help-0

[verbal ermine]

to n

wait nv

i used a different question nice

@woeful pulsar

i pasted the wrong q

because they were similar

its that part iii

and the answer to part ii is

[woeful pulsar]

hmm no wonder

[verbal ermine]

so now i need to get right of the 1st 2nd 3rd 4th term?

[woeful pulsar]

yeah so now you need to take a limit and remove the irrelevant terms

[verbal ermine]

got it thanks

[acoustic bay]

is the channel free now?

[woeful pulsar]

probably?

[radiant pasture]

should be at this point?

[verbal ermine]

yeah it is

[acoustic bay]

can someone help me with this proof? I can send a pic of my work in a few minutes

[radiant pasture]

why in a few minutes

oh i read is as have to send

sorry my eyes are malfunctioning

[acoustic bay]

@radiant pasture not sure what you mean, I had to finish it up and email the picture from my phone to myself

[radiant pasture]

i thought you wanted help within a few minutes as if you had an exam rn, we have a strict policy against doing that

dw

[acoustic bay]

I took ideas from what I can online but I feel iffy on what I have like how do I show that its from t < 1/theta

[radiant pasture]

this is probability theory right

i'm a little rusty on Gamma functions, i can take a look later since i have class rn

[woeful pulsar]

yeah basically we'll have to use the definition of moment generating function

[acoustic bay]

does it look right? I just multiplied by e^tx for my integral but then I got stuck and had to do the whole substitution with Y from an idea I found online but Im not sure if I implemented it right

@radiant pasture bro dont worry about the problems focus on your class, dont get distracted

[radiant pasture]

dw break just clocked in lol

ty for worrying though

[woeful pulsar]

yeah the multiplying by e^(tx) looks right

[acoustic bay]

@woeful pulsar what about the whole substituting by Y? and would you happen to know how I know if its when t < 1 / theta?

[woeful pulsar]

basically is the range where the moment generating function is well defined

yeah so you need to look at the original integral

[normal lagoon]

looks good to me

[woeful pulsar]

so we need e^x to be raised to a negative power

[acoustic bay]

@normal lagoon Thank you for taking a look appreciate it

@woeful pulsar so would a valid reason be because we want to make sure e^-(1/theta - t)x to be less than infinity and this happens when (1/theta - t) is greater than 0?

the e^-(1/theta - t)x is coming from where i substituted the Y btw

[woeful pulsar]

yeah we need to make sure e^-(1/theta - t)x goes to 0 as x goes to infinity

[acoustic bay]

ok thanks guys

@woeful pulsar appreciate it

[woeful pulsar]

WARNING QUESTIONS-2 is landmine

<@&268886789983436800>

DO NOT GO INTO QUESTIONS-2

[still turtle]

Thanks for the warning

I have a question

how do you solve this

[night geyser]

dealt with

[woeful pulsar]

nice thanks

[humble cape]

How would one find a circle with radius r, perpendicular to a given vector? (3 dimensions to be specific)
What I'm really trying to do is find the cone between two 3 dimensional vectors, one being the apex

[woeful pulsar]

So, the two vectors define opposite sides of the slanted face?

if so you can use the angle bisector to get a vector running down the cone

you can calculate this through angle bisector theorem or otherwise

[humble cape]

no sorry, I meant to say two 3 dimensional points

one at the apex (tip of the cone)

[woeful pulsar]

oh, what does the other point define?

is it the centre of the base?

yeah, you can find the plane the circle lies in because you have the normal vector

[humble cape]

yes

So assuming the normal vector is (a, b, c) and the center of the base is (x_0, y_0, z_0)

[woeful pulsar]

what do you mean by finding a circle

is there some sort of form we need to express the circle in?

[humble cape]

The plane is a(x-x_0) + b (y-y_0) + c(z-z_0) ?

