help-0

[robust phoenix]

I did what you said lol

x^2 is 9

9 over 3 is 3

oh nvm

in the 4 over 3 i multiplied by 3 which is wrong and i need to multiply by -3

so it's -1 right ?

[gray isle]

f(-3) = -1
yes

[robust phoenix]

less goo

"A horizontal tangent line is a mathematical feature on a graph, located where a function's derivative is zero. This is because, by definition, the derivative gives the slope of the tangent line. Horizontal lines have a slope of zero. Therefore, when the derivative is zero, the tangent line is horizontal." It's from google

"A tangent of a curve is a line that touches the curve at one point. It has the same slope as the curve at that point. A vertical tangent touches the curve at a point where the gradient (slope) of the curve is infinite and undefined. On a graph, it runs parallel to the y-axis."

[gray isle]

it should be clear if you know equations of horizontal and vertical lines

[robust phoenix]

the slope of a vertical linne is undefined right ?

[gray isle]

yes

[urban lily]

the answer is gonna be equal to -1 if I am correct

[robust phoenix]

yep it is -1

[urban lily]

oh okay thanks

[robust phoenix]

does anyone have the classification of real numbers

so integers whole numbers fractions ratios and so on

[proud bough]

N < Z < Q < R

[robust phoenix]

whole numbers are z ?

I think you missed W

[proud bough]

What is it?

[robust phoenix]

In my book it goes like this

[alpine sable]

whole numbers has 0 thats it

N < W < Z < Q < R

[proud bough]

Z already has 0, though.

[robust phoenix]

N<W<Z<Q<R

[robust phoenix]

but it has negative numbers

[alpine sable]

you could say that for Q too 🙃 "Q has Z tho"

[tight locust]

what is supposed to be the difference between W and Z

[urban lily]

Same thing just added the set "W" which is for whole numbers

[tight locust]

whole numbers are not a real category

[alpine sable]

its for elementary students I believe

[robust phoenix]

Z has negative numbers and postive numbers including the 0 but w doesn't have the negative number it just has 0 and all the postive numbers

[proud bough]

I'm interpreting this as "W is Z but with 0"

[robust phoenix]

yeah

[urban lily]

W starts from 0 but Z starts from negative

[alpine sable]

W is N with 0

[proud bough]

There are different notations for this.

[robust phoenix]

I think Z starts from 0 but goes 2 seperate ways which is postive and negative

[proud bough]

In my country, N = W, and N* = N

[alpine sable]

I have never encountered a set of whole numbers

like a notation or something

[robust phoenix]

ayo

[urban lily]

ig thats more right yeah

[maiden holly]

Does natural numbers start from zero?

[alpine sable]

no

[maiden holly]

Or one

[alpine sable]

1 to infinity

[urban lily]

no

[urban lily]

we work as Neutral numbers as "C" and the Whole "N"

[robust phoenix]

N is all postive numbers so 1 to infinity

[proud bough]

neutral numbers?

C?

[alpine sable]

Natural is 1 to Infinity N
Whole is 0 to infinity W
Integers is - infinity to + infinity Z
Rational is of the form p/q Q
Real has everything including irrational R
Complex has complex numbers C

[proud bough]

Complex numbers?

[maiden holly]

So natural numbers is basically the set of positive Z

[alpine sable]

yes

[maiden holly]

?

[urban lily]

no its Counting

[maiden holly]

Alright thanks

[robust phoenix]

does real have I ?

[alpine sable]

no

Complex has that

[robust phoenix]

i see

[alpine sable]

complex numbers are of the form
z = a + bi

where a and b are reals

and basically all numbers come under complex

[robust phoenix]

so if a number/variable encounters an "I" it's considered complex numbers ?

[alpine sable]

"i"

yes

i^2 = -1

[maiden holly]

Is there a bigger set than complex numbers😂

[robust phoenix]

universe

[urban lily]

how tho?

[alpine sable]

Quaternion Ig

[urban lily]

isnt irrational can be represented on the number line

[alpine sable]

root(-1) is not irrational

[urban lily]

so isnt it subset from R

[alpine sable]

its complex

[robust phoenix]

yep beyond complex numbers only 2 more sets

[urban lily]

Right

[maiden holly]

Really?

[urban lily]

mb

[robust phoenix]

yeah

[maiden holly]

Which are?

[alpine sable]

There is something called Quaternion which might interest you I mean just look up the definition might be enough

[robust phoenix]

Quaternions , Octonions

http://www.maths.qmul.ac.uk/~fjw/goldsmiths/2010/JR/Hypercomplex_text_2010.pdf

[maiden holly]

Lmao didnt know such sets existed

[alpine sable]

might aswell introduce the 196,882 dimension group then

[robust phoenix]

everything after real numbers get weird

[alpine sable]

I actually dont have a clue where they are useful at all

[small cypress]

wait guys for these functions, r the areas where they intrsect the y and x interecpt? No right?

[alpine sable]

imo after complex

[alpine sable]

i dont get you

[urban lily]

thats for sure a lot of dimensions lol

[small cypress]

where they intrsect is neither the y intercept n x intercept right?

[maiden holly]

Haha

[alpine sable]

yup I mean

[robust phoenix]

The greatest thing about math is Math is weird

[alpine sable]

they dont intersect any of the axis so obviously they dont

[small cypress]

math is weird n fun

❤️

[alpine sable]

Math is just fun and beautiful

[small cypress]

https://tenor.com/view/spongebob-maths-spongebobmaths-gif-19232863

[robust phoenix]

How can you even comprehend more than 4 dimensions

[alpine sable]

you cant

[robust phoenix]

https://tenor.com/view/dies-cringe-math-dies-from-math-death-gif-22822700

[robust phoenix]

Yeah ik

[robust phoenix]

metaphorically you can

[alpine sable]

this stuff is mostly used in optimization of stuff if I am right

[placid zinc]

"Comprehend" is vague

One might say that comprehending 4d isn't possible

[finite quail]

hi

[urban lily]

I actually just watched a video of "Veritasium" showing that the c which is the speed of light didn"t exaclty get measured the one way speed rather its the 2

[placid zinc]

But we can still say pretty neat things about these kinds of things, by generalizing notions on 3D

[robust phoenix]

well you know time but its not real time is an illusion

[urban lily]

it was a very interesting video

[finite quail]

help

[alpine sable]

sorry to dismiss you but this is #help-0

[urban lily]

right mb

[proud bough]

Check if they have green eyes. Ask the school guard to let them go.

