help-33

[merry ivy]

where

[smoky siren]

Yes

I'm not going to write it all out in MathJax, but this is what I would do

The point is 1 10 25 is easy to multiply by integers without much pain

[proper zodiac]

Oh wow MATLAB is a great way to show this kind of stuff, very nice

[smoky siren]

Yeah it turned out nicer than I expected

[merry ivy]

what does A(1, : mean?

[smoky siren]

Matrix A taking row 1 and all columns

[merry ivy]

is it the row number?

[smoky siren]

the colon means all the indices

[merry ivy]

so the first >>A :

its basically row 1 + row 3

[smoky siren]

to make a new row 1 yes

[merry ivy]

okay. glad i understand the format

which website is this?

[smoky siren]

This isn't a website

[merry ivy]

what is it?

[proper zodiac]

A software called MATLAB

[merry ivy]

ah.. thanks for the help

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[marsh citrus]

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[timid spindle]

guys, when i compute nullspace which variables do i take as a b c?

[timid spindle]

like which variables do i write the other variables in terms of

the non pivot columns??

like here

[proper zodiac]

You write the pivot variables in terms of the non pivot ones

In the last matrix they have 2 pivot columns in column 1 and column 2, they correspond to variable x_1 and x_2

There is no pivot in the third column which would correspond to x_3

So x_3 is not a pivot variable and so we write the other two in terms of it

[marsh citrus]

@timid spindle Has your question been resolved?

[timid spindle]

oh thnx

[timid spindle]

so just identify all non pivot columns, write those out as is

then represent rest in terms of those non pivots?

thnx mate

[marsh citrus]

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[timid spruce]

whats the best way to improve at mathematics

[marsh citrus]

Please don't occupy multiple help channels.

[woven minnow]

try your best.

no matter what happend keep trying

[timid spruce]

ok thank you

[marsh citrus]

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[marsh citrus]

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[west nest]

part II

my question is

why is it an enlagement of 2^1/3

i thought it would be an enlargement of 2^1/3 /2 which is 2^-2/3

[rapid island]

Did you find the roots of $z^3-1=\sqrt{3}i$

[elfin berry]

azeem321

[west nest]

i just realized issue

my issue

its small to big triangle

nvmd all good thanks

.close

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[graceful leaf]

https://media.discordapp.net/attachments/867389710132707378/972872569822781451/20220508_201604.jpg

[graceful leaf]

Hello

In the proof of theorem 2.27

I suspect that the L taken to be the limit is actually the limsup of the sequence

Is this true

[marsh citrus]

@graceful leaf Has your question been resolved?

[marsh citrus]

@graceful leaf Has your question been resolved?

[still temple]

Hi dense, may i ask, what textbook are you using?

[graceful leaf]

Concise introduction to analysis by Schroeder

[marsh citrus]

@graceful leaf Has your question been resolved?

[still temple]

why do u think that, cos i couldn't find that anywhere in the proof, and it also doesn't have to be true

[graceful leaf]

It's not mentioned such in the proof but taking the inf of upper bounds I thought it had to do something with the lim sup

The proof is written in such a manner that it really makes this very unintuitive

Most proofs of this theorem that I have seen use bolzano weistrass

But this one dosent

Guess it always dosent have to be limsup

Thank you for replying

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[heavy charm]

Im not really sure how to solve this question

<@&286206848099549185>

How do you know the percentage if you dont know the amount shared?

<@&286206848099549185>

.close

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[still temple]

Help

[still temple]

15/2=(b-3), find the missing coordinate which is b

The slope is -2/3

What do I do at this part? 15/2=(b-3) ?

[delicate forum]

15/2=(b-3)? is this an equation?

where does the slope come into this

[still temple]

To find the missing coordinate

[late geode]

if the goal is to find b
simply solve the equation

[still temple]

Which is B

Yes

[late geode]

like you would any other linear equation

same operations to both sides of the equation etc

[still temple]

15/2+3

21/2

10.5

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[flat junco]

,rotate

[flat junco]

how to prove that H is normal subgroup of G

[plucky shoal]

G is abelian, so all subgroups are automatically normal. So just prove H is a subgroup of G

[flat junco]

i know this fact

but is there any other way ?

[plucky shoal]

No

[flat junco]

hmm

[sour relic]

no

[plucky shoal]

why?

[tacit trail]

#❓how-to-get-help

[sour relic]

what has x/lnx to do with Michael's question

[marsh citrus]

@flat junco Has your question been resolved?

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[autumn saffron]

Why pi is irrational number despite being ratio of circle circumference to it's diameter ?

[whole sleet]

Why might you think it is rational?

[prime sage]

well, why is it that sqrt(2) is sqrt(2)/1 and it's irrational

the numbers in the fraction must both be integers for it to be rational

[autumn saffron]

So aren't there any possibilities that both of them will be integers so that we can say pi is rational ?

[prime sage]

not possible

[stoic saddle]

no

it is kind of an ordeal to present a proof that pi is irrational though

(as in, it's much harder than proving that sqrt(2) is irrational, to give an example)

https://en.wikipedia.org/wiki/Proof_that_π_is_irrational

[autumn saffron]

Now I'm thinking that diameter cannot be irrational because it's just a linear measure but is there any way to justify that circumference is only one which is irrational plz forgive if I'm wrong somewhere

[stoic saddle]

you are wrong

it is very possible for the diameter to have an irrational length

any line segment can be used as the diameter of a constructed circle after all

[autumn saffron]

So you mean length can also be of √2 units like that.

