help-0

[terse cradle]

somewhat tbh I struggle hard to learn by text, could u do the working out for the question by steps then I will be able to learn it I work different

[ocean seal]

Chai T. Rex

[terse cradle]

ok i get that

[oak chasm]

Do you remember PEMDAS or BODMAS?

[terse cradle]

Yeah like order of operations etc

Its been a while tho

[ocean seal]

Chai T. Rex

[terse cradle]

btw putting everything into the bot is way better for me

[oak chasm]

Oh, OK.

So, the last thing we do on the left is multiply the 2.

The last thing we do is important here.

So, what's the opposite of multiplying?

[terse cradle]

/

[oak chasm]

Right, so we divide both sides by 2.

Since the last thing is multiplying by 2.

We do the opposite with the 2.

[ocean seal]

Chai T. Rex

[oak chasm]

See how x is closer to being by itself?

[terse cradle]

yep

[oak chasm]

OK, now we do the same thing.

[ocean seal]

Chai T. Rex

[oak chasm]

We square it, and that's it.

So, squaring is the last step.

What's the opposite of squaring?

[terse cradle]

square root?

[oak chasm]

Right.

[ocean seal]

Chai T. Rex

[oak chasm]

See how we got even closer to x by itself?

We got all the way there.

[terse cradle]

yep

[oak chasm]

So, that's how you do a lot of algebra solving.

You get all the xs on one side.

You figure out the last thing you do to calculate it.

You do the opposite to both sides.

[terse cradle]

so we get 12.7

[oak chasm]

,calc sqrt(18^2/2)

[ocean seal]

Result:

12.727922061358

[oak chasm]

Looks good.

,w x^2 + x^2 = 18^2

[ocean seal]

Results provided by WolframAlpha

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

Requested by Chai T. Rex#7323

[oak chasm]

,calc 9 sqrt(2)

[ocean seal]

Result:

12.727922061358

[oak chasm]

Yep, looks good.

[terse cradle]

thanks a tone man ur hands must be tired after this lmao

[oak chasm]

Oh, no, I type a lot.

You're welcome.

[bleak burrow]

Ho

La

[oak chasm]

Hello.

[barren shoal]

What would the answer be here?

[oak chasm]

@barren shoal We can't give the answer, but we can help you solve it.

We have P(no | period 5).

That's what we want.

[barren shoal]

I already know the answer, but I’m trying to see if It’s right.

[oak chasm]

Oh, what's your answer?

[barren shoal]

0.3928, as a decimal.

[oak chasm]

Yes, that's right.

11/28 to be exact.

[barren shoal]

Indeed, thank you for confirming it. Just needed to make sure.

[oak chasm]

You're welcome.

[glacial hedge]

How do I do this? I know im supposed to use the divergence theorem but that Directional derivative is messing with me

<@&286206848099549185>

[hollow pelican]

yo guys does anyone know how to do this?

[ionic jewel]

try physics in #old-network

[warm cloud]

Given that A and B are independent sets, how I get to this line of reasoning?

[ionic jewel]

draw a Venn diagram

they don't even have to be independent

[warm cloud]

I have, I can't understand what -P(A and B) represents

or why it's negative

[ionic jewel]

remove the area in both A and B

it's subtraction

[warm cloud]

I don't understand

[ionic jewel]

fill in your A circle

now remove the area that's the intersect of A and B

done

[warm cloud]

Oh, is it like the A areas from the two terms cancel out, leaving only -P(B)?

[ionic jewel]

i don't know what that means

unfortunately i can't draw a Venn diagram right now

but you can send a picture of what you have

[warm cloud]

this is it right?

[ionic jewel]

i mean that is true but it's nothing like your problem above

oh wait

sec

i was assuming every element is in A or B

[warm cloud]

Elements aren't given, just that the two sets are independent

[ionic jewel]

A intersect not B

[peak forge]

I have doubt it's my assignment but some of them are confusing me

[warm cloud]

essentially the same right? as what i've done

[quaint trout]

A purely algebraic argument:
Since A and B are independent,
P(A and not B) = P(A)P(not B)
Also, P(not B)= 1 - P(B).
So we get,
P(A and not B) = P(A) - P(A)P(B)
But P(A)P(B) is just P(A and B)

[peak forge]

Please help me out

[warm cloud]

ohh i understand

thanks @ionic jewel @quaint trout

[glass flare]

can someone explains the steps to convert this from:

to this

(8) refers to this

dy/dx=-x/y

[quaint trout]

Subtract -2x from both sides

[warm cloud]

it's just algebra

[quaint trout]

Divide by 2y on both sides

Simplify

[glass flare]

so this"

[warm cloud]

you can think of dy/dx as just another unknown here and solve for it

[glass flare]

2x+2ydy/dx=0
2ydy/dx=-2x
dy/dx = -2x/2y
dy/dx = - x/y

[warm cloud]

yes that's right

[quaint trout]

Yes

[glass flare]

then remove the 2's

yeah thanks

[peak forge]

@peak forge how do we do this integers part

[warm cloud]

what did you write in this term?

[alpine sable]

(a small typo, ignore one "minimum of")

[quaint trout]

Do you know how to find the vertex of a parabola? You can either use calculus (derivatives), or you might know a formula like x = -b/2a?

[alpine sable]

yes

[quaint trout]

Okay, how do you do it?

The minimum value is the y coordinate of the vertex. So find the x coordinate of the vertex however you do it, then plug it into the equation to get the y coordinate. That's the minimum.

[alpine sable]

ohk thx

ill try

[quaint trout]

👍

[peak forge]

@warm cloud it's sinx

[warm cloud]

is sinx part of the argument of the log function or is it the base of the log?

[peak forge]

@warm cloud it's in function log

We need to find domain of the function

[rigid smelt]

,rotate

[rigid smelt]

you need to find the domain of this?

