help-36

[final saddle]

@safe elm Has your question been resolved?

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@safe elm Has your question been resolved?

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@safe elm Has your question been resolved?

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@safe elm Has your question been resolved?

[muted sleet]

@safe elm can i use binary search?

[safe elm]

Nope, the instructions given was to use Newton's Method to find the minimum.

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@safe elm Has your question been resolved?

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@safe elm Has your question been resolved?

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@safe elm Has your question been resolved?

[shell dune]

@safe elm Do you still need help

[safe elm]

Yup I do 😢

[empty rain]

<@&286206848099549185>

[novel bone]

3 days 😦

[safe elm]

Is that normal 😅 first time asking for help

[mint orbit]

its an overlap of a lot of specific topics

so its a hard one to help with

like i know matlab but i dont understand the geometry

[safe elm]

Yea I wanna clarify if my understanding of the geometry is correct before I proceed any further

Mainly this:
I've used a parameterised the equation of a superellipse into something similar to polar form to draw the superellipse in part 2.
x = R cos(t), y = R sin(t), where R is a function of t as well.
For a given axes, what I've done is calculated the angle of rotation with respect to the Cartesian x-axes and used a rotation matrix on the superellipse to get a rotated superellipse. Is this the same as what the question is requiring me to do or is scaling along those axes different from simply doing such a rotation

[mint orbit]

thats something I cant help with, sorry

you may reach out to your prof if you are confused about what you are required to do

its unusual to take 3 days to get help for a problem

[cloud zephyr]

Bruh #❓how-to-get-help

[agile perch]

sorry

[jaunty portal]

Hello, I think it's correct what you did here because e1 and e2 are unit vectors, so the supellipse is not scaled, it's just rotated

anyway if you have the parameterization is terms of the angle (polar form), you can just add a phase shift to get the rotation

then add horizontal and vertical shift to get the center

I really don't have a clue on how to get the minimum distance 😵‍💫

[safe elm]

let me show you what i've got so far

[jaunty portal]

yup that's all correct, it's the same thing I got

[safe elm]

The next thing I did was to define expressions 2 superellipses, 1 and 2. so my distance function would be L = (x1 - x2)^2 + (y1 - y2)^2 and substituting the parametric expressions into L to get it in terms of theta1 and theta2.

Then I generate expressions (using diff function in MATLAB because differentiation R(theta) is a pain) for the elements in the Jacobian and Hessian and do a Newton Method minimization of L

I can send over the expressions for the matrix elements a bit later.

I've used excel GRG solver to get the minimum distances and the corresponding thetas, but using a value near those thetas does not always give me convergence to that minimum L I got in excel (usually I get either no convergence or a larger L)

[keen bloom]

yo

[safe elm]

Hi

[wraith tulip]

Gradients are probably the way to solve this, but you might need to change learning rates dynamically for convergence

Anyway, Matlab makes me want to stay away from this

[final saddle]

@safe elm Has your question been resolved?

[safe elm]

I'm not familiar with this. Do you mind elaborating on how I can implement dynamic learning rates?

[wraith tulip]

Basic theory that I was taught (though I must say, never looked into deeply) is that you can multiply the updates by a (geometric) factor.

https://wiki.tum.de/display/lfdv/Adaptive+Learning+Rate+Method

[safe elm]

thanks, i just decided to brute force it with randomly generted initial guesses and take the lowest one (seems to work).

For Q4, since the n is larger, there are some problems with the stability of the newton method.

Do you think geomtric learning rates will help with this?

[wraith tulip]

Well the geometric factor will obviously cause the gradient to become smaller and norm closer to below tolerance, but it could get there too fast even before it reaches any local minimum

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[round rampart]

what do I put here?

[hearty zephyr]

either you need to rewrite the limit,
or take the limit of 2x.
I think the final box is supposed to be the final limit answer.

[round rampart]

ok

[vital crag]

probably use inf or something for infinity

[round rampart]

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[rocky ibex]

.reopen

[final saddle]

Please don't occupy multiple help channels.

[rocky ibex]

other guy didnt help

shapes F and G are similar if that helps

[vital crag]

i closed your other channel

[dawn elk]

find the above side’s length of trapezium f

[vital crag]

.close

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[dawn elk]

hm

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[steep egret]

Can someone help me understand how to look at this circuit? All of the examples in my text were Boolean Gates but they didn't look like this at all. This looks like a more realistic application but I don't understand how to make sense of it. It's asking which values need to be True / False to make the lamp glow. How do I use my understanding of the typical gate logic diagrams from the other screenshot I included, to understand the more realistic circuit? Can I?

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@steep egret Has your question been resolved?

