help-28

[calm tinsel]

uh

first derivative?

[ember shadow]

yes

[calm tinsel]

ok so I see i have to use the first derivative

but what do I sub for x and y?

[ember shadow]

what do you think

[calm tinsel]

I initally thought x=0 as y=1

but I don't think thats right

then the other way around?

[ember shadow]

no

you're told where there is a (local) minimum

[calm tinsel]

I know to find local minimum you find x using the first derivative when y=0

[ember shadow]

not when y=0, a local minimum occurs where y' = 0

[calm tinsel]

y'

my bad

when y' = 0

you find x and you get the x

you sub that into the original y and get the y

[ember shadow]

no, you are given where the minimum is

[calm tinsel]

(1, 1)

[ember shadow]

yes, so you don't need to find the x value at the minimum

[calm tinsel]

yea but what do I sub back in is the problem I'm having

I know how to do it when going forwards but not backwards

[ember shadow]

what is y' again?

[calm tinsel]

y' = x^2 + 2x + C

[ember shadow]

right. so there are 3 "unknowns" there, but you're given 2 of them, right?

[calm tinsel]

mhm

[ember shadow]

so figure out the 3rd

[calm tinsel]

:V

so y' = 1 and x=1 ?

[ember shadow]

no... there is a minimum at x=1

[calm tinsel]

so y' = 0?

[ember shadow]

yes

[calm tinsel]

oh

I see now

then I assume x=1 when y=1 for y(x)

yes?

[ember shadow]

yes

[calm tinsel]

perfect

thank you so much for the help

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[dim compass]

Is f(x,y)=x^3+x^3y + y^3x + y^3 same as y=x^3+x^3y + y^3x + y^3

[gritty rose]

no?

typically one writes z = f(x, y) for surfaces

[dim compass]

Oh it was used in homogenous equation

[gritty rose]

still no?

[dim compass]

Teacher told that if f(xt, yt)=t^n(f^x) it's homogenous equation

[dim compass]

Alright thanks

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[onyx inlet]

https://cdn.discordapp.com/attachments/903481102591750184/1109149454558314536/image.png

[onyx inlet]

I took the LCMs and got (4a-ay)/4y = (ay-5a)/5y

what do I do from here?

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[outer herald]

How would you find a function f, such that

f(x)+f(e^(-x))=0

[outer herald]

I don't really need a solution, but I wonder.

I have computed a solution to this problem by neural network(bro), but I would like to
see is it even possible to actually find it.

Here is what my NN gave as output.

It gives different outputs, so I guess there is a lot of such functions.

Here is red line - actual function f(x)

green line is f(e^(-x))

And if you carefully look they indeed cancel each other

[wise wyvern]

Do you know anything about the function's differentiability?

[outer herald]

it is

[wise wyvern]

Differentiate this equation.

Also there's probably some data missing, that we'll check once you start working.

[outer herald]

f'(x)-f'(e^(-x))e^(-x)=0

Give me a direction

what to search

what to watch

how to find it

branch of mathematics that works on such problems

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[pastel breach]

I'm stuck during half way through my calculations

[wicked gull]

!show

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Show your work, and if possible, explain where you are stuck.

[light sonnet]

,rotate

[light sonnet]

Do you know the formula for area and perimeter?

[pastel breach]

yes

[light sonnet]

And they are?

[pastel breach]

a times b for area

2a plus 2 b for perimtre

this is where im stuck

[light sonnet]

,rotate

[pastel breach]

hope the image is clear

[light sonnet]

Is that 5 an exponent?

[pastel breach]

yep

[light sonnet]

That's the first mistake

Because it's 5 times the area

Meaning 5A

[pastel breach]

oke

let me see if i can solve it now

thank you

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[runic spruce]

struggling to get into that form

[runic spruce]

i got y sqrd = 8t^4 -4t^2

but eliminating t and p ...

[viral jasper]

wdym?

[runic spruce]

going from what i got to their answer by subbing in

im not getting anywhere

final ans only has x and y rather than t and p

[viral jasper]

Did you mean "by eliminating t and p"?

[runic spruce]

but i havent got rid of t yet have I? im confused😭

i think what ive done isnt useful

[viral jasper]

[viral jasper]

I'll give you a hint: I did what you've done so far and I got the solution

[runic spruce]

ok ill keep tryin

[viral jasper]

Do this: Solve for x in terms of t, then figure out what 4(x-1)(2x-1) is in terms of t

[runic spruce]

ok finally got it

thanks

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[neat river]

I need help with this problem please : Among all the circular base cones inscribed in a sphere of radius R, what is the height of the one whose volume is maximum?

[bronze vale]

what have you tried?

[neat river]

Nothing really. I need someone to show me how to do it if thats possible

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[quiet stirrup]

You know the equation for the volume of a circular-based cone. However because it is inscribed in a sphere, it can't get too large because if the height is the diameter sphere, you would have a degenerate zero volume cone. So find a way to relate the volume formula to the sphere by noting that the sphere is uniquely defined by its radius. After that it's just basic calculus and take dV/dh, find critical points, etc.

[neat river]

Could you possibly show me on paper how to do it?

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[woeful hatch]

So I've been trying, badly, to solve this:

[woeful hatch]

and while I understand how to get here (even if the calc notation is really sloppy)

What I don't get is where this comes from

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[woeful hatch]

<@&286206848099549185>

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@woeful hatch Has your question been resolved?

[woeful hatch]

this is just depressing

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[runic spruce]

for 6c

[runic spruce]

in this line shouldnt it be 5.52 instead of 5.65

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@runic spruce Has your question been resolved?