[humble cape]

I actually only need to find one point I think

because I need the cosine and the tangent to the angle of the cone

[humble cape]

I'm guessing this is correct, so how would I now find a point on the circle? I can't just go r in one direction as the plane is very likely to be diagonal

[woeful pulsar]

yeah, the circle is included in the plane

though there's not really a good way to dual space

so it's kinda arbitrary, is there any more context?

[humble cape]

Full context

I have one point and two sphere in R3

[woeful pulsar]

is this math or programming

[humble cape]

programming

[woeful pulsar]

AH

no wonder

we don't really have a nice neat expression

[humble cape]

I need to check if the sphere in between is blocking the light from the point

so I thought a smart way to go about it is construct a cone and check if it intersects with the sphere

[woeful pulsar]

ah, so you don't need an explicit cone

[humble cape]

explicit what?

[woeful pulsar]

you don't need to store the cone explicitly

you just have that idea

[humble cape]

I guess not

[woeful pulsar]

okay you found the radius of the base of the cone?

where's the base of the cone by the way?

[humble cape]

I was going to check the intersection based on this algorithm: https://gist.github.com/jcayzac/1241840

[humble cape]

this is known

[humble cape]

and we know the center of the sphere

[woeful pulsar]

WHAT?

oh no

[humble cape]

is it that bad 😬

[woeful pulsar]

yeah it is

what if the point is very close to the sphere

[humble cape]

it's not, trust me

haha

[woeful pulsar]

oh you only need an approximate algorithm?

[humble cape]

oh, well i don't know. I posted the algorithm above

[woeful pulsar]

how accurate do you need the answer?

[humble cape]

the other option is I use ray sphere intersection

but then I would have to "cast" a lot of rays coming from the point

I just want to check whether it intersects, don't have to know where it intersects

[woeful pulsar]

okay

how accurate do you need the answer?

like if the sphere was a bit outside the cone, is a yes answer okay?

if the sphere is a bit inside the cone, is a no answer okay?

[humble cape]

rather have it be correct all the time

[woeful pulsar]

okay then

firstly, we need to calculate the cone accurately

the centre of the base of the cone is not actually the centre of the sphere

[humble cape]

wait what

[woeful pulsar]

rather, let d be the distance between the light and the centre of the sphere, and r be the radius of that sphere

then the centre of the base of the cone is r^2/d away from the centre of the sphere

if you use the centre of the sphere for the base of the cone, then either the cone will clip the sphere OR the cone will include bits which you don't want

[humble cape]

alright, so then what

[woeful pulsar]

let me draw a 2d mockup

[humble cape]

sure

[woeful pulsar]

slight difference, yeah?

the first one it clips the sphere if you use the radius of the sphere for the radius of the base of the cone

the second one it stops at the tangency point

that's what we need to calculate

it's a well known result from poles/polar or inversion or similar triangles that the centre of the base of the cone is r^2/d away from the centre of the sphere

[humble cape]

yes, that's a good sketch :)

[woeful pulsar]

thx I did it in paint lol

[idle junco]

i sense somebody is doing raytracing

[woeful pulsar]

me too [I sense too]

[idle junco]

XD

[humble cape]

Not even the case haha

[idle junco]

oh lol

[humble cape]

I am trying not to use the ray tracing methods as they all iterate

[idle junco]

cause this is something commonly asked in ray tracing

[idle junco]

why is that a problem

[woeful pulsar]

speed

[idle junco]

space limit?

[humble cape]

Because my code is already slow

[idle junco]

oh speed

[humble cape]

I am namely

[idle junco]

what is the overall objective of the program

[humble cape]

modeling the orbits of the moon, earth and sun

[idle junco]

ohhh

[humble cape]

no, I have not solved the three body problem

it's an estimation

[idle junco]

yeah anything in cse is approximation in the end

[humble cape]

hey this is for maths

[idle junco]

no i mean the orthogonal projection or the 3D graphics

etc

[humble cape]

this was a joke as the three body problem has no general solution

[idle junco]

shadow

[humble cape]

oh ok

but now, I have to check whether there is a solar eclipse

[idle junco]

XD

[humble cape]

and I have to check at every point in time

[idle junco]

that is hard

[woeful pulsar]

ah I see, but are you modelling the sun as a point?