[steep egret]

Still here, just quiet. 🙂

[violet tapir]

F

[steep egret]

Happens lol

I'm just quietly studying all the other topics I got wrong on my practice test while I wait haha

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[supple copper]

I'm trying to do the bottom example expanded out

but what is the integral of cos(t^2)

is there a chain rule or is it just sin(t^2)

[boreal granite]

You need not find the integral

Just assume it is F(t)

that will give you d/dx(F(x^3)-F(2))

@supple copper does this make sense

[supple copper]

yes

wait so

what is F(x^3)

[boreal granite]

you need not write it

just differentiate it using chain rule

And you know its derivative

of F'(x)=cos(x^2)

[supple copper]

ohhhh

okay this makes more sense

thank you

[boreal granite]

You can look at Fundamental Theorem of Calculus

[supple copper]

yeah that's what I'm trying to learn rn lmao

[boreal granite]

If you have partial derivatives

lol

[supple copper]

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[supple copper]

I get what to do when the lower bound is a constant

but I have no idea what to do with this

[magic gyro]

ft

ftc

[tranquil pine]

I’ll solve it and send you an image

[summer vale]

ah yes

[summer vale]

no

don’t

[tranquil pine]

No?

[supple copper]

lol

[tranquil pine]

Ok

[boreal granite]

Do the same as in previous question. It would just be F(x+2)-F(x)

[supple copper]

yes, that's what I'm trying to learn.. but my definition just talks about the lower bound being a constant

oh

[summer vale]

iirc

I asked a similar qn and got this

[supple copper]

hmm okay

one sec

I forgot to actually try something

[vital crag]

~~https://mathworld.wolfram.com/LeibnizIntegralRule.html~~

Err i guess the intention is to write $F(x)$ as a sum of two integrals, each one with one of the x, or x+2 variables

[soft zealot]

riemann

[supple copper]

is it just.. 8?

I think I messed up that sounds wrong

sloppy handwriting sry

[vital crag]

,w [4/2 (x+2)^2 + (x+2)] - [4/2 (x)^2 + x]

[soft zealot]

Results provided by WolframAlpha

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

Requested by riemann#2529

[vital crag]

8 looks right?

if you differentiate the wolfie result wrt to x

[supple copper]

yep

I guess I'm not used to it cuz the other ones didn't have a constant answer

thanks everyone

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[sweet widget]

lim x → infinity x-e^x

[sweet widget]

this is -infinity but how

[spiral quail]

Can u rewrite ur problem more clearly?

[spiral quail]

Thank you

Imagine it’s a race between two runners. The first runner maintains a constant speed throughout the time. But the second runner keeps on speeding up and speeding up his rate of speeding up and speeding up his rate of speeding up his rate of speeding….etc.
Which runner will win the race?

[sweet widget]

yeah so e^x is growing exponentially that's why right?

[spiral quail]

Yup

[sweet widget]

is the bigger infinity

[spiral quail]

Yup

[sweet widget]

is there a mathematical way to show this tho

Like how should i show it

[boreal granite]

You can factor out e^x

[spiral quail]

In the runner analogy u can also think it’s the faster infinity

[sweet widget]

how can you do that

[boreal granite]

e^x(x/e^x-1)

[sweet widget]

ah ok

[boreal granite]

lim of x/e^x is 0

[spiral quail]

WOAHHHH that’s cool

[sweet widget]

yeah that's pretty cool

[spiral quail]

Jasmine I think u would need to know derivative to have a formal mathematical proof. U know what derivative are?

[sweet widget]

Thank you so much!

[sweet widget]

yea yea lol

[trail mango]

i think a clean way is through series

[sweet widget]

ik i was just confused abt this one

[sweet widget]

isnt this a good way to prove this tho?

[boreal granite]

Umm.. I'd use lhopital

But there should be proofs of basic limits

I don't remember

First principle?

[spiral quail]

Idk first principle lol

[boreal granite]

How does your textbooks prove lnx/x

or x/e^x

I dont remember how we did tht

[spiral quail]

At first we did just qualitative observation of their graphs, and then we more formally used lhopital’s rule until either the denominator or numerator wasnt infinity

[sweet widget]

use lhopitals after factoring out e^x?

[spiral quail]

Use it on the x/(e^x), yeah

[sweet widget]

ok great

tysm

[spiral quail]

Np

[trail mango]

oops totally butchered that

[boreal granite]

lol. How does one do that

x/e^x

[trail mango]

for any integer $n\geq 2$, $n-e^n \leq 1 - \frac{n^2}{2!} - \frac{n^3}{3!} - \cdots - \frac{n^n}{n!} \leq 1 - (n-1)$

[soft zealot]

💜𝓁𝒶𝓎𝓁𝒶💜

[trail mango]

i think that's what i was trying to say

[spiral quail]

Woah

We could also use lhopital rule

[boreal granite]

Um.. do we have such inequalities known

ah alright

got it

proving it using derivative, and double and triple

[trail mango]

you mean for what i said?

[boreal granite]

Nvm.. was talking to myself

[trail mango]

looks ok to me, is there an issue?