[stoic saddle]

of course

[autumn saffron]

Ok thx this was very helpful

Can you explain me why decimal notation is given more priority than just fraction with other denominators other than 100.

[stoic saddle]

??

more priority where?

[autumn saffron]

I mean in my school if write answ as like 23/12 or 67/77 they don't allow rather they like to simplify it more and represents in decimal form i.e with denominators in powers of ten.

[stoic saddle]

so your teacher does not allow any fractional answers at all, even on problems that don't say "round to 3 decimal places" or something to that effect?

[still temple]

It's easier you would have to convert this in decimal which will take unnecessary time

[autumn saffron]

I mean if it's not in decimal form at last they don't consider it to be full answer

[civic moss]

Who cares about decimal

That makes no sense

[stoic saddle]

so if the answer to a problem is 1/3 the teacher FORCES you to write 0.33333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333... on the paper?

[civic moss]

Decimal is less “full” than a ratio

Lmao

[stoic saddle]

honestly

it sounds like your teacher is just shit

nothing else

[still temple]

Well this is rational so you can place a bar but what about irrational values

[autumn saffron]

Nah Nah I'm just saying that they want me to write as in decimal notation and not in fraction like 56/45 rather. They want me to convert it into decimal notation and write it as like 1.24

[stoic saddle]

there could be any number of reasons why your teacher would enforce such an arbitrary requirement.

maybe it's because they have a lot of students and have to grade homeworks quickly and don't have time to check whether somebody got a fraction equivalent to the true answer but unreduced

[autumn saffron]

Are you a student ?

[still temple]

Probably for the students to get a 'feel' of the value

[autumn saffron]

Ok

[stoic saddle]

me?

[autumn saffron]

Yes

[stoic saddle]

i'm a university student, yes.

[autumn saffron]

Us ?

[stoic saddle]

no

[autumn saffron]

UK?

[stoic saddle]

no, and i don't like how you keep trying to guess where i'm from.

please stop.

[autumn saffron]

Sorry I will not do that from now

[still temple]

lolol

[stoic saddle]

what's so funny

[main idol]

stop being creepy and asking personal questions

[autumn saffron]

Can you plz solve this . Let the rational number p/q be closest to but not equal to 22/7 among all rational numbers with denominators less than 100 what is the value of p-3q. There is solution of this question in internet but I don't understand it a bit .

[autumn saffron]

Sorry I was just curious really sorry for that

[marsh citrus]

@autumn saffron Has your question been resolved?

[stoic saddle]

Can you plz solve this .
this is a great way to make everyone AVOID helping you with your question(s) outright.

[marsh citrus]

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[shell fable]

can someone help

[still temple]

Well, I don’t know what they mean by solve with square roots, but you can start by factoring out 5x

Then factoring the quadratic

And the roots would be the answer

Like this

[marsh citrus]

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[spice nacelle]

Are u allowed to remove (x-3) now

In nominator and denominator

[bright jay]

No

[spice nacelle]

Ok thx

.close

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[south fog]

Grade 8 - Averages of Statistical Data, please help answer the problem for a, b(i), and b(ii) with steps, thanks!

[marsh citrus]

Please don't occupy multiple help channels.

[bright jay]

Don't open multiple channels

[south fog]

the old one was supposed to be closed but idk how to close it

[bright jay]

.close

[south fog]

ok

.close

[marsh citrus]

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[mild pike]

yo

[mild pike]

is this right?

[gusty briar]

yes

[mild pike]

alr bet

.close

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[pine cloak]

Hi

[pine cloak]

How do you solve this for x?
I know that 85/0.094 can be done and then moved to the left as a division.

But after that, how do you continue?

[marsh citrus]

@pine cloak Has your question been resolved?

[pine cloak]

<@&286206848099549185> any help would be much appreciated

[marsh citrus]

@pine cloak Has your question been resolved?

[marsh citrus]

@pine cloak Has your question been resolved?

[civic moss]

@pine cloak distribute, subtract, combine fractions

[pine cloak]

960.10= 904.2553 * 1.094^x + 1000/1.094^x

(960.10*1000)/904.2553 = 2x1.94 ^x

1061.75768 = 2x1.94^x

I get this

Which I know is wrong

Answer should be 6

[delicate ruin]

What is that [] supposed to mean?

[pine cloak]

The one in the image I sent?

That's a bond price equation

[delicate ruin]

Ok idk what that is in german

[main idol]

The brackets [] sometimes represent the floor function. Check in this case if it is

[pine cloak]

In this case, the brackets are normal brackets, they do not represent the floor function.

[marsh citrus]

@pine cloak Has your question been resolved?

[marsh citrus]

@pine cloak Has your question been resolved?

[signal dust]

Here, as the x is in the power, you would have to take logs of both sides

[marsh citrus]

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[violet lotus]

Hi! I would need some help with equations if anyone is free to help! I have learnt now the base of equations but I don’t know how to solve this tbh. My question is:

[violet lotus]

In an isosceles triangle, one side is x cm.
The other two pages are twice as long.
Perimeter = 75 cm

a) Write an expression for the circumference of the triangle.

b) Calculate the lengths of the pages using an equation.

c) Check that the solution is correct.