[humble cape]

I thought the model was the hard part

[humble cape]

well let's keep things simple right?

[woeful pulsar]

alright then

[humble cape]

unless using 3 spheres is easier

[woeful pulsar]

then I guess we don't really need the accuracy too, honestly speaking

but if you still want to explore the point sphere sphere case, I'll join you

[humble cape]

I am currently checking if a sphere is in between two points

which is MUCH easier

[woeful pulsar]

ah yeah, it's just project the centre onto the line and find the distance

[idle junco]

use the solid angles concept

[humble cape]

I just check whether the distance of the point to the line is smaller than it's radius

[idle junco]

wait by spehere u mean circle?

[humble cape]

no 3d

[woeful pulsar]

it's 3d

[idle junco]

ahhh ok

solid angles then

ig

[humble cape]

sorry but what am I supposed to do now?

[woeful pulsar]

pick how you want to solve the problem

[humble cape]

well I guess I can live with the inaccuracy

[woeful pulsar]

so which inaccuracies will you keep and which will you discard?

[humble cape]

because the moon will move further in between the next point in time anyways

[humble cape]

what do you mean by that?

[woeful pulsar]

ah just wondering if there's anything you are working on

if not I can gracefully leave this conversation lol

[humble cape]

sorry but I'm not getting what you're asking

yes I am working on this problem

[woeful pulsar]

okay, what is the particular formulation of the problem you are working on?

is it still the "point and two spheres"?

[humble cape]

is it easier with 3 spheres?

It's my own model, so I get to choose

[woeful pulsar]

yeah, lemme think about 3 spheres

it's definitely not easier

but idk how much harder

[humble cape]

then let's imagine the sun is a point

because then we can continue with our cone strategy

[woeful pulsar]

alright, so far you got the cone, are you going to use your approximation, or correct that approximation?

[humble cape]

I haven't gotten the cone right? I just have the two points

I can live with an approximation

[woeful pulsar]

then yeah, the centre of the earth and the radius of the earth is a fine approximation

since the distance to the sun is way greater than the radius of the earth

[humble cape]

exactly

but I still don't know how to find a point on the plane

[woeful pulsar]

ah I see, it shouldn't be a problem though, we have all the measurements of the cone to do calculations with it

[humble cape]

a point that is r away from the center

we don't right? We only have the plane, not the circle

[woeful pulsar]

So now we can also find the distance between the centre of the moon and the axis of the cone

we also have the centre and radius of the circle, that's enough to define the cone

[humble cape]

Alright great

so how would I now find the tangent and the cosine?

unless you'd say this (https://gist.github.com/jcayzac/1241840) is not a good way of checking the intersection

[woeful pulsar]

lemme check out

we should work with what we have probably

unless you want to follow that way (which I haven't verified by hand yet)

hmm, but let's consider the plane containing the cone axis and the moon

we want to be able to find that distance

remember we are working in the plane containing the cone axis and the centre if the moon, so hey yeah tan is a good idea

finding this angle looks like a good idea yeah

finding this angle should be easy

@humble cape you here?

[humble cape]

yes I am wrapping my head around it sorry

[humble cape]

this angle seems easy enough yea, even tho the moon is ofcourse not at the same height as the sun and the earth

[woeful pulsar]

yeah

so if you have the red angle, green angle and the angle of the cone, you are more or less done

[humble cape]

I don't see how to get the green one

[woeful pulsar]

hmm, the green angle is part of a right triangle

[humble cape]

how do I find the, in this case, bottom left corner

[woeful pulsar]

bottom left corner?

the bottom left corner of the right triangle is a right angle

you know 2 of the sides

[humble cape]

ah, ofcourse

but what other side than the diagonal side do we know?