[plush egret]

i'm with you, but ultimately im not sure it matters

im getting different values than the solution, too

afaict the test stat should be $\frac{ (5.52-5.7)\sqrt{20}}{0.1} \approx -8.05$

[glossy valve]

jan Niku

[plush egret]

which obviously leads to h_0 rejection

but i could be really really wrong

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@runic spruce Has your question been resolved?

[runic spruce]

Yeah I think either way it’s rejected

Thanks

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[woven frost]

.open

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[woven frost]

.

[woven frost]

How would you set up the integral for this question

[void crest]

Typically, you can use either the shell method or washer method for most problems. The trick is choosing which one make the problem easier. Remember it’s all about the slices. The disk/washer method is slicing perpendicular to the axis of rotation so that the slices create a flat disk or washer when rotated. The shell method is slicing parallel to the axis of rotation so that the slices create thin cylindrical shells like a coke can.

These pictures also tell us how to setup the integral and the bounds of said integral.

[woven frost]

So is the y=4 only for the bounds?

I’m just confused cause typically either the lines intersect or are part of the axis

[void crest]

It can be one of the bounds. The bounds under one method are functions under the other. However, this problem is best setup for using perpendicular slices to the y-axis and adding those disk/washers in the y-direction.

You can pretend there is one more graph here: The line y = 4.

But you don’t need that if you use the disk/washer method for this problem.

[woven frost]

Ah sorry I didn’t add jt

But it’s already just asking for it to be revolves around y axis

Revolved*

[void crest]

Since you’re rotating about the y-axis, the slices perpendicular are in terms of x. The lengths of the slices are determined by the distance from the y-axis, which is exactly the values of the functions. The one furthest from the y-axis minus the one closest to the y-axis.

These create disks with area πr², where r will be the lengths of the slices.

Then you sum, i.e. integrate, all these stacked slices from the smallest y-value to the largest y-value enclosing the area.

[woven frost]

So to determine the lengths of the slides in this question you would do y-y/2

Slices*

[void crest]

The functions are in terms of x; so, x - 2x

Imagine drawing a perpendicular line from the y-axis to the line y = x. What would the length of that line be?

When x = 2 what’s the length of the line segment between the y-axis and the line y=x?

[woven frost]

Wouldn’t it be just 2

[void crest]

Ecxacyl

It will always be x for whatever value of x

[woven frost]

Okay I understand this part

[void crest]

The same is true for 2x

So outer minus inner.

[woven frost]

But then how would you set the integrals in terms of y

[void crest]

Then sum / integrate all the disk/washer in the y-direction (bottom to top)

Ahh yes. I see. I was thinking in terms of the picture. You are correct. Since we’re integrating in terms of y, you do indeed solve the two functions in terms of y.

[woven frost]

Ah ok

[void crest]

which would be what you said.

[woven frost]

So the length of the slices would be y/2?

From y-y/2

[void crest]

Let’s check to see if that makes sense looking at the picture

Looking at y=0 would the slice appear to be 0 in length?

[woven frost]

Yeah

I think

[void crest]

And at y = 4, would it appear to be length of 2. We can see that the length is from x=4 to x=2; so it does appear to be the case.

The slice* is from

[woven frost]

What would be the next step in setting up the integral

[void crest]

Now, these are disks; so don’t forget to square the lengths and multiple by π

[woven frost]

So just pi (y/2)^2

[void crest]

for each value of y from y=? to y=?

[woven frost]

Could you elaborate on that chase that lost me

Cause*

[void crest]

pi (y/2)² is the area of a disk for each value of y in the picture.

To get the volume you add all of these disks stacked on top of each other.

starting at the bottom y = 0 to the top y = ?

(adding means integrating)

[woven frost]

So 0 to 4

[void crest]

And I think you got it! You have everything you need for the integral to find the volume of rotation.

[woven frost]

I have a question then

[void crest]

The disk method is based on the volume formula for a cylinder: V = πr²h. Here, r is the length of the slices in the x direction and h is what you get when you integrate all of those in the y-direction.

[woven frost]

I tried doing the question before and I got it wrong

And the integral set up is

3/4 piy^2

Where did the 3/4 com from

Come*

Well I can see where the /4 came from

But not the 3

Unless I’m just messing up algebra

[void crest]

Sorry. I misspoke. When you’re finding a washer it’s area of the outer circle minus area of the inner circle.

So each radius is squared.

y² - (y/2)²

[woven frost]

Ah

Okay thank you

[void crest]

no worries.

[woven frost]

Thanks a lot actually

👍

[void crest]

You’re welcome.

[woven frost]

Have a good one

[void crest]

Have a good evening

[woven frost]

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[normal thicket]

Which function defined on R by f(x)=x for every x in R, is continuous in R?
Ans A. identity function
B. constant function
C. dirichlet function
D. Riemann functi
I want to know which book has these topics? I searched it in function topics but didn't find it

[gritty rose]

Calculus should cover the first two

[normal thicket]

They pick up these function seperate?

Like metric function(distance)

[stiff musk]

the question doesn't make sense... if the function is defined by f(x) = x, then how could it be the constant function etc?

[gritty rose]

Just google any calculus book and look at examples. They should have a lot. If you need more real analysis is also more in depth and has more complicated examples

[normal thicket]

Answer is identity function

[gritty rose]

You probably just fumbled the translation

f(x) = x is the identity function

The rest of the information is irrelevant

[thick minnow]

if you're not comfortable in english then you can tell me in Hindi otherwise the question doesn't make sense

[normal thicket]

I wanted to know that these options are taken up separately and made this question?