[peak forge]

@rigid smelt yes

[rigid smelt]

so the argument of log_10 is a bit wonky, usually we would want a product because its easy to deal with (easy to check the sign)

[peak forge]

Actually domain function

[rigid smelt]

so try simplifying the argument of log_10 to a product

[peak forge]

Okay

[alpine sable]

I have a Circle with Radius R
How can I get the co-ordinates of every Point inside the circle?

[rigid smelt]

channel is used, please move

[plush thunder]

Range?

Anyone?

[vale wigeon]

does {} mean fractional part?

[plush thunder]

Yes fractional part function

[vale wigeon]

and what progress have you made so far?

(i'm guessing none...)

[plush thunder]

Actually

[0,1/4)

But

Yk…

[vale wigeon]

there is a huge difference between "can someone do this problem" and "here's this problem, i got this answer for it but i'm not sure"

[plush thunder]

Okay my bad
Lemme ask again

Can someone do this question
I haven’t studied the topic well

[vale wigeon]

you got the answer as [0, 1/4), yes?

that looks wrong to me unfortunately

[plush thunder]

🥲 no wonder why I came here right

Yes

I also used an app called photo math

It doesn’t really show you how it’s done

[vale wigeon]

...

well don't use photomath, for one

[plush thunder]

Yeah..

[vale wigeon]

it's useless precisely because it doesn't show you how it's done

anyway

[plush thunder]

Exactly

[vale wigeon]

@alpine sable channel busy please move

[alpine sable]

sry

[vale wigeon]

you're essentially asking for the range of sqrt(-x^2 + 2x - 3/4) for x in [0,1)

one sensible move is to complete the square under the root to get sqrt( -(x-1)^2 + 1/4)

then it becomes clear that the largest value of this is sqrt(1/4), or 1/2, achieved at x=1

and the smallest value is of course 0

[plush thunder]

Wait

[vale wigeon]

here's a graph if you want

[plush thunder]

Alright
0 to positive 1

That doesn’t make any sense

I tried making a graph

Well

[vale wigeon]

the fractional part ranges from 0 to 1

[plush thunder]

Ah yes

Alright I think I got the answer

[-1/4,1/4)

[vale wigeon]

no..

no!!!

[plush thunder]

And that’s the range of the whole function

Wh

[vale wigeon]

no!!!!!!!!!!!!!!!

[plush thunder]

Yo wa

[vale wigeon]

how can the range of sqrt(whatever) include negative numbers in the first place!!!!!!

and why do you limit yourself to 1/4 when sqrt(1/4) isn't 1/4 but 1/2!!!!!!!!!!!!!

[plush thunder]

I-

[vale wigeon]

look at the graph!!!!!! can you not see it goes up to 1/2!!!!!!!!!!!!!!!!

do you not read what i say?

[plush thunder]

Fuck

[0,1/2)

[vale wigeon]

do you not read what i say??? does it not occur to you that the person helping you has something useful to say and you should read what they say????????

[plush thunder]

I just said I haven’t studied the topic and wanted to complete my assignment

I’m kinda late in the night

It’s

It would be helpful if you just helped me with the answer

I’d be thankful

[vale wigeon]

we don't give out answers here

[plush thunder]

Alright just tell me

Is x the dependent or independent variable

That’s all

Oof

Thanks anyway!! @vale wigeon

[vale wigeon]

DON'T THANK ME WHEN I'VE DONE NOTHING TO HELP YOU.

[warm cloud]

relax

[void mirage]

Hi, so I am stuck on this last question.

For every 100,000 kWh of total energy a data centre consumes, 20,000 kWh of that total energy is used for purposes other than powering IT equipment (i.e. for lighting, cooling, etc.)

What is the power usage efficiency (PUE) for this data centre? Type a number given to two decimal places into the box.

Any help is appreciated

<@&286206848099549185>

[alpine sable]

in this step why didnt they divide by det(A)?

[pearl marlin]

How can you say ?

Use v =u+at( a is here retardation)

[dull onyx]

can u not post the same question in multiple channels

[pearl marlin]

Just simple calculation

[smoky harness]

Hey can I have help please

Anyone good a math

[distant otter]

what do you need help with

[smoky harness]

This mf thing its like a puzzle aswell I think

have to evaluate the ceiling

[strong furnace]

<@&268886789983436800>

[smoky harness]

Does noone know how to do the ceiling thing ?

[rigid smelt]

someone probably does and will help if you patiently wait

[smoky harness]

Ok

[glad night]

hello can I please have some help for trigonometry homework?

Sorry I couldn’t upload a clearer image

I thought that I would start with cutting the triangle in half to get 2 right angle triangles but I messed up extraordinarily

So I think I need to work out another interior angle

[jagged imp]

f(x)=1/2-x seems to work but idk how to prove that its the only solution or if its the only solution

I don't think you need to know or prove that its the only solution to find ceil(f(2021))^2 but I would like to solve it thoroughly

[gray isle]

use trigonometric rules/laws that can apply to non-right triangles

[glad night]

I haven’t learnt how to use those do you know which one I would use?

[gray isle]

in this case, you'd want to apply the ||cosine|| law

[glad night]

okay let me have a look

[teal epoch]

Law of Cosines. Just substitute these and you'll get x.

[glad night]

Oh my okay thank you everyone I’ll update y’all to see how it goes 😭

[jagged imp]

@smoky harness if this helps you

[gusty kestrel]

alright heres the problem

https://media.discordapp.net/attachments/817776552674328670/866263540185038928/IMG20210718182110.jpg?width=935&height=701

https://media.discordapp.net/attachments/817776552674328670/866263552150208522/IMG20210718182128.jpg?width=935&height=701

[gray isle]

are you stuck on part b)?

[gusty kestrel]

yep

[gray isle]

consider isolating cos(2x) in your equation

[gusty kestrel]

i still don't understand how to do after isolating cos2x

@gray isle is this it?

