mystic saffron]

hm

[night dagger]

no worries

thanks for the previous help

.close

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[lethal relic]

How would you solve this

[mystic saffron]

he has given you the solution

all you have to do is develop (x+3)(x+4)x

[lethal relic]

So foil it?

[mystic saffron]

wait no

i'm wrong

[lethal relic]

How did u come up with that equation

Oh

[mystic saffron]

the last one is equal to 20 not 0

[lethal relic]

Ye -2

-20

[mystic saffron]

i think i have found a polynomial that passes these three points

try to consider a polynomial of the form f(x)=ax^2+bx+c

then replace the x with the conditions given in the question and solve the system of equation

[lethal relic]

Wdym

[mystic saffron]

you have f(x)= ax^2+bx+c

id you replace tge x by 0 what do yiu get?

[lethal relic]

Yes but what would I plug

[mystic saffron]

0 -3and -4

you have the value of these from the question

[lethal relic]

yea

Wouldn't I just write it as x^2(x+3)^3(x-4)=-20

[mystic saffron]

i dont think

[lethal relic]

The. How would u write it

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[mystic saffron]

i tryed to solve for it

i got to 7*(4th root of x)-sqrt(x)=12

i don't know where to go from there

I feel like you don't have to solve it to get the sum

i just don't know what to do

if it was cuberoot(x) instead of 4th root of x, the answer would be 0

since it's the sum

Please help me

<@&286206848099549185>

[quasi sparrow]

Try setting t = x^(1/4) and use quadratic formula in t

[odd edge]

@mystic saffron Has your question been resolved?

[mystic saffron]

ok but in that case, there will be an i

right

like the imaginary number

and i don't want to deal with that because it's asking for the sum

unless the number under the sqrt is nonnegative

but thanks for the idea

i'll give it a try

who knows

there might not be an i

[lime root]

idk if there actually will be a complex root since I havent solved this q myself but if a complex number is one of the roots to an equation, its conjugate is also a root

so the imaginary part would cancel out in the sum

[mystic saffron]

ok

thanks

but what's a conjugate

[lime root]

the conjugate of a + ib is a - ib

[mystic saffron]

oh

ok

tysm

[lime root]

np

[mystic saffron]

@quasi sparrow @lime root both helped a lot, tysm

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[wild flax]

HELP

[wild flax]

HELP ME

HELPP

ITS URGENT

HELP ME

PLEAS

[wild flax]

https://www.youtube.com/watch?v=uIV031bnmFA

which one do i use

for that first question in the vid

[mystic saffron]

give a time stamp..

[void yew]

uh

[odd edge]

@wild flax Has your question been resolved?

[wild flax]

fuckin failed it

[odd edge]

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[mystic saffron]

How do you find a square root? I know this is a dumb question but I just never learned and I can’t watch youtube right now and this is kind of my last resort. I never learned how to.
And, I’m not talking numbers like 25. I know how to do that.., but I’m having trouble with ones like 0.35
And just other numbers without the use of a calculator

[mystic saffron]

For me, I tried ignoring the decimal. And I’ve been stressed and I haven’t been able to do basic math. It’s probably real simple

And so I am just trying to think of what the square root of 35 is?

And just how to do other equations as well

I will be sleeping soon, but I will check in the morning, or if someone could send me a dM that would be great

[quasi sparrow]

There are calculus techniques

[mystic saffron]

I haven’t learned calculus yet haha

But, possibly if you explain it I will learn?

[quasi sparrow]

This is a good start
https://www.khanacademy.org/math/ap-calculus-bc/bc-series-new/bc-10-11/v/maclaurin-and-taylor-series-intuition

[lofty spade]

You could learn the long division technique for finding a square root if you really want to do it by hand

[lofty spade]

Or you could start with guess and check

The square root of 36 is 6, and the square root of 25 is 5, so the square root of 35 is between 6 and 5

Then you could calculate the square of 5.8 to narrow it down further

[mystic saffron]

Ah this seems the easiest; thank you so much.. I will definitely look at these other methods to study over the weekend though. Thank you a lot. Do you think you could give me a question that is not a perfect square that I could try out?