I have real anaysis book which has riemann integral only

[thick minnow]

umm... okayyy

[thick minnow]

so did you make up the question?

Or like can you post take the picture and post it here

[normal thicket]

No i was solving previous year question

[thick minnow]

previous year NET question or GATE question?

[gritty rose]

Just screenshot it next time

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@normal thicket Has your question been resolved?

[normal thicket]

Yeah sure

[normal thicket]

No Delhi teacher exam TGT

[thick minnow]

I... okayyyy..... the longer I look at it, the worse it gets

[normal thicket]

May I ask which exam you are preparing for?

Can I dm you?

[thick minnow]

you can just tell here

I am preparing for the NET maths exam

[normal thicket]

Which attempt?

[thick minnow]

2nd

[normal thicket]

Can you tell me which book you read for calculus?

Any coaching center?

[thick minnow]

wdym calculus, single variable calculus isn't in syllabus

we have real analysis

[thick minnow]

I found few PDFs from a telegram link

I can post it here if you want

[normal thicket]

Yes please share or dm

[thick minnow]

sent

close this channel if you're done

[thick minnow]

as for this I think it's just meant to ask what is f(x) = x called

for some reason extra info is given that it's continuous on R

[normal thicket]

Yes. Thank you all

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[stable quarry]

Hello, I have kind of a hard to explain question. I have 5 Litres of bleach and I need to dilute it evenly among these bottles. I need to dilute 0.325mL of bleach per litre of water. I need to find out how many bottles I can fill up using 5 L of bleach. Each bottle is 1 Litre.

[empty sapphire]

so each bottle is 1 Liter and you need 0.325mL to make a cleaning solution for that 1L bottle

you have 5 Liters total so we can use dimension analyis here

[stable quarry]

Yes

[empty sapphire]

bare with me one moment

shit sorry my laptop died I'm typing on my phone. Someone else better handle this it's hard to do Latex over mobile.

Sorry 😦

[stable quarry]

😭

[empty sapphire]

also, is it supposed to be 0.325mL, 0.325L or 325ML?

[stable quarry]

0.325 ml

[empty sapphire]

.325 ML is tiny. That would be the most concentrated bleach ever, lol

but ok I'll try over mobile

[stable quarry]

ty its kind of a theoretical thing im trynna workout

[empty sapphire]

ah ok

so if we convert 0.325 mL to L, we get 0.000325 L of bleach needed for a solution.
If we have 5 L total of bleach and a single bottle need 0.000325L of bleach to make a cleaner, then you can fill 5/0.000325 = 15384.6153846, or about 15,384 and about 2/3 total bottles

is 15,384 bottles and a not quite so full bottle

here's the math behind this (also I was able to find my charger and log back on 🙂 )

[stable quarry]

aaaa ty i see where i went wrong. I did 0.000325 / 5 and then did unnecessary calculations with that number haha ty very much

[empty sapphire]

yeah np!

[stable quarry]

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[torn jolt]

Hii, i was simply playing with linear transformations (i am currently watching the 3blue1brown course on linear algebra) and in the video no 3 he speaks about transformations based on the basis vectors that we can modify the basis vectors to obtain a new formula to calculate the position of any vector.

Now i was playing with several of such transformations and then randomly i kept imaginary numbers as ab expriment, just to see what happens. Turns out we need a new dimension or a new axis to define these transformations. Am i right or am i mising something, please help.

The pic above is just me applying a single transformation to 2d vector and as you can see, the x-coordinate and the y-coordinate is a sum of 2 imaginary number, now we can add a new axis in this scenario but what about when we bring in the z-coordinate too. I am stuck, help me

[torn jolt]

This is the pic i am talking about

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[torn jolt]

No

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@torn jolt Has your question been resolved?

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@torn jolt Has your question been resolved?

[torn jolt]

No

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@torn jolt Has your question been resolved?

[stiff summit]

Where are you stuck?

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@torn jolt Has your question been resolved?

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[faint valley]

What do I do now there is no way they wanted me to solve this in this way

[alpine wolf]

help me with prime factorization pls

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[cloud furnace]

prove that a^n + b^n is divisible by a + b if n is odd

[cloud furnace]

i dont even know where im supposed to start

[sharp flame]

Probably induction

n = 2p - 1

[cloud furnace]

i dont have that yet

[sharp flame]

divisible for all natural numbers p

Oh

[summer echo]

factoring

[cloud furnace]

hm?

[summer echo]

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

this for example

[cloud furnace]

ah

would that hold true for all odd integeres n tho

with a+b being a factor

[sharp flame]

It would

[summer echo]

This is just the case n = 3, you will have to find similar factorizations for other n

[cloud furnace]

ohk

thanks

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[sonic scarab]

Prove that with any real number a, b such that $0 < a, b < 1$, the following inequality holds:
$\sqrt{ab^2 + ab^2} + \sqrt{(1-a)(1-b)^2 + (1-a)^2(1-b)} < \sqrt{2}$
Use the Cauchy-Schwarz Inequality.

[glossy valve]

Khwu

[sonic scarab]

I have thought about factorising into sqrt ab(a+b) and sqrt (1-a)(1-b)(2-a-b)

And with that used Cauchy but it does not lead me to the correct proof

This is an Olympiad problem

<@&286206848099549185>

I would appreciate any help

Please

This is a very interesting problem guys <@&286206848099549185>

[full forum]

@sonic scarab Has your question been resolved?

[sonic scarab]

<@&286206848099549185>

[full forum]

@sonic scarab Has your question been resolved?