[serene flame]

oh, the channel is still active, i'm sorry, i'll move

[gray isle]

yeh, pretty much

[gusty kestrel]

oh thx

[gusty kestrel]

its fine don't worry

[serene flame]

too late i moved it to ch 2 :/

[alpine sable]

can u guys help pls

[gray isle]

whoops misread the question

[gray isle]

you could start considering that the last digit of n^k depends on the last digit of n
and the last two digits of n^k depends on the last two digits of n

[smoky harness]

zpv dBnf uif xspOh xBZ Mpm OPpC

[vestal storm]

i got a quick question

[smoky harness]

Are those brackets?

[vestal storm]

no the modulus sign

why is the vertex at -5,-3

.

[noble crypt]

haha caught you emoji thief

[vestal storm]

its not....

.

[glass lichen]

cause |x| was moved 3 down and 5 to the left

so $(0,0)\to (-5,-3)$

[ocean seal]

Mosh

[vestal storm]

ohhh ok

i get it

ty

[crystal cape]

how to do this

[plucky crow]

split the sums

[alpine sable]

hey i didn't get that... how would you solve for y in that thing? how does modulus change the graph? cause

y + 3 = |x + 5| has a different graph and
y + 3 = x + 5 has a different graph

I just don't get it

[crystal cape]

can u elaborate?

[plucky crow]

so the right sum if you expand it becomes sigma x^2 -100x +2500

then split them

[crystal cape]

yeah

and?

[plucky crow]

so sigma x^2 = 671 + 100 sigma x -2500sigma1

and what goes on the bottom and the top of these sigma signs are x=1 and 22

[smoky harness]

Anyone have a clue of this puzzle?

[noble crypt]

which game is this

[timber coral]

Of a group of elephants, half and one third of thehalf went into a cave,
One sixth and one seventh of one sixth was drinking water from a river.
One eight and one ninth of one eighth weresporting in a pond full of lotuses
The lover king of the elephants was leading three female elephants; [then], how many elephants were there in the flock?

[crystal cape]

i havent done such sums before

how would i find the variance

[timber coral]

This problem is from Leelavathi, can somebody tell me how to solve it

[plucky crow]

using the variance formula

[crystal cape]

could u show how?

i havent done this before

[uneven dew]

anyone?

[misty mountain]

what is the number of permutations for 3 things with 2 ways it can permutate

[shell widget]

@uneven dew $\omega = \frac{\theta}{t}$

[ocean seal]

Sup?

[shell widget]

angular velocity = angular displacement / time taken

[uneven dew]

thanks alot

[misty mountain]

?

[serene flame]

shouldn't it be 3 choose 2? correct me if wrong

or actually not

3 times 2

[misty mountain]

no the number of permutations

eg, if you have a set of 3 switches with two modes "on or off" what is the number of different permutations of on or off that you can put those 3 switches in

001, 010, 100, 101, 110, 011, 111, 000

let 1 be on and 0 be off

[misty mountain]

this is what I got

only 8

so does that mean 3^2 = 8

help

obv 3^2 = 9

but shouldn't their be another combination

[shell widget]

3 objects, each has 2 options. So 2 * 2 * 2 = 8

[misty mountain]

why isn't it 3^2?

I might've been taught this wrong :/

like 2 is the number of permutations, and 3 is the object

[serene flame]

i was indeed wrong

[misty mountain]

why are we multiplying the options by the number of objects?

shouldn't it be the other way around?

[misty mountain]

sorry let combinations be x and objects being (n) so n^x, not x^n

wait never mind, I get it now

for example the if 3 switches have 1 permutation, how many permutations can the 3 switches have

and let the 1 permutation be (1)

so it would be (1)

or (1), (1), (1)

which is the same

so 1 different combination

[ruby current]

would (b) would be false for a=b=-1 ?

[teal epoch]

Yes
You can't split radicals for negatives

[ruby current]

the answer key says true

[teal epoch]

does b says any explicit restrictions or something?

[ruby current]

nope

[teal epoch]

huh
weird-

[ruby current]

i mean it’s a true statement in general but i don’t think they had this case in mind

[teal epoch]

let me check it up again real quick-

[strong furnace]

in general is all cases

this is not considering all cases

should be false

[misty mountain]

so (a) would be equal to pp+qq so p^2+q^2

[teal epoch]

we talking about b if you haven't know already-

[teal epoch]

if there is one case that is false despite most cases being true well that's false

[ruby current]

that’s all it says for (b) lol

[ruby current]

ok good point

fair enough

[strong furnace]

I mean not to excuse this at all but if its a lower grade and complex numbers are not introduced kinda like the old breed of mathematicians you don't even consider the case where negatives are under radicals

[ruby current]

this is in james stewart essential calculus

it’s one of the diagnostic tests

[strong furnace]

bruh

[misty mountain]

oh we talking about complex numbers

[strong furnace]

stewarts has been getting bad cases on this server a lot

[misty mountain]

wym?

oh nvm

[ruby current]

also what does rationalize the expression mean when you don’t have a radical in the denominator like in (b)

[misty mountain]

how do I expand (p+q)^2

[ruby current]

you still multiply by the conjugate right? but what does this achieve

[strong furnace]

this looks like it leads to limit evaluation used in finding derivatives

[shell widget]

in part (b), the conjugate is sqrt(4+h) + 2

[strong furnace]

so its just multiplying by conjugates (my guess)

rationalize is a weird word imo

[ruby current]

p² + 2pq + q²

[misty mountain]

what are the steps

[ruby current]

umm do you know how to multiply two binomials

do you know FOIL or something like that

most students just have that formula memorized but you can get it yourself too

[ocean seal]

Nonexisty

[ruby current]

that

[misty mountain]

got it, thnx

[misty mountain]

nah

[teal epoch]

FOIL - First, Outer, Inner, Last

[misty mountain]

how do I apply that?