[boreal granite]

nope

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[tranquil pine]

help...

[tranquil pine]

ok so

do not judge me because my mind is blanking and I am being extremely dumb

why did they put a 0 place holder

like what was the point

[void crest]

hi

the stuff in the 10th slot its * 10

same for the stuff in 100ths slot

uve to *100

same as adding 2 0s

[tranquil pine]

dumb it down for me

ok so

[void crest]

just

imagine u are multiplying 10 with 12

and u do this long multiplication thing

u just get 12

well

0 + 12

but this 12 is from the 1 from the 10s place

so uve to *10

like

[tranquil pine]

ok wait give me a sample problem

[void crest]

36 * 12 =

36 * (10 + 2)

so we first do the *2

we get 72

then we * 10

which is the same as we * 1 and we * 10 later

and * 10 is the same as adding a 0 behind

[tranquil pine]

wait why * 10

[void crest]

well

36 * 10

= 36 * 1 * 10

lol

i feel weird

ok maybe

if its 36 * 26 instead

so like

its

36 * (20 + 6)

so first we do 36*6 = idk something

then next we do 36 * 2 * 10

so we find 36 * 2

and the * 10 is the same as adding a 0 behind

[tranquil pine]

856

[void crest]

idk how else to explain it

[tranquil pine]

wtf

i genuinely do not understand how i forgot to do multiplication

ok wait give me a problem i can try 😭

[void crest]

okwell

idk

some1 else can explain it btr

mayb

ima dip now

[tranquil pine]

oh

ok then

OH I GET IT

im so dumb goodbye.

.close

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[void crest]

oh

cool

yayyy

💕

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[round rampart]

wat

[round rampart]

<@&286206848099549185>

guys?

this is like my last problem

<@&286206848099549185>

[tranquil pine]

It wants it in exact form which you can’t get by reading it off a graph

At least I assume that’s the problem because your answer is correct just not in exact form

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[cedar tulip]

how did they get the last $\Sigma \frac{1}{a^{2}} = \frac{q^{2}-2pr}{r^{2}}$

[soft zealot]

Night Wølf

[magic totem]

$$\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}=(\frac{1}{a}+\frac{1}{b}+\frac{1}{c})^2 -2(\frac{1}{ab}+\frac{1}{bc}+\frac{1}{ca})$$

[soft zealot]

秋水

[cedar tulip]

damn never thought binomial formulas could work with trinomials too 😅

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[jolly eagle]

How can you determine if this graph f(x) is negative?

[vital crag]

Do you know what it means for a graph to be negative

[jolly eagle]

hmmm well i initially thought that the graph is negative when the slope was decreasing but that only determined the behavior for f'

besides that i dont really know what it means for a graph to be negative

[vital crag]

It's when the function is below the x axis

I.e. when f(x) < 0

[jolly eagle]

ohhh so even if it starts out positive because it goes below the x axis it is negative?

[winter pecan]

For all x > 5, the graph is negative

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[austere sinew]

any idea on how to prove: For all x, (x is different to P(x) ) , where P(x) is power set of x

[rain compass]

so you want to show P(x) is not equal to x?

am i understanding

[austere sinew]

yup

[rain compass]

what is your definition of P(x)

[austere sinew]

P(x) is the set of all subsets of x

y is an element of P(x) iff y is a subset of x

[rain compass]

consider x. is x a subset of x?

[austere sinew]

yes

[rain compass]

what class is this for?

[sturdy cypress]

2^n is never n

[rain compass]

i want to say that x in P(x) but x not in x, but we may be dealing with more

[rain compass]

what if x is infinite?

[sturdy cypress]

they don't have the same cardinality even coincidentally

ah ok

sounds fair

[austere sinew]

i'ts introduction to set theory

zfc axioms

[rain compass]

ok i doubt any of my arguments would be solid then

you can repost your question if you want

[austere sinew]

the exercises is show that everyone of these are different:

do you think that prove P(x) /= x is a good idea?

[rain compass]

not sure tbh

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[gilded crow]

I don't understand how to show this is an equivalence relation and am struggling to understand the wording of the problem...

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[vast coral]

For what x y z is this mateox regular

[vast coral]

https://cdn.discordapp.com/attachments/540211747613704221/1039986838741450772/unknown.png

[desert mantle]

calculate the determinant

[vast coral]

@desert mantleand what after

[desert mantle]

well when is the determinant zero

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[crisp fiber]

for b

why did they multiply by 12!

because i stopped at 10C6 * 8C6

does this have something to do with the inclusion-exclusion principle?

i think im just missing something?

