help-0

[placid steeple]

i am sorry

[wild marten]

$(1/2) = 2^{-1}$

[ocean seal]

Om3ga

[wild marten]

and same for others

[placid steeple]

which one do i select?

[wild marten]

wdym?

[placid steeple]

the options

[wary stream]

We're not here to give answers

[wild marten]

that you have to solve

[placid steeple]

ok

sad

[wary stream]

You use the info given to find it yourself

[wild marten]

I gave you the best hint possible

[placid steeple]

okk

i dk anything abt this and my sir expects me to submit this by tmrw

[wild marten]

there's another technique that is to be used, but you'll have to figure that out :)

[placid steeple]

i will watch youtube tutorials and learn it somehow

[wild marten]

yes, gl

[placid steeple]

thanks

[edgy cape]

If you don't know anything about logs at all use this: https://www.youtube.com/watch?v=kL8Mx0gBDiw&ab_channel=TheOrganicChemistryTutor

[placid steeple]

thankss buddy

[shut temple]

[charred flint]

so you want to prove the 2nd equation, which is A=..., using the 1st equation

you can do this by seeing if an arbitrary element in A is there, and if an arbitrary element not in A is there

like is a \in A inside both A and one of the B_i's?

[slim fog]

Not a math question per se, more a historical one: why are functions called functions?

[fringe shoal]

They define a system which has an input and an output. That system performs some FUNCTION on the input

[slim fog]

This seems a little forced

[strange shale]

You should try proving that any arbitrary element of A belongs to the other set and vice versa

[strange shale]

why?

[slim fog]

I am not a native English so correct me if my intuition is wrong but, as far as I’m aware, the term function is used to mean the purpose of something (i.e the function of a hammer-the purpose of a hammer) or to indicate that something works how is supposed to. A more natural way of saying would have been : the system performs some transformation on the input

[strange shale]

There is another definition according to google:-
4. a thing dependent on another factor or factors.
"class shame is a function of social power"

y is a function of x

y=f(x)

[strange shale]

Does that make sense?

[edgy cape]

can I use this channel?

[strange shale]

sure

[slim fog]

The justification seems kinda circular.

[strange shale]

Only if that very defintion came from math itself

[slim fog]

yes

[strange shale]

where are you subbing y=0

in your derivative?

[edgy cape]

yes

[strange shale]

you need to do it in the original function

and plug the value of y in the derivative

[edgy cape]

but if I sub y=0 at the derivative doesn't that give me the gradient at that point

[strange shale]

no...

[edgy cape]

o

[strange shale]

wait...

[edgy cape]

wait when I sub y=0 into the og eqn then I get an x value

but I differentiated with respect to y

[strange shale]

yeah i said something stupid i am sorry

I am sleepy

[edgy cape]

ok its fine

[shut temple]

Oh thrn it id easy thanks

[edgy cape]

I am not sure how to do a). I differentiated to get 2e^2x+6e^-2x but idk what to do next

[charred flint]

should be 2e^2x+6e^-2x

(and both of those terms are positive)

[storm abyss]

How do u resolve this?

[edgy cape]

sorry thats what I did

I mistyped

thanks

but what am I supposed to do with that

[charred flint]

e^something is always positive

[edgy cape]

how am I supposed to show that mathematically

[sand pawn]

Ok, anyone needs help now?

[storm abyss]

yes me

[sand pawn]

Go ahead, state your issue

[storm abyss]

^this

[edgy cape]

what

cant you find another channel

[charred flint]

it's just a basic fact you can appeal to

2e^2x+6e^-2x>0 because e^x>0 for all x

[tribal temple]

Does any1 know how to do this apparently this is incorrect

[storm abyss]

man u here?

[sand pawn]

x<0

[edgy cape]

when I graph e^x and find a y value using x=0 it gives me y=1, so the function can't be greater than 0 it hs to be >=

[storm abyss]

ops wait

[charred flint]

hm? e^x never equals 0

[storm abyss]

yes but how do u reach the result?

[edgy cape]

I did this with e^-2x and e^2x with the same result

[charred flint]

yeah it's just a small fraction on the left side of that graph

[sleek apex]

Hey.

[edgy cape]

but it still means e^x isn't >0

[charred flint]

I don't understand your argument

[sand pawn]

Hmm, I am finding your problem to be complex

[edgy cape]

im not arguing im confused, I need to show that e^x >0 or e^-2x>0 or e^2x>0 and I don't know how and when I graph the functions and calculate a y value using x=0 it gives a value meaning that the functions do =x and are not greater than x

[alpine sable]

can someone help me with this?

[charred flint]

looking at x=0 tells you nothing about whether e^x>0

it's the y-value that's bigger than 0 here

[fast patio]

the question is not clear enough

[alpine sable]

better?

[fast patio]

i mean, it doesnt explain what it wants

[fast patio]

oh, ok, no I got it

@alpine sable can you send this question again in #help-9 ?

[alpine sable]

sure

[fast patio]

i think other people were working here

[edgy cape]

ok what does it mean when e^x > 0 . I thought it meant when you plug in x=0 it should be a math error

[charred flint]

nah it means for every x you plug in you get a positive number

like e^2 is around 8 which is positive

for the graph it means everything is above the x-axis

[alpine sable]

help

[charred flint]

@alpine sable you can figure out the bottom right angle, and the triangle having 2 equals sides means it has 2 equal angles

[edgy cape]

ohh that makes sense thanks. So should I just show how when x=0 y=1 which means that e^x>0 for the 'show that' part

[charred flint]

x=0 y=1 doesn't mean anything for this

you just say it's because e^x > 0 for all x

[edgy cape]

oh so there's no way to prove that

[alpine sable]

i dont get it

[edgy cape]

thanks @charred flint

[charred flint]

yeah there's no simple proof that the question wants you to say

@alpine sable see where to use this?

[alpine sable]

is the answer 56?

[alpine sable]

180-68/2?