[dull onyx]

its the one the person above just showed u

basically this

sorry for not cropping</3

[misty mountain]

(p+q)^2

so um

[quaint pond]

i have a very basic question

So if I have an interval from [0;100]

and I want to find how many of them are divisible by say 2

I would divide 100 by 2

lets say I want the numbers to be divisible by 7

then I would divide 100/7

and my question is why does it work

[alpine sable]

using -1 would extend the thing to complex numbers, which if not in your curriculum, basically means it is true

[quaint pond]

because 100/7 gives me 14.285... and i know that thats 14 numbers that can be divided by 7 in the interval of 0 to 100 but again I dont understand it.....like why

[crude rose]

Because 7 can have fourteen multiples of itself before it becomes greater than 100

So there must be 14 numbers in 100 divisible by 7

[quaint pond]

ohh right so that 0.285... could also be an indicator of how close 100 is to the next number that can be divided by 7?

[crude rose]

Yea

[alpine sable]

in this case you would just rationalize the numerator too because it can be rationalized (a + b)(a - b)

[quaint pond]

thanks

[zealous gyro]

hey guys I’m a bit ashamed to ask this, but I am in a state of oblivion

[indigo jetty]

for the first one, the minus sign is applied to the terms in the brackets, but for the second one the minus sign is applied to the sin term

[zealous gyro]

Why is it like that

[crystal cape]

cause in the first one the minus sign is before the bracket

[teal echo]

by convention basically

[crystal cape]

in the second one its after the bracket

[zealous gyro]

What’s the convention

[teal echo]

you do operations left to right

[zealous gyro]

Okay thank you for clarifying that

[teal echo]

np

[zealous gyro]

I’m doing math after a while

Just doing revision and that made me blast my mind for some reason lol

I was multiplying the minus inside and was thinking why am i getting a different equation all together

And then started thinking why am I multiplying in the first place lol

So one good habit of mine I guess is what ever I substitute, I just out brackets

I guess that’s a good standard to not get confused?

[crystal cape]

yes

[alpine sable]

Hey guys how do I find intervals of x here: x^2 + x + 1 > 0

Well you do notice that you have a quadratic

you could complete the square

I'm getting squareroot of a negative number dead end

Show your working

For more information look up quadratic polynomial inequalities

√((x-2)^2 )> √(-3/4)

there

dead end

[gray isle]

show all work

before that

[alpine sable]

what you mean?

[gray isle]

how did you get that

[alpine sable]

Alright wait

[vale wigeon]

you definitely screwed up somewhere

[even before the square-rooting both sides step]

[alpine sable]

x^2 + x + 1 > 0 ---> x^2 + x + (1/2)^2 + 1 > (1/2)^2 ---> (x + 1/2)^2 > 1/4 - 1 ---> (x + 1/2)^2 > -3/4 ---> √(x + 1/2)^2 > √(-3/4)

[vale wigeon]

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

this step was entirely unnecessary.

if you know a thing or two about squaring, then you can look at the inequality (x + 1/2)^2 > -3/4 and immediately conclude it must be true no matter what the value of x is.

[alpine sable]

ohh

Thanks

[sterile beacon]

can someone help me with this exercise?

there it says "Calculate"

where a = 7

amd b = 14

[oak chasm]

@sterile beacon Do you know about Euler phi function?

[sterile beacon]

yes, somehow

idk how to apply it

[ocean seal]

Chai T. Rex

Chai T. Rex

Chai T. Rex

[oak chasm]

So, what's that?

[sterile beacon]

yeah, what's that

[ocean seal]

Chai T. Rex

[oak chasm]

,w {EulerPhi[29], EulerPhi[EulerPhi[29]], EulerPhi[EulerPhi[EulerPhi[29]]]}

[ocean seal]

Results provided by WolframAlpha

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

Requested by Chai T. Rex#7323

[oak chasm]

So, we have all the phis.

Now, a = 7 and b = 14, so let's do this.

So, a mod 4 is 3.

a mod 12 is 7.

b mod 28 is 14.

b mod 29 is 14.

[ocean seal]

Chai T. Rex

[oak chasm]

Any questions so far?

[sterile beacon]

yes, how did 7^7 become 7^4

[oak chasm]

Because, the base is done modulo 29. The first exponent is done modulo phi(29). The second exponent is done modulo phi(phi(29)). The third exponent is done modulo phi(phi(phi(29)).

So, 7 was the third exponent.

So, it's done modulo phi(phi(phi(29))), which is modulo 4.

Oh, I made a mistake.

7 modulo 4 is 3, which I originally said.

Let's redo that.

[ocean seal]

Chai T. Rex

[oak chasm]

OK, now do you have any questions?

[sterile beacon]

so basically, 7 converted to 3 because phi(phi(phi(29))) is 3 ?

[oak chasm]

Because phi(phi(phi(29))) is 4.

So, that's the modulus for the third exponent.

So, what's 7, modulo 4?

[sterile beacon]

oh, so with that result you do 7 mod 4 no?

[oak chasm]

Yeah, that's right.

Which is 3.

[sterile beacon]

then after that

you just do the power

and repet the phi(phi(

but this time just 2 times phi phi

[oak chasm]

Yes, this time it's the second exponent, so two phis: phi(phi(29)) = 12 is the modulus.

[sterile beacon]

and then 343 % 12 no ?

[oak chasm]

Yes, that's right.

[sterile beacon]

good

now I understand

but then?

[oak chasm]

OK, now same thing.

[sterile beacon]

14^7 is too much

[oak chasm]

You can do binary exponentiation.

[wind flicker]

can anybody help me?

[oak chasm]

@wind flicker Sorry, channel is busy.

[wind flicker]

aw man

alr

[sterile beacon]

what's that?

[ocean seal]

Chai T. Rex

[oak chasm]

We repeatedly square until we have a power right under the exponent we want.

We then add together those exponents we need to get the power.

At each squaring, we reduce modulo 28 to keep the number small.

Does that make sense?

[sterile beacon]

somehow.. but we have mod 29

not mod 28

[oak chasm]

No, this is the first exponent.

So, it's modulo phi(29) = 28.

[sterile beacon]

ohh

ok, it makes sense

[oak chasm]

So, that's the cheap way to do a power with moduluses.

[ocean seal]

Chai T. Rex

[sterile beacon]

yes, that's easy 🙂 that's the part that I really understand

[oak chasm]

Yeah, this takes some practice.

