help-13

[pseudo merlin]

Becuase it has opposite sides that are congruent but they arent parallel?

[tribal pasture]

Rhombus has parallel sides

[spice kraken]

it's true

[pseudo merlin]

bro chat gpt is aliar

is the original statement true

[mighty shuttle]

!nogpt

[cedar kiln]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[pseudo merlin]

it works sometimes

A quadrilateral with two pairs of parallel sides is a parallelogram?

[mighty shuttle]

even then, don't trust it for maths

[tribal pasture]

Yes

[mighty shuttle]

yes

[pseudo merlin]

so this statement is true

if this statement is true then the contrapositive is also true

the converse is true

and now all i need is the inverse wait

wait

is inverse

Not p => not q

or not q => not p

[tribal pasture]

converse is not always true

[pseudo merlin]

but we established that the converse was true

[tribal pasture]

this is contrapostive

[pseudo merlin]

oh ait

wait

we havent

[pseudo merlin]

no we said its true here

so what is the inverse

[spice kraken]

inverse is contrapositive to converse

[pseudo merlin]

if the opposite sides of a quadrilateral are not congruent, then it does not have two pairs of

[spice kraken]

since converse is true so is inverse

[pseudo merlin]

parallel sides

[pseudo merlin]

what do u mean by this

if converse is true then inverse is true?

then if original statement is true then contrapositive is true?

so then all these statements are true

[tribal pasture]

statement p=>q

converse q=>p

inverse not p=>not q

Contra postive not q=> not p

[glacial bridge]

When we say Frequency = 1/(2×π))×angular frequency, how do we compute that?

Because if we consider the projection of a ball moving around in a circle, we can say that ω = 2πAN/t

{Here N is the number of oscillations, A is amplitude, and t is time}

And f = 4AN/t

By that means, f = (2/π)ω

And not f = (1/2π)ω

Can anyone help me with this one?

I've been scratching my head over this for a whole day

[spice kraken]

a statement is equivalent to its contrapositive

and the inverse is equivalent to the converse

[pseudo merlin]

oh

ok thanks

.close

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[summer kayak]

The temperature distribution $T(r)$ within the cylinder wall ($1 \leq r \leq 2$) is determined by the differential equation:

$$
r \frac{d^2T}{dr^2} + \frac{dT}{dr} = 0 \quad
$$ The outer side of the pipeline, at $r = 2$, is cooled by the surrounding air with a temperature of $T_e = 20^\circ$C.
$$
k \frac{dT}{dr} = -\alpha(T - T_e) \quad \text{at } r = 2 \quad
$$ a) Discretize the equation using central finite differences for $N = 4$. Use boundary conditions (9) and (10). Print out the system matrix and the right-hand side with all elements. The derivative in the boundary condition at $r = 2$ can be approximated using a first-order difference approximation:

$$
k \frac{T_{N+1} - T_N}{h} = -\alpha(T_N - T_e).
$$
Use this boundary condition to eliminate $T_{N+1}$ in the last equation of the equation system. Let k = $\alpha$ = 1

[wraith dagger]

afealway

afealway

[summer kayak]

Btw Te is the temperature outside which is 20 and T0 is inside witch is 450, is this equation wrong because I keep getting incorrect result when I solve for the vector T. I have been stuck at this problem because no matter what I do I can't get it right. The problem is larger than this but it builds upon it so if I am correct here then I should be there too.

[cedar kiln]

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[summer kayak]

<@&286206848099549185>

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@summer kayak Has your question been resolved?

[summer kayak]

Not yet

[mighty drift]

just react to the bot

[cedar kiln]

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[wise badger]

The question :
Using integration by parts, demonstrate that for k € [0,n-1] P(k) => P(k+1)

I started by translating the property with the given formula

Then I did the integration by part

I'm not sure what I wrote, if anyone can confirm

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[north cipher]

how to render latex by bot?

[coral jewel]

$your latex here$

[cedar kiln]

@north cipher Has your question been resolved?

[north cipher]

Can anyone help me with recursive relation

$f(n) = \sum_{i = 0}^{n - 1} f(i) \cdot f(n - i - 1) \cdot (i+1)$ and $f(0) = 1$

I solved it using generating function and reached

$(dy/dx) = (1/x) - (1/y)$ and $y(0) = 0$

[wraith dagger]

mexomerf

[north cipher]

where coeff of x^n is f(n - 1)

Can anyone help me find f(n) in O(n) or O(nlogn) or O(nlog^2n) time complexity

sorry for bad latex

I want f(n) mod some value ofcourse

change

$f(n) = \sum_{i = 0}^{n - 1} f(i) \cdot f(n - i - 1) \cdot (i+1)$ and $f(0) = 1$

is correct relation

[wraith dagger]

mexomerf

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[dark birch]

Hello can anyone help me with a problem of loci of complex numbers

[cedar kiln]

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[summer lintel]

not too sure on these absolute things

if i rasie the entire leftside by ^2 does that change the sign

[crimson sedge]

which side

there are multiple eqn

[summer lintel]

is not not only one

[crimson sedge]

what

[summer lintel]

also, is that jjk spoiler

in your profile pciture

[crimson sedge]

idk im a manga only i just found this online

anime only*

[crimson sedge]

basically you're asking if the inequality sign changes?