[charred flint]

,w (180-68)/2

[ocean seal]

Results provided by WolframAlpha

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

Requested by Plurmorant#1811

[charred flint]

nah, close though

the triangle angles are a little different

here are where the equal angles of an isosceles triangle are

[sand pawn]

ans is 44 degrees

[charred flint]

so y, the angle you want to find, is the non-paired angle

[strange shale]

@sand pawn this is a place of learning not for just getting answers...

[sand pawn]

Yes but he haven't specified what he wanted though

That's why I gave him raw answer

[strange shale]

It’s the general etiquette here to not give answers directly... we help here... just like Pluromont is doing

[sand pawn]

Ok, I will keep that in mind next time, Thanks for letting me know

[torpid summit]

does someone speak spanish?

[fast patio]

hola

[torpid summit]

my math problems are in spanish lol

[fast patio]

dime que pasa

[torpid summit]

eso es lo que pasa

[fast patio]

ordenada es la coordenada y

abscisa es la coordenada x

do you want me to explain this in spanish or english? lol

[torpid summit]

spanish

[fast patio]

ok

[torpid summit]

o como te sea mas comodo

[fast patio]

para que sea mas comodo, yo te lo explicaria in portugues

[torpid summit]

perfeito kkk

eu nao prestei muita atencao nas aulas

entao agr estou bem perdido

[fast patio]

ok, é o seguinte

[sand pawn]

Buddy can you take a proper snapshot? I cannot see anything well

[fast patio]

ele quer que vc encontre um ponto P

mas ele diz que o ponto P tem segunda coordenada 3

entao é P=(x,3)

e ele tb diz que a distancia de P até um ponto A=(-2,-4) é raiz de 65

vc sabe como encontrar distancia entre dois pontos num plano cartesiano?

[torpid summit]

nao :c

vou tentar terminar

obrigado

[torpid summit]

entendo

[fast patio]

para encontrar a distancia entre 2 pontos num plano cartesiano, vc faria pitágoras

desenhando a questao, ficaria algo desse tipo

a distancia de A até P é $\sqrt{65}$

[ocean seal]

Jessiquinha

[fast patio]

e o cateto vertical parece ter 3+4 de tamanho

e o cateto horizontal parece ter x+2 de tamanho

entao, usando pitágoras:

$(\sqrt{65})^2=(3+4)^2+(x+2)^2$

[ocean seal]

Jessiquinha

[fast patio]

aí voce resolve a equação e descobre a abscissa do ponto

@torpid summit tudo bem?

[torpid summit]

opa desculpa nao vi a mensaem

muito obrigado

vou terminar

[fast patio]

ve se fez sentido p/ voce

[torpid summit]

fez sim

esse bot e top

[fast patio]

eu nao falei aqui

mas é importante lembrar que distancia é sempre um número positivo

entao as vezes é bom usar módulo

[high salmon]

How do you actually use a box plot??

[sand pawn]

Do you still need help on it?

[dim oasis]

That’s a lot of quarter rule to make a box and whisker plot

[high salmon]

Quarter rule?

[dim oasis]

The grid, I’ve never seen a box and whisker plot made on a huge grid like that

[high salmon]

Blame my professor

[dim oasis]

That’s the kind where you make a box representing the IQR and lines (or “whiskers”) for the full range of the data

They look like this

[high salmon]

Yes I understand

[dim oasis]

Is your question what they can be used for or how to draw the one in your problem?

[high salmon]

I've drawn it, but it asks for me to use the data in the plot

Which I can't seem to grasp

[dim oasis]

Hm

I see the problem now

If 23 seconds is the lower quartile, than 75% of the data is higher than 23 seconds

[high salmon]

Ah i see

So 180

[dim oasis]

My brain assumed it would be normally distributed which confused me but since it’s measured in quartiles it’s easier than I thought

[high salmon]

Much appreciated, thanks very much

[dim oasis]

[edgy cape]

For my derivative I got ln(2y+3)+[2(y+4)/(2y+3)]. And for part (ii) to find A I think I need to substitute y=0. And when I do that I get 3.76 and the mark scheme says the answer is 0.27. Where did I go wrong?

this is the mark scheme

[fast patio]

wolfram agrees with you at (ii)

[edgy cape]

what

[fast patio]

actually

i found something between 4 and 4.5

[wicked blaze]

hello can someone help me with forces, it isnt hard

[edgy cape]

what did you find

[wicked blaze]

the exercice 5, why is it cos^-1 and not just cos

[fast patio]

oh shoot, i didnt see it was talking about gradients

sorry

[edgy cape]

so am I right?

[wicked blaze]

plz 😭

[edgy cape]

it says Fx= F*cos(a) so Fx/F =cos(a) and you use arccos aka cosinverse aka cos-1 of the Fx/f to find a.

revise this

[wicked blaze]

thank uuu

[edgy cape]

also please find an empty channel next time I was kinda using this

[wicked blaze]

sorry i noticed it next time i will :(

[edgy cape]

right

[spiral sparrow]

Where can i learn the basics of modulo arithmetic. I often find myself needing it in competition math but I don't think its taught on my course

[edgy cape]

https://www.khanacademy.org/computing/computer-science/cryptography/modarithmetic/a/what-is-modular-arithmetic

[dim oasis]

I figured some of it out just by playing around with it

[spiral sparrow]

thank you

[dim oasis]

There’s a way that you can mentally calculate days of the week of any date and that uses modulo a bit

[spiral sparrow]

In my case I need to know the fundamentals since I need to use it in proofs

[dim oasis]

Yeah khan would be the way to go then, I just use it casually

[hardy acorn]

could someone help

[dim oasis]

Quite possibly

[alpine sable]

can anyone help me with two equations with variables, preferably in voice, please.

[quasi heart]

You have to use the reciprocal of the function. Therefore it is 1/3.76 = 0.27

[edgy cape]

why

[quasi heart]

Because in a y-axis, x-axis diagram, y indicates the function or f(x) and x the variable

[edgy cape]

Thanks I understand

[edgy cape]

to get B do I find the value of y when x =0 in the og eqn and then plug that y value into the derivative

[quasi granite]

We have 3 urns, and each has 6 balls. First has 6 white balls, second has 3 white and 3 black balls, and third has 6 black balls. After choosing an urn at random, we draw a ball. What's the probability of the ball being from the first urn, if the ball was white?