[mystic saffron]

Thanks! I’ll check it out

[lofty spade]

Yes, it is the easiest, but also slow and tedious

[lofty spade]

You could try finding the square root of any number that isn't a perfect square, like 2,3,5,6,7,8, and so on

[mystic saffron]

Okay will do. Thanks a lot

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[woven vortex]

How do I go about balancing the chemical equation: C16H10N2O2?

[fair prism]

This is just a chemical, not an equation. What is the other part

[woven vortex]

There’s not anything else to it, I’m wanting to balance it because I need mole ratio

[worthy moat]

You can't balance a chemical

, w C16H10N2O

[clever fjord]

Results provided by WolframAlpha

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

Requested by ericsson6890

[woven vortex]

Oh okay, well I’m needing to calculate the yield percentage (of synthesized indigo) based on 3.95 grams of acetone and 0.5204 grams of 2-nitrobenzaldehyde that were used.

and from what I was told, I’m needing to convert these numbers before I can calculate the % yield?

[odd edge]

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[woven vortex]

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[next granite]

so

For ii

I am stuck

I am using a table

And I'm getting the answer 0.15

I'm using a karnaugh map

[mystic saffron]

i or ii?

[next granite]

ii

[mystic saffron]

wait why do u need a k-map for this

?

[green elm]

does the prime just mean complement?

[next granite]

im learning it and decided to use it on it

[next granite]

yes i think so

should I send a picture of the k-map?

[mystic saffron]

ive never seen anyone use a k-map outside of electrical engineering classes

[green elm]

i mean you're given P(A ∩ B), why can't you find the probability of its complement?

[mystic saffron]

idek how its used for this

[next granite]

I'll send a picture of my k-map. Maybe you can see what I did wrong

[green elm]

i don't know what a k-map is, just pause and think for a moment

if i tell you that the probability of some event is 0.45, what is the probability of its complement?

[mystic saffron]

do u have to solve with a k-map? just draw a venn diagram bro lol

[next granite]

I'm trying to learn the k-map cuz I thought it will be easier for me in future years :/

[mystic saffron]

okay show the k-map

i dont get how its used here

[next granite]

Alright one sec

[mystic saffron]

i used k-maps for circuits and combinational logic when i took EE classes

[mystic saffron]

,rrcw

bro this is not a k-map 💀

[next granite]

oh

it showed that on the title of a video im watching

[mystic saffron]

send the video

[next granite]

https://www.youtube.com/watch?v=YdfFVpeZPlU&list=PLyOCXF304crYx2E07OlOhF8-XyKtDXwRy&index=5

go to the start of video

1 minute 21 sec

[mystic saffron]

idk what this persons talking about

ive never heard anyone say a k-map is a probability table

https://www.youtube.com/watch?app=desktop&v=RO5alU6PpSU

this is a k-map

for circuits and stuff

boolean algebra

[next granite]

oh. So is the video incorrect or smt

And can i still use the table

[mystic saffron]

well its wrong in calling it a k-map

its just a probability table

[next granite]

Do you know what I did wrong in the probability table?

[mystic saffron]

,rrcw

how tf do i rotate it

[next granite]

ill rotate it and send it again

one sec

[mystic saffron]

ok bet

[mystic saffron]

ok

[next granite]

so yeh. I followed the steps in the vid

[mystic saffron]

so the 0.05 shows A intersect B right?

[next granite]

yep

[mystic saffron]

and ur asked to find the complement of (A intersect B)

so u want the complement of 0.05

so

1-0.05?

[next granite]

Oh???