[sterile beacon]

from where did you learn to do all of this stuff?

my teacher is so egoist, didn't even tell us how to solve the exercises even after the exam

[oak chasm]

Oh, from programming, abstract algebra, and number theory.

[sterile beacon]

yes.. I know the chapters, I mean the resource

book, videos?

[oak chasm]

Oh, I don't remember the book name for number theory.

Let me see if I can find a web page.

[sterile beacon]

ok

[oak chasm]

Euler's theorem: https://en.wikipedia.org/wiki/Euler's_theorem.

[sterile beacon]

well, I knew about this theorem, but I didn't know that I can apply it like you just done

[ocean seal]

Chai T. Rex

[sterile beacon]

with multiple powers

[ocean seal]

Chai T. Rex

Chai T. Rex

Chai T. Rex

[oak chasm]

Now for the exponent of the exponent.

[ocean seal]

Chai T. Rex

[oak chasm]

Does that make sense?

[sterile beacon]

yes it makes sense

thank you so much

[oak chasm]

You're welcome.

[sterile beacon]

are you a teacher ?

[oak chasm]

No, I just spend some time helping out online.

[sterile beacon]

ok.. thank you so much stranger from the internet

[oak chasm]

No problem.

[alpine sable]

Hey can someone help me solve a math problem

Some guy needs to save 1500 bucks from something

Every he gets either 5 or 10 bucks and it's a 50% chance

So if he goes 10 bucks every day it would take him 150 days and if he gets 5 bucks it would take him 300

How much would it take him if he got 5 one day and 10 the next

[novel siren]

he gets 5, 10, 5, 10, 5, 10, etc. each day ?

[alpine sable]

Yes that's how interpreted it

[novel siren]

then every 2 days he gets 15 bucks

[alpine sable]

Like is there a formula for this kind of thing

[alpine sable]

Oh I'm an idiot

D says cone

https://cdn.discordapp.com/attachments/713904284206628887/718684206711963668/image0.jpg

15

what

thats what I said

[glass lichen]

dont troll

[alpine sable]

@light berry can u help

with the problems I sent

[glass lichen]

clearly not if they cant do basic addition

[alpine sable]

oh true

whats year 1

im not from india or europe

or canada

[gray isle]

so around 8yrs old?

[alpine sable]

um

huh

[gray isle]

<@&268886789983436800>

[alpine sable]

u are a funny trolelr

if ur 5 u cant be on discord ecksdee

uh yeah

lol

[glass lichen]

Yeah that's why Ram pinged...

[alpine sable]

oh

lol

<@&286206848099549185> sorry for ping but may I get help for the two geo questions I sent

no

1 is trapezoid

I initially got trapezoid but than my friend got

right triangle

so now im confused lol

than*

[glass lichen]

there they go

[tame falcon]

[alpine sable]

lol 😄

[gray isle]

its a little ambiguous what you're actually folding in the second step

[alpine sable]

ye im a bit confused

would it be an isosceles right triangle

as well

[gray isle]

i.e. whether you're folding such that both corners will meet the middle
or whether you're only lifting one corner

[alpine sable]

ah both corners are supposed to meet? o.O

tbh i got a trapezoid and an isosceles right triangle

[gray isle]

in the case of lifting only one corner, that step wouldn't change the shape
so its most likely the former

[alpine sable]

and I havent learned proofs yet so idk how to prove either of those shapes

[alpine sable]

if u dont mind can u draw a diagram

I ended up just drawing a square

[gray isle]

where you'd life both corners, and you'd get a trap

[alpine sable]

and a diagnonal

[gray isle]

do you have a tissue?

[alpine sable]

yes

[gray isle]

that's more or less a square

experiment with that

[alpine sable]

yeah

I got both shapes

so now I am confused

[gray isle]

lifting one corner doesn't change the shape, and you'd still have a right triangle
so they probably wanted you to lift both corners

in which case you'd get a trap

[alpine sable]

sorry whats a trap

I lifted both corners but i got two resulting shapes

so nwo I am confused

[gray isle]

abbreviation for trapezoid/trapezium depending on where ur from

[alpine sable]

ah

but I also got a small isosceles right triangle so now im confused

[gray isle]

wdymb y getting btoh

if you do a fold you should only get one shape

[alpine sable]

sorry can u like repeat the steps

so like

I

folded

the tissue

and unfolded the second corner

and got two shapes

[gray isle]

wdym by unfold

noone told you to unfold anything

thought it would be pretty self explanatory with a square sheet in front of you

[modern oak]

I keep on getting 0 after various attempts but the answer key says it is 2

Can anyone explain how this is?

[gray isle]

how are you getting 0?

[alpine sable]

OHH

thank you

[alpine sable]

@gray isle sorry for the ping but may u help me with this problem a swell

[modern oak]

I simplified it to (1- cosx)/ x^2) ^-1

But I do not know how to proceed from here

[alpine sable]

im confused

[gray isle]

that doesn't explain how you got 0

[alpine sable]

what is theta^2

[modern oak]

I just plugged it in

But i know that isnt the right way

[alpine sable]

wait so theta is 0

?

[modern oak]

ya lim theta -> 0

[gray isle]

trying to plug 0 in directly gets you 0/0,
which is indeterminate and not to be conflated with 0 just be cause you see a lot of 0s

consider applying conjugates and the limit identity for sin(t)/t as t→0

[modern oak]

Alright I'll try that out

I photo mathed it and for some reason it simplified (1-cosx)/x^2 to 1/2

and then they applied the negative power to make it 2

But i dont understand how that would work

[gray isle]

its a less common limit identity

[modern oak]

Ok thank you

[alpine sable]

for the third step thats how I was stuck

lmao

[chilly garden]

how do we test how random something is?

is there a mathematical evaluation function for a sequence of numbers that can provide a sort of randomness coefficient?

[alpine sable]

yes there exists randomness tests but im not too knowledgeable on them

[glacial hedge]

How do I do this?