[summer lintel]

yeah

can i just do this

[crimson sedge]

no cuz that's not how you square expressions, you need to distribute

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

[wraith dagger]

45

[crimson sedge]

(in general)

[summer lintel]

but i am not squaring it

or

i am jsut

if i square t he enitre thing

then it sqaureroot goes away

[crimson sedge]

yes but you have

$\sqrt{1 + \frac{1}{x^4}} + \sqrt{1 + \frac{1}{x^2}$. Squaring this doesn't equal $1 + \frac{1}{x^4} + 1 + \frac{1}{x^2}$

[wraith dagger]

45
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[crimson sedge]

(in the denominator)

[summer lintel]

so i cant jus sqaure

the individual

terms

[crimson sedge]

yeah you can't

[summer lintel]

oh ok

unlucky

[crimson sedge]

this is correct, though

because the sqrt is applied to the entire term

[summer lintel]

2 + 1/x^4 + 2*sqrt(1 + 1/x^4)*sqrt(1 + 1/x^2) + 1/x^2

so i need this

$$ 2 + 1/x^4 + 2*sqrt(1 + 1/x^4)*sqrt(1 + 1/x^2) + 1/x^2 $$

[wraith dagger]

// mav

[summer lintel]

$$ 2 + \frac{1}{x^4} + 2\sqrt{1 + \frac{1}{x^4}} \cdot \sqrt{1 + \frac{1}{x^2}} + \frac{1}{x^2} $$

[wraith dagger]

// mav

[crimson sedge]

indeed

[summer lintel]

and

2 1
1 - -- + --
2 4
x x

i cant copy my from the document

1 sec

[crimson sedge]

u can send ss

[summer lintel]

$$2 + \frac{1}{x^4} + 2 \cdot \sqrt{1 + \frac{1}{x^4}} \cdot \sqrt{1 + \frac{1}{x^2}} + \frac{1}{x^2} $$

[wraith dagger]

// mav

[summer lintel]

bruh

wrong copy

1 - 2/x^2 + 1/x^4

not too hardf to write like this

i'll need to somehow get rid of these squareroots

@crimson sedge

<@&286206848099549185>

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.close

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[rustic spire]

https://media.discordapp.net/attachments/903430333096132618/1209972871988908153/image.png?ex=65e8de0c&is=65d6690c&hm=ad056c69982725fc6edc7ba618cfa6b466d70c9b3695270c319270206e23f4d6&

[rustic spire]

What is longer, the green line EB or black lines EA and AF

The angles were easy but idk about length

No cosine

I cannot use cosine

[granite hound]

are you asking which one is longer, EB or EA + AF?

[rustic spire]

Yeap

[granite hound]

EA + AF is longer

It's a condition for three line segments to form a triangle

[rustic spire]

I think you are misunderstanding the problem

AF is not a full side

Look at it again and you will see

[granite hound]

Oh I'm sorry

I see now

[rustic spire]

No worries

[granite hound]

EB = EA + AF

[rustic spire]

I think i could use the trapezoid on the top with 3 known sides using cos to get 4th and then know the lenght but

No cosines

[rustic spire]

How did you get the lower EB length

[granite hound]

I didn't get EB length

[rustic spire]

Upper EB and EA are same

Because of it being whatever the english word for same length triangle

[granite hound]

umm

you mean

triangle EGA?

[rustic spire]

But lower. How did you compare with AF

[granite hound]

uhhh

[rustic spire]

Yeah

[granite hound]

I don't understand your question

so can i just explain

[rustic spire]

Ok

[granite hound]

Let G be the intersection of BE and AC

then angle CAB = 36

and angle EAG = 72

so angle EGA = 72

so EA = EG

and now connect FG

and triangle FCG and triangle FCB are congruent

so angle CFG = 54

-> angle GFA = 72

-> angle FGA = 72

->FA = GA

but GA = GB

so FA = GB

therefore EA + AF = EG + GB = EB

got it?

[rustic spire]

Wait a sec

[granite hound]

take ur time

[rustic spire]

Oh yeah

I see it

[granite hound]

yay

[rustic spire]

Thanks a lot

[granite hound]

my pleasure

[rustic spire]

Its all about the isosceles triangles

[granite hound]

yea

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[glacial steppe]

Physics problem

Is that not how net forces work?

Net force is the sum of all forces?

[lusty pawn]

you might want to post the question on the physics server

[glacial steppe]

Didn’t know there was one

[lusty pawn]

see #old-network

you'll find the server

[glacial steppe]

Found it

[lusty pawn]

👍

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[short agate]

I am in diff-eq class and we are solving for initial value problem that is in the second order. We get to the point where we do the quadratic equation thing and solve for a variable (s) = -1 +/- i. When he plugs it back into the exponent of e, he comes out with s1=e^-t cos(t) and s2=e^-t sin(t). I get that this has something to do with eulers formula, but I don' t get where the rest of it went.

[short agate]

eulers formula says that it would be s1=e^-t (cos(t) + isin(t)) and s2=e^-t(cos(t) - isin(t)) right?