[woeful pulsar]

radius of the moon

[humble cape]

right, right

[waxen willow]

Hi guys

[woeful pulsar]

what is Hz?

urgh capitalisation is messed up

please use consistent capitalisation

[woeful pulsar]

Try doing the first part where you do z/w?

[waxen willow]

I did it but someone was saying it was wrong ?

Thats the answer i did

[woeful pulsar]

check your working

w = -1+i

you divided by -1-i

[mossy oracle]

Could someone help

[waxen willow]

So is it because i put the 1 infront of the i ?

when it should be on its own ?

[woeful pulsar]

which diagrams make sense and which don't?

[woeful pulsar]

erm... your first line is wrong

[waxen willow]

is it that line where the mistake is ?

[woeful pulsar]

no, earlier

[humble cape]

thanks Element

I'm back on track

[woeful pulsar]

you did it? nice

[humble cape]

on the highway

[waxen willow]

Why is dividing the first part by W wrong ?

is it suppose to be Z ?

1+7i

[woeful pulsar]

you cancelled the (-1+i)

[waxen willow]

Oh so it suppose to be -1-1i instead of +1-1i

[alpine sable]

Suppose I have the linear congruence 5x [congruent] 8 (mod 5) can't I multiply both sides by 5 and then I get 25x [congruent] 40 (mod 5) and since 25 [congruent] 40 (mod 5) cause 5 divides (25-40) then I obtain x [congruent] 1 (mod 5) Why can't I do this ? what's wrong with it ? I don't understand

[woeful pulsar]

$5x\equiv 8\pmod{5}$

$25x\equiv 40\pmod{5}$ (okay)

$x\equiv 1\pmod{5}$ (not okay, since you divided by 5 and 5 is not coprime to the modulus, it's like dividing by 0)

[ocean seal]

Element118

[alpine sable]

well like

If I have a congruent b mod m and c congruent d mod m then a .c congruent b.d mod m

same thing here

I have 25 congruent 40 mod 5

@woeful pulsar I didn't quite understand

[woeful pulsar]

yeah

How did you get $x\equiv 1\pmod{5}$?

[ocean seal]

Element118

[alpine sable]

yeah my bad

I think I can't divide by 5

my bad

[chrome willow]

find x?

[woeful pulsar]

similar triangles?

[chrome willow]

not gonna lie i am not even sure. but i did get 5 as an answer by doing 18/9x = 8/20 and then cross multiplying and then solving from there

but i dont know if thats the right way to do it

[woeful pulsar]

yeah your intuition on what works is correct

the way you can rigourise it is to extend the two lines to meet at an intersection point

that would give you the similar triangles

[chrome willow]

Okay thank you for your help

[spare hill]

hi, i'm trying to work thru this example

but I'm not sure what this part is: [1, -2+2i]_T

[glass lichen]

that's the eigenvector

[spare hill]

idk why when i use Symbolab's eigenvector calculator, it doesnt come up as the same

[glass lichen]

eigenvectors arent unique for a given eigenvalue

[spare hill]

oh? so there are many eigenvectors?

[glass lichen]

yes, there's an entire subspace

the eigenspace of the eigenvalue

[spare hill]

ahh

darn, i wished symbolab would me the steps thru these specific eigenvectors used in the example

[glass lichen]

$Ker((3+2i)I-A)$ to be specific

[ocean seal]

moshill1

[spare hill]

ah, this is the one used specifically in the example?

[glass lichen]

well you want an eigenvector for $\lambda = 3+2i$, so you need to find the basis of the $(3+2i)-$ eigenspace

[spare hill]

ok

[ocean seal]

moshill1

[spare hill]

got it. i'll try that with the example again. thank you so much! this clarifies a lotttt

[tender portal]

hi is this channel free now?