[maiden holly]

Wait wtf

😂

[finite quail]

wtf

[placid zinc]

Indeed, in order to measure light speed like that, you'd need an instrument that can signal faster than light

[robust phoenix]

?which is impossible nothing can have more speed than light

[placid zinc]

Indeed, we can't measure speed of light with one beam from A to B

Gotta bounce it

[urban lily]

exactly, therefore we cant be sure if the light goes in all directions at the same speed or not(gotta stop there cuz its the question channel)

[robust phoenix]

if someone hears the thunder after he sees the lightning by 10 seconds it means he is 3,43km away from the lightning right ?

[stray turtle]

Can anyone solve this?

[robust phoenix]

-3^3 is -27

[proud bough]

Don't crosspost.

[maiden holly]

Can we use induction for this?

Or isit unnecessary

[stray turtle]

yeh induction is also fine

[alpine sable]

would I be able to solve for theta_L if there are two instances of it?

[urban lily]

Is this right guys or did I mess up in smth?

[exotic meteor]

may I get help?

[urban lily]

send your question and if someone can help, they will try to solve it

[exotic meteor]

i need da hel

p

[alpine sable]

So do you know what the mean and the median are?

[exotic meteor]

no

[urban lily]

Mean: Mathematically. the mean can simply be defined as the list of numbers that are used to describe a central tendency. The method to calculate mean is simple enough, the variables need to be added and divided by the number of items in the overall sample. Assume a data value, say x1, x2, … , xn

So, the formula for calculating the mean is given as:

Mean = (x1+ x2+ … + xn)/n

Here “n” is the total number of sample items.

Median: Median, on the other hand, can simply be defined as the number that is found in the middle of the set. Median is an essential quantity that can be used for separating the available sample into two; the higher half sample, as well as the lower half sample, can be procured in this method.

To proceed with the process of finding the median of the given data, first, arrange the given set of numbers on the ascending order, and then determine the middle value from the centre of the distribution. This condition can be suitable if we have an odd number of observations. But, in case of even number of observation, there is no single median value. So, in this case, add the two numbers in the middle and then divide it by 2. The obtained value is taken as a median value.

[exotic meteor]

what the

[maiden holly]

Mean=average

[exotic meteor]

ik what they mean

avg of PM class is 50 and avg of AM class is 80

[alpine sable]

now you just have to do the median

[exotic meteor]

wouldn't it be pm?

[alpine sable]

which is basically lining the results up in order and finding the middle number

if there are two middle numbers you add them up and divide by two

[exotic meteor]

wait so is the answer AM AM?

ye or no

[alpine sable]

yeah i checked the median

but not the mean

so if you're confident with the mean then yes

[urban lily]

isn't the median the same in both?

its the middle number

[exotic meteor]

im confused

was i right or was i wrong

[alpine sable]

the median or AM is 75 the median for pm is 50

[exotic meteor]

so am am right?

cus am pm would be wrong

[alpine sable]

you have to verify yourself man

[exotic meteor]

BOI ur right ngl

well the higher mean is AM and the higher median is AM

sooooooooooooooo

[urban lily]

.

[exotic meteor]

ayo brother

can i lemme know if I got some of these right

u

[alpine sable]

aight real quick

[alpine sable]

but i got my own homework to do hahah

[exotic meteor]

i messed up on 4, i fixed the +'s and made it ,'s

[alpine sable]

wait i mean 1 is right

[exotic meteor]

is 2, 3 and 4 right?

[alpine sable]

2 is right

3 is right

just write 1 number for 4

[exotic meteor]

whats missing in 4?

[alpine sable]

so add all the ones from q3 and then put a single number

[exotic meteor]

me confusion

write an example

[alpine sable]

so 1+0+81

is 82

instead of writing the whole equation just put down a single number like you did in q1

[exotic meteor]

oh so add it together?

[alpine sable]

yeah

[exotic meteor]

78?

[alpine sable]

ye

[exotic meteor]

can u do one more?

with me

so im like fully sure

[alpine sable]

nah man i gotta do my own work

[exotic meteor]

pain

[alpine sable]

you got the hang of averages

just read what they want carefully

[exotic meteor]

alr

ty homie

apex 2k damage badge hammer emoji

[umbral hatch]

lol

[alpine sable]

From a box containing 4 dimes and 2 nickels,
3 coins are selected at random without replacement.
Find the probability distribution for the total T of the
3 coins.

what does the capital T refers ?

[umbral hatch]

i think total?

[alpine sable]

oh ok

[vernal dragon]

how do I solve this kind of equation

is it second order ordinary diff?

r^2+r+ g * angle = 0

[alpine sable]

what does it mean by find the equation of the x axis?
the x axis of what?

[umbral hatch]

x axis is the same for everything

[alpine sable]

?

[placid zinc]

The x-axis is an object, not a description of something else

[alpine sable]

what does it mean then by find the equation

[umbral hatch]

ok putting it this way, u see the x axis, the x always changes, but something is always 0

can u think what what something is?

[alpine sable]

y?

oh ok

I get it now

wait why did you delete ur message

is it wrong

[umbral hatch]

no

[alpine sable]

t why did you delete ur message

[umbral hatch]

I was recollecting my mind

[alpine sable]

ok

[umbral hatch]

i thought i wrote too quickly

so i was making sure

[alpine sable]

so when they say x axis, they mean the coordinate plane right?

[umbral hatch]

ya

[alpine sable]

ah ok

[alpine sable]

Hi guys, how do I find this?

I think the answer is y=x--5 but I didn't use any specific formula to find it

since I just experimented

[amber urchin]

Parallel means that in function y=ax+b both functions have the same a

So you need to find a function that is y=1x+b that also includes a point (2,7)

[alpine sable]

is there a formula or substitution i need to do in order to find it?

[umbral hatch]

substitution

[alpine sable]

what would I need to substitute in order to find it?