[boreal granite]

12 different positions

What you did is assuming it doesn't matter what position one gets

[crisp fiber]

how does multiplying by 12! account for different positions?

i dont fully understand this

[tranquil pine]

10C6 and 8C6 is just to select a unordered subset of 6 men and women respetively

but after that you are supposed to assign them to 12 different positions

[crisp fiber]

oh

oh ok it just clicked

[tranquil pine]

cool 😅

[crisp fiber]

again this slipped my mind

thanks :P

i kept using combinations

[tranquil pine]

sometimes just phrasing the reasoning in a particular way helps out a tonne

[crisp fiber]

true

.close

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[hallow wren]

can i please get help on this

[tranquil pine]

what have you tried?

[hallow wren]

i tried by doing fof by n times

[tranquil pine]

be careful about simplifying, you are losing information about the domain

you cannot multiply top and bottom by 0

the way to think about this, is to first find the domain of f_1

[hallow wren]

so its by placing x as 1?

[tranquil pine]

huh? wdym

[hallow wren]

x=1

for f_1

?

[tranquil pine]

yes, that's in the domain

but we want the whole domain

try and think about what values are undefined

[hallow wren]

-1?

[tranquil pine]

yeah

now for f(f(x)), the inside f(x) cannot be -1. So when is f(x)=-1?

[hallow wren]

x=-2

[tranquil pine]

yup, so whats the domain of f_2?

[hallow wren]

everything except -2

[tranquil pine]

theres another value that x cant be

[hallow wren]

-1

-3/2

[tranquil pine]

yeah

just -2 and -1

[hallow wren]

ohk

[tranquil pine]

yeah, thats for f_3

do you spot the pattern now?

[hallow wren]

so i need to find f(1-4) and see what can not be the value of that function?

so my domains are R - {-1,-2,-3/2,-5/3}

[tranquil pine]

yes

[hallow wren]

and for second subquestion : my answer should be -(n/n-1)

no but it wont be true for n = 1 and 4

[final saddle]

@hallow wren Has your question been resolved?

[hallow wren]

@tranquil pine

[tranquil pine]

no it isnt

I think its related to the fibonacci sequence

[hallow wren]

Ohh

i got the general equation for numerator but still finding denomenator

[tranquil pine]

should be the same equation for both numerator and denominator

[hallow wren]

but it will be 1 then

[tranquil pine]

its shifted by 1

the bottom is one term slower than the top

-1 - n/(n+1) = -(n+2)/(n+1)

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[remote sedge]

Help

[remote sedge]

This

Please

Anyone

[spiral quail]

For problem E

It should be minus pi 8^2 not plus

Because there a circle’s worth of area is taken away from the box’s top and bottom face

Actually one circle’s worth taken away from the top side, and another one taken away from the bottom, so that makes 2 circle’s worth of area taken away. So not -pi 8^2 but -2 * pi 8^2

[remote sedge]

Thanks

I made the sphere one

[spiral quail]

You solved that one?

[spiral quail]

Wdym

For problem D

They mixed up radius and diameter

They are supposed to use radius when calculating area so pi 3^2, but they did diameter and did pi 6^2

[remote sedge]

Yeah

[remote sedge]

When you put ^ it means the number is like little and up right?

[spiral quail]

Yup

2^2 means 2 to the power of 2 which is equal to 4

[remote sedge]

Okay

[remote sedge]

But the result stays the same right?

[spiral quail]

When they calculated the area that wraps around the cylinder, they did circumference of circle times height, but they used diameter instead of radius when they calculated circumference

Idk about the result

,calc 2 * pi * 3^2 + 2 * pi * 3 * 8

[soft zealot]

Result:

207.34511513693

[spiral quail]

No the result is not the same

[remote sedge]

Mkay

[spiral quail]

Need anything else?

[remote sedge]

But in the composite shape one

it changes too?

[spiral quail]

Which problem?

[remote sedge]

This

And also help with this one but only the side

Since I have the right side

[spiral quail]

In problem E, they correctly used radius to calculate circle area and circle circumference. Radius is half of diameter, and diameter is 16 so radius is 8

Can u refer to the problem number?

[remote sedge]

3

And 4

[spiral quail]

Gtg eat dinner sorry

[remote sedge]

Oh okay

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[remote sedge]

.close

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[fallen reef]

,w solve 1-2\sin^2 ((3\pi)/2)

[soft zealot]

Results provided by WolframAlpha

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

Requested by dopediscorduser#4906

[fallen reef]

I don't understand this

If [ 1-2\sin^2 ((3\pi)/2) = \cos 2(((3\pi)/2)]

[soft zealot]

dopediscorduser

[fallen reef]

[cos(\frac{6\pi}{2}) = cos (3\pi)]

[soft zealot]

dopediscorduser

[fallen reef]

Nope nevermind

.close

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[quiet basin]

How do i get j 0.0024

[void valley]

,calc 1/425

[soft zealot]

Result:

0.0023529411764706

[void valley]

approximately 0.0024

[quiet basin]

Ty

What do i put into the calc to change it over to get them numbers

How does 107.59 change to 76.08

[boreal granite]

r<theta = rcos theta +j rsin theta

@quiet basin

[quiet basin]