[quasi heart]

Yes that's it. You'll get 6 if I'm not mistaking... And if you use the reciprocal it'll give you 1/6 = 0.17

[edgy cape]

Ok thanks a lot

[wicked plank]

can someone help me with something

[dim oasis]

Hello why are you pinging randomg people?

[quasi granite]

No, just the one I asked

[upper bone]

It's hard

:(

[tight echo]

Can anyone tell me if this question makes sense?

[upper bone]

Solve the equation in R

;-;

Ikr

can u help me

pls

[tight echo]

Why

[upper bone]

Tf

why 6 pings

[tight echo]

Cause it's annoying

[upper bone]

<@&268886789983436800>

[sly mantle]

b&

[tight echo]

Lol

[upper bone]

lol

[west rivet]

hello! could someone help me understand how to solve this problem?

[mighty bison]

Hey could someone help me with the law of sines, the question is what is the biggest angle with the sides: 6,5 cm 7,2 cm and 9,8 cm

[west rivet]

:(

my mom cant help me with that

[mighty bison]

dw about him just some weird kid who is trying to be funny

<@&268886789983436800>

😐

[sly mantle]

b&

[mighty bison]

thanks

[wicked blaze]

so there is this force that is 100N and it doesnt mention the friction force but the solution says that the friction force is -100

why

[slate kayak]

Maybe the physics server can help you

[wicked blaze]

do u have a link

[prime flax]

does anyone know how to solve c

the answer i wrote for a is 55 charge to mamxiumize profoti and then 10571 is the maximum profit

and her profit if tickers free is -22704 dollars

but what is c asking

how do you set up the eqaution?

[waxen crow]

Any swedish people that can help me with a math problem in my book?

[formal sigil]

need help guys

find 2 consecutive integers such that 2 times the smaller number is 19 less than 3 times the greater number

[alpine sable]

hello, does this equal to 1.19?

[formal sigil]

im using this question

[bleak ridge]

,calc 1.1-0.06/2*log(1/0.001)

[ocean seal]

Result:

0.89276734163054

The following error occured while calculating:
Error: Undefined function ln

[formal sigil]

i beed help

[bleak ridge]

Uhhh

Consecutive integer 1 is a
Consecutive integer 2 is b

a + 1 = b

Obviously

Then uhhh

[formal sigil]

why is a=b+1

[bleak ridge]

2a = 3b - 19

[formal sigil]

isnt a smaller than b

[robust crow]

How do I call it ?

[bleak ridge]

Oh yeah you're right

[onyx flower]

idk how to do this but i just did it liek quadratic

20<=5x<=30

do i choose 20?

or 30

does it matter?

[bleak ridge]

You can just solve the system of equations from there

[bleak ridge]

Wdym

Are you solving the limit by plugging in close values?

[onyx flower]

yeah im doing the epsilon delat proof

so |x-5|<1

4<x<6

[bleak ridge]

Oh

[onyx flower]

20<5x<30

what number do i choose?

does it matter

i mostly always do the right number but sometimes i see people doing left number as well

[bleak ridge]

I forget how to do those things and I just learned them

One sec

I learned them with only one side to the inequality

And you just mess with it until you can prove that a value of epsilon exists for the delta or whatever

[dusky palm]

is this all correct?

also can I simplify any of the sqrts?

[dusky palm]

<@&286206848099549185>

[raven rover]

Idk if (12)^2 + (√11)^2 = (2√73)^2

It isn't

[dusky palm]

no, the length of the left side is 2sqrt73

i didn't add anything to get there

[raven rover]

This right triangle can't exist

Pythagorean Theorem

This assumes that the vertical side is perpendicular to the horizontal side

But given your calculation of base * height =, you're assuming that it is perpendicular

[upbeat isle]

Hi my teacher gave me the question "The decimal .23 is a rational number. Explain why this statement is true." I thought it was an irrational number...? right?

[dusky palm]

my teacher said that that she made it up on the spot so its probably not an actual right triangle

but said to just go with it

[raven rover]

You can't use that figure, then

[raven rover]

0.23 is a rational number because it can be expressed as a ratio of two integers. In other words, you can take an integer, divide it by another integer, and get 0.23. This makes 0.23 a rational number.

[oak chasm]

@upbeat isle After the 23 is a repeating 0. If you get a repeating thing at the end, it's rational.

That's why 0.33333 with 3 repeating forever is rational. It's 1/3.

[upbeat isle]

Do you just know that 0.23 is rational by knowing what 2 integers expressed as a ratio equals that?

[raven rover]

Yup

[oak chasm]

To show why it's rational, you take the nonrepeating part 0.23 and write it as 23/100 (the bottom has 2 zeroes after 1, just like 2 places after the decimal place).

[upbeat isle]

wth xd

[oak chasm]

23/100 = 0.23.

[upbeat isle]

oh ... right

[raven rover]

If you can find a way to express a number as the ratio of 2 integers, then that number is rational.

[upbeat isle]

i see

[oak chasm]

Then the repeating part, you use 9999 with as many 9s as the repeating part.

0 is the repeating part and it's one digit, so it's 0/9, and then the repeating part is after 2 decimal places, so you do 0/900.

So, 23/100 + 0/900.

To do it with 0.33333 with 3 repeating, you do 0/1 + 3/9.

,calc 1/7

[ocean seal]

Result:

0.14285714285714

[oak chasm]

That has 142857 repeating forever.

So, it's 142857/999999, which reduces to 1/7, which is what you started with.

[raven rover]

I think this guy is just learning rational and irrational numbers

Not necessarily number theory - or at least that feels like number theory

[alpine sable]

What are 5 digit prime numbers?

What does the 5 exactly mean?

[raven rover]

prime numbers with 5 digits, i'm guessing

5 is the number of digits in the prime number

[alpine sable]

yeah

im dum

can these be converted into letters?