[royal finch]

no

It says that e^it = cos(t) + isin(t)

[short agate]

Yes that’s what I thought, but there is also the 1 at the beginning. So if you make that the exponent of e^t then you get e^-t+it

I just don’t get where the rest of the rulers formula is going. He’s only using one part and canceling the other somehow

[royal finch]

Noone can explain what they are doing if you don't show what they are doing. The first thing you should do is rewrite that as e^-t e^it

[short agate]

Yea sorry I’m just kind of in a hurry

Let me write it down and send a pic

[royal finch]

You only need two linearly independent solutions. You should look at which ones they are "canceling" and see if you really need it.

[short agate]

Here’s what the prof wrote in notes

[royal finch]

They probably explained this already elsewhere in the notes. That is a bit of a leap.

[short agate]

He doesn’t though

[royal finch]

Take e^((-1+i)t) and e^((-1-i)t) as your solutions, call them u_1(t) and u_2(t), respectively. Then take y_1(t) = u_1(t) + u_2(t) and y_2(t) = u_1(t) - u_2(t).

[dire geode]

just expanding what jessica said, read this if you don't have notes/a book on it
https://tutorial.math.lamar.edu/classes/de/ComplexRoots.aspx

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[pseudo trellis]

How could I solve this problem?

[cursive nacelle]

using implied differential

[pseudo trellis]

Hmm, what is that?

[cursive nacelle]

differencing considering y is a function of x, example:

[dire geode]

https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-2-new/ab-3-2/v/implicit-differentiation-1

[pseudo trellis]

yikes

thank you, i'll try it out

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[languid plume]

A given sinusoidal function has a period of 3, an amplitude of 7, and a maximum at (0, 2). Represent the function with a sine equation and a cosine equation.

what i did first is solve for the cosine function, and in the image is the equation I got.
But changing the equation to sine moves the graph to the right and fails to meet maximum (0,2)
So I added a phase shift for sine, my question is if what i did is correct to solve this, i need guidance

[candid dragon]

the derivative of the function will satisfy (0,0) since there is a maximum at x=0

start with y=Asinkx + Bcosmx

[cedar kiln]

@languid plume Has your question been resolved?

[languid plume]

y=7sin(2pi/3 x) + 7cos(mx)?

i dont think they would allow me to use derivative also

[languid plume]

<@&286206848099549185>

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[unreal cape]

Hello I'm struggling with this problem: "Consider a sphere of radius 2 centred around the origin. Calculate the volume of the part of the sphere that is sandwiched between the 𝑥𝑦-plane and the plane at 𝑧=1 parallel to the 𝑥𝑦-plane" I have attatched my workings, the correct answer should be \frac{11\pi}{3}

[dire geode]

!ss

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[unreal cape]

solution used cylindrical coordinates and yeah I could and I understand the solution workings, but I cant find what I have done wrong with spherical?

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[solar tendon]

If a point charge is situated at the very center of a solid cube. What will be the amount of flux that will pass through each of the faces of the cube?

[solar tendon]

I don't know where to even start to answer this one

help

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[cedar kiln]

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[flint plinth]

!status

[cedar kiln]

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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[near summit]

<@&286206848099549185>

[flint plinth]

!15min

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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.

[near summit]

step 1

1

1. I don't know where to begin.

[flint plinth]

can you find the radius of the circle?

[solid dragon]

find the radius of the circle using pythagoras theorem

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[dense locust]

How do I figure this out

[dense locust]

I know the cos graph, 90, 270

c^-1 (+4/5) gives 36.8

c^-1 (-4/5) gives 143

Oh ok

no isee

[opaque pivot]

cosx is negative for 180 < A < 270, so it's -4/5

[dense locust]

Yeah

143

Yeah

cheerio

.close

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[dense locust]

.reopen

[cedar kiln]

✅

[dense locust]

I got a question

sin^-1 +5/13 gives you 22.6 and -5/13 gives you -22.6

They both dont give you more than 90 degreese

What am I supposed to do

[open yew]

its 5/13

cuzz sin is postive in 1st and 2nd quadrant

[dense locust]

so your telling me it goes like this?

Oh yeah it does

I get the positive reason

[open yew]

see how till pi

its above x axis

[dense locust]

Yeah

ok gottchya

thank you

[open yew]

if B lies between pi and 2pi

then its -ve

[dense locust]

Yeah

Becuase it has

yeah

yeah

thanks for the double check

:3

Victor

[open yew]

have a nice day bud

[dense locust]

You TOO!

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[hearty anchor]

Hi, I don't exactly have a math question that I need help with but I'm looking for someone who's willing to tutor me about geometry🥲 I'm having a hard time understanding. Thanks🙂

[dense locust]

https://tenor.com/view/rabbit-no-nope-shake-head-gif-8690926

[cedar kiln]

@hearty anchor Has your question been resolved?

[hearty anchor]

sorry I just realized its not a worksheet question or anything, I'm just rlly eager to understand the concept of geometry like the arcs and stuff🙂

I'll do anything pleaseee🙏 🙏

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[sacred swan]

1000$

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[hearty anchor]

u too late brauh

[sacred swan]

No please

I'm good with even

950$

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[vagrant mist]

Do you have any tips to start thinking about statements as equations?