[nova totem]

Draw a diagram first

By "page" do you mean side

[violet lotus]

Yes sorry

i used translate

Since it’s not in English

[nova totem]

I see

Draw a diagram of a triangle

With respective side lengths

[violet lotus]

Okay

done

[nova totem]

Show me

[nova totem]

Yeah so now label the sides

[violet lotus]

Ok

[nova totem]

Now construct a formula for the perimeter

[violet lotus]

Ok

Oh btw

On my paper

It says that the perimeter is 75 cm

Sorry forgot to mention it

[nova totem]

Oh okay

Yeah that's important lol

So let P be the perimeter

[violet lotus]

Ok

[nova totem]

Construct an equation, $P$, in terms of $x$

[elfin berry]

Umbraleviathan

[violet lotus]

Okay

What’s next?

[fair fox]

Are you trying to construct triangles with constraints?

[marsh citrus]

@violet lotus Has your question been resolved?

[nova totem]

What is your equation

Sorry I had to do something lol

[violet lotus]

i don’t have one

I need to make one

And idk how

[fair fox]

Have you been able to find a answer?

[marsh citrus]

@violet lotus Has your question been resolved?

[violet lotus]

.close

[marsh citrus]

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[still temple]

Can someone explaim how they got the first equation in this solution?

[marsh citrus]

@still temple Has your question been resolved?

[still temple]

<@&286206848099549185>

[marsh citrus]

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[still temple]

Hi guys is this approach correct?

[still temple]

@cedar forge for your reference

[marsh citrus]

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[oak void]

how do i deffrenciate -250/x?

[oak void]

250/x = 250x^-1 right?

[still temple]

yes

[oak void]

thanks

[still temple]

@oak void do you know d/dx of 1/x?

[oak void]

x^-1?

-1x

[still temple]

nope

that's wrong

[oak void]

-1x^-2

i mean

[still temple]

nope, you can't differentiate 1 over X with power rule

[proper zodiac]

?

[oak void]

so you can't differenciate 1/x?

[still temple]

fuck I'm wrong

soory

[proper zodiac]

you can and its this

[still temple]

I'm fuking dumb, I thought its integration

I'm out

[oak void]

💀

[still temple]

now my brain will remember this embarassing moment until I die

[marsh citrus]

@oak void Has your question been resolved?

[oak void]

.close

[marsh citrus]

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[oak void]

how do i got from f'(x) to f(x)

[late geode]

integration

[oak void]

oh yeah, im stupid

🤦‍♂️

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[high belfry]

hey can anybody explain to me how the term "∫udv = uv - ∫vdu" works?

[prime sage]

product rule i believe

like (uv)'=uv'+u'v

[high belfry]

do you have any explanation on how it works? or know like a video

[prime sage]

oh

[high belfry]

yeah exactly but i dont get the upper term

[prime sage]

do you mean how to derive the formula or how to use the formula

[high belfry]

i was trying to do ∫f(x)g(x)dx = ∫f(x)dxg(x) + ∫g(x)dxf(x) but that seems wrong

[high belfry]

derive

[prime sage]

so like (uv)'=uv'+u'v

[high belfry]

this one

[prime sage]

and the integrate both sides

[main idol]

https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/ab-diff-1-optional/v/product-rule-proof

and then
https://www.youtube.com/watch?v=q_BP4LyvdOA

[high belfry]

thanks

.close

[marsh citrus]

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[still temple]

in RHS how it converted

[prime sage]

-8 = -10 + 2

[still temple]

thx man

.close

[marsh citrus]

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[still temple]

help plz

[prime sage]

ngl i dont see any mistakes, you sure you got the equations right?

[still temple]

heres the whole equasion

it wants it done in that way

maybe my equasions at the top are wrong

[prime sage]

what are your variables?

[still temple]

RaTa=760 which is the basic rate problem

RsTs=220 same thing but for salieri

[prime sage]

what i meant is that R is rate and T is time right?

[still temple]

yeah

[prime sage]

Ts = 2Ta is wrong i think

[still temple]

oh

why

[prime sage]

Amadeus took twice as long

so Ta = 2Ts

[still temple]

oh

omg im stupid

tysm!

[prime sage]

np

[marsh citrus]

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[arctic gale]

Hi

[arctic gale]

,rotate

[arctic gale]

How to calculate the surface of a sector with centerangle 1/6pi

1/6*180 degrees = 30 degrees

So my guess would be 1/6 *pi *r^2

[marsh citrus]

@arctic gale Has your question been resolved?

[marsh citrus]

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[prisma trellis]

Hello guys

[marsh citrus]

Please don't occupy multiple help channels.

[prisma trellis]

I’ve been waiting for hours to get help

I’ve tried so many times to find the value of n, can anyone please help me try finding n?

[proper zodiac]

,rccw

[prisma trellis]

Wdym?

[prisma trellis]

So does that mean n=18 is the first value of n?

[still temple]

First integer solution, but then again im not entirely sure if in ncr you can put n in terms of fraction or not 💀

[prisma trellis]

How did you get 17.0168?