WOW

I was looking at prime A and prime B column

Cuz i thought

The prime thing multiplies

onto both a and b

AHHHH

Understood

Thank you very much

[mystic saffron]

np

[next granite]

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[tame ember]

so if GH is parallel to IL

[tame ember]

in a proof does that create a side or a angle

and where does it create a side on GH or IL?

or both

[void yew]

wat

[tame ember]

He

[void yew]

if GH and IL are parallel then they never meet

[tame ember]

I know but does it create a side or angle

[void yew]

What does that mean

[void yew]

You mean like when you have a transversal between 2 parallel lines?

[tame ember]

Yea

Like does it create side or anagle

[void yew]

That usually gives you places to apply corresponding or alternating angles

[tame ember]

Is corresponding a side

[void yew]

but not much to do with sides

[tame ember]

Oh ok

Where would I place the angle

[void yew]

Well the only transversal is GK

And there's not any immediate alternating angles

[tame ember]

Yea I placed a angle at I

[void yew]

What are you tryna prove in this exercise?

[tame ember]

Nvm it’s good

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[radiant vigil]

answer in the book says k is -17 i can't find where i went wrong someone help

[lofty spade]

for (a)?

[radiant vigil]

yes

[mystic saffron]

Look right to me did you maybe copy the question wrong

[radiant vigil]

yeah thats what i was thinking too

[mystic saffron]

X^3

You put x^2

[radiant vigil]

oh

thanks

xD

[mystic saffron]

Happens

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[wary tapir]

I had a difficulty understanding the step before the answer.

The question is about derivation.

[wooden python]

,rccw

[wary tapir]

Ty.

<@&286206848099549185>

[lilac wharf]

Sur quelle étape plus précisément tu bloques?

Pour passer du deuxième au troisième terme?

[wary tapir]

Oui.

Surtout comment Epsilon just showed up.

[lilac wharf]

C'est le développement limité en x=0 de ln(1+x)

[wary tapir]

Om, i didnt reach that yet in uni. Thanks.

👍

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[tacit vault]

im very confused about how models work

could someone at least give an example of a model and explain why it would be false in the first part of 1

[odd edge]

@tacit vault Has your question been resolved?

[tacit vault]

<@&286206848099549185>

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[royal herald]

i understand the 3/(50 * 50 * 50) cuz 3 ways to get exactly 2 days * probability of it happening

but where does the 49 come from

[mystic saffron]

that solution answers something different than the question

the question gives the probability of the flag being chosen on exactly 2 days, and the question asks for the probability of choosing it on at least 2 days

[royal herald]

wait wait

im sorry

this is the entire thing

[mystic saffron]

regardless, suppose you have three blanks and a choice of 50 characters to fill therein with the condition that two of them have to be the letter a. In how many ways can you do that?

one way is aXa, the other aaX, and the last is Xaa

now, theres 49 choices to put for X if you need a twice

[royal herald]

ah ok

so

3 ways to arrange aa in that 3-letter combo

wait

[mystic saffron]

yes, and then X too has 49 choices to be filled

you can look up the principle of multiplication as well

suppose you have some 50 characters again and now you want to find the number of three letter strings that contain “a” at least once

how’d you do that?

[royal herald]

number of strings with 1 a + number of strings with 2 a's + number of strings with 3 a's

[mystic saffron]

thats accurate

and if the problem were the winconsin flag being selected at least one day, this would have been the answer

[royal herald]

ok i think im starting to understand

thank you @mystic saffron

[mystic saffron]

youre welcome

[royal herald]

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[tulip carbon]

Ok let me explain rq

[nimble lava]

what should we find here

and can u translate

[tulip carbon]

so person 1 frode works with the areal of a fogire frode means that the area of the square abcd with sides (x+3) kan be explained like x^2 + 6x + 9

show here how frode can explain that this is correct

now i did do this in class by my friend next to me explaining it but i dont understand this fully

this is an exam example

[chilly moss]

this is a way to understand why $(x+3)^2 = x^2 + 6x + 9$ geometrically

[clever fjord]

A Note

[tulip carbon]

huh?