So would that be 45cos 107.59 in a calc

[boreal granite]

no the other way around

[quiet basin]

Ok ty

Ok the math aint mathing

I still cant get it

Dw math is now mathin🐒

Ty

https://tenor.com/view/yes-sweet-hell-yes-pump-it-gif-22136641

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[hushed garnet]

Hello, I'm having some problem and idk if someone can help me, but I'm trying to find an equation on desmo where I can get those red dots on my green line. My coords are made by iteration in C#, I'm trying to understand but I'm really bad a this

[hushed garnet]

So basicly I need a straight line going to the corner where the black rook is

[dry light]

Comedy

Is Desmos in radian or degree mode

Make sure it's in the correct mode

[hushed garnet]

😮

[dry light]

Seeing cos(60) = -0.9 makes me think it's in radian mode

The slope of the line is going to be the tangent of the angle between the line and the x axis

[hushed garnet]

Oh boy... Ok I don't even know how to change the mode XD... Oops I'll look more into it

[dry light]

Top right corner

The gear

Click it, click degree

[hushed garnet]

Ok so that mean im gonna use the tan for the green line

[dry light]

Yes

You can just do $f(x) = \tan(60)x$

[soft zealot]

Umbraleviathan

[hushed garnet]

😮 Thanks! I'm sorry for my lack of knowledge lol

[dry light]

Np

[hushed garnet]

I don't have a gear on the top right, I suppose it's the one on the left on my screen?

Anywya I guess I'll google at this point, thanks!

[grim badger]

Click the wrench

[hushed garnet]

It indeed was! Oh wow XD. Oh wow hahaha

So I'll multiply X by the tan of 60 and it's gonna work alright

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[fallen reef]

How did they rationalize this

[summer vale]

multiply root 2 num and denom

[fallen reef]

yes but

[\frac{\sqrt{1-\frac{\sqrt{3}}{2}} * \sqrt{2}}{2}]

Not right

[soft zealot]

dopediscorduser

[fallen reef]

I don't follow how this gets your to 2 - \sqrt{3} in the numerator

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[scenic notch]

does anybody know what this symbol means \sum _{n=0}

[scenic notch]

\sum _{n=0}

bruh

[grim badger]

$\sum _{n=0}$

[soft zealot]

dldh06

[scenic notch]

how do i type in a symbol in this server

yeah that's it

I keep seeing this thing pop up but I have no idea what it is

[grim badger]

It's summation

[scenic notch]

what's that

[grim badger]

If you don't know that yet, I suggest doing your own research or hold off until you learn it in school

[scenic notch]

Bruh

I'm so curious though

[grim badger]

Then research

Google it

[scenic notch]

It's so hard to google these weird math symbols

and I never even know the name of what they are

[grim badger]

.

[scenic notch]

i see

thanks

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[sterile warren]

Hi can you help me

[sterile warren]

How many solutions is there for f (x) = 0

And why

My teacher so busy helping everyone so can’t get help lol

[void crest]

lol

it depends on f

[sterile warren]

Oh

I see

[tranquil pine]

crazy right?

[sterile warren]

Here is th graph like

I didn’t see it was a part of this 1

[tranquil pine]

f(x) =0
how many times did the function pass thro the y axis

[sterile warren]

3

1*

Oh I see

On C it’s 0

My answe was y = 0

[tranquil pine]

f(x) = 0
y=0

[sterile warren]

I have another question pls

[tranquil pine]

im sorry i was looking somewhere else

y=0
and x€R

[sterile warren]

Oh

[tranquil pine]

so 3

[sterile warren]

3?

So x axis and not the y axis

Y = f (x)

Y is 0 in C I think

[tranquil pine]

if the question is how many times is f(x) = 0
then how many times was the y-axis 0
if the question is how many times f (0) then it means how many times was the x-axis 0

[sterile warren]

Ye it’s y = 0 answer prob like on C

[tranquil pine]

y =0
then how many times did it cute the x-axis

cut**

[sterile warren]

Oh

I see

3

3 points

I was thinking wrong

The rate of change of this do u have any idea how to do

The rate of change for the curve

Is the first sentence

And then interval

Decide rate of change for curve y……. in interval 1……..

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[limpid torrent]

Instantly c and d are ruled out but how do I know if it is absolute maximum or not, I think it’s B

[limpid torrent]

It is the greatest value on the interval

So would that make it the absolute min on that interval

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[limpid torrent]

.close

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[wooden veldt]

why is this a valid thing to do? does it have a name?

[scarlet sequoia]

It's composition of functions

If two functions f and g are equal everywhere (i.e f(x) = g(x) for all x)

Then for any other function h, $f(h(x)) = g(h(x))$

[soft zealot]

rafilou2003

[wooden veldt]

ah I see

thank you

[scarlet sequoia]

Here the function h is the inverse function

No problem

[wooden veldt]

yep got it

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[stuck owl]

How can I use the top fact to form the first part into the second part?