[glass lichen]

Wdym

[alpine sable]

I'm trying to decrypt this

[oak chasm]

@alpine sable Those are the first ten prime numbers after 10007.

[alpine sable]

Yes I know that

[hushed pasture]

@rich ginkgo yes it is correct

[prisma mountain]

cant seem to understand how to find the inverse of this

[vapid oak]

how would you go about finding the inverse of other functions?

[prisma mountain]

i dont think its possible, but the algebra is where im lost

well u swap the x and y right? and solve for x

[vapid oak]

yeah

im gonna try and solve it myself to see what to do

[honest tartan]

Recall that only bijective functions have inverses.

[prisma mountain]

be my guest lol, my brain crashed

bijective?

[honest tartan]

In this case, you must analyse the function separately for x >= 0 and x < 0.

[honest tartan]

Both injective and surjective.

[prisma mountain]

first time hearing these terms sorry, but i see

[honest tartan]

a.k.a. one-to-one and onto.

[prisma mountain]

ah alright

[prisma mountain]

any luck? if not np

[vapid oak]

This guy is right here

however his explanation sounds like it confused you so I can reword

Since the original function doesn't pass the horizontal line test, it won't have an inverse function so you need to analyse it piece by piece

[prisma mountain]

yeah i understood what he meant more or less, just not seeing what piece by piece implies in this case

pinged u as u mentioned u were going to attempt it lol, mb

[vapid oak]

I tried attempting it but yeah, you have to do it separately

basically means, when x is negative and the absolute values take effect, what is the inverse function? and then you have to work out when x is positive what is the inverse function?

and then idk sort of bring that together, im not the most familiar with this topic so im not the best at explaining it

[prisma mountain]

yeah no problem, u explained plenty

i will try this method, bizarre question regardless, would be simple to just say it has no inverse

[upbeat isle]

Hi when i solved an linear inequality with an absolute value thing, I got x<8 and x<2, how would i write this in interval notation?

cus when i try to plug one equation into the other because of the absolute value sign, they dont work

Original equation is absolute value of ( x-5 ) < 3 if that helps

[vapid oak]

so |x-5|<3

[upbeat isle]

yea

[vapid oak]

well one of these answers is wrong

because, for example -10 is within the range of your two inequalities but |-10-5|=15 which is not ❤️

[upbeat isle]

am confused

dude my brain literally stops functioning as soon as i see an sbolute value

[vapid oak]

ok so i would recommend going back to the inequality and trying to solve it again, be a bit more careful

[alpine sable]

Are you guys done here?

[vapid oak]

well i mean i dont think we're done here, and even so you could have gone to one of the other channels which havent been used in hours if you were confused

[clever folio]

Assume t is in X then expand the defn for being an elt of X (what the set builder notation for X says) then expand the defn of divisibility. Try to relate that to Y.

[tranquil tulip]

can someone help me i have to find where i can put the stereo so that the lines to speaker a and speaker b will be the shortest

[clever folio]

Do you know how to prove one set is a subset of another set?

I do not understand why you are confused by t then.

An elt of X

(Sry typo)

To show something like A is a subset of B you assume you have an elt of A and show it must be in B also. That's all I'm doing with t.

[clever folio]

The shortest path between two points is the line connecting the two points.

[clever folio]

Or like, that's what I mean by saying "assume t is in X" (or assume t is an element of X).

[alpine sable]

bizarre is that a jojo reference?

[prisma mountain]

always has been

[alpine sable]

oh my god

my entire existence is uprooted

I will now move on

By ur enlightenment

Oh wise one

[warm verge]

how can someone help me with this?

is this possible?

[brisk bough]

Hi! Quick question, may i use this server to ask about the questions from a school assignment? Thanks!

I currently don't have one now, i'm just asking if i can

[blissful nest]

what im doing

[low topaz]

2 is a number

[brisk bough]

Ahh so it's mostly the purpose of the server, i see

[onyx flower]

im stumbled

xcosx+sinx=0

explain how do i do this

i get -xcotx=1

[placid zinc]

Can't solve algebraically

[shadow reef]

My teacher did this in class but could some one explain how she simplified x^3-27 I got everything else

[buoyant kayak]

difference of cubes formula

[north needle]

Factor theorem

[buoyant kayak]

$a^3-b^3=(a-b)(a^2+ab+b^2)$

[jade token]

isn't it ab?

not 2ab?

[north needle]

X^3 - 27 = 0
X = 3 is a factor
Therefore (x - 3) goes into x^3 - 27

[ocean seal]

a disappointing son

[ebon tiger]

My friend gave me this problem

I have some intuition for it

The coefficient of x^t is (-1)^n where n is the number of 1s in its binary representation/the sum of its digits in its binary representation

But I haven't been able to manage anything else

[charred flint]

mathematica says it's 1

[toxic canyon]

Please help Derive the recursive formula for butterfly sequence (aka figurate numbers):

[toxic canyon]

Please help Derive the recursive formula for butterfly sequence (aka figurate numbers):

Example of figurate numbers⬆⬆
Please help Derive the recursive formula for butterfly sequence (aka figurate numbers):

[mellow linden]

quick question, when you multiply fractions you don’t change the denominators right? just reduce and multiply

[toxic canyon]

That's right.

Please help with my question ⬆⬆⬆ @crisp iron

[placid zinc]

@toxic canyon
Can you describe the pattern in English? If I gave you some random member of the butterfly sequence, what would you do to get the next one?

[toxic canyon]

@placid zinc i added an example figure, but maybe not helpful?

[placid zinc]

I get the pattern haha. I'm asking if you do

[toxic canyon]

Yes, i do get the pattern. Here is S4

the triangle increase by, with explicit formula

[placid zinc]

Oh. Well, you're done with that formula

[toxic canyon]

but i really struggle with derive the recursive formula.

ask i posted a littel bit over.

[placid zinc]

Or wait, you mean "the triangle" by the part in green?

[toxic canyon]

This is the formula for both green part's

My problem is with this:

derive this recursive formula.. 😕

[placid zinc]

Can you describe the pattern in English? If I gave you some random member of the butterfly sequence, what would you do to get the next one?