[umbral hatch]

dont channel hop

[umbral hatch]

ok so u know equations of parallel lines have same gradient?

[alpine sable]

yeah

the answer is k(2x-2y+10=0), k is a constant

we can have multiple answers

this is one

thats it

if it is wrong please tell me

i know that since they are exactly parallel that they have the same gradient but i still am unsure on what to subsitute

[umbral hatch]

ok cool so what can u establish already about the equation of the required line?

[alpine sable]

dude just go with the relation of if two lines are parallel, the ratio between the first two co-efficients are equal but are not equal to the ratio of the third constnat

[umbral hatch]

we cant have multiple

[umbral hatch]

it has to pass through 2,7

[alpine sable]

aah yes but still what i gave will be correct ig.

[umbral hatch]

yea yea ik ur method

[alpine sable]

i mean the answer i gave

[umbral hatch]

i find mine easier to understand tho

[alpine sable]

ok

[civic vigil]

with explanation please

[alpine sable]

i mulitplied the first two coefficients with some constnat, then substituted 2 and 7 in x and 7 in y and found k.

[alpine sable]

what should we do there

is it an equation or should we simplify it

ask your question like an adult please.

[civic vigil]

simplify

[umbral hatch]

lol

[alpine sable]

ok fine then

[umbral hatch]

take the LCM

[sinful juniper]

Study Exercise 3:

Given a₁₀ = -47 and a₁₅ = -77, find a₂₀
how do i find the difference for this
is there some formula?

(another discussion took place after i sent the same message in questions 1 channel)

[alpine sable]

is subtracting by -10/4 the same as subtracting by -2.5?

[carmine lion]

uh yea?

[alpine sable]

because if subtract 6 by -10/4 I get 3 1/2 but when I subtract by -2/5 I get 3.5

3 1/2 does not equal 3.5 tho right?

[carmine lion]

it does...

[alpine sable]

3 times 1/2 is 1.5

[carmine lion]

no

its 3 + 1/2

have you learned how mixed fractions work

[alpine sable]

oh wait it's plus?

[carmine lion]

yea?

[alpine sable]

wait brain fart

[carmine lion]

lmfao

[hard bloom]

Uhh... Can someone give me the solution of this question and show me how you got it?

[alpine sable]

8/6=m/12

m=16

[carmine lion]

uhh

[umbral hatch]

find scale factor or do what @alpine sable whichever easier for u

[alpine sable]

can someone explain why this is a negative at the two ends

[carmine lion]

maybe try and factorise

wait lemme try

[alpine sable]

wrong equation whoops

^ this is the correct equation for the graph

[hard bloom]

Thank you!

[hard bloom]

Thank you!

[alpine sable]

please dont give out wrong answers but since this looks like a test I'll pass ||you took m/12, and m is not the length of any side of the shape, its a fraction of it|| ||another thing it should be 6/8 = m/12 considering logic, and not correctness||

[alpine sable]

oh right it is wrong, i glanced over it and I didn't realize that the 12 counted that whole side mb

[umbral hatch]

@hard bloom

[hard bloom]

Yes sir

[umbral hatch]

read the above

[hard bloom]

Yeah i realized that when i typed in the answer, i doubled checked and it seemed odd but i also came up with 16 because he said i could do m/12.

[hard bloom]

ah nah its just maths online, they give us that so we can practice working on maths

[alpine sable]

if it is, my hints should suffice ||probably try substracting lengths||, if it isn't well idk

[tender plinth]

anyone know what the inverse of a factorial function would be?

or if there even is one

[humble tinsel]

if this channel is free imma just post my question

i basically need to find an and bn for this furier series

and im kinda stuck on the part of solving the integrals

i do not know if im supposed to make this series have x be in [-1;1] or just to do it

the things i do know are omega, the period, and the fact that f is an uneven function

[harsh belfry]

I've been working on this question for quite some time and I can't seem to figure out how where to go next

After I finally simplified my question to

`x⁶ + h³ + 3x²h + 3xh²

       hx`

I was unsure on where to go next

What should I do?

[fervent anchor]

I will use h in place of delta x simply because it's easier to type
((x+h)^3 - x^3)/h
= (x^3 + 3x^2h + 3xh^2 -x^3)/h
= (3x^2h + 3xh^2)/h
= 3x^2 + 3xh
If you then take the limit as h --> 0, you will get 3x^2.

[vale wigeon]

^^^^^^^^^^ you're missing a bunch of these

[harsh belfry]

I need to take a moment to read through that

Let me write it down real quick

[fervent anchor]

Thx for letting me know :) I almost forgot it

[placid zinc]

You're tripping yourself up by using arrows, when you really should be rewriting the entire line with small simplifications, and doing rough work to the side

It's a problem when you are at the bottom of the page, and have to look at the top to figure out what you're doing. That's a lot of work that can derail you

[harsh belfry]

What happened at this part?

I'm not sure how you got rid of some of the h

@fervent anchor

Also thanks a bunch.

I can see alot of the mistakes I made.

[harsh belfry]

Yeah, you're right. In the future I will work my problems out that way.

Its easier to trace back what I did that way and correct errors

[placid zinc]

Cancelled h from top and bottom

[harsh belfry]

I mostly added the arrows to make it easier for others to follow

Ahhhhh thanks

I don't know how I didnt think of that

Morning brain

haha

[placid zinc]

That cancellation ends up being what makes the limit easy - it gets rid of the hole in the graph

[harsh belfry]

Because I wrote my work in such a way I missed that the second function is negative

Im taking that advice to heart

Thanks.

[placid zinc]

"easy" meaning you can do this algebraically

Not necessarily saying that this is easy to do haha

[pale cloud]

When is the discriminant used?

I know it’s to like find how many solutions for a quadratic but I don’t know when to use it or what it gives

[alpine sable]

so like, you are asking how to use the discriminant to find the number of solutions?

@pale cloud

[pale cloud]

No like if a question say there’s one solution and ask me to find c

[alpine sable]

do you have any problems specifically that you are struggling with?

[alpine sable]

this doesn't really involve any knowledge about discriminants

let me ask you, do you know what y=c looks like? like is it a horizontal line or a vertical line?