[still temple]

I didnt, i put it in a calculator

[prisma trellis]

Oh ok

Do you know anyone who can explain it

[still temple]

@ramanujan

[marsh citrus]

@prisma trellis Has your question been resolved?

[marsh citrus]

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[agile phoenix]

Find the inverse of the following functions algebraically. Is the inverse a function? Why or why not?

3. g(x) = (4/3)x - 7/3

[agile phoenix]

I changed it y = (4/3)x - (7/3)

then changed it again to X = (4/3)x - (7/3)

i got stuck after that

[fleet dagger]

it should be y on right side

after 4/3

[agile phoenix]

oh i meant (4/3)y

I got stuck after those step

[fleet dagger]

rearrange stuff to leave y alone

and that's your inverse function

just make sure g is bijective

[agile phoenix]

should i do like 4y-7/3

[fleet dagger]

sure, then multiply by 3, add 7, and divide by 4

[agile phoenix]

i will just get y alone then

.close

[marsh citrus]

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[agile star]

Hello I have a Question.

I have this circle, which draws values from -1 3/4 pi to 1 3/4 pi and which linearly fall off towards 0 depending on the distance from the center.

The red lines move forward and rotate based on the value of the pixel they are on (flow field style):
(prevHeading + pixelValue - prevDirection)

Now my issue is, that on the left side where the transition is, there is no smooth transition. the lines dont flow through the border (blue lines).
The seem to shift away (green arrow) the further they are from the center.

What could I do so the lines flow through the borders?

[odd crest]

i don't really understand what you mean

[agile star]

If you look at the right side of the image the lines flow naturally, on the left, the lines dont pass the black white border. (white would be 2pi and black -2pi). At those borders the value seem to fall off.

[nova tree]

So you want it to spin around the circle?

[agile star]

yes

[odd crest]

this is a vector field?

[agile star]

I think it could be interpreted that way yes

[odd crest]

what is the black white border supposed to do

what is the thing you want?

[nova tree]

Isn’t it because the pi’s zero out

Causing a straight line

[odd crest]

well the arctan can cause issues

[agile star]

this looks more like a vector field

[odd crest]

idk if you use that

[nova tree]

Once it enters the circle it’s forward speed should be reduced to 0 so it just goes in circles without travelling forwards

[odd crest]

i feel like you need to explain what it is and what you want it to do

[nova tree]

Cuz when it travels forwards it leaves ur spinning sphere

Cuz it’s got a range

Actually that wouldn’t work either cuz they lines would just form a circle

What is the point of this

[odd crest]

that's my question

like explain please

cuz i can't help if i don't know what we're talking about 😄

[nova tree]

Ur right lol

[agile star]

just visualisation I would like to get a vortex looking thing xD

[odd crest]

could you try change the strength of the vortex

making it much stronger than the leftwards thing?

[nova tree]

Wait why are the lines straightened out on the left

Wouldn’t that just push out

[agile star]

yes that is the problem

[nova tree]

It should be in a circular motion

[odd crest]

the vortex is going counter clockwise

but the speed to the left

is too big

[agile star]

yes that is what I would like a circulat motion

[odd crest]

it causes this weird problem

[agile star]

I dont use speeds I use pixel values to determine rotation

[odd crest]

the thing is

this looks like a vector field of only left

combined with a vector field of rotation

just added together

[agile star]

the value 0 is interpreted as left

[odd crest]

you want this?

[agile star]

ah so you think at the edges there sould be no lines at all

yes

[nova tree]

It would be nice if ur lines had a directional head

[agile star]

ok wait

[nova tree]

Ok that’s better

Right so arrows on the left should push right into the sphere and arrows on the right should push left

[agile star]

true on the right theres the same issue, and I understand now what Katherine is saying with the two vector fields combined

[nova tree]

Yh he’s right

[odd crest]

the area surrounding the circle

what colour is it

and what value does it give?

[agile star]

0

[odd crest]

what does 0 represent?

cuz it needs to represent no direction

[agile star]

well right movement

true

[odd crest]

you want to create a vortex using the colours of the pixels as direction values right?

[agile star]

yes

[nova tree]

If the outside of the circle has a value of 0 and no direction wouldn’t it just stop before entering the circle?

[agile star]

yes that is an issue

[odd crest]

what if you change 0 to be up?

instead of right?

or rotate the picture 90 degrees clockwise

[agile star]

I can try

[nova tree]

I feel like you need another force to push the lines into the Center or counteract the acting force of the lines so it don’t just go off screen

So what if we just like surround the vortex with a circle that pushes lines into the vortex

[agile star]

so that's 0 = up:

oh down

[nova tree]

That looks better

Maybe

[odd crest]

this is what you want

where there is a very shallow spiral inwards?

[agile star]

yes

but I also see my problem now, the "force" of the spiral needs to be stronger than the general direction of 0 otherwise the vectors will allways pull out of the spiral

[odd crest]

what are you doing with the values?

to get this?

[nova tree]

Wouldn’t a circular force pushing inwards but not stronger then the vortex force work

[agile star]

I create a point then from there i create a new point (distance, 0) rotate that new point by (heading ofLine + pixelValue - previousPixelValue) and offset it by the previos point.

line is (prevPoint to currentPoint)
not sure if this is understandable

[odd crest]

what's heading of line?