I see you've put a few boxes over important parts, but I still haven't heard you describe the actual change that happened between S3 and S4

[toxic canyon]

The S(n+1) make me unsure.. I am more used to Sn = S(n-1)

[languid gate]

what the coefficeint of n PLEASE

[toxic canyon]

Hmm, I am not sure if I understand..

[languid gate]

that

[toxic canyon]

4 = coefficeint
1/2 = coefficeint

right?

[languid gate]

im bad at this i dont even know whats a coefficeint

[toxic canyon]

aaa, i was thinking you where trying to help me out... I am in the middel of e problem here. 😅😅

[languid gate]

its the number in front of the varieble someone told me

[toxic canyon]

Changes between S3 --> S4 @placid zinc

[placid zinc]

Can you describe the pattern in English? If I gave you some random member of the butterfly sequence, what would you do to get the next one?

That is, if I gave you dots, how would you add more dots to get the next one?

[toxic canyon]

To get
S2 = S1 + 9
S3 = S2 + 9 + 2
S4 = S3 + 13 + 2
S5 = S4 + 15 +2

To find Sn, you must add Sn = S (n - 1) + (??????), n = ?? @placid zinc

[fair rover]

someone please help

[toxic canyon]

Maybe try another channel. I am in the middle of something here😅😅

[fair rover]

alr

[split slate]

$f(x)=\frac{1}{x},\ g(x)=\sqrt{x}\ \ \text{Does }f(g(x))\text{ exist? Why/Why not?}$

[ocean seal]

HappyAlt

[alpine sable]

5-7 only

[kindred warren]

two lines are parallel if they have the same gradient

for 5, i would rearrenge both equations to make y the subject

then if they have the same gradient then they are parallel

if the product of their gradients equals -1 then they are perpendicular

[inner sentinel]

how would i go about solving this

[kindred warren]

a + b = 9

rearrange it to make b the subject

[inner sentinel]

would i find the derivative of (a^2(9-a)^2)/81 and find the critical points

[kindred warren]

oh you already did it

[kindred warren]

yes

and figure out whether they are local maximums or local minimums

then find the different between them

[inner sentinel]

thats where im stuck at

[kindred warren]

ah

[inner sentinel]

i found 3 critical points how do i find if its min or max again

[kindred warren]

ok so can you tell me the three points

[inner sentinel]

plug it into the derivative and if its concave up or concave down?

[inner sentinel]

x=0, x = 9/2, x=9

[kindred warren]

alright

[late parcel]

Is this channel open now?

[kindred warren]

no

if a point is a local minimum, then the x value directly to the right of it has a positive gradient and the x value directly to the left has a negative gradient

[inner sentinel]

oh yaa

[kindred warren]

so you can test for each poin

point

[inner sentinel]

so test for the points next to it by plugging it into the derivative?

[kindred warren]

yeah

[inner sentinel]

alr i will try it

also cant i just plug in the critical points themselves

[kindred warren]

that would just give an answer of 0

which wont help

[inner sentinel]

oh yeah

[alpine sable]

help

[late parcel]

Wait

[inner sentinel]

so i tested a point to the left and right of 0 and i got 0 to be minimum

[late parcel]

@alpine sable it’s D

[shadow cedar]

can someone help me with this?

im kinda lost here

[alpine sable]

ohh ye my first answer was correct ok tyyy

[kindred warren]

ok now test the other points

[coral temple]

Answer whenever idc, how many in stage 10 and stage 50. Not really math it’s just idk a thinking thing

[inner sentinel]

for the maximum?

[kindred warren]

yes

[inner sentinel]

wait but a point to the left of 9 is negative and the right of 9 is positive so doesnt it mean thats also a minimum

[kindred warren]

yeah

and then 9/2 is a maximum

[inner sentinel]

but since the question says find the difference between the max and min which min am i subtracting from 9/2

[kindred warren]

they both have the same value

0

so doesnt matter which one

[inner sentinel]

wdym they have the same value 0

[kindred warren]

the both have a y value of 0

(0, 0) and (9, 0)

[inner sentinel]

ya

[kindred warren]

so the minimum occurs when x is 9 or when x is 0

and the maximum occurs when x = 4.5

[inner sentinel]

so i can do (9/2) - 0 to get the answer

[kindred warren]

No

9/2 is what x is

you have to find the value of a^2b^2 / 81

[inner sentinel]

oh find the y of it?

[kindred warren]

yes

which would have an exact value of 81/16 i believe

[inner sentinel]

yes

[kindred warren]

yes

[inner sentinel]

wait that makes sense now tysm

[kindred warren]

so 81/16 - 0

is just

81/16

[inner sentinel]

yeah

thanks

[cunning raven]

quick question do I use chain rule for this derivative

please @ me

[gray isle]

you'd start with product rule @cunning raven

and then a small application of chain rule after

[cunning raven]

yeah thanks a lot for confirming

[sick phoenix]

hi i’m lost can anyone help

[kindred warren]

since RW and ST are parallel then angles TCR and WRS add to 180

and we know that the angles in a hexagon add up to 720

there for we have 720 - 110 - 120 - 180

which is 310

there fore the remaining angles (x and y)

must add up to 310

[sick phoenix]

ohh so we don't need to find the individual value of x and y?