[pearl badge]

you should write a table with phrases and what they mean as an equation after that practice by underlining the words and under them write the corresponding equation

[vagrant mist]

Alright, I'll try it.

[pearl badge]

which phrases do you have?

[vagrant mist]

There are questions that I know have problems that are easy but I still can't get the result, the responses are a mess...

[pearl badge]

yup

[vagrant mist]

To transport 321 boxes, including large and small ones, 7 trucks were hired. The boxes
large ones were transported by 4 pickup trucks, each
truck carrying the same number of boxes.
The small boxes were transported by the other 3
trucks, each truck carrying the same number of boxes. Knowing that each truck
carrying small boxes transported 9 boxes more than
that each truck carrying large boxes, the total number of small boxes transported was

This one, I'm doing one or two question per day

My answer was

tb = truck with big boxes
ts = truck with small boxes

4tb + 3ts = 321

tb = ts + 9

4tb + 3ts = 321
4ts + 36 = 321
4ts = 321 - 36
ts = 285/4
ts = 71,25

but we can't transpor half of a box

[cedar kiln]

@vagrant mist Has your question been resolved?

[cedar kiln]

@vagrant mist Has your question been resolved?

[solid dragon]

your equation is wrong

its ts = tb + 9

[limber robin]

4b+3s=321
s-9 = b
4(s-9)+3s=321
7s-36=321
7s=357
s=51?

[solid dragon]

@vagrant mist it should be this

[vagrant mist]

yes, that's correct. Thanks!

[solid dragon]

if you have no other questions, u can close this channel by typing .close

[vagrant mist]

.close

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[quaint scaffold]

.reopen

Hey guys whats this technique called ? Multiplying the fraction like that. Its from calc one but i forgot what its called exactly. Trying to brush up on it for calc 2

[analog pagoda]

Its called expanding the fraction

[quaint scaffold]

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[unborn scroll]

Hello, if I have a 2x2 matrix such as
[76, 40]
[58, 46]
how would I manually (by hand) do the math for the fast fourier transform to convert it into the the frequency domain? Any help would be appreciated
This is a scaled down version of an exploration im doing on fourier transform in image processing

[cedar kiln]

@unborn scroll Has your question been resolved?

[cedar kiln]

@unborn scroll Has your question been resolved?

[unborn scroll]

<@&286206848099549185>

[silk hound]

@unborn scroll how much idea do you have of DFT (Discrete Fourier Transform) ?

[unborn scroll]

i've researched the topic alot

in my report I derived it to this

sry

[silk hound]

Ohh great

Then what's the issue ?

I mean, that is the 2D representation of DFT

[unborn scroll]

Yes I understand but in my project its a 16x16 image

so DFT is too many operation

I kinda need to learn how to do FFT manually

[silk hound]

"Computing a 2D transform of X is equivalent to computing 1D transform of each column of X, and then taking 1D fourier transform of the result."
-MATLAB

[silk hound]

FFTs (or even DFTs), especially for image processing are seldom done manually. Majorly it involves softwares doing it for. But if you so want to explore the logic of all behind it, try expanding this formula and convert it into matrix format.

FFT is just breaking the DFT into three matrices (A)(B)(P) so that it becomes easier for the comupting time.

[unborn scroll]

lets take the matrix i provided above
[76, 40]
[58, 46]

lets say these are intensity values for the pixels aka brightness

how would i apply the fft

cuz you said break up the dft into 3 matrices

[unborn scroll]

can I have the link to the paper or website?

[cedar kiln]

@unborn scroll Has your question been resolved?

[silk hound]

https://medium.com/swlh/the-fast-fourier-transform-fft-5e96cf637c38

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[crimson sedge]

How to prove that f(2x)=2f(x) is injective given that f: Z+ —> R. I’m new to analysis and can’t understand how to approach this problem. Should I find the f(x) first?

[crimson sedge]

what do you mean by finding f(x)

because there could be many different types of f(x) which have the identity f(2x)=2f(x)

[solid juniper]

yea, you are supposed to show any function f with that property is injective

[tepid sail]

here's how you start off the proof

let $x_1, x_2 \in Z+$ s.t $f(x_1) = f(x_2)$

show that $x_1 = x_2$

[wraith dagger]

nosqldb

[cedar kiln]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[wraith dagger]

nosqldb

[solid juniper]

also the problem does not seem right…. e.g. take f(x) = 0

[cedar kiln]

@crimson sedge Has your question been resolved?

[dire geode]

!original

[cedar kiln]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[dire geode]

oh oops already sent

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[bright sorrel]

how did this happen?

[bright sorrel]

why is x=1/2ln(y)

my thought process is e^x=y
xln(e)=ln(y)

x=ln(y) somewhat?

it's e^2x=y

[silk hound]

It's probably e^2x=y. That would explain the 1/2

[bright sorrel]

yeah

ty

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[oak harness]

can anyone explain how to do this: Where does the line y=-(1/e)x +2 intersect with curve y=ln(x) - i have been trying to learn logs but i dont quite get it

[open yew]

y=-(1/e)x+2?

can you write it on a paper? or use the bots? it isn't clear

[oak harness]

sure

[silk hound]

Simple observation. x=e

[oak harness]

would i sub x into e

[silk hound]

Sub ?