[pale cloud]

Using the discriminant, it gives me this questions answer

[pale cloud]

It’s a horizontal line meaning the point touches the x line

[alpine sable]

Y

(-y,0)

is the answer

[pale cloud]

What

[alpine sable]

wdym x line? do you mean x-axis?

ohh wait

[pale cloud]

Yea

[alpine sable]

no, that's not the answer.

so y is a variable?

i thought y was a constant lol

and please do not give away answers.

[alpine sable]

no, that's wrong, you aren't said it touches the parabola on the x-axis, but on some other horizontal line.

[pale cloud]

Oh

Yea it touches the line on where c is

[alpine sable]

the line doesnt exist

so once again, this doesn't involve any special knowledge of discriminants

[pale cloud]

….

[alpine sable]

because the only line that touches one point of the parabola, it is the y-axis, but it is given that the y value is a constant

[pale cloud]

But I’m watching a video and the guy used discriminant

[alpine sable]

can i see what they did? clearly there is a method that doesn't involve any knowledge about discriminants and the number of sols

hey al3dium

[alpine sable]

but if they have one method that does involve, you are free to use it guess. but that looks like overcomplicating

let me see

hey it is simple infact they were just finding the y value

but they gave y=c is a line

which is weird as

if y is a constnat

then the line will be parallel to x axis

[pale cloud]

What are u talking about “y constant”

[alpine sable]

so it should touch paral bola at 2 points

[pale cloud]

I don’t even know what that mean

[alpine sable]

they stated in the question as y=c for some constant c

it means

y is not a variable

it is a constant

[pale cloud]

Yes it’s the y axis why

[alpine sable]

no the y axis is x=c and y being a variable

if y is constant the line is parallel to x axis and if x is constant the line is parallel to y axis

only in direct relations like y=mx

[pale cloud]

..

[alpine sable]

i mean yeah, you can use what they did, but essentially you can just find the maximum of the parabola, since it will be only point that it will only intersect once a horizontal line

[pale cloud]

But why did they did that

[alpine sable]

what they did is more of around-the-corner solution but i guess it's good

[pale cloud]

Discriminant show how many solution it has

Not the solution

[alpine sable]

where did i say the opposite?

[pale cloud]

No u say “u can use that” but idk how to use it

For future problems

[alpine sable]

wait so you are saying the parabola will have a point that is not 100%smooth

okay, their method is rather unintuitive but if you insist, let me try to explain what they did

well in calculus terms it doesnt sound weird but yaah it is weird, it is like corner point of a circle

just mentioning there is a much more intuitive approach to it

[pale cloud]

So

What did they do

[alpine sable]

x + 1 = x

Find x

x doesnt exist

so they essentially thought, the parabola y=-x²+5x touches the x-axis once, but as they are looking for when it touches the y=c, they "added" a +c in the original parabola so that they can find instead where that original parabola hits y=0. which if you think about it, it's just the same problem, but just manipulated into a new one with the same solution. and now is when they use the discriminant knowledge, as they are trying to find where y=-x²+5x+c hits y=0 once, and that once tells us that the discriminant=0, so they just solve the equation discriminant=0, where they find c.

@alpine sable please stop giving away misleading info.

ohh sorry

i just shared what i k

but again, this method is rather unintuitive and wouldn't recommend it

no malicious thought

[pale cloud]

Then what method is good?

[alpine sable]

can you just ping what wrong stuff i just said so i wont say it again, i am not joking

no method isn't "good", just that their method was unintuitive, what i mentioned above is rather intuitive if you know simple knowledge about parabolas

[alpine sable]

here

[pale cloud]

How do u find the maximum

[alpine sable]

do you know about $x_{\text{max}}=\frac{-b}{2a}$

[ocean seal]

Al𝟛dium

[pale cloud]

Yes that’s the x coordinate of the vertex

[alpine sable]

well then, if you find that coordinate, you can plug it into y, to find the y-value of the maximum, and hence the value of c

[pale cloud]

Do it work for other problems like this?

Is there any key words that I need to know in the word problem to use this formula?

[alpine sable]

the reason is a simple as, note that the only point where a parabola can be hitten once, it's at the maximum/minimum, so that's what we are looking for.

[pale cloud]

What if it’s hit twice

[alpine sable]

it is the maximum if the parabola faces down, minimum of it faces up

you are not getting through the point i'm trying to make, the problem was talking about hitting the parabola once, and that only happens at the max/min

there is no other point that can be hitten once with a horizontal line

[pale cloud]

Yeah I understand

[alpine sable]

yes sorry kenny i completely forgot that parabolas have a vertex point of turning

[pale cloud]

Every time when a parabola hit once, it happens at the max and min because there are no other line for it except y=x?

And since I’m trying to find that, I need to find the maximum or minimum?

[alpine sable]

yes it is like the perfect tangent of the parabola exists there

it exists in other places too

but you dont have to you know

do any approximations

[pale cloud]

Is this problem a maximum or minimum

Or do it no matter

I just need to find x of the vertex and plug it In to find y

[alpine sable]

well normally, if the a value is positive then the parabola faces the positive side of y axis

then this value will be the minima value

[pale cloud]

So this is negative

It’s maximum

[alpine sable]

if the a value is negative then the parabola faces downwards so then this value will be maximum value

[alpine sable]

no no listen, if it faces up, then the least value on the y axis

will be the minima value

if the graph faces down then the vertex value will be the maximum

of the y values that exist

[pale cloud]

No if it’s pointing down it’s the maximum and this is the graph

That is pointing down

[alpine sable]

yes i said the same thing right

[pale cloud]

I said the same thing but u said no

[alpine sable]

maybe i misunderstood

[pale cloud]

I meant to say the a is -

[pale cloud]

So do I do this? Al3dium

[alpine sable]

what do you mean with the last part you wrote? also be careful, i'm talking about horizontal lines, no other problem will have the same strategy, what i rather recommend is to have all the tools about parabolas, and have a good intuition about them and about the problem.

and please be careful, every time when a parabola is hit once with a horizontal line, it can only possibly happen at the max/min

let me show graphically

[pale cloud]