i dont understand what the square does at all

forget the 3y and x^2

what is the stuff on the side

[chilly moss]

a square with a side with length of (x+3)

can be seperated into four parts

[tulip carbon]

so on the bottom it is x + 3

and on the blue its x^2 because x*x

[chilly moss]

yes

[tulip carbon]

and the same for all 4

then i just do the math that x^2+6x+9

is the proof that this is correct or?

because i have to prove its right

area off a square is side*side

[chilly moss]

It would be correct if it's supposed to evaluate the understanding of that square

[tulip carbon]

ok now another thing

[chilly moss]

can you translate

[tulip carbon]

shorten the fraction

[chilly moss]

in general, we don't care about a = 0 and b = 0 situation when doing that

because it would be not possible to make a or b zero

this is the conclusion--> so you can divide it by ab

[tulip carbon]

i am confused

i need like step by step explanation like first we do that etc etc

[chilly moss]

1> you cannot divide by zero
so a is not zero, and b is not zero

2> you can divide both numerator and denominator with the same number(if the number is not zero)

$\frac{6a^2b}{15ab^2} = \frac{6a^2b/ab}{15ab^2/ab}$

[clever fjord]

A Note

[tulip carbon]

what does this leave us with

6^2/15^2

[chilly moss]

$\frac{6a^2b}{15ab^2} = \frac{6a^2b/ab}{15ab^2/ab}$ = $\frac{6a}{15b}$

[clever fjord]

A Note

[chilly moss]

and, 6a and 15b are both divisible by 3

so 6a/15b = 2a/5b

[tulip carbon]

but why do we get 6a is it because we have a^2 that ab only removes one ab

[chilly moss]

think of $6a^2b$

[clever fjord]

A Note

[chilly moss]

$a is multiplied two times and b is multiplied one time a^2b$

wait..

i gotta hate this bot

so

dividing by ab means, removing the one time multiplication of a and b each.

[lime root]

$a$ is multiplied two times and $b$ is multiplied one time so $a^2b$

[clever fjord]

nalin

[chilly moss]

so as the result, $a^2b/ab = a$

[clever fjord]

A Note

[lime root]

so as the result, $\frac{a^2b}{ab}$ would result in $a$

[clever fjord]

nalin

[tulip carbon]

because?

a*a+b and we remove ab

[chilly moss]

in math, $ab$ means $a$ x $b$

[clever fjord]

A Note

[chilly moss]

likewise, $a^2b$ means $a$ x $a$ x $b$

[clever fjord]

A Note

[lime root]

likewise, $a^2b$ means $a \cdot a \cdot b$

[clever fjord]

nalin

[tulip carbon]

yeah right because like 2a or 2b

[chilly moss]

to make it even more simple, $\frac{a^2b}{ab}$ = $\frac{a \cdot a \cdot b}{a \cdot b}$ = $a$

[clever fjord]

A Note

[lime root]

nice

[tulip carbon]

but why the fraction removing ab

[chilly moss]

in fraction, you can multiply or divide the same number on numerator and denominator
(with the exception: divide by 0)

[tulip carbon]

is it like a pizza where the pizza is ab/ab which is

[chilly moss]

numerator means the number above the stick in fraction, denominator means the opposite

[tulip carbon]

alright

its correct but not finished if u get what i mean

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[mystic saffron]

Is abcosx + abcosx = to 2abcosx or 2a2bcosx

[mystic saffron]

former

[mystic saffron]

What

2abcosx?

yes

Thanks

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[cold viper]

Hi

[cold viper]

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[obsidian nebula]

Hey

[obsidian nebula]

I am trying to find how long a projectile would take to move through a parabola

I have calculated the angle of launch, the height of launch and initial speed

The angle is 8.468

The height 2.3 meters

[green elm]

do you have an equation for the height vs time?

[obsidian nebula]

And speed 17.88 m/s

No

How do I do that

[green elm]

have you seen such an equation before? looks something like:

$y(t) = y(0) + v(0)t - \frac{1}{2}at^2$

[clever fjord]

Bungo

[green elm]

where y(0) is the initial height, v(0) is the initial vertical velocity, and a is the acceleration due to gravity

[obsidian nebula]

Maybe this

Or nah?