[sonic scarab]

<@&286206848099549185>

.close

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[hazy dove]

.reopen

hey

[hazy dove]

can anyone help me with this math equation

I love math, it's just that geometry is my weakness😭

<@&286206848099549185> hellooo😭😭

[full forum]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

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Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

@hazy dove Has your question been resolved?

[hazy dove]

absolutely not

<@&286206848099549185> it's exactly 15 minutes now, can anyone help me with this thing now please?😭

[quiet needle]

@hazy dove dm

[hazy dove]

okay

can anyone help too?😭

anyone?

another 15 minutes has passed

and yet still no one

<@&286206848099549185> hey????😭😭

I'm loosing hope

[alpine wolf]

<@&286206848099549185> i need help with prime factorixation

[hazy dove]

ay ay why you taking my channel?

you tryna take it?

[full forum]

@hazy dove Has your question been resolved?

[hazy dove]

No

[silk oar]

What's the question?

!status

[full forum]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[pure kite]

Where is the drawint

Drawing

[hazy dove]

oh

here it is

I don't really get it

are you guys still there?

[pure kite]

https://youtu.be/kXcG6oYh3i8
Maybe you can watch this

[full forum]

@hazy dove Has your question been resolved?

[hazy dove]

Yes

[full forum]

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[arctic cove]

help me with all of these please

[full forum]

Show your work, and if possible, explain where you are stuck.

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[hardy folio]

Need help on the last question where it's asking for an equation where the two surfaces meet using the z variable

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[hardy folio]

How am I supposed to find the answer to the last prompt? "Write an equation for where the two surfaces meet using z."

[pure sandal]

when both surfaces meet both equations are true

||sub one into the other||

[hardy folio]

so do I just solve this like system of equations?

[pure sandal]

idk

it sounds wrong

i got ||z = 1||

[hardy folio]

that is correct

what did you sub in ?

[pure sandal]

z = root x2+y2
x2+y2 = 1

so z = root 1

[hardy folio]

bruhhhhhh

it was that simple im a n idiot

[pure sandal]

imma get screamed at by the helpers

cus

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[strong cliff]

did I do the (3x + 3)^2 wrong?

[strong cliff]

I think I got the wrong answer

[jade root]

foil it out

[strong cliff]

I tried to

and It was something like 1600

pls someone help

^ i want to be able to solve these kind of equations for the 9th grade nationals

[hallow marsh]

dude (3x+3)^2 equals 9x^2 + 9 + 18x

[strong cliff]

eee

Oke

[hallow marsh]

look (x+y)^2 = x^2 + y^2 + 2xy

[strong cliff]

Why the 2xy?

[hallow marsh]

just multiply

[strong cliff]

Doesnt make sense :/

I mean like yes I belive ya all that it’s true

[light sonnet]

$(a+b)^2 \neq a^2 +b^2$

[glossy valve]

dldh06

[strong cliff]

it just seems silly

[hallow marsh]

do this multiplication
( x+y)^2 = ( x+y)(x+y)

[strong cliff]

alr

the yx * yx step explained it well

ty everyone

also

when you do these kind of ”opening brackets” stuff, do you always plus the different parts together

like in this examples

example*

^

[light sonnet]

do you always plus the different parts together
What exactly do you mean?

[strong cliff]

Well for example 2(a + b)

so you’d have 2a + 2b

right?

[light sonnet]

Yes

What about it?

[strong cliff]

Aaa so we add +s

[light sonnet]

Where is s from?

[strong cliff]

pluses

[light sonnet]

Oh

[strong cliff]

I meant it at pluses

the +s

Oke

well ye except for if you have a -

oke i understood everything now ty everyone :))

.close

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[peak dome]

.close

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[torn jolt]

Is this right

[atomic blade]

Yes

[torn jolt]

Does the x become to the second?

Like -6sinx^2-3cosx^3

[atomic blade]

What

No

That makes no sense

Why would -6x sin(x) become -6sin(x^2)

[torn jolt]

So what would it become

@atomic blade

[atomic blade]

What you have is fine

[torn jolt]

That’s the final answer?

.close

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[vestal tide]

would this be 1 when approaching from both sides?

[empty sapphire]

correct

[vestal tide]

FUCK YEAH

[empty sapphire]

lol

[vestal tide]

im doing the line through the x axis method

[empty sapphire]

I'm not familiar with that one, but if works for you then great! 🙂

The thing with limits to remember is that a limit exists if the left hand limit and the right hand limit "approach" the same value. Even though f(2) does not exist (hence the open circle), the limit does in fact exist and equals 1

[vestal tide]

And if both limits are approaching different values its DNE right?

[empty sapphire]

correct

the LH and RH limits might exist individually but the general limit would not at that point

[vestal tide]

Ok, I see

I have one more question

whats the difference between the open circle and closed circle on the graph?

its to show inequalities right?

[empty sapphire]

you mean at the point? It just means that value doesn't exist for that function. It's not part of the domain for the function

so in your example in your problem, the domain would be (-inf, 1)U(1, inf)

[vestal tide]

alright cool

If I have anymore questions I will give you a shout

.close

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[empty sapphire]

just open a new channel and let someone filter in naturally. I'm not always here and we don't encourage pinging individuals 🙂

[vestal tide]

Sounds good!

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[short quest]

hey

[short quest]

can someone help me :3

is the numbers correct.?

[spice orchid]

check yourself on a calculator

[short quest]

how do i do that

[spice orchid]

well how did you get those numbers in the first place?