[stuck owl]

Someone told me to switch the sums but if I do that its not equivalent anymore. And even if I do switch the sums then how can I justify setting the i=j to i=0?

[stuck owl]

Ignore this. I cant just swap the sums and replace one part with 2^i because its not a lone sum but a sum of a product

So im stuck and I dont know how to tackle this. The above is only my guess at how to solve this. I dont know if it even works. (As in: I have the left formula and I am trying to evaluate it. My guess is that I need to do those steps above to get to 3^n)

Currently trying some stuff to work backwards from the second part to the first

[distant hawk]

If you have experience in computing double integral, then it is much like the trick you will do when you want to "swap" order of summation.

That is, sketch out the current "summation region" first, and then try to reverse the way you sum things.

There shd be many good online resources to help you learn this trick. https://mathinsight.org/double_integral_change_order_integration_examples

[worldly vale]

I would suggest writing out a table of all the (i,j) pairs you're going to be running through in the double sum, and see if you can use that to help you switch the order by thinking about what values j takes for a fixed i

[stuck owl]

I have done this just now

Now I need to do that last step at the bottom

[worldly vale]

yeah this is good, its just a different way of counting what things you have

which step?

[stuck owl]

the question marks at the bottom

[worldly vale]

oh

[worldly vale]

do this then

like
(0,0)
(1,0) (1,1)
(2,0) (2,1) (2,2)
.
.
.
(n,0) (n,1) (n,2) ... (n,n)

and instead of fixing a column (j) and going through rows(i), fix a row and go through a column

[stuck owl]

you mean a table of all the things i sum together so like: (nC0)(0C0) + (nC1)(1C0) etc

okay

[worldly vale]

no

just the (i,j) pairs

here, we fix a j and i goes from j to n

this is the first column of what i wrote when we let j=0

then j=1 is the second column

im just listing the (i,j) pairs in a suggestive way

[stuck owl]

Ah yeah. Will that help me here where I have a product? I dont see how I can replace the second part or just one sum without breaking things because of the nCi in the beginning

[worldly vale]

if you go through and swap the sums correctly, youll be able to pull the nCi out of the second sum bc the second sum will only be going through j and nCi does not depend on j

[stuck owl]

Okay Ill try it

[stuck owl]

cant i finish this by symmetry?

it goes from 0 to i and the other goes from j to n

I feel like it should be possible to argue that the two sums are the same because nCk is nC(n-k) or something like that

[worldly vale]

there is no need to consider what is actually in the sum when switching the order

then switch would work the same no matter you were adding up

[stuck owl]

even in this case? It seems like it doesnt work if I switch it

because of i equals j

[worldly vale]

if you still have i=j then you havent switched correctly

it becomes this

[stuck owl]

so that would be how it should be switched? Ill try to understand it more

[worldly vale]

yes thats the correct switch, and this^ is the way to think about it

[tired walrus]

both of these double summations sum over pairs (i,j) with 0 ≤ j ≤ i ≤ n

[stuck owl]

Thanks that helped me understand it.

.close

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[wide nova]

yo

how can i calculate this limit

f being derivable at a

[tired walrus]

xf(a) - af(x) = xf(a) - af(a) + af(a) - af(x)

[fleet latch]

Have you tried L'Hospital's rule ?

[wide nova]

nah not really not allowed to use it

[wide nova]

oh then it is f(a) - a * f'(a)?

[fleet latch]

oh not allowed to use, then we gotta solve it in a lovely way

[tired walrus]

nor do you need it

[tired walrus]

yes, should be.

[wide nova]

okkk

smart method

tysm

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[fleet latch]

wow, Ann outsmarted me

[wide nova]

yup xD

[fleet latch]

good one.

[wide nova]

aight thanks guys

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[final saddle]

@dense moat Has your question been resolved?

[cloud zephyr]

have you tried anything?

[candid eagle]

^ We aren't going to solve the problem for you.

[cloud zephyr]

@dense moat

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[polar wing]

i need help with generally, roots of unity, cyclotimic polynomials, and primitive roots.

[polar wing]

i dont quite get their connections

and maybe some understanding of each one of them

i understand this example^

i want an intepretation of this formla definition^

I dont understand this

hmm i have an ok understanding of unit roots

[worldly vale]

pick something specifically you want clarifying, there's a lot going on

[polar wing]

yeh it's because the pages are referencing each of the key terms from other pages

im not sure which concept is the first to learn

and go on

since the overlapping

[worldly vale]

well i mean chronologically would make the most sense i would think

[hearty zephyr]

probability primitive root

[polar wing]

ok so what's the motivation of writing the nth root to be this form?

[worldly vale]

what alternative form would you write it in?