[agile star]

this = currentPoint - previousPoint;
atan2(this.y, this.x)

[odd crest]

atan :S

[nova tree]

Is this maths or a type of coding language

[agile star]

coding language sorry

[nova tree]

Python?

[agile star]

java

[nova tree]

E

Alright I’m guessing atan is a def function

Right?

[agile star]

what do you mean?

[nova tree]

It’s a sub program

Right?

You’ve imported this.y this.x to replace two variables?

Yo ngl idk any Java

[agile star]

so I checked what atan2 does. It says:
Returns the value of the first argument raised to the power of the second argument

[nova tree]

Ok so

Ur doing this.y this.x^this.y?

[agile star]

pretty much where this.x is (currentPosition - nextPosition).x

[nova tree]

Alright

How do you know next position

[agile star]

wait no it's y^x

[odd crest]

atan2 is the arctangent function

but a special one

[agile star]

pseudo code:

next position is:
next_position = vector2(distance, 0)
next_position.rotate(prevHeading + currentPixelValue - previousPixelValue)
next_position.add(currentPoint)

[odd crest]

this is really dependent on the right pixel values btw

[agile star]

yes and the pixel values are:
angle from centerpoint + pi/2

[odd crest]

why - previous pixel?

[agile star]

so it's just a deltaRotation otherwise if there where all 0 for example the lines would not go straight

[odd crest]

i don't really understand

the previous heading + pixelvalue makes sense

wait

wouldn't it just be current pixelvalue?

cuz that already is angle from centrepoint + pi/2

[agile star]

true!

Ok I changed that and you are right

still looks the same

[odd crest]

previousheading + pi/2?

[agile star]

I just rotate nextPosition by pixelValue

angle from centerpoint + pi/2 are the pixelvalues

[odd crest]

can you make it in colour?

[agile star]

yes blue?

[odd crest]

you could try to make it in 2 pieces

for example have it so that blue colour gives everything a rotation

[agile star]

ah you mean like adding a dimension

[odd crest]

i think ultimately the way you're trying to do it is not gonna work

i think the picture you use should be different

you could make it a black disk with a darker inside

and just use the darkness as a measure of how much to rotate

[agile star]

well eventually I dont want to show the values it would be just the lines reacting to the values

ah yes I see

[odd crest]

so heading = angle from origin - pixelvalue * pi/2

• cuz that's counterclockwise

which is better

😄

[agile star]

where pixel value would be distance

[odd crest]

from origin

yes

this would result in

[agile star]

I have actually two values to play with, the opacity of the pixel and the pixelValue

[odd crest]

i said it exactly opposite way around 😄

what you have now with pixelvalue * pi/2

needs to be other way around

as in 1 - pixelvalue

if the pixelvalue goes from 0 to 1

(maxvalue - pixelvalue) * pi/2

[agile star]

yes that is a nice spiral!

[odd crest]

also the outwards thing can be inwards if you add 180 degrees

i think

angle from origin - (maxvalue - pixelvalue) * pi/2 + pi

[odd crest]

it will flip it from counterclockwise to clockwise

apart from the fact that it applies to a square

it looks good

a spiral vortex

[agile star]

yes I'm thinking about the square thing

but I like the result

Yes I think I can work with that, thanks to both of you. Would it be alright Katharine, if I messaged you once I have another question about this? So I don't have to re-explain the whole process? I think I can go from here though

[odd crest]

is good

[marsh citrus]

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[frigid nimbus]

can someone explain these to me?

It's too complicated for me

like can somoene simplifiy what they're saying like in simple words?

[fossil mulch]

ah im not sure if i can explain you pefectly but ill give a try to make u understand

[frigid nimbus]

sure @fossil mulch

[fossil mulch]

alright so basically here , they're trying to find the maximum/minimum value of function

[frigid nimbus]

i know what maxima and minima are but the problem is i don't understand why we're doing a second derivative and i don't understand any step after that

[fossil mulch]

ohhh alright

gimme a min

look at this pic

so basically when we do df/dx = 0, they're tryin to find the point where the slope is 0

[frigid nimbus]

righrt

[fossil mulch]

so after finding the points, there might be two cases 1) the curve might be downwards as in 1st pic 2) the curve might be upwards as shown in 2nd pic

and in the first case it'll be the maximum coz look the curve in first pic, isn't the top most point is the maximum one?

[frigid nimbus]

yep

[fossil mulch]

so by doing second derivative we'll know if the curve is upwards or downwards, if we get d²y/dx² <0, it means the curve is downwards and it gives the maximum value

and if we get d²y/dx²>0, it means curve is upwards and it gives the minimum value as in the 2nd pic.

did u understand this?

[frigid nimbus]

i am thinking

i can't wrap my head around why doing the second derivative would tell us if the slope is upwards or downwards

doesn't the first derivate already do that

[fossil mulch]

first derivative gives us the point where exactly the slope is 0, in other words look in to the picture, it gives the point where that dotted line is meeting the curve

see this one, first derivative gives the cordinates of that red point.

[frigid nimbus]

i need to understand the fundamentals

so

the derivative of any function gives us the slope of that function at any point

right?