Substitute ?

[oak harness]

is this just basic knowledge i need to know because otherwise i dont understand how im just supposed to know that

[oak harness]

yes

[oak harness]

for reference im still in grade 10

but i like learning new maths

[silk hound]

It's observation. Y=-(1/e)x+2 has -ve slope for x>=0. And y=ln(x) has +ve slope for x>=0. This means they WILL intersect.

[oak harness]

observation?

[silk hound]

These types of questions generally have answers right in front of the eye, like substituting x=0,+-1. Worse case scenario x=+-2. But not more than that

[silk hound]

You know, noticing some peculiarities, or something common between the two. That stuff.

[oak harness]

is it like a function

ln(x) ik has something to do with logs

[silk hound]

Yes ln(x) is the natural logarithmic function, log_e_(x)

I don't want you to think in terms of functions or equation. Interpret math in terms of graphs and flow of lines and curves, things will be much more visible.

For better help try plotting these graphs on desmos.

[oak harness]

so is this question asking for the co ordinates of the intersect

if so how would i find those from ln(x) = - (1/e)x +2

without ploting a graph

[silk hound]

That's the thing. You can't solve this equation analytically. You have to realize and notice the fact that this equation gets solved at x=e

I mean you can write x=e^y and x=2e-ye and then TRY using the Taylor series.

[oak harness]

would this qualify as a proven answer?

[cedar kiln]

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[livid peak]

can i get some help on how to start this pls

[silk hound]

Put x=0, you get y intercept. Put y=0, you get the x intercept. Now we know e^kx is a decreasing graph. Draw the graph and make it pass through the x and y intercepts.

[oblique prawn]

when u plug in -infinity what do u get

[livid peak]

oh ok so make x=0

to find y intercept, like a normal graph

yea yea ty

will do

[livid peak]

does x = 0.59 sound approximately right

im not sure if my rearranging was correct

i did:
0 = e^3x - 6
e^3x = 6
3x = ln(6)
x = ln(6) / 3

[silk hound]

Yeah exactly this is correct.

Whatever this value turns out will your x intercept.

[livid peak]

👍

ty

[livid peak]

sorry do u mind explaining what asymptotes are quickly pls

i looked explanations but theyre a bit complicated

or how i would identify them

[silk hound]

Take y=1/x for example for x>=0

Here as x tends to infinity, y tends to 0 but never actually approaches it.

Then x=0 is an asymptote of the equation.

[silk hound]

Ansymptotes mostly occurs when a function is reaching infinity at a finite x value or atleast is tending to some value.

[livid peak]

okay

so its kinda like an imaginary line which stretches to infinity and gets close to a curve

[cedar kiln]

@livid peak Has your question been resolved?

[silk hound]

Yes it is.

[cedar kiln]

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[charred ermine]

i forgot how to expand (2x + 6)² - 9 💀

[crimson sedge]

$(a+b)^2 = (a+b)(a+b)$

[wraith dagger]

45

[charred ermine]

.close

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[crimson sedge]

just want to make sure, the area of these integral is 5,3 ?

(16/3)

Area = integral of [4-4x -(4-x^2)] dx
Area = integral of (-4x+x^2)dx

<@&286206848099549185>

[crimson sedge]

yo

so ur trying to find the area between 4-x^2 and 4-4x

?

[glad blaze]

wat

watttttttttttttttttttt

[crimson sedge]

?

[crimson sedge]

yes

[crimson sedge]

whats the axis of rotation

the x axis, y axis, sm oher line?

other*

about the x axis? The picture looks like this perhaps?

?

[crimson sedge]

idk, I haven't learned about rotation yet

i assume this what u trying to find

the area enveloped by the 2 lines

"Calculate the area of ​​the region (y=4-x^2) bounded by the (y=4-4x)."

The question is simply written that way.

hmmm

How do we know whether the area of ​​the shaded area is on the right or left?

I am also confused

its enveloped

so the one you did

cuz it doesnt have to stop at the x axis

it has to be surrounded on all sides by sm sort of line or asymptote

so this is what u've been given

ah

yh

generally, they woulda given an axis of rotation if ur using the washer method tho

I don't see the cutoff point before 😄

[crimson sedge]

wdym

i zoomed out a bit

on desmos

but it woulda looked like this

it says about

'about the y-axis'

My teacher hasn't taught me about finding the area of ​​a rotated volume, this question is only about the area of ​​a flat plane.

these are the formula

oh

my teacher didnt teach it on a flat plane

only on a rotated volume

got a bone to pick with my professor now

there's an easier way???

Next week we will learn about the integral area of ​​a rotated volume

[crimson sedge]

nah

[crimson sedge]

how about the answer?

[noble owl]

This was so fun in my first year of uni omg

[hazy escarp]

i think theyre looking for this bit

[crimson sedge]

so, its integral of [(4-x^2)-(4-4x)]dx, start from 0 to 4?