How do u know that one point is intersecting the horizontal line

[alpine sable]

,w plot y=-x²+5x & y=6.25

[ocean seal]

Results provided by WolframAlpha

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

Requested by Al𝟛dium#4084

[alpine sable]

look at this, if you try to draw any other horizontal line to cut with the parabola, it will intersect twice other than at the max

[pale cloud]

Yeah so there will be 2 roots

[alpine sable]

if you disagree, try yourself to draw horizontal lines, you will eventually notice it

[pale cloud]

And y=c is a horizontal line right

[alpine sable]

i mean, yes but that's beside the point i'm trying to make, roots are only used when y=0. but in this case, we were talking about y=c not the y=0

[pale cloud]

So is it a horizontal line

Y=c

[alpine sable]

yes, but not necessarily y=0, which you seem to be obsessed with

[pale cloud]

Y=0 mean the horizontal line is at the x axis right

[alpine sable]

which is exactly why the discriminant knowledge doesn't really helps us here

[pale cloud]

But y=c is something different

[alpine sable]

yes

[alpine sable]

yes any function f(x)=c where c is a constant is a horizontal line that is parallel to x axis

[alpine sable]

yes as well.

[pale cloud]

So the horizontal line of y=c is somewhere else and we don’t know

So we need to find it by finding the vertex which is where the point touches

Or intersects?

[alpine sable]

yes

[alpine sable]

where the point touches once the horizontal line

[alpine sable]

yes

[pale cloud]

What

[alpine sable]

he saying that only at the vertex it is possible for a horizontal line to touch the parabola once.

[pale cloud]

Yes

So it touches y=c once

And we need to find the vertex so we can find where it touches

[alpine sable]

yes y=c is the horizontal line, and this line touches the vertex once.

touches once, be careful.

[alpine sable]

yes

touches ones only

[pale cloud]

And the touching part is a y value so to find the vertex I need to do x=-b/2a and that give me the x value of the vertex so I need to find the y and that’s my answer

[alpine sable]

yes.

see bro, any line touches the parabola ones, but for it to be a parallel line to the x axis and touch the parabola ones will be the vertex.

[pale cloud]

If it touches twice then it will have 2 roots meaning it’s just 2 points and just find the 2 x’s right

[alpine sable]

thats why they stated the line is y=c

[pale cloud]

Idk what u mean

[alpine sable]

i think you are getting confused due to me

[alpine sable]

no, that's what i'm trying to get you through, we are talking about y=c, not y=0, so the knowledge about the roots doesn't helps.

i will stop speaking

[pale cloud]

Yes I know y=c now but what will it be if it touches 2 points

[alpine sable]

it will be a linear function

if it is a straight line

dude you are of which grade

just for the sake of simplicity in explaining

[pale cloud]

I’m 12th

[alpine sable]

which country

then we will have infinite solutions, since there are infinite horizontal lines that will touch the parabola twice

[alpine sable]

for that particular y value only, for any y value you will have only 2 solutions

not only for 0

[alpine sable]

what are you saying?

[pale cloud]

😭

[alpine sable]

dont cry chill out dude

[fickle crow]

What line to touch twice at that y value is what I think he is saying

[alpine sable]

can you tag the message you are replying to

[sinful iris]

hello

[pale cloud]

Whattt are u guys saying I don’t even know what we are talking about

[alpine sable]

@pale cloud the problem you suggested about a parabola that touches y=c twice will have infinite solutions, if you imagine it in your head, you can make infinite horizontal lines that will touch twice

[alpine sable]

dont mess it up just listen to aladin guy he is explaining well

[pale cloud]

But u show it only touches the point once so what do U mean infinite

[pale cloud]

Yeah since both sides is going down and the lines could be everywhere

Any*

[alpine sable]

i think you are getting the point but you are explaining it weirdly

[pale cloud]

Wait let me draw a picture of what I’m thinking

[alpine sable]

let me show what i mean by infinite sols

,w plot y=-x²+5x & y=1

[ocean seal]

Results provided by WolframAlpha

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

Requested by Al𝟛dium#4084

[alpine sable]

,w plot y=-x²+5x & y=2

[ocean seal]

Results provided by WolframAlpha

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

Requested by Al𝟛dium#4084

[alpine sable]

,w plot y=-x²+5x & y=3

[ocean seal]

Results provided by WolframAlpha

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

Requested by Al𝟛dium#4084

[alpine sable]

this can keep going on forever.

well you have only 2 solutions for every y value right.

all these are touching twice.

please say yes.

[alpine sable]

can everyone else please don't interrupt me? i feel like we've already been clear that any interruptions will confuse more kennyy.

@pale cloud yes, you can see that we can make loads of horizontal lines where it touches twice hence we will have inf sols

[pale cloud]

Yep

And u can’t find those solution because u need more info right

[alpine sable]

well you can't find the solution since you have infinite solutions, and hopefully you understand that you can't write them down

[pale cloud]

Ohhhh

So I will never see a problem that require me to find 2 solution because it’s infinite?

If y=c

[alpine sable]

i mean, you can find one, and answer with "infinite solutions" but that's all

[pale cloud]

Ohh okay I think I get it now

So back to this one

I want to explain it to make sure I know what I’m doing

[alpine sable]

alright.

but i have to go in like a few minutes

if i don't get to answer you now, i will eventually

or anyone else can answer too

[pale cloud]

So in this question y=c and the parabola touches the y=c at exactly one point so it means that I need to find the vertex since it touches at one point so I do x=-b/2a to find the x value and plug it into y and I get my answer

[alpine sable]

yes.

good job

[pale cloud]

Yay tyy

[alpine sable]

you're welcome.

what is the function for the orthogonal line to y = 3x + 3

can u help me @alpine sable?

i am sorry but can you just say what are ortho gonal lines just asking.

@alpine sable

hey

dude dont send those stuff here

[alpine sable]

2 lines that when they meet each other, they make a right angle

ohh thanks

but the line you gave is a linear one

yh

so then it has infinite orthogonal lines right

no

i got a similar result but i just wanted to check

what is the function for the orthogonal line to y = 3x + 3
can it be -1/3x + ]-inf,+inf[?

can anyone explain how does a linear function graph line not have infinite othogonal lines

[urban lily]

$ x^2 + y^2=4 prove that: y^3 /frac{d^2y}{dx^2} -4=0

bruh idk how to use it brb imma type it

can someone help me with this I can't get it to work

diff calc

[gray isle]

what have you tried?