Its in the section called divergence theorem

but i have no idea how to use the divergence theorem

@crisp iron

<@&286206848099549185>

[drowsy bloom]

Is it possible to solve for x

[gray isle]

insufficient info

[ionic jewel]

,w pi/4+pi/3= 5pi/12

[ocean seal]

Results provided by WolframAlpha

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

Requested by 兔子#6562

[chilly garden]

if anyone more knowledgeable on em could answer me that'd be great, ty

[tiny ledge]

I swear that's meant to be 7pi/12

[thick shard]

x² - 3² = x² - 9. Is this correct?

Or, should it be:
x² - 3² = x² + 9?

[tiny ledge]

The first one

[thick shard]

How? I'm confused. Why isn't -3² = +9. I mean - 3 • -3 = +9? Please, explain.

[tiny ledge]

In that form, it would be -(3)²

[thick shard]

Ah.........................................................

That was!!!!!!!!

Thanks a trillion!!!!

[thick shard]

@tiny ledge

[tiny ledge]

How would I intuit this?

[thick shard]

I think the side having "x" length could vary and the hypotenuse does not have any defined length, so... Change in the side having "x" length have change in the hypotenuse. So, there are infinite answers?

[tiny ledge]

nvm i got it

[alpine sable]

how would i do this

[warped phoenix]

[b, c] --> -8
[d, e] --> -31.1...
[a, b] --> 8
[c, d] --> -26

was it [a, b] because it was positive? my logic was that the biggest increase is [d, e], -31.1...

??

[velvet pelican]

that's the biggest decrease

notice the - sign

[warped phoenix]

but the question isnt asking for the greatest increase

its asking for the greatest avg rate of change

which is [d, e], isn't it?

[velvet pelican]

in terms of magnitude yes

[alpine sable]

note: i found out the problem is impossible so disregard sorry

[warped phoenix]

so by greatest they mean positive?

[velvet pelican]

looking at the answer i'd assume so

[warped phoenix]

they couldve been more clearer 😦

should i assume they always mean the greatest positive change unless otherwise told then?

[velvet pelican]

the wording is a bit ambiguous but if the other similar questions also mean that then they probably want to teach it that way

[main panther]

Easy problem but I’m completely blocking

Blanking

,rotate

[ionic jewel]

geometric series means its multiplied by some number each time

so lets let the ratio be r

$$t_3 = 864$$
$$t_4 = 864(r)$$
$$t_5 = 864(r)(r)$$
$$t_6 = 864(r)(r)(r) = 4$$

[ocean seal]

bunny

[ionic jewel]

and you can solve the last equation for r

[main panther]

Tysm

[willow jungle]

If bob buys 78 watermelons and eats 17.59345340/78 of it how much does bob have

[ionic jewel]

what

,w 78 - 17.59345340

[ocean seal]

Results provided by WolframAlpha

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

Requested by 兔子#6562

[celest anvil]

critical point is 2/sqrt5

but there's only 1

[glass lichen]

Well how did you get the one critical value?

[celest anvil]

the other ones are i and -i

[glass lichen]

Yeah cause you didnt do the math yourself

you just went to wolfram

apply Fermat's Theorem properly and fully, and the math yourself

[celest anvil]

nah

[warped phoenix]

lol

anyway

how do i figure out the periodicity of a function from a table?

ik you can figure out if there is periodicity by seeing if there is a pattern in the outputs

but im not sure how to know what the period is

[oak chasm]

What's the table?

[warped phoenix]

@oak chasm

the outputs display a clear repeating pattern, so ik periodicity exists, im just not sure what the period is

[oak chasm]

OK, so it looks like cosine.

But the way you guess at the period is to look at the repeated values and how far apart they are.

1s are separated by 2 pi.

0s are separated by pi.

-1s are separated by 2 pi.

You take something like the LCM of those.

LCM(2 pi, pi, 2 pi) = 2 pi.

Does that make sense?

[warped phoenix]

2pi isnt a multiple of pi though is it?

[oak chasm]

It's a multiple and an integer multiple.

You multiply pi by 2 to get it.

So, 2 pi is a multiple of pi.

[glacial hedge]

How do I find the surface integral of (x+y+z) over the triangular surface with vertices (1,0,0) (0,1,0) and (0,0,2)

[slender marten]

parameterise the surface in two variables... r(x, y) = <x, y, the surface as a function of x and y>...

You can find a normal to the plane from those three points to get the equation of the plane or other ways.

[burnt bolt]

learning limits right now and I am very confused. How is this not 0?

[true pulsar]

One can see by factoring that (x^2 - 4) = (x - 2)(x + 2)

[burnt bolt]

wouldn't that be 0 * 4?

[glass lichen]

Yeah... that's why you finish simplifying before evaluating the limit

[burnt bolt]

Mosh are you agreeing that it is 0 or 4

bc simplified its (2 - 2) * (2 + 2)

so I'm confused if it was an error in this course or not

[true pulsar]

He's saying that you need to cancel out the (x-2)'s on the top and the bottom

[burnt bolt]

ohhhhh

i see

thank you.

[glass lichen]

Yeah, further simplify..

[lapis ore]

So during my lecture on trig substitutions, my teacher said that when there is a number minus something squared (1-9x^2) underneath a square root, you can think of it as sqrt[1-(3x)^2]. I understand that you are just taking the square root of 9, but what allows us to do this and how does this make sense? How does 9x = 3x. I mainly just want to know where I can learn more about this method and what this method is called, thanks.

[true pulsar]

9x =/= 3x 9x^2 = (3x)^2

It is essentially the same idea as u substitution, which I assume you are familiar with?

[lapis ore]

oh wait I was thinking of it as (9x)^2 not 9(x)^2

I see how they are the same thing now lol

[true pulsar]

👍

No idea how you plugged in things to get this. But no, you can't

Erm no you just use something like x = 3sint to substitute

No need for imaginary numbers

[burnt bolt]

I don't understand how this simplifies to 5x + 1. Is the order of operations different with limits?