[crimson sedge]

idk how t do it a 2d plan

only rotated

[crimson sedge]

xD

😭

like i said, got a bone t pick with professor

[hazy escarp]

yeah its just integral of top - integral of bottom

[crimson sedge]

but we used those formulas t find the area of the 2d plane

[crimson sedge]

should I put a minus in front? because some of the area is below the x-axis?

[crimson sedge]

i see :>

[hazy escarp]

dont think you need to

[crimson sedge]

okay then tysm

the answer is 10,6 = 32/3

.solved

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[crimson sedge]

.reopen

[cedar kiln]

✅

[crimson sedge]

.solved

[cedar kiln]

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[hazy escarp]

😭

[crimson sedge]

for sm reasn that answer dont sit right with me

idk tho

[cedar kiln]

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[fair bloom]

Correct?

Any way I can check it myself using some online calculator

[carmine bronze]

Looks good. 👍

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[fair bloom]

bet ty

[fair bloom]

.close

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[hazy dawn]

did my professor solve this integral correctly

this is what I got

I dont understand how my professor arrived at his answer

[tepid sail]

hmm I'm a lil confused here bc I know that the first term should be multiplied by w^2 no?

[hazy dawn]

hmm

let me see

I think my answer is wrong for sure

[tepid sail]

nvm the professor is right

the steps are just messed up

and A_0 and A_1 are switched p sure

[hazy dawn]

he has no w constants on the first term

[tepid sail]

here

this is good but

A_0 and A_1 is mixed up

[hazy dawn]

yeah I messed up on the bounds of integration

[tepid sail]

it's all good

[fair bloom]

which math level is this?

[tepid sail]

it's like calculus (the level above pre calc)

[hazy dawn]

thank you

[fair bloom]

these are like triple integrals

calc 2? or 3 i meant

[tepid sail]

yeah it's a simple extension of one integral

[tepid sail]

anyway np!

[fair bloom]

not calc 1 tho

[hazy dawn]

lmao I put the 1/2 on the outside

and forgot to remove the 1/2 on the inside

[tepid sail]

yeah and you kept in

[hazy dawn]

im sleeping

[tepid sail]

other than that

u should be fine

have fun it's a friday night!

[hazy dawn]

thanks

[tepid sail]

good night!

[hazy dawn]

you too

.close

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[neat haven]

im currently doing a trigonometry problem regarding angle of elevation, and i have .1051=150/x (150/x as a fraction) and i dont know what to do in order to get x to be by itself

[teal meadow]

multiply both sides by x, divide both sixes by 0.1051

[neat haven]

okay thank you!

[teal meadow]

i gochu

[neat haven]

.close

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[drifting dove]

Go away

[cedar kiln]

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[charred gyro]

Hello just asking if this looks right

[charred gyro]

Can't be bothered to get exact number

[cedar kiln]

@charred gyro Has your question been resolved?

[charred gyro]

<@&286206848099549185>

damn, it's busy today

DFsdfdsfsdfsdf

I'll give it another 15 mins

[drifting dove]

Hi

[charred gyro]

ello, wdy think of above paper?

[brazen kestrel]

,rotate

[charred gyro]

^

[brazen kestrel]

I have 10.699 months

so looks right

for future reference you can easily check this sort of thing by entering it into desmos as $0.02x^2-0.6x+9.18=5.05$

[wraith dagger]

The Hat of DMing

[brazen kestrel]

that'll solve it for you

so you can verify your solution

[drifting dove]

What if you wanted to do it urself

[charred gyro]

okay thank you

[charred gyro]

oh like that?

wait sorry I'm moving to another building just a moment

[cedar kiln]

@charred gyro Has your question been resolved?

[charred gyro]

exactly

[charred gyro]

what if you were doing it during a test and you don't have access to desmos

[viscid pine]

.close

[charred gyro]

shush

[brazen kestrel]

I simply meant you can use it to verify your answers for this sort of thing

[charred gyro]

oh, to like check your answer

[brazen kestrel]

yeah

[charred gyro]

lol, yeah I understand now

here's another actually
how would you do (px)^2 +4px -12 = 0

cause you end up with both a x^2 and a p^2

I'm not used to equations having two such types

would u like to see my working?

nvm

.close

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[worldly walrus]

Ok that’s a better image

I’m not sure where to begin

[violet flume]

try starting here

[wraith dagger]

jan Niku

jan Niku

[violet flume]

hint: ||how can you make 1/3 c into 2c?||

[silk hound]

Dude, just multiply with 6.

[cedar kiln]

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[gilded barn]

I know how to do vertical and horizontal line tests, but I'm confused on the wording of putting countries on a axis?

It should automatically pass the vert line test

so its ___ to one

and assuming at least two people have been born in the same country, it should be many to one right?

[silk hound]

Okay. Rather than using tests, look at this question as a simple real life question and try to answer it that way.

[gilded barn]

I'm answering based on a graph not on a word based result

[gilded barn]

and therefore the b) condition would just be everyone is born in a different country right?

[silk hound]

Exactly. Try not to in this case. It'll help you understand Relations and Functions much better.

[rocky harness]

A better way to picture relations is arrows between sets

[silk hound]

Exactly, Now, you're getting it.

[silk hound]

Haa yes this still a better way than vert and horz lines.