[short quest]

#bots

umm

i did this

,calc 6*sin(3(0)/2)

[glossy valve]

Result:

0

[short quest]

,calc 6*sin(3(15)/2)

[glossy valve]

Result:

-2.9230470747631

[short quest]

,calc 6*sin(3(30)/2)

[glossy valve]

Result:

5.1054211472047

[short quest]

but idk if i did it correctly

[spice orchid]

the TeXit calculator here takes radians, not degrees

,calc sin(360)

[glossy valve]

Result:

0.95891572341431

[spice orchid]

see that would be 0 if it was degrees

[short quest]

oh..

oh?

so how should i use the calculator

for this

I sohuld erase all of them then?>

[spice orchid]

enter your radian values rather than your degree values

[short quest]

,calc 6*sin(3(pi/2)/2)

[glossy valve]

Result:

4.2426406871193

[short quest]

like that?

[spice orchid]

yes that is now correct

[short quest]

,calc 6*sin(3(0)/2)

[glossy valve]

Result:

0

[short quest]

,calc 6*sin(3(pi/6)/2)

[glossy valve]

Result:

4.2426406871193

[short quest]

umm?//

,calc 6*sin(3(pi/12)/2)

[glossy valve]

Result:

2.2961005941905

[short quest]

,calc 6*sin(3(pi/6)/2)

[glossy valve]

Result:

4.2426406871193

[short quest]

,calc 6*sin(3(pi/4)/2)

[glossy valve]

Result:

5.5432771950677

[short quest]

,calc 6*sin(3(pi/3)/2)

[glossy valve]

Result:

6

[short quest]

,calc 6*sin(3(5pi/12)/2)

[glossy valve]

Result:

5.5432771950677

[short quest]

,calc 6*sin(3(pi/2)/2)

[glossy valve]

Result:

4.2426406871193

[short quest]

,calc 6*sin(3(7pi/12)/2)

[glossy valve]

Result:

2.2961005941905

[short quest]

am i doing tihs correct so far?>

@spice orchid can u verifiy

[spice orchid]

im not going to also do those calculations

[short quest]

,calc 6*sin(3(2pi/3)/2)

[glossy valve]

Result:

7.3478807948841e-16

[short quest]

can you do atleast one.

lol

[spice orchid]

if you've inputted it into the calculator correctly then you're probably fine

no

[short quest]

this my second time putting it in calc

i dont want to get it wrong again

but okkk

,calc 6*sin(3(2pi/3)/2)

[glossy valve]

Result:

7.3478807948841e-16

[short quest]

,calc 6*sin(3(2pi/3)/2)

[glossy valve]

Result:

7.3478807948841e-16

[short quest]

umm?/

,calc 6*sin(3(3pi/4)/2)

[glossy valve]

Result:

-2.2961005941905

[spice orchid]

use something other than a texit calculator

https://www.wolframalpha.com/

[short quest]

ok

what do i do with this..

i have to apy?

pay?

[spice orchid]

no?

[short quest]

Could i use desmos calc instead

[spice orchid]

yes of course

[serene hazel]

if you want the full steps then yes you need to pay

wolfram can be used on textit too

[short quest]

im using desmos

its alot easier

[serene hazel]

,w calc 6*sin(3(3pi/4)/2)

[glossy valve]

Results provided by WolframAlpha

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

Requested by Kenzy#2227

[serene hazel]

alright thats good

[short quest]

,w calc 6*sin(3(5pi/6)/2)

[glossy valve]

Results provided by WolframAlpha

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

Requested by bagsss#1204

[short quest]

,w calc 6*sin(3(2pi/3)/2)

[glossy valve]

Results provided by WolframAlpha

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

Requested by bagsss#1204

[short quest]

,w calc 6*sin(3(11pi/12)/2)

[glossy valve]

Results provided by WolframAlpha

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

Requested by bagsss#1204

[short quest]

,w calc 6*sin(3(pi)/2)

[glossy valve]

Results provided by WolframAlpha

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

Requested by bagsss#1204

[short quest]

,w calc 6*sin(3(13pi/12)/2)

[glossy valve]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by bagsss#1204

[short quest]

,w calc 6*sin(3(7pi/6)/2)

[glossy valve]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by bagsss#1204

[short quest]

,w calc 6*sin(3(5pi/4)/2)

[glossy valve]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by bagsss#1204

[short quest]

,w calc 6*sin(3(4pi/3)/2)

[glossy valve]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by bagsss#1204

[short quest]

,w calc 6*sin(3(7pi/12)/2)

[glossy valve]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by bagsss#1204

[short quest]

,w calc 6*sin(3(3pi/2)/2)

[glossy valve]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by bagsss#1204

[short quest]

,w calc 6*sin(3(19pi/12)/2)

[glossy valve]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by bagsss#1204

[short quest]

,w calc 6*sin(3(5pi/3)/2)

[glossy valve]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by bagsss#1204

[short quest]

,w calc 6*sin(3(7pi/4)/2)

[glossy valve]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by bagsss#1204

[short quest]

,w calc 6*sin(3(11pi/6)/2)

[glossy valve]

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Requested by bagsss#1204

[short quest]

,w calc 6*sin(3(23pi/12)/2)

[glossy valve]

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[short quest]

,w calc 6*sin(3(2pi)/2)

[glossy valve]

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[short quest]

ok i done it

FINALLY

@spice orchid @serene hazel

how do i graph this now

[spice orchid]

each circle out from the center is (presumably) 1 unit

so for each angle just go the appropriate amount of units away from the middle

[short quest]

hm

do i graph

it 0-360

so around like 28 times??

[spice orchid]

you have 24 different points to plot

[short quest]

oka

THIS SEEMS GOOD RIGHT?

i think im doing it

IM SOHAPY

[spice orchid]

that does look like it could be a flower

[short quest]

these numbers

are getting negative

how do i graph these?