[kindred warren]

nope

it's impossible to find their angles with this much information

[sick phoenix]

ah ok got it, tyvm ^.^

[kindred warren]

np

[alpine sable]

someone pls help

[kindred warren]

i think i found the answer

ok if we call the amount of 15% alcohol that we need 'x' and the amount of 5% alcohol that we need 'y'

we can make an equation that x + y = 10

we also know that 10% of the solution will be alcohol, so 0.15x + 0.05y = 1 (the '1' comes from 10% of 10)

so we have a simultaneous equation

x + y = 10 and 0.15x + 0.05y = 1

if we solve it x = 5 and y = 5

so each type of alcohol should have 5 gallons

@alpine sable

[alpine sable]

makes sense

so it would be 5, 5

[kindred warren]

yes

im not 100% sure tho

im more like 70% sure

[alpine sable]

i think i might be different

[kindred warren]

you can type that as the answer if you want

[alpine sable]

Given the arithmetic series an = a0 + d(n - 1), with a0 = 5 and d = 10, find the sum of the first 30 terms.
help me pls

[kindred warren]

@alpine sable was it correct

[alpine sable]

whelp

[slow wraith]

can't get this question right (its for an exercise) can anyone help>

[kindred warren]

since you have a y intercept you already know what c is

so y = ax^2 + bx + 12

then since (3, -3) is a point

-3 = a(3)^2 + b(3) + 12

but (3, -3) is also a turning point so if you find the dy/dx you can sub x = 3 into that and it will become 0

then you have a simultaneous equation

equation 1: $9a + 3b + 12 = -3$

[ocean seal]

Tra-Guy

[kindred warren]

equation 2: $6a + b = 0$

[ocean seal]

Tra-Guy

[kindred warren]

i got equation 2 from finding the derivative then substituting x = 3

using these two equations you can find a and b

did you get the answer

[slow wraith]

can anyone help

[alpine sable]

i still don't get it

[kindred warren]

oh

it's hard to explain

but can you figure out the simultaneous equation

[alpine sable]

my teacher didnt explain about that she just sent a yt link about it.... and thats the only way we can answer that

[kindred warren]

oh

interesting

do you havent learnt about derivatives

[cunning raven]

channel in use, also this is physics question?

[glass lichen]

do you know vertex form..?

[nimble mulch]

Is this channel free now? That dude doesn't seem to be responding

[glass lichen]

there's 9 other channels + the topic channel... you dont need to wait on a channel

[nimble mulch]

yeah sorry I will move to some other channel

[alpine sable]

ohhh, i see, so the final answer is gonna be?

[alpine sable]

u were right btw

[kindred warren]

nice

[alpine sable]

it's so aids to solve tho lol @kindred warren

is this right

[kindred warren]

yes but i dont think you rounded the first one correctly

[alpine sable]

what would it be rounded to?

[kindred warren]

it should be 17.68

i used a calculator and that it what it said

[alpine sable]

is this the best way to express the language accepted for this DFA? unless I'm missing something

[alpine sable]

ur right

this good?

[kindred warren]

yes

[raven kraken]

Does anyone know how to do geometry proofs?

[unique sun]

i might

does anyone know how to solve this

[fair osprey]

Like statement reasons?

[alpine sable]

this good guys?

[kindred warren]

ye

[kindred warren]

we can use the same logic from the previous question

x + y = 5

0.15x + 0.1y = 0.7

[alpine sable]

ok

i got it then

[kindred warren]

so 4 gallons of 15% alcohol and 1 gallon of 10% alcohol

[alpine sable]

damn u solved it for me lol

i just solved it

[kindred warren]

ye

[alpine sable]

im taking intermediate algebra

and collegfe algebra

and this shit is the hardest thing ive encountered so fart

far

[kindred warren]

are you in the US

[alpine sable]

yea

[kindred warren]

cool

im in australia

[alpine sable]

so the first is 4

and second is 1

right

[kindred warren]

ye

what grade are you in

[alpine sable]

sophmore year of college

@kindred warren

[kindred warren]

pure acid is 100% acid right

[alpine sable]

i dont think so

[kindred warren]

oh

well if it is

then

you need 6L of pure acid

and 12 litres of 10%

wait is sophomore year second year

in university

[alpine sable]

yeah

2nd year

[kindred warren]

so is that 19-20 year olds

damn

[shut depot]

<@&286206848099549185>

What is meant by consecutive points?

Like I don't understand what is meant by that or can visualize it

[pliant flume]

can someone help me with using the point slope form of the equation of line which is refering to the inverse of f(x)

[shut depot]

@alpine sable

Just watch or google how to do fractions: https://www.khanacademy.org/math/arithmetic/fraction-arithmetic

[grim delta]

thats the same

unless it asks for mixed numbers for whatever reason just leave it as an improper fraction

if you want to convert TO an improper fraction from a mixed number all you have to do is take the whole number, multiply it by the denominator of the fraction and add the numerator to the product
thats the numerator of the fraction, the denominator stays the same as the original fraction

so for 3 3/4 3*4+3 is 15 and then denominator is still 4 so 15/4

np

[undone garnet]

If a matrix A^(31) is a zero matrix(size: nxn) then what would that tell us about Matrix A (size: nxn)?

[maiden raptor]

anyone able to help

[undone garnet]

<@&286206848099549185>

[wild shard]

it is f'(g(x)) * g'(x) by means of the chain rule

[craggy niche]

Thank u

[spark reef]

is this right

[wild shard]

it is also a zero matrix?

[spark reef]

since the first derivative has only one variable you just find that derivative for the second right

[devout summit]

You didn’t apply chain rule while differentiating the second time.

[tight rover]

is this channel occupied?

well i will

i'm stuck on this, why should it be the fundamental limit (1+1/x)^x?

[wispy urchin]

??

[devout summit]

Substitute x=3k and limit turns to\$\lim_{k\to +\infty}\left(1+\frac{1}{k}\right)^{3k}$

[ocean seal]

Euclid31415

[tight rover]

ooooh brillant

thank u euclid

[pallid cape]

Can a someone help a homie out?

[oblique mural]

yes

[desert sand]

Can someone help me on question 6

[pliant zephyr]

the pic is not clear

pls zoom in and send it

[pliant zephyr]

perimeter=OP+SO+SR+QR+QP
OM=OS=7 SR=C/8 (r=7) ,QP=C/6(r=14),QP=7

[desert sand]

Thank you

I can help

2s + 6 = 14

2s = 14 - 6

2s = 8

s = 8/2

s = 4

Do u understand why s is 4?

Alr just use the same method

And you can solve the others

Np

[crude flax]

can someone help me too?

[desert sand]

In?

[crude flax]

im having trouble understanding this

[desert sand]

I'm supposed ur looking for k?

[crude flax]

yes

[desert sand]

Is there any more details or smth?