[green elm]

probably that can be derived from the equation i wrote above

but you can also just solve it directly using the equation i gave,

just solve for the time when y(t) = 0

assuming you want the projectile to end up at y=0

[obsidian nebula]

Sure

Thank you

Wait

[green elm]

btw, the formula in your screenshot doesn't appear to involve time, so it could not be used to answer "how long"

[obsidian nebula]

Okk

That one is for maximum range

[green elm]

yea that makes sense

[obsidian nebula]

The one you gave me is a parabola as well

[green elm]

yes, the motion will always be a parabola (assuming there's no air resistance, just gravity)

[obsidian nebula]

X2 is the time

It would take

Is this right?

[green elm]

i don't know, i didn't plug in numbers and solve, how did you get that answer?

[obsidian nebula]

Plugging in the values on the last function

But something I noticed is that it didn’t consider the angle

Angle of launch ***

Is there a function which involves the angle?

[green elm]

in my equation, v(0) is the initial vertical velocity

that will involve the angle

you take the initial total velocity and multiply it by the appropriate trig function of theta

[obsidian nebula]

Ohhh ok

It would be the initial velocity times the sine of the angle right

[green elm]

yes correct

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[mystic saffron]

How do I make 90° triangle I need it to apply sin tg or cos

[noble forge]

Draw a perpendicular from T to UV

[mystic saffron]

yeh

that would make 30 degrees at top

[noble forge]

no

Think carefully. Hint:||Angle sum property||

[mystic saffron]

am i doing it correctly?

[noble forge]

no

Do you understand what I mean by perpendicular?

[mystic saffron]

yeh

like

90 degrees at bottom

wait

[noble forge]

Can you canculate this angle

[mystic saffron]

yeh

oke thats good

what is the blue

degrees

[mystic saffron]

did you put ? thereE?

OWH

I GET IT

thx alot beard guy

how can i be this stupid wtf

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[spiral jetty]

hi, id just like some help/affirmation with a proof question. I struggle a lot figuring out how to deconstruct proof questions and where to start. for this particular question, ive decided to go with a direct proof approach, and will use the red part of the statement to show that the blue part is true hence completing the proof

[spiral jetty]

is this the right approach? my first step that ive taken is to actually write down what it means for c to be a factor of ab

which from my lecture notes ive gathered is that c = q * ab + r

ah but wait im stupid, in this case for c to be the factor, the equation would be ab = c*q, no remainder since it is a factor, right?

[grizzled tide]

what is the hcf

highest common factor?

[spiral jetty]

yeah highest common factor

, im tryna figure the answer out for myself/get close to a solution before the model answers come out, i just always struggle with getting started

the lecturer said that we should try to use bezouts theorem/identity on this question

[odd edge]

@spiral jetty Has your question been resolved?

[spiral jetty]

ye i think i worked out the rest of the proof, key word is think hahaha

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[true fog]

Not sure how to do this

[true fog]

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[jagged maple]

Hi, can someone help me? I have to prove this assertion:

x isn’t an integer => x² isn’t an integer

[jagged maple]

Nevermind

!close

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[lusty hazel]

I need help with why I'm getting a negative answer by doing modular arithmetic here

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@lusty hazel Has your question been resolved?

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[foggy lotus]

What is meant by “decently defined” in the following is that for every x from the definition area, the corresponding y value is actually in the target area.
The SurInBi dance school in Unendlichland (like infinity land) is starting a new dance course. The women and men each receive a number. There is a real number for every one
x ∈ [0;6] a gentleman and for every real number y ∈ [0;5] a queen.
Now the dance course leaders are thinking about how they should put the dance couples together.
Sura suggests allocation according to y=ax(x-6).
How must a be chosen so that the assignment is properly defined and surjective, i.e. every lady is asked to dance?