[urban lily]

I did get the y'' but its no where near the R.T.P

I can write it and send here

my attempt

[gray isle]

note that y' can be isolated from your first derivative

[alpine sable]

@gray isle, can you write it like this: y = -1/3x + ]-inf,+inf[?

Or is that notation weird?

[gray isle]

notation is weird

[alpine sable]

i mean it technically works since b can be any value

i also edited it

[gray isle]

no

bad notation

[alpine sable]

how'd you write it?

[gray isle]

y = -x/3 + b
where b is in the reals

[alpine sable]

real numbers?

[gray isle]

yes or (-inf,inf) or ]-inf,inf[ or equivalent representation

[alpine sable]

okay

[urban lily]

well yes but I do not see where its gonna help, Isn't the derivative coming from both should be the same?

[gray isle]

that y' can be subbed in to your equation for the 2nd derivative that also contains y'

which allows you to simplify

[urban lily]

oh so I should try substituting in 2nd dev with (2x/2y) not the y' itself?

[gray isle]

whut

wdym

sub your y' with whatever y' is equal to

[urban lily]

the y' if isolated equals to 2x/2y

[glass lichen]

also y' != x/y

[urban lily]

yea thats what I meant

[gray isle]

unless i really fked up my algebra, the signs in the question seem wrong. can you double check Mosh

[ancient saddle]

Hello, I suggest to multiply by y^2 on both sides in the last equation

[glass lichen]

yeah should be +4

cause y'' will have -(x^2+y^2)

[fervent anchor]

Calculas😮

[ionic jewel]

whats the question here

[urban lily]

a miserable attempt from me to solve this

but it seems that I need some break cuz clearly I cant focus getting to solve it lmao

[urban lily]

It became more terrifying than it is

[ancient saddle]

Oh sorry, notice that (y^2) * (y')^2 = x^2

[gray isle]

take it one step at a time

[alpine sable]

@vivid fulcrum infinity?

[glass lichen]

clearly not.

[urban lily]

nah

[alpine sable]

Prove me wrong

[glass lichen]

it says digit

[vivid fulcrum]

i dont think so

because the question impleis its a digit

[glass lichen]

so it's an element of Z_10

[vivid fulcrum]

implies*

[still spruce]

I have a question

[alpine sable]

@still spruce Question away you must

[still spruce]

Its a probability question

[glass lichen]

shut up if you're going to promote rule breaking.

[alpine sable]

Triggered

[glass lichen]

channel is in use, ie you cant post here

use a different channel

[still spruce]

I have a 1 in 95000000 chance of getting the green light, everything else is red

[glass lichen]

channel still in use.

[still spruce]

and i get 95000000 tkaes

[gray isle]

https://media.discordapp.net/attachments/487651208048410627/807545463669653514/unknown.png?width=400&height=256

[still spruce]

Im sorry

[glass lichen]

[vivid fulcrum]

LOL

[urban lily]

im not quit sure but i guess it has smt to do with the i^n thing

[rocky timber]

you're talking like Yoda lol

[alpine sable]

Exactly

[urban lily]

AHAHAHAAH

[alpine sable]

And @glass lichen is triggered that I just talked like yoda

[gray isle]

the question should've been to prove
$$y^3\dv[2]{y}{x} + 4 = 0$$
continue from:
$$2x + 2yy' = 0$$
and first isolate $y'$

[ocean seal]

ℝamonov

[glass lichen]

Not triggered, just annoying when you have idiots promoting rule breaking

• trolls

[alpine sable]

Still anal about the rules.

[fervent anchor]

😂

[vale bough]

[urban lily]

so first of all its +4 not -4?

[glass lichen]

yes

[urban lily]

okay cool

when we isolate y'

y'=-x/y

right

[glass lichen]

yes

[urban lily]

ill try to substitute again in the last one

[gray isle]

and you can sub that in to what you had earlier,
alternatively you could differentiate this again

[urban lily]

in this case should I substitute in y or y' or y''?

[gray isle]

y is y

[urban lily]

sry the last 2 only clearly y doesnt have y'

[gray isle]

y" is y"

you're next immediate goal would be to get an expression for y" or y^3 y" in terms of y

sub your y' with whatever y' is equal to

[urban lily]

in which step exactly in the 1st dev I got or should I get the 2nd dev first then sub with the equal to y'?

[gray isle]

... do i have to repeat myself again?

your second derivative has both y" and y' in it(which you don't really want)

you can get an expression for y' from your first derviatve

[urban lily]

okay got that

[gray isle]

sub that value into the equation involving your second derivaitve

[urban lily]

understood

[gray isle]

after doing that, that equation won't have y' in it anymore

only x,y and numbers, (which you DO want)

[fervent anchor]

This is how you find the second derivative of any parametric functions

[boreal whale]

100x84239y.3-344x-3e-c3

[valid warren]

my teacher taught us the wrong way to solve derivatives and I basically got a 65% doing the right method

just ask your teacher before submitting

[boreal whale]

100x84239y.3-344x-3e-c3

[fervent anchor]

Wdym?

[boreal whale]

i need tutor help pls :( i have no time to do after school

[alpine sable]

last digit of 6^n is always 6 and 1^n is always 1 should be enough

[urban lily]

Thank You All! @gray isle @glass lichen @fervent anchor

[meager jay]

I was trying some variations of frensel integral, and I found this using desmos

Can someone help proving it?

I have tried a lot, by solving both indef and def, but no progress

[alpine sable]

It's not a u-sub right?

[meager jay]

The indef integral involves polylogarithms, and I'd like to avoid that

[meager jay]

I don't think so, I have tried many elementary subs

The problem is the discontuinity at x = -pi/6

[alpine sable]

It's not a u-sub because a u-sub will require their to be another function outside of the function. Which there isn't so u-sub is out of the question

[meager jay]

I have also tried tan(x/2) = u sub, but didn't get anything

[limpid scarab]

What’s 2+2

I’m stuck on that

[meager jay]

pls don't spam

[jade birch]

At this point have you checked if the antiderivative exists?