[rocky harness]

If you see many arrows mapping to one element, the function won't be one-one

[gilded barn]

so...
a) Many to one
b) Every person must be born in a unique country

[silk hound]

But the best one is still logic building. It helps you with improving common sense.

[rocky harness]

You can't really classify it as many one, since we don't know if everyone was born in different countries or not

All you can say is that it is a function

It wouldn't be many one if everyone was born in different countries for example

[gilded barn]

alright thats fair

[silk hound]

Yes but the likeliness of everyone being in a different country is very less.

[gilded barn]

i kinda said that tho, I've got to avoid assuming things

[gilded barn]

from answers btw

alright I'm more confident with the thought process, thank you

.close

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[true lotus]

f(x) = x/2 - 1/2
g(x) = (x+1)/4
f(g(x)) + 2g(f(x)) = 0

how do i calculate this?

[silk hound]

Calculate what ?

[true lotus]

f(g(x))

is it just g*x?

[glass bluff]

isn't g of x defined?, i think you just use substition

[upper abyss]

f(g(x)) is f, with g(x) plugged into it

[silk hound]

Yes

f(g(x)) = g(x)/2 - 1/2

Now substitute g(x)

[true lotus]

so i just put g(x) for x in f(x)?

thanks

.close

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[vital pumice]

i just dont understand what to do

like is letter a, x^2=4ay ??

whats "form of the equation"?

[shrewd crag]

parabola form

[vital pumice]

like the standard ones?

its asking what standard parabola form was used?

[cedar kiln]

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[tawny drum]

Help with problem 9,10,and 11 pls

[royal loom]

, rotate

[royal loom]

Please ask only about 1 problem at a time

[wicked mantle]

Do you want answer or what?

[royal loom]

!nosols

[cedar kiln]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[wicked mantle]

Chill

I know the rules xD

[wicked mantle]

!status

[cedar kiln]

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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[tawny drum]

i know how to do number 9

i tried many times but i keep getting nowhere

idk how to do the others

[royal loom]

!show

[cedar kiln]

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

[royal loom]

For #9

[tawny drum]

for 9 i just simplified it to the form of : x+iy = 4+3i

but i couldnt do it

i got a denominator of x^2 + y^2

[stray nest]

doesn't x²+y² remind you of something?

[wicked mantle]

[tawny drum]

um no

diference of squares is minus

[stray nest]

well recall the definition of |z|

it's just that squared

[wicked mantle]

gl, I’ll leave for other channels

[tawny drum]

ohh

still kinda stuck

now i have (x-3iy)/|z| = 4+3i

[stray nest]

oha re you solving the 9th one?

[tawny drum]

yeah

[stray nest]

that definitely will not do it then

you can only compare the imaginary lart to the imaginary and the real part to the real

if you're getting a

(x-3iy)/(x²+y²) = 4 + 3i

you should just split that numerator and compare both parts of the number

you'll get two equations simultaneously solving them should yield x and y

[tawny drum]

um

is it x=4

y=1

nope its wrong

bruh

i did

(x/x^2 + y^2) - (3iy / x^2 + y^2) = 4 + 3i

(x/x^2 + y^2) = 4

(3y/x^2 + y^2) = 3

xy=4

x/y=4

got the last 2 equations by isubstituting x^2 + y^2 into the two equations

[cedar kiln]

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[vast apex]

Don't know how to approach this limit 😦

[cedar kiln]

@vast apex Has your question been resolved?

[crimson sedge]

hint: [ \parens [\bigg] {\f {n + 2} {n^{1 + \f1n}}}^{!n} \cdot \sqrt[n] {(3n + 1)!!} \sim 3\sqrt{3en} ]

[ancient iris]

is this chanel free?

[sacred grail]

chanel is very expensive

[ancient iris]

bro

can u help

[crimson sedge]

[vast apex]

How did you get that? Can you pls explain

[sacred grail]

to get a crude estimate on $\sqrt[n]{(3n + 1)!!}$, pair up the small and large terms together

[sacred grail]

actually maybe this is too crude

i was hoping for a more elementary argument but maybe you'll just have to rewrite it as approximately [ \map\exp{\f1n\sum_{i = 1}^{(3n + 1)/2} \log {2i}} ]

[sacred grail]

the sum is handled using a riemann sum argument

[cedar kiln]

@vast apex Has your question been resolved?

[cedar kiln]

@vast apex Has your question been resolved?

[raw gulch]

Hi there. first at all, think of creating product of two limits, one walks to number e powered to certain number, it is easy, and the second limit is a nice example for using Stolz-Cesaro theorem. If you have never heard about it, find it and read ab it and make few initial tasks before you touch your given problem here.

that is all

[cedar kiln]

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[young shale]

Is it possible to express F as a function in terms of

[young shale]

ωg/ω0

in:

I don't think it is, but this has really agonized me for quite a while so its not impossible that im missing something

/close

.close

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[golden bough]

Part C, how do I prove the parameterization is bijective in a rigorous manner

[golden bough]

having $u^3*v^3=(uv)^3$ is trivial

[wraith dagger]

pacmanboss256

[golden bough]

.close

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[dry solstice]

Have I done something wrong? I'm getting 2 values for the coefficient of restitution