I don't quite understand this question

I've just been taking whatever power x is to for f(x) and the number after the function for a

That method doesn't work for 31 b tho

[glass lichen]

$f'(c)=\lim_{x\to c}\frac{f(x)-f(c)}{x-c}$

[ocean seal]

moshill1

[glass lichen]

@tender portal

[tender portal]

That the definition of a derivative

How do I apply it to 31 b?

Oh

[tender portal]

Thanks I got it

[willow bluff]

Hello I’m just learning the sin and stuff. Can someone help me out?

[glass lichen]

,rotate

[glass lichen]

is it a test?

[nocturne swift]

im confused

[willow bluff]

Nope. Hw check

[limpid spade]

so its a right angle, and you need to find x

which identity would you use? sin,cos or tan?

[limpid spade]

How much 4in is yard? and also whats 12ft and 20ft in yard?

[willow bluff]

Sin?

[tender portal]

do conversions then multiply height, width, and length

[limpid spade]

Why sin?

[willow bluff]

🤷🏻‍♂️

[limpid spade]

If you used sin show me what u would do

[willow bluff]

Sin 43 = 26/h

[limpid spade]

how do u come at 43 and 26

[tender portal]

I don't understand 32 now

if I use the definition of the derivative wouldn't f(x) for 32a just be cos(pi+h)

[candid sluice]

so the defn of a derivative at a is $\lim_{h \to 0} \frac{f(a+h) - f(a)}{h}$

[ocean seal]

Pappa

[tender portal]

Yes

[candid sluice]

what is f(x) in your case

and what is a

[tender portal]

is f(a+h) the same as f(x)

[candid sluice]

well

f is some function

more clearly

f is the function that is being differentiated

so what function are you differentiating

[tender portal]

Yes ok

cos(pi + h)?

oh cos pi ?

[candid sluice]

cos pi is a constant

the function is cos x

but a = pi

so putting all this info into our defn

[tender portal]

I don't quite understand how you got to this

[candid sluice]

sure

so i want to find the function that is being differentiated

so i write x as a placeholder

[tender portal]

Ok

[candid sluice]

and ill call my function f(x)

its just a name for the function we are differentiating

[tender portal]

Ok

[candid sluice]

and its input is x

[tender portal]

Yes

[candid sluice]

the function we are differentiating is cos

[candid sluice]

so putting in that input you get f(x) = cos(x)

[sinful shore]

So I would have to find the inverse of Function F, and then plug in function H into F right?

[tender portal]

ahhh ok

and cos(pi) = 1

alright

[candid sluice]

check your unit circle

[sinful shore]

anyone know?

[candid sluice]

cos(pi) is not quite 1

[tender portal]

on the unit circle is it not?

[candid sluice]

jesus thats a bad image

[tender portal]

Oh it's -1

nvm my bad

[candid sluice]

epic

[tender portal]

yeah that makes sense

so for 31a I would follow the same steps

[candid sluice]

yeah

its just jazzed up notation to scare you

[tender portal]

the function I am differetiating is x^1/2

[candid sluice]

the same idea

[tender portal]

and the delta x + 1 is just a constant

within the function

[candid sluice]

yes

[tender portal]

That clears it up so much thanks

The left part is always the function I am trying to differentiate

and the right is the output of the constant that I put into that function

[candid sluice]

you should probably think of the left part as the function plus some small nudge

so sqrt(1+delta(x))

delta(x) is a small nudge

[alpine sable]

I know this is a math server but can someone please help me with this earth science question you can dm me please.

[candid sluice]

and then sqrt(1) is the constant

[tender portal]

what do you mean by a small nudge

[candid sluice]

uhh

so have you seen the visual interpretation of the derivative

[tender portal]

right now I just understand that the left part is the function I'm trying to differentiate

[upbeat stone]

i need some help on how to find the missing value given the mean

[tender portal]

The tangent line to the function?