[fossil mulch]

yep

rightt

and second derivative

[frigid nimbus]

what does it mean to take the second derivative of a function?

[fossil mulch]

tells us how the curve is behaving, if it's going upwards or downwards

did u get this?

[frigid nimbus]

nope

the second derivative is the first derivative of a new function

what is this new function?

[fossil mulch]

new function is "first derivative of actual function"

let's take an example wait

[frigid nimbus]

ok

[fossil mulch]

so here the function is -3x²-6x-4

so the first step is to derivate it

and we get -6x-6

now we'll have to equate it with "0" to get the point where slope is 0

so -6x-6 =0

we'll get x=-1

did u understand till now?

[frigid nimbus]

i still dont get what the second derivative of a function signifies

like what is it on the graph

the first derivative is a function that will give u the slope of the function at any given point

[fossil mulch]

ok now we've got the point (x,y) =( -1,-1)

[frigid nimbus]

what is the second derivative?

[fossil mulch]

this tells us if it's maximum or minimum at that particular point

[frigid nimbus]

i will watch a video on second derivatives first

i think i am not clear on those

[fossil mulch]

yeah try with video. may be you'll understand there better.

[frigid nimbus]

yeah

[still temple]

The second derivative tells if a graph is concave up or concave down

[frigid nimbus]

why would it do that?

or

how does it do that?

[proper zodiac]

think about the tangent line, the second derivative will tell you how that tangent line changes as you move x

[frigid nimbus]

well the tangent line doesn't change

it's a line

[proper zodiac]

as you move x

[frigid nimbus]

y changes yeah

but the slope of the tangent line remains constant

[still temple]

As you increase the value of x the slope increases continuously in concave down graph

[frigid nimbus]

okay so the second derivative is not the function of a line, it's the function of a set of lines right?

[still temple]

Not a single tangent line the tangent line for all different points of a graph

[frigid nimbus]

okay i will watch a 3blue1brown video rq

on higher order derivatives

they help me a lot

[marsh citrus]

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[frozen jolt]

so this is a circle question
im stuck on how to find the angle of 2
i have already found angle 1 based on the central angle theorem that the measure of a central angle is equal to the measure of the intercepted arc
finding angle 2 is where im stuck

[marsh citrus]

@frozen jolt Has your question been resolved?

[marsh citrus]

@frozen jolt Has your question been resolved?

[frozen jolt]

<@&286206848099549185>

[frozen jolt]

.close

[marsh citrus]

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[frozen jolt]

this is sad

[marsh citrus]

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[severe cedar]

Can i get the rotation from a Rodrigues axis represention to be equal to a rotation matrix constructed from roll pitch yaw?

[severe cedar]

I just want to know if they are equivalent.

[marsh citrus]

@severe cedar Has your question been resolved?

[marsh citrus]

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[elfin gale]

Given an equation x² - xy = 23, where x and y are natural numbers, what is x + y?

[elfin gale]

im confused

like x(x - y) = 23?

oo wait

since 23 is a prime number, so the only possible values for x and (x - y) are 23 and 1, aren't they?

ohhhh now i get it ok ok thanks @west lichen

.close

[marsh citrus]

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[distant charm]

hi

im having a hard time trying to solve this proof

so i've tried finding similar angles as to find similar sides if similar angles

but it doesn't seem to work out within the range of the given

[marsh citrus]

@distant charm Has your question been resolved?

[distant charm]

<@&286206848099549185>

[prisma scaffold]

Hi, so the way I did this was by showing that both triangles share all three angles

[distant charm]

how would one do that?

i've tried an it just doesn't seem to work

at least for me

[prisma scaffold]

There is more than one way to label these angles but we will need to label 2, I labelled CBD as x and BCE as y

Now we just have to fill in all the angles that can be expressed in terms of there labeled angles

To get BCE and EAD, we will need to draw some extra lines

Draw lines 3 lines from B, C and D all going to the centre of the circle called O

Since triangle BCD is isosceles, we can find angle BCD as 180-2x and therefore the angles BOC and COD are both 2x

[distant charm]

ok

reasonable enough

but quick thing, i know you explained all this, but i think our teacher doesn't really expect extra lines to be drawn

[prisma scaffold]

Oh

[distant charm]

yeah sorry

i didn't want to interrupt mid way

[prisma scaffold]

No it's alright, I was just gonna explain why angle BAE was the same as CDE etc but you already know that, as you have labelled then as thr same color

We since CBE and CDE are the same size since triangle BCD is isosceles, then BAE and EAD are the same

They will all be x using my labelling

So the three angles of both triangles are x, y and 180-x-y

After you have filled them all in and you don't need to draw extra lines

[distant charm]

alright

thank for the help man

sorry for the slight misunderstanding in the beginning

[prisma scaffold]

Sorry, I meant BCE was y not BCD

But you can label them any way you want, then just fill in all the rest

[distant charm]

aight

.close

[marsh citrus]

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[unkempt wraith]

I dont really know why im struggling with probability so much but if someone is willing to vc with me to help walk me through that would be awesome

[still temple]

so, the all possible ways to take 6 cards out of the maximum possible way of ordering around 46 cards into 6 cards each where their order doesn't matter

[unkempt wraith]

that would be 9,474,296,896 possibilities?