[spice orchid]

you would go in the opposite direction

[short quest]

where is 2pi

in the map

it doenst matter

ig

umm do i make a flower now..

[full forum]

@short quest Has your question been resolved?

[full forum]

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[short quest]

bruh

[short quest]

my question needs answers

is that correct

[visual cape]

What's your question?

@short quest

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[alpine vigil]

Proofs assignment question.

[alpine vigil]

Would it be sufficient of a proof to do the following:

Let there exist z = a+bi
Let there exist w = c+di
where a,b,c,d are real numbers such that wz=1

After multiplying wz we obtain

wz = ac-bd+(ad+bc)i

As ad+bc is real, this must equal 0 (sketchy reasoning not sure how to improve)

Then from our assumption ac-bd=1, and d/c = a/b

and d/c = a/b

This part feels especially tricky for me, I'm not sure whether this would count as proof by construction?

@floral scroll

[onyx glen]

first three lines are kind of meh

also d/c = a/b is not only incorrect but relies on neither b nor c being 0, which you cannot say

have you already learned how to divide complex numbers? like, informally? @alpine vigil

[alpine vigil]

I know the basics of dividing complex numbers, not sure what exactly is needed but I can learn more if needed

[onyx glen]

well can you tell me what 1/(a+bi) would be?

[alpine vigil]

Hmm, is it (a-bi)/(a^2+b^2)?

[onyx glen]

well, now i am going to ask you the very same question

is is true that (a+bi) * (a-bi)/(a^2+b^2) = 1?

and is (a-bi)/(a^2+b^2) always defined for a+bi ≠ 0?

[alpine vigil]

For the first question, only if a,b≠0
For the second question, it looks to be that way...

I'm a bit confused, where might division of complex numbers come into the proof?

[full forum]

@alpine vigil Has your question been resolved?

[alpine vigil]

<@&286206848099549185>

[alpine vigil]

<@&286206848099549185>

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@alpine vigil Has your question been resolved?

[full forum]

@alpine vigil Has your question been resolved?

[full forum]

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[gentle anchor]

I know it's a quadratic

And that b = (m+4)

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[upper patrol]

hey

[upper patrol]

quick question

if you know f(x) is an odd function

is (f(x))^2 an even function?

[spice orchid]

Plug -x in and see what you get

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[empty tulip]

Can someone please help me with this question?

[stiff summit]

!status

[full forum]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[empty tulip]

I’m currently stuck on step 1. So do you know how to solve part a and b?

[stiff summit]

Do you understand the question?

[empty tulip]

Kind of but idk what value of t would best fit both f(t) and g(t)?

[stiff summit]

When in doubt you could always try 0 or 1

[empty tulip]

Okay so do you just sub in 0 or 1 into t to find both f(t) and g(t) as the coordinates right?

[stiff summit]

Yes

[full forum]

@empty tulip Has your question been resolved?

[empty tulip]

Well 0 and 1 will not work since both are not rational numbers. So I decided to go with 1/3 and got N = (13/5, 13/15) but how do you solve part b?

Idk how to find k

[stiff summit]

Check the definition of a rational number

[stiff summit]

Did you solve question 3? You could look at that, might give you a clue

[empty tulip]

This is what I did for Q3, but how you solve for k given what I did before?

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[tardy lotus]

A car is going uphill with a speed of 20 ms^-1. The hill has a slope of 30° with the ground. If rain starts falling at a rate of 6ms^-1 vertically to the ground then in what angle would the the driver see the rain fall?

[dim compass]

Draw the situation

[tardy lotus]

I tried to solve it out by considering the road flat but the rain falling at angle of 30° with the ground. Then I used vector addition to solve but I got a wrong answer

[dim compass]

It's already given that road is tilted with a slope of 30° though?

[tardy lotus]

Yes but to solve this problem easily I did that

[dim compass]

Also it would be more accurate to say that road and hill are the same here

You can say that rain is falling at angle of 30 degree with respect to flat road

[tardy lotus]

Yes but I considered it horizontal to the group

[dim compass]

But not the uphill

[dim compass]

group?

[tardy lotus]

Ground*

[dim compass]

I mean it would be better if you could show your comprehensive understanding of the question through drawing

[tardy lotus]

The driver going uphill would see it falling at angle of 30° wouldn’t he?

[dim compass]

Where in the question was this mentioned?

Are you asking for the confirmation of your answer?

Which you got to be 30°

[dim compass]

You considered the uphill is horizontal with respect to the ground?

[tardy lotus]

It's 60° not 30° sorry for that

[tardy lotus]

My answer is wrong

[dim compass]

Ohh

Yes with respect to horizontal uphill it's 60 degree

With respect to vertical of car it's 30°

So your answer is correct

[tardy lotus]

The x component of the rain fall with respect to the road is 6cos60°. So the rate at which the driver will see the rain hitting the car will be 20-6cos60

Then I found out the y component and used trigonometry. I got tan-1(6sin60/(20-6cos60))

,w tan^(-1){6sin60/(20-6cos60)}

[glossy valve]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by Mushfiqur#7459

[tardy lotus]

,w 0.2967 rad to degree

[glossy valve]

Results provided by WolframAlpha

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

Requested by Mushfiqur#7459

[tardy lotus]

It's not the correct answer

[dim compass]

Y component velocity of rain will be 3√3 right?