One is the correct one

[crimson sedge]

e varies from 0 to 1 💀

[subtle hinge]

e ranges from 0 to 1

lol

[crimson sedge]

lol

[dry solstice]

Yes I know

But idk why I get two answers, one of which is correct

[cedar kiln]

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[neat reef]

Find a probability space where following conditions are satisfied:

a) Probabilities A_1 and A_2 are independent
b) Probabilities A_2 and A_3 are independent
c) Probabilities A_1 and A_3 are independent
d) A_1, A_2 and A_3 are not independent

[cedar kiln]

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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[neat reef]

2. I have begun but got stuck midway.

[cedar kiln]

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

[neat reef]

I know about the first three conditions should look like, however not sure about the fourth... And can't think of any example sastified all four conditions

[cedar kiln]

@neat reef Has your question been resolved?

[upper abyss]

A1 has to be independent from A2A3, or else we can break up P(A1A2A3)

It's a lot of constraints, haha. I suggest using unknown variables for things

[wispy marten]

Hint: consider a fair coin you throw twice.

Let $A_1$ be the event: The first throw gives heads. \
Same for $A_2$, but with the second throw. \
Finally let $A_3$ be the event: we observe exactly $1$ heads and $1$ tails on the two throws.

[wraith dagger]

all matrices are invertible

[wispy marten]

@neat reef

This is the kind of exercise you learn once, and you just learn the typical idea

You can do the same with two dice throws, but it's a little more subtle

[fair geyser]

i don't understand what this says

[neat reef]

@wispy marten it is possible to define A_1 = A_2 in this example?

[wispy marten]

No

If A_1 = A_2, then these events are not independent

[neat reef]

So I dont understand your hint, A_1 is and event when we have head and A_2?

[wispy marten]

The coin is thrown twice

[neat reef]

Allright

[wispy marten]

A_1 is the event where you have heads on the first throw

A_2 is the event where you have tails on the second throw

Naturally A_1 and A_2 are independent

[neat reef]

I see

[wispy marten]

You can also verify that A_1 and A_3 are independent

Same for A_2 and A_3

(do the computations)

However, A_1 , A_2 and A_3 together are not independent

[neat reef]

So A_3 is the event with two throws where we are getting exactly one head and one tail

@wispy marten

[wispy marten]

Yes

[neat reef]

Let me do computations

But how can I define the probability for A_3? Of course for A_1 and A_2 the probability of getting head resp. tail is 1/2

@wispy marten

[wispy marten]

I did not understand your last sentence

Of course for A_1 and A_2 the probability of getting head resp. tail is 1/2

[neat reef]

So

P(A_1) = 0.5 and P(A_2) = 0.5

[wispy marten]

Yes

[neat reef]

So P(A_3) = 0.5*0.5 = 0.25

@wispy marten

[wispy marten]

Non

There are 4 possible outcomes when you throw a coin twice

HH, HT, TH, TT

H for heads, T for tails

[neat reef]

Sure

[wispy marten]

The first letter is for the first throw

And the second letter is for the second throw

Now since the coin is fair, all these 4 outcomes happen with same probability (here 1/4)

With this information, what is P(A_3)?

[neat reef]

It should be 1/4 = 0.25

@wispy marten

[wispy marten]

No !

[neat reef]

...

[wispy marten]

How many outcomes have 1 tails and 1 heads exactly

[neat reef]

2 outcomes HT or TH

@wispy marten

[wispy marten]

so 2/4

[neat reef]

Right

[wispy marten]

Now it only remains to compute the probability of intersections

[neat reef]

So P(A3/A1) = 0.5 and the others...

Therefore we can see they are independent

@wispy marten Okay, I'll try

[wispy marten]

What is A3/A1?

[neat reef]

It should be P(A_1 ∩ A_2 ∩ A_3) = P(A_1)*P(A_2)*P(A_3) = 0.5^3 = 0.125

@wispy marten Probability that the event A_3 occurs if A_1 occurs before... Conditional probabilty

[wispy marten]

We write |

not /

[wispy marten]

This won't be the case

[neat reef]

Allright, thanks

... hmmm

@wispy marten How so?

[wispy marten]

You only have 4 outcomes with probability 1/4 for each

See how many of them satisfy the requirements for each intersections

[neat reef]

Only 2 of them satisfy the requirements, those are HT and TH

So the answer should be 0.5

@wispy marten

[cedar kiln]

@neat reef Has your question been resolved?

[neat reef]

Or I should be thinking that A_1 happens, what is 0.5 and then A_2 what is also 0.5 so A_3 = P(A_1)P(A_2) = 0.50.5 = 0.25

@wispy marten

[neat reef]

<@&286206848099549185>

[cedar kiln]

@neat reef Has your question been resolved?

[cedar kiln]

@neat reef Has your question been resolved?

[cedar kiln]

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[prime island]

https://i.gyazo.com/340b4fc1a93ab4128f1b0c9f42e71218.png

[prime island]

I got this far

I have no idea what to do next

I want to plug y into the derivative equation but it looks like it gives back 0

[flint plinth]

what do you get if you plug y back in to the original equation

[prime island]

Ill try that

am I doing this right?

[flint plinth]

should be x^6 in the last term?