I have a deadline for this task which ends in 60mins, really appreciate any help.

I tried to find a by putting in x=6 and y=5 but the result is 0...

[low locust]

why do you have a deadline

ah I see. midnight you have to turn it in I assume

[foggy lotus]

yes

[low locust]

11 pm is truly the best time to start with stuff. anyway

what you for example dont want to happen is that you plug x in and get 1000 back

what you should get back should be in [0,5]

[foggy lotus]

yes

[foggy lotus]

we have weekly test and a part is obligatory, the task i am on right now is for bonus points for the exam but i would like to take them with me

it's this task (this is in german) there was another function where you had to find a suitable a, this worked fine: 1/5 is the right answer for a1

[low locust]

have you done the hint and sketched the situation?

[foggy lotus]

yes, with geogebra where i could change the a on a scale

is it right that the graph has to go through the point (5|6)?

[low locust]

no

6 isnt in the codomain

[foggy lotus]

does it have to look something like this, the vertex has to be on y=5?

and the function should go through x=0 and x=6

[low locust]

yes

[foggy lotus]

but how can i find an a that transforms the graph that it fulfills these 3 conditions?

[low locust]

well you know the x value where the vertex is

its in the middle of the roots

[foggy lotus]

ah youre right, i forgot about this.....

its x=3

ok ok

yeah then its y=-9a

its equal to y/-9=a

putting in 5 for y

gives me the a

✅

thank you very much

sometimes you try so hard to find a solution that you overlook the easy steps

[odd edge]

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[wicked folio]

Anyone able to proof read my ()?

I suck major donk at order of operations

I've tried all kinds of different possible

100^2 / 2 * 100 * (120-100)

Like, what is up with this?

[odd edge]

@wicked folio Has your question been resolved?

[wicked folio]

"The arrival rate squared, divded by 2 times the service rate, multiplied by the difference in the service rate and the arrival rate"

Taken from the video lesson

I also looked through the eBook to maybe see if there was a diagram I missed that reveals my missing number

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[tender reef]

can anyone help me understand how to do this as the fractions make me confused

[odd edge]

@tender reef Has your question been resolved?

[quasi sparrow]

What part don't you understand

[tender reef]

here is my working so far but

[tender reef]

how to solve the problem

[quasi sparrow]

Each dive choice is independent

So you just multiply the probabilities

[tender reef]

top x top
bottom x bottom?

for example:

2/5 * 2/5 = 4/25
4/25 * 2/5 = 8/125

[quasi sparrow]

Yup

[tender reef]

it was that simple all along

thanks man

.close

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[desert marlin]

So I've completed the first part about proving that inequality, and I have some ideas for the second part, but it is really quite difficult and I keep getting stuck.

[clever fjord]

Austin

Austin

[desert marlin]

But, I am completely stuck and out of ideas at this point. Don't really see how to use our inequality and what it might tell us as we continue. Any help is appreciated

<@&286206848099549185>

[merry finch]

@desert marlin

coose

[odd edge]

@desert marlin Has your question been resolved?

[odd edge]

@desert marlin Has your question been resolved?

[odd edge]

@desert marlin Has your question been resolved?

[iron bear]

if i rewrite the inequality as
[
\abs {q \sqrt 2 - p} \ge \f 1 {100q}
]
does that make it more clear?

[desert marlin]

No, but, make “what” more clear?

[iron bear]

i'm trying to rewrite it in a form so that it is more clear how you should apply the inequality

[desert marlin]

Okay then no I don’t see how that is more applicable

[iron bear]

okay how about if i rewrite it with different letters

[
\abs {n\sqrt 2 - m} \ge \f 1 {100n}
]

[iron bear]

recall that you are trying to prove something along the lines of
[
\sin(\pi n\sqrt2) \ge \text{something larger than $n^{-5}$}
]

[modern sundial]

I've never seen this problem before but it's a pretty elegant exercise

[desert marlin]

I don’t see anything from the new letters

Especially if n and m integers which they are

[iron bear]

do you have any ideas on how you can bound sin from below?

the problem is how close nsqrt(2) could be to an integer right?