[sweet ibex]

$(5x+1)(x+3) = 5x^2 + 16x + 3$

[ocean seal]

JW

[burnt bolt]

what

yours is dif from my screenshot bc you still have the (x+3)

[glass lichen]

yeah... cause the x+3 cancels

[burnt bolt]

thank you mosh

and texit

[stoic crest]

can someone explain to how completing the square of a quadratic works. thx

[copper wedge]

im getting back into algebra after a year, so how would u solve this

|2x -4| - 8 = -2

[stoic crest]

😦

[glass lichen]

what have you tried?

[copper wedge]

well im not sure if |2x-4| means 2x +4 or not

[glass lichen]

it means |2x-4|

[copper wedge]

then what is the purpose for having | around it instead of (

I thought something like |-2| meant 2

[glass lichen]

it's absolute value bars, not brackets

and yes, it does

but you dont know the sign of 2x-4

[copper wedge]

so it would still be 2x -4

[glass lichen]

when 2x-4>0, yes

[copper wedge]

so the answer is 5

[glass lichen]

no there are 2

[copper wedge]

and negative 5?

[glass lichen]

$\abs{2x-4}=6\implies 2x-4=\pm 6$

[ocean seal]

Mosh

[glass lichen]

since if |x|=a, then x=a and x=-a make it true

[copper wedge]

plugging in 6 does not work tho

[glass lichen]

yeah cause it's not the answer

[copper wedge]

so its +- 5

[glass lichen]

no

finish doing the algebra

$2x-4=\pm 6$

[ocean seal]

Mosh

[copper wedge]

yea sorry im lost i dont know what other answer besides 5 would work

[ionic jewel]

isolate x and see!

[glass lichen]

2x-4=-6

is the case you're opting to ignore

[copper wedge]

how would 2x-4 = -6

|2x-4| - 8 = -2 would have 2x -4 = -6 and 2x-4 = 6

wat

fuck

nv

[glass lichen]

yeah

[glass lichen]

and for this reason 2x-4=-6 @copper wedge

[copper wedge]

nvm its 2x -4 = 6 or 2x -4 - 6 = 0

[stoic crest]

?

[sweet ibex]

there are lots of videos on youtube that will explain it well

[stoic crest]

ive watched a few. they just show how to do it and not why it works

[sweet ibex]

the idea is using the identity $(x+\frac{b}{2})^2 = x^2 + bx + \frac{b^2}{4}$

[ocean seal]

JW

[sweet ibex]

this is always true, and you can confirm this by multiplying out the brackets

[stoic crest]

ye but why do u do that to B

[sweet ibex]

what do you mean?

[stoic crest]

i know the formula but i dont get how it works. i know i dont need to know why it works but it helps me remeber it

[sweet ibex]

it works because of the identity above, you are essentially using a trick to write the equation in a different, but equivalent way

subtracting $\frac{b^2}{4}$ and adding $c$ to both sides of the identity gives $(x+\frac{b}{2})^2 - \frac{b^2}{4} + c= x^2 + bx + c =0$

[ocean seal]

JW

[sweet ibex]

from there you simply rearrange the equation $(x+\frac{b}{2})^2 - \frac{b^2}{4} + c =0$

[ocean seal]

JW

[stoic crest]

ye but like why do u divide B by 2... i dont understand it

im not very good at math so i might just be missing something obvious but yeah

[sweet ibex]

the reason you divide by 2 is because $(x+\frac{b}{2})^2 = (x+\frac{b}{2})(x+\frac{b}{2})$ and if you multiply out those brackets you get $x^2 + bx + \frac{b^2}{4}$. If you didn't divide by two you would have $(x+b)^2 = x^2 +2bx + b^2$, but this does not look like the equation that we are trying to solve, which is $x^2 +bx +c = 0$.

[ocean seal]

JW

[stoic crest]

ah so i was just being dumb. thx lol

[winter salmon]

i found t1 and t10 i can't find tn+1- tn

[glass lichen]

what have you tried to getting t_(n+1) -t_n

[winter salmon]

omg im so dumb nvm i found the answer

[glass lichen]

[waxen schooner]

How could I create something along the lines of this on a function graph?

[midnight shard]

that exact sine wave or just a section of any sin wave

[waxen schooner]

Yeah, but how would I offset it before 1, and make it go back up to 1?

[midnight shard]

hmm i dont know exactly what youre asking

something like this?

oop gtg sry

[alpine sable]

Hey guys when I'm taking the negative square root in an inequality, do I change the sign?
for example: (x + 2)^2 > (5/4) if I take the negative root of 5/4, do I change the sign to < ?

[topaz scaffold]

Negative square root?

$-\sqrt{\frac{5}{4}}$

?

[ocean seal]

RipeOrange

[topaz scaffold]

This?

[tribal laurel]

wat function best models the growth if the roc is 0.5?

[rich basin]

how do we do this using quotient rule

[topaz scaffold]

#help-1

[rich basin]

i mean reverse chain rule

[topaz scaffold]

Which one is quotient rule? Idk the names

[tribal laurel]

ummm

[topaz scaffold]

Oh you can't just expand?

[rich basin]

you can, but i want to know how to do it with reverse chain rule

[topaz scaffold]

I don't think you can

[rich basin]

why?

[shut rampart]

i have a question

[topaz scaffold]

Another channel please

[shut rampart]

I'm confused on how i got 10/12 on this certain question

ok

[tribal laurel]

can anyone answer mine first :c

[topaz scaffold]

We can sub $u = (x + \frac{1}{x})^2$

[tribal laurel]

T^T

[ocean seal]

RipeOrange

[rich basin]

yeah

why not sub u as x+1/x

[tribal laurel]

wat function best models the growth if the roc is 0.5? help pls

[urban cypress]

help pls

[topaz scaffold]

And if we differentiate we get $du = (1-\frac{1}{x^2}) ,dx$

[ocean seal]

RipeOrange

[topaz scaffold]

And we don't have the $(1-\frac{1}{x^2}) ,dx$ to sub in the du

[ocean seal]

RipeOrange

[topaz scaffold]

What does ROC stand for?