[limpid scarab]

I’m not spamming

[meager jay]

go to #help-1 pls

[limpid scarab]

Why

[meager jay]

so that we can use feynman?I didn't get you

<@&286206848099549185>

(reposted)

[plucky crow]

,w integrate ln(1+2sinx)

[ocean seal]

Results provided by WolframAlpha

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

Requested by Syphax#3869

[meager jay]

,w integral ln(|1+2sinx|) from -pi/2 to pi/2

[ocean seal]

Results provided by WolframAlpha

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

Requested by Delta0001#1968

[jaunty hatch]

why am i retarded

[ancient obsidian]

Don't worry you're not the only one

[alpine sable]

He's not the only ass that really stinks

[fervent anchor]

Oh wait

I forgot there's 1+2sinx😅

[maiden raptor]

I would like to create a little contest to see who can solve this the fastest, this is just contemporary math nothing crazy

[meager jay]

and there is an ln() also lmao

[chrome salmon]

Seems like no one wants to participate

[maiden raptor]

right? i guess they cant solve something like this lol

too hard for them

lol

[chrome salmon]

Or they aren't intrested

[glass lichen]

Or cause that isnt the point of the help channels

[alpine sable]

But what if 0 was equal to 1

[glass lichen]

That im aware no algebraic structure has the same additive and multiplicative inverse

so that'd never happen

[alpine sable]

U are wrong i think

[glass lichen]

Ok, prove me wrong then

[alpine sable]

Ok

[chrome salmon]

Its good until you think that you are the only one to think it

[alpine sable]

0+0=1

[glass lichen]

no

[alpine sable]

But

If

We suppose

0=1

Then

0=1

[glass lichen]

then you'd have 1=2

[chrome salmon]

Lol I expected better

[glass lichen]

and 2=3

and 3=4

etc

[alpine sable]

Hm

[glass lichen]

so your system is just 0

[alpine sable]

Doesnt seem like a problem to me tho

[glass lichen]

so 0 cant be equal to anything else, contradiction qed

[alpine sable]

But

[fossil birch]

Hlepm me i am in the 7th grade 🙂

[alpine sable]

If it was

[glass lichen]

no buts

you're wrong

[alpine sable]

And everyone was wrong

Then?

[glass lichen]

Yeah no clue what you're even saying anymore

0=0, 1=1

[desert flint]

can u help dray

[alpine sable]

Option 1

[desert flint]

plz..

[fossil birch]

THX

[alpine sable]

@fossil birch It's A

Yeah

[chrome salmon]

Yes he will be helped

[desert flint]

cuz im too dumb

🙏🏼🙏🏼

[glass lichen]

Damn, 2 people back to back not knowing how to help

[alpine sable]

Calculus is literally false tho

[glass lichen]

It isnt

[alpine sable]

Newton was probably drunk

[wary stream]

You don't give out answers here

[alpine sable]

High on apple meth or smn

[glass lichen]

Ok, finitist spotted

[alpine sable]

What is a finitist

[glass lichen]

rejects the concept of infinity

[fossil birch]

too bafd

bad

[alpine sable]

I dont

[glass lichen]

so why is all of calc false?

[alpine sable]

Hmm

[wary stream]

Goal of the server is to teach people concepts, not give answers

[alpine sable]

Ill have to think a while

[fossil birch]

too bad

[chrome salmon]

No dray

No

[alpine sable]

Dumb idiot newton didnt write it in a day he took a bunch of decades so give me a break

[alpine sable]

Thanks, but don't you think you should tell @alpine sable too? because he gave the answer here too

[alpine sable]

I mean it was literally a 1+1 question

[glass lichen]

wow, developing an entire branch of math takes more than a day of thinking, I had no idea \s

[alpine sable]

the more you know

But you told him option 1, which is the answer

I spit on newton

[glass lichen]

You did it too, so you're not really in the position to condemn

[alpine sable]

Kilogram better

I set a dog on fire once

[alpine sable]

Here comes Anal mosh to the rescue. lol

[glass lichen]

Not my fault you cant follow rules

[alpine sable]

And the dog inturn set its puppies on fire

Dumpster fire

[wary stream]

What is this nonsense you are saying?

[sly mantle]

@alpine sable you're close to a mute

[alpine sable]

I AM LITERALLY DISPROVING CALCULUS

[alpine sable]

Ok

But if 1+1 is 2
Shouldnt 2+2 be 3

[chrome salmon]

On discord?

[glass lichen]

no

clearly not

[coral pagoda]

oh boy...what is happening...

[alpine sable]

Hmm

I think

[glass lichen]

unless you have some fucked up definition of +

[alpine sable]

I disagree

One could

[glass lichen]

It's 0, what do you expect?

[alpine sable]

I think we should burn all of newton's work

[sly mantle]

@alpine sable i think you're a troll & should soon stop this convo

[alpine sable]

Ok

@alpine sable show us how you disprove newton

[sly mantle]

no, don't encourage further convo from them

[alpine sable]

@sly mantle hes provoking me now

Ill tell him in dms

[sly mantle]

you will not

[alpine sable]

U all gonna miss out on some revolutionary discoveries

[sly mantle]

b&

[chrome salmon]

Oh banned

That's a good abbreviation

[ionic jewel]

i hate s&

[glass lichen]

Damn, now I won't get to see the attempt at disproving all of calc

[sly mantle]

anyone continuing that particular convo will follow suit

move on, stick to hw help

[alpine sable]

@sly mantle Did we just have a dreadful encore of Twisted Karma?

[sly mantle]

encore means repeat, which i hope doesn't happen

[coral pagoda]

That definitely happens sometimes, especially when the question is rather difficult.

[alpine sable]

@sly mantle So this hasn't happend before?

[coral pagoda]

I've taken my shot at helping some people on here, but I've been stuck a fair few times.

[sly mantle]

not in the same day

[alpine sable]

ok

[glass lichen]

it was 25+(-25)

[fervent anchor]

Oop😅 sry

[coral pagoda]

Ah, I didn't see the context

[balmy star]

are these problems considered hard for someone in 11th grade?