[crude flax]

no this is it

it only says to find the unknown angle of k

[desert sand]

Ok erm there are two isosceles triangle

Wait no

Yes

Bcoz 7j isnt the final answer

Erm back to the triangle thing

So there's re two isosceles triangle

[pliant zephyr]

ΔADCcongruent to ΔBDC
then angle ADC=BDC
ADC=180-2**17
=146
k=360-2*ADC
=360-292=68

[desert sand]

Ok nvm

[maiden holly]

Bruh

[desert sand]

Lol

[crude flax]

angle D = 180 - (17+17)
= 180 - 34
since ADC = BDC
k = d x 2
= 34 x 2 = 68

is this correct?

[pliant zephyr]

yep

[crude flax]

ok thank you

[pliant zephyr]

np

[crude flax]

I have another question

[desert sand]

I have a stroke reading that xD

[crude flax]

lol

[desert sand]

<BOC is 130°

Wait how do I angle thing

[pliant zephyr]

and OB=OC

[desert sand]

^

[pliant zephyr]

then 130=180-2d
2d=50
d=25

[crude flax]

erm

[desert sand]

Yea

[crude flax]

let me try to put it in my format -_-

[desert sand]

Ok so angle O is 130°

[crude flax]

130 because 180 - 50 right?

[desert sand]

Yup

[crude flax]

okay

[desert sand]

Not rn give us another few min sorry

[crude flax]

so then cant we just do 130 divided by 2 and get c?

[desert sand]

Actually yes u can do that

[fluid knot]

wron pic

[crude flax]

do then its just two steps right?

[desert sand]

@fluid knot Pls give us a few min here

[fluid knot]

oh ok 👍

[desert sand]

Yup

[crude flax]

whats the point of the other triangle and circle then -_-

[desert sand]

Bcoz it's a isosceles triangle

[desert sand]

It's just making us to feel confused

Lol

[crude flax]

lol

ok thank you

[desert sand]

Np

@alpine sable what's your question again

Hmmm

@alpine sable sorry I couldn't help you with this

But as far as I know expression is just explaining the sentence using numbers

@fluid knot and your question?

[fluid knot]

this my question

[desert sand]

Eh

I suck at linear equations

[fluid knot]

oh lol

[desert sand]

Sorry

[fluid knot]

its for me its also hard but algebra kinda easy

[desert sand]

Same same

[crude flax]

sorry for asking again but i am confused by this -_-

[devout summit]

This is a rhombus

4x=x+60

[crude flax]

erm

[inner sequoia]

what the shit where did n^9 come from

[clever folio]

Could it be a typo?

Seems like the original had n^1 in the denominator but meant to put n^9?

Well hmm

Actually the whole line on the bottom seems wrong.

4/18 is not 1/3 for example

[inner sequoia]

oh shit yeah what the hell?

[clever folio]

Are they claiming that's the soln?

[inner sequoia]

yes lmao

happens couple times, ill report it to my teacher

[clever folio]

Good idea.

[sage hornet]

Hey guys I just have math question could anybody help me? “Jessica Drives to work in 35 minutes if she increases her average speed by 5km/h she saves 5 mins how far away from work does she live?

[clever folio]

"Jessica drives to work in 35 minutes" at what speed?

Are they referring to her avg speed with that?

[inner sequoia]

first off convert 5km/h to km/m
would be more useful since you're talking in minutes

[clever folio]

Seems like a distance=rate * time prob.

I guess they mean 35 min at her avg speed so let r be her avg speed and d be the distance

So d=35(r in km/h) and d=30(r+5 both in km/h)

The first is because at whatever her average rate she gets to work (distance d) in 35 minutes.

The second is because if she increases her speed by 5 she saves 5 minutes to travel the same distance.

You can probably figure out how to solve it from that

OneCore is right about unit conversions though so you'll need to do that stuff too.

[sage hornet]

I’m not sure how this question is related to solving systems of equations my math teacher has put this on our exercise sheet for solving systems of equations

[clever folio]

You have two equations

[sage hornet]

Oh yeah

[clever folio]

One is for her avg speed the other is for when she goes a little faster

[sage hornet]

now I get it

[desert fable]

i dont get what the question is asking ...

can sb pls help 😢

"The frog stops when it lands on one of the two lines." so doesnt it stop after the 1st jump ....

[thorny cave]

anyone know how to find LENGTH C to D using sine rule

[half crypt]

To kids here :) if you need this

[limber urchin]

The frog jumps over the line first before landing

[alpine sable]

what's the value of a, b, and c of it?

[kindred warren]

a = 5/3, b =-10, c = 12

[alpine sable]

y = 1666666667/1000000000x² - 10x + 12

oh wait its wrong lol

uh oh

[kindred warren]

What the

it's just $y = \frac{5}{3}x^2 - 10x + 12$

[ocean seal]

Tra-Guy

[alpine sable]

the final ansswer is gonna be?

???

@kindred warren

[kindred warren]

ye

a = 5/3, b =-10 and c = 12

[crude flax]

can someone help please i dont understand it

[alpine sable]

anyone knows howmuch is |z*w| if z = 1+3i, w = -2 +5i

a = 5/3, b =-10 and c = 12

[kindred warren]

yes

[kindred warren]

Since it is a parallelogram, 4x = x + 60

[crude flax]

i dont really understand what you mean by it

[kindred warren]

It is a rule

[alpine sable]

[crude flax]

so i have to find the value of the variables

how do i do that

[kindred warren]

On a parallelogram, the opposite angles are equal

[kindred warren]

4x = x + 60

[kindred warren]

Whats wrong

[crude flax]

what is x +60

[kindred warren]

The angle on the shapr

Shape

[alpine sable]

what's the a, h and k of it?

[crude flax]

but then how do i write the values

[kindred warren]

Did you get the right answer for the other one?

[kindred warren]

Using the equation 4x = x + 60

You can find what x equals

[alpine sable]

it's not a exam or something my dad gave it to me for practice and he's still not home so.