[still temple]

$\frac{6}{\frac{n!}{(n-r)!r!}}$ I think this should be it

[elfin berry]

please request a new nickname

[still temple]

wait

hmmm

so let say

[unkempt wraith]

are you able to vc?

[sleek lake]

this is too short to vc about

46 choose 6 = 9366819

[still temple]

that is to total possible combinations for which order doesn't matter

this implies that

if we pick one out of that group there may be one that is the same but different order

so that would be asking how many ways can we arrange 6 cards

where the order doesn't matter

🤔

[sleek lake]

it means that can't happen

[unkempt wraith]

without repitition would be 6,744,109,680 possibilities?

[still temple]

Oh

[still temple]

Oh wait I must I've mixed it up

my bad

[sleek lake]

yes "doesn't matter" is too short to convey the real meaning

[still temple]

so that would imply that it's only 1/total combination

as all numbers must be there

🤔

[sleek lake]

yes

[still temple]

yeeeet

that is hella low

🦦

$\frac{1}{\frac{46!}{(46-6)!6!}}$ I think this should be it

[elfin berry]

please request a new nickname

[still temple]

$\frac{(46-6)!6!}{46!}$

[elfin berry]

please request a new nickname

[marsh citrus]

@unkempt wraith Has your question been resolved?

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[quick dagger]

A boy has 100 Hershey's kisses in his backpack before morning recess. During recess, he eats 30, gives 10 to his friend Ali and another 10 to the supervisor. How many Hershey's kisses does the boy have left. Include and algebraic expression as well.

[quick dagger]

please I need helppp

[hazy lion]

which part is giving you a problem

[quick dagger]

I need help with the solution and especially the algebraic expression

where do you use x in this question??

pleaseeee

[hazy lion]

x is what the question is asking for

[quick dagger]

hmm

so x=100-30-10-10

because you would have to subtract the amount he gave away/ate from the amount he had before recess, right?

because I did this question on an online test and I did this but I got a mark off

[hazy lion]

idk that looks right to me

[quick dagger]

yeah

I am gonna have to ask my teacher

thanks for your help bro

because the other option was like x=100-30-10x2

^no brackets

and another one was x=100-30+10+10

no brackets

because you have to follow bedmas

or pemdas if you are american

[hazy lion]

how dumb they try to trick you to force you to get it wrong

to me it seems like u got it right but

good luck

[quick dagger]

yeah its annoying

thanks for your help 🙂

see you later bro

.close

[marsh citrus]

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[marsh citrus]

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[inland coyote]

hey

[inland coyote]

could someone help me take first order conditions for this

lagrange

[marsh citrus]

@inland coyote Has your question been resolved?

[marsh citrus]

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[tepid quiver]

find the area of this intersection of cos(x), sin(x) and tan(x)

[whole sleet]

weird

Well, splitting it vertically will work

Left area = ∫ tan(x) - sin(x) dx (0, a)
Right area = ∫ cos(x) - sin(x) dx (a,b)

Where a is the x-value of the intersection between tan and cos
And b is the x-value of the intersection between sin and cos

Oh wait, I guess b = π/4

But a is going to be a strange number

[tepid quiver]

[whole sleet]

Yeah this is a "use tech" kind of problem

[tepid quiver]

I have a genius idea

$$\int_{0}^{\frac{\pi}{2}}\cos\left(x\right)dx = 1$$

[elfin berry]

Chunkin

[tepid quiver]

right that's the area of the blue

what if you then find the area of the green and pink

and subtract that

😳

cuz then u don't have to use all 3 at a time

[tepid quiver]

any idea how to find green or pink

[proper zodiac]

pink: find that intersection

[still temple]

try to find those

[whole sleet]

You're about to do the same problem with more steps, I think

[proper zodiac]

int the appropriate functions before and after that intersection point

[whole sleet]

Ultimately you'll still need to find the green, which has a strange value for the endpoint

[proper zodiac]

you can probs get green by integrating the inverse functions

[tepid quiver]

wait but guys

[proper zodiac]

imagine flipping it in x-y, those'll be the inverse functions

[tepid quiver]

tan(x) and sin(x) only intersect at 0 (and multiples of pi but that's outside the scope)

[proper zodiac]

why are you looking at that

[tepid quiver]

^

[still temple]

try to find those and then - them

[tepid quiver]

😳

ok

[proper zodiac]

wasn't that literally the idea you just had chunkin?

[tepid quiver]

$$-\int_{0}^{\frac{\pi}{2}}\cos\left(x\right)dx+\left(\int_{0}^{\frac{2}{3}}\left(\cos x-\tan x\right)\ dx+2\int_{0}^{\frac{\pi}{4}}\left(\cos x-\sin x\right)\ dx\right)$$

[elfin berry]

Chunkin

[tepid quiver]

I think it was a bit different

cause mine excluded the area we are trying to find

uh duz this look right

$$-\int_{0}^{\frac{\pi}{2}}\cos\left(x\right)dx+\int_{0}^{\frac{2}{3}}\left(\cos x-\tan x\right)\ dx+2\int_{0}^{\frac{\pi}{4}}\left(\cos x-\sin x\right)\ dx$$

[elfin berry]

Chunkin

[marsh citrus]

@tepid quiver Has your question been resolved?