[tribal laurel]

rate of change

thx

[glass lichen]

Just expand it tbh

[urban cypress]

can u help me next?

[topaz scaffold]

Yes it's much better

[topaz scaffold]

I'm assuming this is exponential

[tribal laurel]

ye

[rich basin]

@glass lichen what about if it has higher powers, that means expanding it will be a problem

[glass lichen]

I mean yes, but then binomial theorem

[waxen schooner]

Yeah exactly

[urban cypress]

@glass lichen can u help me

[rich basin]

I just want to know how to use reverse chain rule for this

[topaz scaffold]

So each term is 1/2 the last one I'm assuming which is just 0.5^x

[urban cypress]

this is my question

[glass lichen]

channel is in use clearly

[tribal laurel]

wdym

[urban cypress]

wha

[glass lichen]

#❓how-to-get-help #rules

[urban cypress]

okie

oh

ok

[topaz scaffold]

Mmm let us move to another channel

[tribal laurel]

ok

5?

nvm

[rich basin]

@glass lichen I jsut want to know how to use reverse chain rule for this

[glass lichen]

Yeah I dont really see the u sub you'd even do

[glass lichen]

Told you already its in use

[urban cypress]

its not anymore they moved to a diff channel

[glass lichen]

this channel is still in use by Bortuo

besides, there are 10 channels... you dont need to be heartset on using the 1st

[rich basin]

@glass lichen i tried substiuting the u

u for x + 1/x

(u)^2

and then reverse differentiating it

[topaz scaffold]

It... worked?

[rich basin]

No it doesn't

i graphed both of my answers on desmos and it does not work

[glass lichen]

yeah cause you dont have the u'dx

[rich basin]

Can you explain what the u

dx

is

Don't we have the udx

@glass lichen Why do we need the udx when we can find it using reverse chain rule, instead of just subsituting

[glass lichen]

cause you're asking about u-sub

[rich basin]

Okay, then how about just using reverse chain rule

[glass lichen]

You wouldnt use u-sub for this problem, like I pointed out

[rich basin]

okay, then how would we do it using reverse chain rule

[topaz scaffold]

You can't

[rich basin]

I just don't get why you can't

[glass lichen]

cause u'dx isnt present

so you cant get the du to do the u integral

[rich basin]

Why do we need the u`dx

[glass lichen]

cause that's part of u-sub...

[rich basin]

couldn't you just make the constant 1 that is right next to the equation be u`dx

[glass lichen]

$(f\circ g)'(x)=g'(x)(f'\circ g)(x)$

[ocean seal]

Mosh

[glass lichen]

so clearly you need the inner function's derivative in the integrand

[topaz scaffold]

Here

Think about it this way

When you use the chain rule on something like f(x)^3

[rich basin]

yeah

[topaz scaffold]

It becomes $3f'(x) \cdot f(x)^2$

[ocean seal]

RipeOrange

[rich basin]

yes

[topaz scaffold]

There's that f'(x) that pops out

[rich basin]

yeah

[topaz scaffold]

So if we want to do the reverse of the chain rule, we have to have that f'(x) somewhere

Which we don't have in the integral you gave us

[rich basin]

like in the function right

can't we get f`(x)

because we know that it would be the differentiation inside the f(x)

[topaz scaffold]

We can't get it

[rich basin]

we can just differentiate the inside the get it

[topaz scaffold]

Notice here that both f(x) and f'(x) are present

[topaz scaffold]

Then we don't have the f(x)

[rich basin]

wouldn't the f(x) be the equaiton that i gave

[alpine sable]

yo uh

[topaz scaffold]

Well you either have to use the thing inside the square as the f(x) or the f'(x)

Can't do both

[topaz scaffold]

Post in another channel please

[alpine sable]

uhm

which one

[rich basin]

but then if we declare one as f(x) we can find the f`(x)

[topaz scaffold]

Yea, but we need that f'(x) to be somewhere in the integral

[rich basin]

like typically those within a power usually are unchanged when differentiated

and we can use that principle to find the integral

[glass lichen]

literally any not in use..

[rich basin]

what would be an inequation that would be applicable for using the reverse chain ruld

[topaz scaffold]

Ehhh?

[topaz scaffold]

$\int \frac{(ln^3(x)}{x} ,dx$

[rich basin]

there is a guy called eddie woo and he used the chain rule without the u`dx

https://www.youtube.com/watch?v=Fqh00tHfVP0

[ocean seal]

RipeOrange

[rich basin]

for that equation

[topaz scaffold]

You don't have to

But it's pretty much the same process

[rich basin]

wouldn't that be 1/x dx

make the u be ln^3(x)

[topaz scaffold]

Well you sub u as ln(x)

[rich basin]

and then du/dx = 1/x

du = 1/x * dx

[topaz scaffold]

Yup

[rich basin]

substitute du

wait do you substitute 1/x as du/dx

or do you substitute du

@topaz scaffold but then why was the chain rule applicable in eddie woo's video

[topaz scaffold]

du

Or you can multiply the x over and sub dx = x du

And the x's will cancel in the integral

[topaz scaffold]

Lemme watch it 😅

[glass lichen]

well in the example Woo does, the u'dx is present

$u=3x+1\implies\dd{u}=3\dd{x}$

[ocean seal]

Mosh

[glass lichen]

$\int (3x+1)^7\dd{x}=\frac{1}{3}\int u^7\dd{u}$

[ocean seal]

Mosh

[rich basin]

what would you sub the u for ?

i mean the du

@glass lichen , like im' really confused with what the du you may. be sub as

[glass lichen]

dx=du/3

[rich basin]

what would be du in terms of numbers?

[glass lichen]

du=3dx

like I said

[rich basin]

wouldn't that just be back at the start?

[topaz scaffold]

No cause your integral gets simplified to 1/3 • ∫u^7 with the u sub

[rich basin]

wouldn't the 1/3 cause the du substitute to cancel out