[crude flax]

how do we find what x is

[kindred warren]

Ah ok

[kindred warren]

Do you know how to solve linear equations?

[kindred warren]

Can you send the entire questions

[kindred warren]

Ok

Ill do it

[crude flax]

No

[alpine sable]

'ight

[kindred warren]

Do you want me to just tell you the answer

Or do you want me to try and work you through it

[alpine sable]

just the answer, i'll just review it by myself

and if i still dont get it

[kindred warren]

Ok

[alpine sable]

i'll ask for u:>

[kindred warren]

So h = 5

k = 2

And thats it

Lol

[alpine sable]

*h = 5 k = 2 *

[kindred warren]

Yes

[alpine sable]

that's all ?

ohh ok time to review it i;ll be back if i still dont get it tysm!

[kindred warren]

Yeah there is no 'a' because the question didnt specify and 'a' in the equation

[clever sleet]

does anyone here know about edgenuity, anyone ever taken it before for a school class?

[somber gust]

I have question about basic probability. I'm trying to figure out the chance of a given minecraft world with every block. With 775 blocks, but I don't know how to do compounding probablity (if one block has 1 /775 chance of being a block type, what is the chance that a second will have that same block type as the other one, so on for another 2.304e+17 blocks

[cloud mirage]

@plain pike

@plain pike

[vale wigeon]

@somber gust minecraft worlds are not generated with a uniform distribution on every block

[somber gust]

I know that I'm curious how many combinations there are

[vale wigeon]

the number of possible worlds if you throw away all worldgen considerations and just fill all 2.304e17 blocks arbitrarily?

then there are 775^(2.304e17) possible worlds

a number so stupendously large you couldn't even describe it as "astronomical"

[somber gust]

yeah ok, i'll forget about it

[native notch]

the world gen goes beyond 30,000,000 blocks in each direction (it technically goes to the 32 bit integer limit) and with the caves and cliffs update, world height will be well over 256 blocks. around 512 I think.

Which gives you 2.36118323924e+21 possible places for blocks.

and like Ann said, if you disregard worldgen and fill every block randomly, you get 775^(2.36118323924e+21)

I don't know if you're accounting for block states, but that doesn't matter at this big a scale. Basically very big number

[limber thorn]

how do you find the derivative of ... (x^2-1)-1

[vale wigeon]

you want the derivative of x^2 - 2?

[limber thorn]

{(x^2-1)-1} maybe this makes more sense?

derivative of whats inside the bracket

[vale wigeon]

$(x^2 - 1) - 1$ is the same as $x^2 - 2$.

[ocean seal]

Ann

[marble sparrow]

may i get some help on this please

[vapid oak]

One thing to help you get started: what is the maximum possible digit sum under those restrictions?

and then try and restrict it down to 29

[marble sparrow]

got it

could you help me with this one?

[vapid oak]

sorry definitely not my strong suit, maybe someone else could help

[marble sparrow]

no worries

[half crypt]

[vast isle]

does anyone know the formula for these two 😭

[jagged imp]

what exactly are you trying to do with those shapes

[slim sparrow]

where did the "(x-2)" came from?(highlighted with red)

[devout summit]

Is it just 1? f(0) can only be 0 hence, f(1) can only be 1 and soon we get that f(x)=x for all values in domain.

[vale wigeon]

are you asking "why did the num and denom get multiplied by (x-2) and not something else?" or are you asking "what is even happening here?"

[vapid oak]

since you are allowed to multiply both sides of a fraction by the same value without changing the fraction, they have multiplied both the numeratora nd denominator by (x-2) to utilise the difference of squares in the denominator

[slim sparrow]

thanks for the answer mate

[vapid oak]

well this is one of my fav questions

basically there are 9/10 ways to lose right?

so the probability of spinning 110 times and losing is (9/10)^110

which is...

gimme a sec

0.0009%

[devout summit]

But we need losing 109 times and winning 1 time right?

[vapid oak]

sorry what was the question

the chances of spinning 110 times and only one of them being jackpot?

aah

does it necessarily have to be the last spin, or only 1 of the 110?

[devout summit]

I don’t think so.

Question would have stated it then

[vapid oak]

well then I think the probability would be $(\frac{9}{10})^{109} \cdot \frac{1}{10} \cdot 110$

[ocean seal]

Omfish

[devout summit]

\left(stuff \right) to fit inside brackets nicely btw

[vapid oak]

do you get why?

lmk if you need an explanation

[devout summit]

$\binom{110}{1}\cdot \left(\frac{9}{10}\right)^{109}\cdot\frac{1}{10}$

[ocean seal]

Euclid31415

[alpine sable]

This is actually hard: Can you find a bijective function from R to R × R?

i cant solve

that

can you help me?

[fringe turret]

my answer is 112

1/1/2

am i right or somethin

[vapid oak]

well thats not a fraction

so im not sure what that number is

[fringe turret]

hold on

this is my answer

[vapid oak]

correct

[fringe turret]

ok thank u

[vague iris]

Hello can imaginary numbers be plotted on the number line?

[magic geyser]

well number line is only for Real numbers I think

so no

only the real part of the complex number I think

[vague iris]

what lmao

i think somethings going on w ur auto correct

[magic geyser]

oh yes

sorry

[vague iris]

lmfao

but getting back to my question
imaginary numbers cant be plotted in the same plane as real numbers?

[magic geyser]

well the imaginary number is an y value and there cannot be y values on the number line right?

[coarse agate]

hii can anyone help me with polynomials?

[magic geyser]

Essentially, an imaginary number is the square root of a negative number and does not have a tangible value. While it is not a real number — that is, it cannot be quantified on the number line — imaginary numbers are "real" in the sense that they exist and are used in math

@vague iris

[magic geyser]

[vague iris]

Im trying to solve this rational inequality
I got stuck getting the critical values. Im not sure if i should plot that +-2i

@magic geyser

[coarse agate]

we have to think about a real life problem that is polynomial like in the picture with solution and procedure

[vague iris]

that just substitution i think then simplify it

[coarse agate]

how do u simplify it? @vague iris ? sorry for ping