[polar wing]

i can't name anything but this form came up of nowhere,?

hmm theres an explanation of angle i think

the benjamin person explained yesteryda

[worldly vale]

roots of unity are in general complex numbers, theyre written in polar form here, polar form plays particularly nicely with multiplication

[soft zealot]

ΣAC

[polar wing]

yeh but the pic i sent is not represneted as the sum of angles

but 2kpi/n

like where did these stuff come from

[worldly vale]

well what happens if you raise them to the power of n?

[polar wing]

2kpi i

the n in denominator gets cancelled

2k pi is the angle?

[worldly vale]

yeah

so what do they become

[polar wing]

why choose to represent the theta as 2k pi?

cause that makes the value to be 1?

ahhh ok

nice

[worldly vale]

yeah, so you see how they're all roots of unity

[polar wing]

yesyes

and when they are graphed on the complex plane

they are polygons

[worldly vale]

its slightly more complicated to show that that actually is all of them and we're not missing any, but i wouldnt worry too much

yeah regular n-gons

[polar wing]

okok

[polar wing]

can u explain the concept of primitive roots?

cause its relations with modular arithmetic is so confusing

like why is it like this?

and this

[worldly vale]

primitive roots in Z_n* are just the elements such that you can reach any other element by taking repeated powers

they can "generate" the group

[polar wing]

I’m really confused 😭

Be back in 15 min

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[solar bridge]

I am dealing with the triangle numbers

[solar bridge]

is this the correct way to write this

or should it be k(k+1)/2?

because n(n+1)/2 is just a closed form of this right

[sturdy cypress]

yes

i mean, i don't know

it doesn't make sense to write k if you don;t use the k, but it's not clear why you're asking about Σ something in the first place

[solar bridge]

i need to find t_1, t_1 + t_2, etc

which is this equation but instead of n i need to match the variable at the bottom right

[sturdy cypress]

it is not this equation

[solar bridge]

so this way

[sturdy cypress]

you;re glitching hard

[solar bridge]

im confused lol

when i want to compute t_1

[sturdy cypress]

you kinda skipped over the equal sign

like what

there was an equal sign, you erased it, and you got something really new

[solar bridge]

you mean this?

[sturdy cypress]

right, you invented a new equation that looks like this but without the equal sign

oh i see

[solar bridge]

but isnt this the basic summation formula? which adds 1 + 2 + 3 + ... etc

wait

[sturdy cypress]

yeah that was smart, that's what they asked for

[solar bridge]

oh so the question is just asking me to plug in the values and get results

[sturdy cypress]

no that's what i thought

but they are asking for sum of triangular numbers and you don;t have something for that to plug into

actually no idea how to do this

well, I guess yeah, you maybe are supposed to just do "the basic summation formula" and add up the results

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[heady slate]

what topic is this

[tranquil pine]

definite integration

by substitution

[median mural]

im praying for you

[tranquil pine]

but I need help not prayers

[void valley]

what u can say about x - 1/x for 1/2 < x < 2 ?

or in other words check signs of x-1/x in the interval 1/2 < x < 2

[tranquil pine]

yeah already cleared that step ... lemme share my solution (I got the wrong answer)

[void valley]

it should be decomposed into

[soft zealot]

Modus

[heady slate]

wtf

[void valley]

oh ye

you did that

[tranquil pine]

the actual answer is e^(3/2) -1

idk how

[void valley]

aa

d/dx (x-1)/x isn't 1/x^2 + 1

it's 1/x^2

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[slender cargo]

guyssss pls

is it right

i probs did something wrong 😭 😭 😭

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@slender cargo Has your question been resolved?

[frail badger]

why did i get pinged here

[slender cargo]

.close

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[rotund veldt]

this is the function f

How can I tell if it will be continious or not?

[tranquil pine]

it isn't

u can tell because it has a denominator with a variable in it

generally those won't be continuous

[rotund veldt]

but if it would have a domain then it would be continuous

?

[tranquil pine]

no

if that were the case the domain would always be (-inf,inf)

there would be no point in finding the domain

the point of finding the domain is to determine its continuity

the continuity of f(x)

[rotund veldt]

but i just read that these are continious:

i dont get whyy

[tranquil pine]

because they simplify

[rotund veldt]

so they arent actually continious?

[tranquil pine]

no

but u can simplify them

that causes asymptotes

[rotund veldt]

oh okay

so if it were an asymptote it would be continuousus

[tranquil pine]

no

well

yes

well

no

[rotund veldt]

lol

[tranquil pine]

if u think about the graph of the function

[rotund veldt]

Wth is this lmao

Some quantum physics function

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[tranquil pine]

how would i answer this?

as u can see i have the slope intercept form of that general form equation

im not sure what i should do now though

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[delicate halo]

Need help with Q18

Just don’t know how to change the limits

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@prisma hedge Has your question been resolved?

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[final saddle]

@autumn jetty Has your question been resolved?