[dreamy trench]

,w int_0^b(tanx-sinx) dx + int_b^(pi/4) (cosx-sin(x))dx

[elfin berry]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by EndTimes#8053

[dreamy trench]

,w int_0^(2arctan(1/2(1+sqrt(5)-sqrt(2(1+sqrt(5))) (tan(x)-sin(x)) dx

[elfin berry]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by EndTimes#8053

[marsh citrus]

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[dreamy trench]

A = sqrt(sqrt(5)/2 - 1/2) - 1 - 1/2 log(1/2 (sqrt(5) - 1))

[marsh citrus]

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[robust talon]

okay, so i dont understand composite functions, and my teacher refuses to help me. i am compleatly lost

[still temple]

find the possibility of the case that getting 10 people to sit circling a round table and of them of being selected 3 people sitting side by side?

<@&286206848099549185> help

[lavish raft]

welp

[bright jay]

One, this channel was taken by someone else. Two, you have to wait at least 15 minutes before pinging helpers

[lavish raft]

damn 3?

[bright jay]

Look up resources, khan Academy is good

[lavish raft]

oda is better

[bright jay]

Did I ask for your opinion?

Because I don't care

[lavish raft]

so do i

[marsh citrus]

@robust talon Has your question been resolved?

[robust talon]

sorry

[marsh citrus]

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[robust talon]

i straight up forgot i opened this

[marsh citrus]

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[inland bay]

3. A lighthouse, 50 metres high, is on a cliff. From a ship, the angle of elevation of the bottom of the lighthouse is 44° and the angle of elevation of the top is 49°. Find the height of the cliff.

[inland bay]

Can someone solve it for me, I opened I ticket before but no one explained properly how to do it and just gave vague clues. Also someone else closed my ticket.

[main idol]

start by drawing a picture

[inland bay]

I did

Someone told me to use sin on smaller triangle and cos on larger one

I’m stumped

[main idol]

share your picture

[main idol]

,rotate

[main idol]

where's the lighthouse

[inland bay]

It’s the 50m

Below it is the cliff

On the left side

[main idol]

what is that 50?

oh it's 5 degrees

[inland bay]

Yes

[main idol]

what is this supposed to be

sin(theta) = ?

[inland bay]

Yes

[main idol]

Oh is that opp / hyp ?

[inland bay]

Yh

He told me to use it to find h for right angle triangle

[main idol]

what is this equation supposed to be?

you have 2 h variables. are they the same?

[inland bay]

No mb the h on the left side is H as in Hypotnuse

Small h is cliff height

Since opposite of the angle is 50(lighthouse height)+h(cliff height)

Angle being 49

[main idol]

Oh so you have 2 equations and 2 unknowns

[main idol]

re-write this with proper H and h as you said

[inland bay]

Ok

[main idol]

Then write an equation for $\sin(44^\circ)$

[elfin berry]

riemann

[inland bay]

What?

[main idol]

,rotate

[main idol]

Isn't that a 9?

[inland bay]

Yes

49

[main idol]

So write an equation for sin(44)

Use your diagram

[inland bay]

Umm ok

Like that

[main idol]

Right

Do you know how to solve a system of 2 equations with 2 unknowns?

[inland bay]

Uhhh no

Explain plz

[main idol]

https://www.mathplanet.com/education/algebra-2/how-to-solve-system-of-linear-equations/solving-systems-of-equations-in-two-variables

Solve for one variable in one equation, then plug that into the second equation

[inland bay]

Ok lemme investigate

I don’t think I’m doing this right 😅

[main idol]

use foil here

then solve for h

[inland bay]

Ok

Like that expland left bracket

[marsh citrus]

@inland bay Has your question been resolved?

[inland bay]

Wow, try fingers but hole

No sights of jou ahead

[marsh citrus]

@inland bay Has your question been resolved?

[marsh citrus]

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[jagged abyss]

the line y = -2x + 4 crosses a and b

show the radius for the circle that goes through the dots A, B and origo is sqrt5

[young nova]

Do you know how to find the x and y intercepts of a line?

And do you know how to find the distance between two points

Oh actually wait I sorta misread the question.

The circle part seems a bit trickier than I had thought

Were you taught how to find the circle passing through 3 points?

google is giving me a fairly straightforward method but I ideally want to use the one you leaned in class

It's ok if you don't remember

[marsh citrus]

@jagged abyss Has your question been resolved?

[jagged abyss]

okay

.cllose

.close

[marsh citrus]

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[peak viper]

Idk where have i gone can someone help me ?

[peak viper]

°wrong

[nova totem]

I'm sorry what

Is this

$\sin{\left(\frac{x}{2} + \frac{π}{4}\right) = 1$?

[elfin berry]

Umbraleviathan
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[nova totem]

It looks like you have an = in the argument

[peak viper]

Yeah it has =

[nova totem]

I think that's a typo

[peak viper]

I dont get it

[nova totem]

Because that doesn't make sense

It should be + or -

Given the location of = on the keyboard, I think they meant +

sin(0.25π) ≠ 1 so

Like

I'm thinking they meant + instead of =

They forgot to hold the shift key lol

[peak viper]

Lmao ,
Ok i ll let him know