[glass lichen]

yeah

I'd say they're hard for grade 11

[coral pagoda]

It is highschool algebra, but they are certainly a bit more involved than typical problems.

[glass lichen]

more so it's just bigger questions as opposed to difficult concept

[balmy star]

oh ok thanks!

[fervent anchor]

Speechless😞

[balmy star]

why?

[coral pagoda]

It's tedious for the very sake of being tedious

[glass lichen]

computational difficulty as opposed to conceptual

[coral pagoda]

I have my feelings about this decision with designing problems.

[jade birch]

||so I take a break to go munch on sth and I miss the origin of the great calculus disproving?...||

[alpine sable]

I'm trying to find the distance between one corner of a cube and the middle of one of its faces

I know the first image is inccorrect but I can't see how. Geometrically they both look the same to me and I don't understand why the value of produced"R" is different for the two methods

[coral pagoda]

Yea, you just added wrong

Both answers are correct. But s^2+1/2s^2 should be 3/2s^2

[ocean seal]

.itsjustnai

[light coyote]

I have to check the convergence or divergence of this,
I used the ratio test and I'm getting 0/0. is that a valid case for convergence ?

[coral pagoda]

First, probably a good idea to slow down a bit. What does the fraction converge to?

Hopefully you can see it immediately

[light coyote]

1 ?

[coral pagoda]

correct

Okay, now here's the thing. If 1 aspect of the sum converges, then the other one must converge in order for the entire sum to converge.

Note a sum converging, does NOT mean its parts have to converge.

Okay, now the question is does tanh(n) converge?

[light coyote]

umm so if I use ratio test on that it becomes
tanh(n+1) / tanh(n)
limit of tanh approaching infinity is 1
so that converges to 1

[coral pagoda]

It sure does!

So we have two converging pieces, 1 and 1.

Now the limit of the a sum is equal to the sum of its limits (provided they converge)

So we have $\lim a_n=1-1=0$

[ocean seal]

dackid (jump king +)

[light coyote]

Alright, what does this mean though?

So it converges to 0?

[coral pagoda]

100% correct

[light coyote]

Niceeee, thank youu 😊

[coral pagoda]

Happy to help 🙂

[deep quiver]

-5i(1/8i)

Tell this question

a+bi

Complex number

@alpine sable

??

Telling it not ?

Not conjugate

Just real and imaginary part

[wary stream]

Is this from a book?

[deep quiver]

Just tell

[wary stream]

What?

I'm asking to see what the exact question is

[stuck jolt]

Lmao, wdym just tell

Do you not want to know why?

[deep quiver]

Tell answer

[wary stream]

I can't

[deep quiver]

Why you dumb

[wary stream]

Because I don't understand the question

[deep quiver]

You all are dumb

[stuck jolt]

Watch what you say

[maiden holly]

😂 What the hell

[deep quiver]

All are dumb ass

You don’t know simple question

[wary stream]

This is not helpful information at all

[stuck jolt]

The information you are giving us is not helpful, and please refrain from using insults

[deep quiver]

What

I told

Full question

This is from complex number a

[wary stream]

It is not helpful information

Do you have the exact question to post?

[deep quiver]

Express that following question in the form of a+bi

[alpine sable]

-5i(1/8i) rationalize

[wary stream]

Now that's a bit more helpful

[deep quiver]

That is the question then -5i(1/8i)

[wary stream]

Then just saying complex number

[stuck jolt]

Well, took you a while to finally tell the question

[alpine sable]

He said it

Before

[deep quiver]

That first part

Of example 2

[wary stream]

But not in a very clear fashion

[alpine sable]

You wrote it down wrong

[maiden holly]

i^2=-1?

[fervent anchor]

this is the complete question?

[wary stream]

The picture is

[stuck jolt]

That is just 5/8

[deep quiver]

Yes

[alpine sable]

Multiply them

[stuck jolt]

Like example 2 is just 5/8

[deep quiver]

K thnx

[stuck jolt]

I mean, hopefully you know how I got there

But it is quite straightforward I mean

[deep quiver]

K

I’m checking you all

[alpine sable]

(5/8)+0i if you need it in that form specifically

[maiden holly]

Nani

[deep quiver]

Yeah real part is 5/8 and imag part is 0i

[alpine sable]

Did I pass

[deep quiver]

Yes

Lol

[stuck jolt]

Yes

[deep quiver]

@fervent anchor

Want the hell you are typing

@maiden holly

[maiden holly]

Are helpers like trained professional mathematicians or are they just passionate volunteers ?

😂

[fervent anchor]

@deep quiver the question wasn't complete

[deep quiver]

Now completed

[strong furnace]

you will find some of both

[deep quiver]

Check my dm

[stuck jolt]

They are a bit rude, ik

[deep quiver]

He or she ?

[fervent anchor]

Btw) use (a-b)² = a²-2ab+b²

[deep quiver]

@fervent anchor

Check dm

[stuck jolt]

They

[wary stream]

Stop pinging people

[stuck jolt]

ˆ

[deep quiver]

..

[sly mantle]

@deep quiver watch your attitude toward others

[glass lichen]

the latter

[alpine sable]

@maiden holly I tutor math as a side job. Here I volonteer, it helps me keep sharp

[maiden holly]

ah icic

[stuck jolt]

<@&286206848099549185>

[alpine sable]

Did you just @ yourself

[sly mantle]

@stuck jolt as a helper you should know to use the ping after 15min pass with no reply

[stuck jolt]

Tbh, I did not even know that

[sly mantle]

see #❓how-to-get-help

[alpine sable]

Read the rules lol

[rigid wind]

the rule is mentioned like every 15 minutes

[stuck jolt]

Anyways, what is done is done... Does anybody have an idea on how to do this?

[alpine sable]

No clue

[maiden holly]

Nani did a helper just break a rule lmao😂

[stuck jolt]

Lmao, tbh I did not even know that it was a thing

[maiden holly]

Haha

[stuck jolt]

I will repost it so people see it

Well then

[slender girder]

captain can you pls help?

[sly mantle]

@slender girder pls use an unoccupied channel