[autumn jetty]

<@&286206848099549185>

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@autumn jetty Has your question been resolved?

[autumn jetty]

no

[fossil geyser]

Have you made any progress on your own? What have you tried so far

@autumn jetty

[autumn jetty]

I just don’t get how you work with GH, HI, IJ

like how do you express that

[fossil geyser]

GH + HI = GI
HI + IJ = HJ

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[magic abyss]

a soccer team has 3 possible outcomes when playing a game, win, loss or draw, chances of winning is 80%, a loss 15% and a draw 5% calculate the chance of the team winning the 2nd match in a tree diagram

[prisma niche]

Have you tried drawing out a tree?

[magic abyss]

It's a question my brother got in his exam

[prisma niche]

My question still stands

[unkempt heart]

I don’t think we are allowed to help with exam questions

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@magic abyss Has your question been resolved?

[magic abyss]

its a after exam question

not a current

I memorized

it

[magic abyss]

/close

.close

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[latent cloak]

For a, the first number has to be 2-5, and the last number has to be 2 or 4 yeah?

[grave adder]

wait "" "" _"

wait but how is 2-5?

for the first?

like would that not b e odd?

since 3 is is within 2-5?

[latent cloak]

It only matters if the last digit is even

[grave adder]

oh so the first and second does not matter

unless it says so

[latent cloak]

Well it also has to be above 200

So it cant be 1

[grave adder]

wait but only the end determines if it is odd or even?

k

btw do u know wut it means by case 1?

and case 2?

like is it just stating the parameters for the question?

[latent cloak]

Because if it is 3 or 5 for the first number, then the last number can be 2 or 4, but if it is 2 or 4, the last number could only be the oposite

[grave adder]

wait so case 1 is saying that it can either start with 3 or start with 5?

like the number 3

or is it saying possibilities

[latent cloak]

Both cases are posible, but they have different equations for the ammount of numbers

The number

[grave adder]

wait but why is it only 3 or 5?

like once the end is even could u not use another even number for the front?

[grave adder]

right?

[latent cloak]

Well imagine this

If it starts with a 3 or a 5, the equation would be 2 * 4 *2 for the possible numbers, but you would also need cases for the second number

[grave adder]

oh true

wait so would there not be 4 different possibilities of 3 or 5 being paired up with 2 or 4

[latent cloak]

Like if it was 34, the last number would have to be 2

But if it was 35, the last could be 2 or 4

[grave adder]

like the numbers can not be repeated?

[latent cloak]

I think so

But i have class rn, i cant help for a sec

[grave adder]

k just pls answer when u have time

so like if i use 3 in case 1 can 3 not be used again for any section in case 2?

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[forest cedar]

$2^{\frac{x}{2}}\left(1-3^{\frac{x-1}{2}}\right)+1-3^{x-1}=0$

[soft zealot]

『Marius』

[forest cedar]

I am thinking that somehow i need to create another 1-3^(x-1)/2

somebody else gave me an advice that 1 - 3^(x - 1) = (1 - 3^(x-1)/2)(1 + 3^(x+1)/2)

but if i multiply the 2 parenthesis I don t end up at 1-3^(x-1)

[tranquil pine]

the (x-1)/2 should be all in the exponent

$1-3^{x-1}=(1-3^{\frac{x-1}{2}})(1+3^{\frac{x-1}{2}})$ is a difference of two squares

[soft zealot]

Toby

[forest cedar]

so this is (a+b)(a-b) im not going to expend it , im just trying to understand how to see this type of expression if I find a similar equation

[tranquil pine]

well here we have one 1-3^{(x-1)/2} already, so ig it makes sense to try and factor that out

[forest cedar]

yeah I was thinking about that but I guess I don t have enough practice to see what I have to do after that in this type of eq

thx anyways 😄

.close

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[fluid gale]

where do i go from here

[low egret]

What have you been asked to do?

[fluid gale]

verify the identity

i’m working with the left side

[low egret]

Oh right

Well I would just write $\tan^4\theta$ as $\tan^2\theta \cdot \tan^2\theta$ and rewrite one of the squared tangents as $\sec^2\theta - 1$ (I am assuming you're aware of that identity)

[soft zealot]

Sid

[fluid gale]

so you wouldn’t take the fraction route?

could you tell me why i should go into sin cos

is it because the other side doesn’t have sin cos, so it would be better to preserve the tan and sec right

[low egret]

Just cumbersome

[low egret]

You can go by rewriting those as fractions and it would still verify things but it's just gonna be more work

When you write it in terms of sine and cosines you'll have to use sin^2 + cos^2 = 1

tan^2 = 1 + sec^2 is nothing but that identity rephrased

So it always helps save two steps (one converting to the fractions and the other converting from the fractions when you're almost done)

[fluid gale]

So when approaching verifying trig problems, always try to think of a way that doesn’t involve converted to fractions correct?