6sin60

[tardy lotus]

Yes

As per my calculations

[dim compass]

Then √(Vy^2+Vx^2) should be the answer

[tardy lotus]

They told me to find the anglee

[dim compass]

Oh it's asking for angle

Mb

You can you tan theta = Vy/Vx

[tardy lotus]

I did

[dim compass]

And that's what you did

Oh

Did you try substracting 90 to it

[tardy lotus]

Yes

[dim compass]

Maybe the angle is being asked with respect to vertical?

Oh

[tardy lotus]

This is what they did

[dim compass]

20 sin60 is the horizontal component of car's velocity

[tardy lotus]

Yes

[dim compass]

And 20cos60 is the vertical component

Why did they add 6 and 20cos60?

If anything there should be substraction

Because 6 is vertically downward and 20cos60 is vertically upward

[tardy lotus]

Yeah

[dim compass]

I have opinionated that they might be wrong but still

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[mental bolt]

Can I replace all the characters here at the beginning? Or untie the brackets first and replace all the characters in the brackets later?

[last vapor]

Replacing now should work

[mental bolt]

Or this?

Well my teacher said otherwise… (my teacher’s calculations) @last vapor

<@&286206848099549185>

[hot herald]

commutative and associative property pretty much allow you to multiply in any order
use parentheses if needed

-ab = -(ab) = -(a)*b

[full forum]

@mental bolt Has your question been resolved?

[mental bolt]

What

[hot herald]

having -(p)(q)
you could distribute the - to the p first to get
(-p)(q) then multiply to get the expanded product

you could also multiply those p and q together first
-(pq)
and then distribute the - sign

etc

both approaches would be valid from the properties of multiplication

[mental bolt]

I don’t understand still @hot herald

[hot herald]

using an example like
-(x+2)(x+1)

[mental bolt]

You’d change every sign

So

-x-2

-x1-1

Ez

[hot herald]

you could do
-(x^2 + 2x + x + 2)
(-x-2)(x+1)
both are valid

So
-x-2
-x1-1
Ez
NO, that's not how that works

$-pq \redneq -p \times -q$

[glossy valve]

ℝamonov

[mental bolt]

So the teachers calculation is right?

@hot herald

[silk oar]

What he wrote in this sentence is right

[mental bolt]

Ok Papi

[full forum]

@mental bolt Has your question been resolved?

[mental bolt]

So -(x+1)+(5+x)

So, (-x-1)(-5-x) @silk oar

<@&286206848099549185>

[mental bolt]

<@&286206848099549185>

[mental bolt]

<@&286206848099549185>

[mental bolt]

.close

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[merry ingot]

Hey guys, currently stuck with a counting Problem, or actually I dont know if my solution is correct + I was wondering what concepts I should study in order to master these problems. Here is the problem:

Consider the letters ABCDEF. How many arrangements are there, if the letter A is before B and B is before C?

My solution/approach:
I basically looked at the possible cases by fixing A, B, or C and tried to calculate the total number of arrangements like that.

ABDEFC => 4! = 24
ABDEFC => 4! = 24
ADEFBC => 4! = 24
ADBCEF => 3x2!x3! = 36
ADEBCF => 3!x3x2! = 36

So in total I have 144 possible arrangements.

[full forum]

@merry ingot Has your question been resolved?

[patent matrix]

Yeah I think that's a good argument. I think for clarity, it might be easier to bold A, B, and C

Or maybe just use blank spaces for D-F

So you have
A _ _ _ _ B C
A _ _ _ B _ C
A _ _ B _ _ C

ah the spaces dont show up

But I hope I still made the point clear

A - - - - B C

A - - - B - C

A - - B - - C

etc

I think you might be missing a few cases but I think you hit the nail on the head

Maybe its more systematic to start
A B C - - - -
A B - C - - -
A B - - C - -
A B - - - C -
A B - - - - C

Wait, better yet

A B C - - - -
A B - C - - -
A - B C - - -
A B - - C - -
A - B - C - -
A - - B C - -
A B - - - C -

etc

Feels like the triangle numbers are showing up

Feels like its going to be something like $4! * \sum n C 2 $

[merry ingot]

Ah thank you

I think I kind of lack a systematic way of writing down the specific cases and calculating it

The last one might help, ill try it again with that and calculate it

[patent matrix]

Awesome, you're welcome! I'd love to know what you get.

[merry ingot]

@patent matrix Okay I think I solved it...

Consider for example AB-C-- or AB---C or -A-B-C, its always one of these cases where you have the - all next to eachother (AB---C), all split (A-B-C-) or in a 2:1 split (A--B-C). For each of these cases, there are 6 possible arrangements. Therefore, we just need to find out how many cases there are, which is a stars and bars problem. We have 3 letters and 4 possible bins to create with the -. So the total number is (n+k-1) choose (k-1) = 6 choose 3 = 20.

Therefore, in total there are 20*6 = 120 possibilities.

[patent matrix]

I think you still might be missing some, because A need not be the first letter in the sequence, right?

Doesn't -ABC-- satisfy the requirements as well?

-AB-C-
-AB--C

right?

[merry ingot]

Yeah true but isnt that covered through using the stars and bars formula

[patent matrix]

Oh it might be. I'm actually pretty unfamiliar with stars and bars

So if you says it does, I will take your word

Okay, so if that's the case, I think you got it

[merry ingot]

I hope so

I hate these problems haha

Thank you for your help :) Ill mark it as solved now

[patent matrix]

Oof that's a hit point of damage. I think counting is so fun!

You're welcome! Glad I could support

[merry ingot]

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[torn jolt]

When one root of the quadratic equation x^2 + ax + 6 = 0 is 3 + 7i, find the values of the other root and the real numbers a and 6.

[wise wyvern]

Do you realise the other root HAS to be the conjugate of the first one?