[desert marlin]

Yes basically

Because if it is then we get sin0 basically

Which is not good

[iron bear]

so here, this tells you exactly how close

[desert marlin]

I’ve had that inequality from the very beginning

I just have 0 clue how to use it

[iron bear]

i've rewritten the inequality in a form that makes it more obvious to apply

[desert marlin]

I know you think it is somewhat obvious from your rewrite but it is far from that for me, if I am being honest

[iron bear]

i am just giving you some direction without giving it all away

i can give some more hints

[desert marlin]

Yes please

[iron bear]

essentially the idea is you can extract out the ``integer part'' of $n\sqrt2$ by writing
[
n\sqrt2 = (n\sqrt2 - m) + m,
]
where you can choose $m$ to be the closet integer to $n\sqrt2$

[iron bear]

then, $\sin(n\pi x)$ will ignore the $m$ part

[desert marlin]

We have sin(n sqrt2 pi )

[iron bear]

more specifically,
[
\abs {\sin(\pi n\sqrt2)} = \abs {\sin(\pi(n\sqrt2 - m) + \pi m)} = \abs {\sin(\pi(n\sqrt2 - m))}
]

[iron bear]

imagine $n\sqrt2 - m$ to be quite small, close to $0$

[iron bear]

what would you do here to put a lower bound on the quantity on the RHS

[modern sundial]

Personally the way I see the problem is that your inequality you are given tells you that sqrt(2) can only be approximated by a rational p/q up to an error. That error is very small, so I can use the fact that the argument of sin(x) is very close to 0 to strategically construct an inequality only for the misbehaved parts I care about.

[desert marlin]

If it close to 0, sinx approx x, so our bound can be the nsqrt2-m which we have a lower bound for

[iron bear]

indeed

can you make that lower bound precise?

[desert marlin]

1/100n

In absval

[iron bear]

kind of

im thinking of something like
[
\sin(x) \ge \f {2x} \pi \textqq{for} x \in [0, \tf\pi2]
]

[desert marlin]

How do we know x in that range

And why /pi

[iron bear]

this is the secant line connecting the origin to the first positive vertex on the graph of sin(x)

you use the fact that sin is concave on that interval to construct this lower bound

*and you can assume that $x = \abs {\pi(n\sqrt2 - m)}$ is within that range because you choose m to be the closest integer to $n\sqrt2$

[desert marlin]

So not using sin(x) approx x?

We are using this instead

[iron bear]

well this is not a precise statement

[desert marlin]

Indeed

[iron bear]

it is a statement about the limiting behaviour near 0, but the x we are talking about here is not quite limiting

[desert marlin]

But it is precise that in that interval sin(x)>= 2x/pi

[iron bear]

indeed

[desert marlin]

So what were we doing with this Lower bound again?

[iron bear]

so from this, we can say
[
\abs {\sin(\pi n\sqrt2)} = \abs {\sin(\pi(n\sqrt2 - m))} \ge \f2\pi \pi\abs {n\sqrt2 - m} \ge \f 2 {100n}
]

[desert marlin]

So when dividing by that

The thing we get

Is less than if we instead divided by

2/100n

[iron bear]

yep

[desert marlin]

So then boom

Snow tysm for your help. I wish I was more enthusiastic rn

This problem has exhausted me

[iron bear]

all g

[desert marlin]

Last night me and denasxite were making progress

So I didn’t want to go to bed and miss out on solving it

Because I’ve been stuck all week

But I was up until 4am

And had to quit

[iron bear]

oof

[desert marlin]

And now today been working on it since probably

4/5 hours ago

So it’s just

Killing me

[iron bear]

[desert marlin]

But I appreciate your help a lot

Was simpler than I expected

[iron bear]

np

[desert marlin]

.close

[odd edge]

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