For all the coefficients to be real.

[onyx glen]

did you miscopy a b as a six...?

[torn jolt]

that’s what the translation says

[onyx glen]

well it is kind of strange that they would ask you to find the value of the real number 6

because 6 is... well, 6

are you absolutely certain that this symbol was definitely a six and NOT a b on paper

[torn jolt]

probably a b 😬

[onyx glen]

yeah exactly

[onyx glen]

in that case, this point stands.

[torn jolt]

okay sorry for the unnecessary help channel, I solved it

.close

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[normal thicket]

@gritty rose no instructions. I uploaded this question somewhere with title short method

[normal thicket]

Sorry for pinging you because the channel is closed due to time out

[gritty rose]

Yea so what does the title say

[sharp flame]

I think you can do something by adding 0

And splitting the fraction

Honestly maybe just

$\tan \frac x2 = u$

[glossy valve]

NEONPerseus

[sharp flame]

Bad idea don't

[normal thicket]

I tried this too

But it became complicated

[sharp flame]

Yes

[normal thicket]

It says nothing related to the question

@gritty rose

[full forum]

@normal thicket Has your question been resolved?

[normal thicket]

Sorry for pinging you again

[quasi bolt]

I’ll try to solve it

[normal thicket]

Yes. Please

Send your video@quasi bolt in dm

Youtube link

[quasi bolt]

Wtf is this integral, not even python can integrate it

[white geyser]

you would approximate this one realistically

[quasi bolt]

Its an indefinite integral, wdym approximate?

[white geyser]

realistically, as in, in real applications. can you solve this?

[quasi bolt]

Probably not

[white geyser]

yeeeeeaaaaah no short way to get to that i dont think

[quasi bolt]

lmao

[quasi bolt]

What did you use?

Google colab?

[white geyser]

wolfram

[full forum]

@normal thicket Has your question been resolved?

[normal thicket]

I am waiting for riemann answer

@gritty rose

[full forum]

@normal thicket Has your question been resolved?

[torn jolt]

u sub?

[normal thicket]

What?

[normal thicket]

I didn't understand

[torn jolt]

u substitution is a method for integrating

[normal thicket]

.close

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[unique lintel]

Hello

[covert wing]

[unique lintel]

‘(A,C)α₁ — (A,B)α_ — (B,A)β₁ — (_,Α)α₀’

[wispy shadow]

helloo

can someone help me with this problem?

[unique lintel]

Man

What are u doing

This is my channel

[covert wing]

Create your own help channel, delete the questions here.

Read #❓how-to-get-help

[wispy shadow]

wait wait wait

[unique lintel]

How do I make the bot do the pciture of the problem?

[covert wing]

This question concerns a game called Families.

The game is played by three players, each starting with a hand of four cards. There are three families in the game: $\alpha$, $\beta$, and $\gamma$, and each family contains four cards.

The game proceeds with players asking questions of the form: Player A asks Player B, "Do you have any cards from family $\beta$?" Player A can only ask this question if they already hold some $\beta$ cards. If Player B has any $\beta$ cards, they must answer "Yes" and give one of them to Player A. We notate this question and answer as $(A, B)\beta_1$. If Player B has no $\beta$ cards, they must answer "No," and we notate this as $(A, B)\beta_0$.

If a player receives a card after a positive response and ends up holding four cards of the same family, they must declare the family they constitute, and those cards are removed from their hand and the game. We notate this as $(-, A)\gamma_4$, for example, when Player A declares a family of four $\gamma$ cards.

A player continues to make moves until they receive a negative answer. Then, play passes to the next player in alphabetical order $(A\to B\to C\to A)$.

If a player declares a family of cards and holds no remaining cards in their hand, they have won the game, and the game stops.

If a player lies about their hand or makes a statement that creates a logical contradiction, they have lost the game, and the game stops.

To prevent trivial wins, no player may start with all four cards of the same family.

In the examples that follow, each move in the game is separated by a dash, —.
‘$(A,C)\alpha_1$ — $(A,B)\alpha$ — $(B,A)\beta_1$ — $(,Α)\alpha_0$’

[unique lintel]

`

(A,C)α₁ — (A,B)α_ — (B,A)β₁ — (_,Α)α₀
what should be in each blank space? Explain your reasoning carefully. `

Can you help solve it?

[covert wing]

I can't, sorry, but I just created that LaTeX output for you

[unique lintel]

Bruh why can nobody help

[stiff summit]

Where did this question come from

[full forum]

@unique lintel Has your question been resolved?

[stiff summit]

Do you have a link

If you knew which field of maths it was from, you might be able to ask it in the relevant channel

So, what field of maths is it from?

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[nova wing]

how do i find a?

[torn jolt]

Is it said anywhere that D, F, and B are aligned?

[nova wing]

nope

[torn jolt]

What about A, F, and E?

[nova wing]

this is all that's given

[torn jolt]

I guess I'm gonna have to assume that if points look aligned then they are because otherwise this is unsolvable

Find AFB first and then it should become obvious

Wait a second actually no

[nova wing]

yeah

i'm really stuck😭

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@nova wing Has your question been resolved?

[nova wing]

<@&286206848099549185>

[kindred oriole]

working on it

[nova wing]

tyty

[kindred oriole]

This is not the answer, just my first lot of working/thinking it out

130 = x+a *

[torn jolt]

That's obvious

[nova wing]

👍

[kindred oriole]

I'm trying to do it with some simulantous equations but everything just keeps canceling

[torn jolt]

There has to be some construction to be done

I think drawing a line DF parallel to BC should be a way

[nova wing]

hopefully it is, i truly have no clue

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