[candid sluice]

yes

[tender portal]

yes

[candid sluice]

and we approximate it by secant lines

[tender portal]

yes

[candid sluice]

where the points are super close etc

[tender portal]

yep yep

[candid sluice]

so delta x is just the distance between them

its not a constant

the f(a) part is a constant

[tender portal]

ah ok

[alpine sable]

What is the equation for y?

[tender portal]

but like f(x) = x^1/2 and in 31a the x is just (1+delta x) right?

[candid sluice]

yes

[tender portal]

y = 2x

[candid sluice]

x is just a placeholder for the input of the function

[tender portal]

wait no

[alpine sable]

how do you know that

[tender portal]

y = 1/2x

[tender portal]

alright ty

[alpine sable]

thought it wqas

y = 0,5x

[tender portal]

same thing

[alpine sable]

at the start

but i checked

and its not true

checked on mathway

[tender portal]

oh wait thats not 0.5 its 0,5?

[alpine sable]

oh yeah

[upbeat stone]

i need some help on how to find the missing value given the mean <@&286206848099549185>

[alpine sable]

What is the value of the expression ** 5s - 7 ** when s = 3

15s - 7 or 8s

[cold roost]

Stop bumping your question @upbeat stone , and do you even have any thing posted?

[upbeat stone]

my thing posted?

do i need a screenshot

or do i just type it

ok so 11,12,7,3,x what do i do to get a mean value of 8

how do i find the x

[limpid spade]

5*(3)-7=8

[alpine sable]

5 * 3 - 7

Is there any proof about this ? What is this called? Currently I am learning sets and subsets 🙂 I dunno what characteristic function this is called.

I share with you my method of solving for congruence systems

[alpine sable]

@limpid spade do you just replace 3 with s so 5 * 3

[limpid spade]

Yeah duh what else can u do

[sinful shore]

can someone help me with a problem ?

no one helping me

[limpid spade]

What question

[sinful shore]

how would u do this

[alpine sable]

Atleast a name about the proof of this?

[sinful shore]

also waiting on this one

<@&286206848099549185> please help

[daring sonnet]

Hey can someone help me with a question

I’m so lost on what to do

[limpid spade]

Iron and Noob other channels

[daring sonnet]

What

Ok

[limpid spade]

Post on other channels

[daring sonnet]

Ok

[limpid spade]

Other channel

[bleak crane]

oops

[alpine sable]

Can someone help me with this?

[proud oracle]

^^

confused i havent been payin attention for this unit

[sinful shore]

@proud oracle photomath it

[proud oracle]

but photomath dont do word problems

:/

[rustic kiln]

5 is c

[proud oracle]

thank you

[sinful shore]

can u help me

[sinful shore]

.

[alpine sable]

draw a tangent to the circle

and the length of the blue thing

[rustic kiln]

1 is D

The answer is just written wrong

[proud oracle]

for mine?

[sinful shore]

for mine

[proud oracle]

oh shit lol

[rustic kiln]

Wait no

[rustic kiln]

No

[rustic kiln]

Sorry o was looking at the wrong one

[rustic kiln]

1 is D

[proud oracle]

okay thank you

[ripe vigil]

ok so im doing a project about angle of elevation, we have to make our own word problem i made one but dont know how to solve it can someone help me with this

this is what i made

[lofty kelp]

.

[alpine sable]

ask in an unoccupied channel please

[ripe vigil]

my bad i didnt see anyone typing

[lofty kelp]

LOL

[alpine sable]

ABCD is a parallelogram, what properties of parallelograms may be useful here?

[lofty kelp]

AB=CD

[alpine sable]

well they don't tell us AB or CD

we have the lengths BE and BD

so try to think of a property related to the diagonals of a parallelogram

point E is the intersection of the two diagonals

[lofty kelp]

yesz

[alpine sable]

you need to use the fact that the diagonals bisect each other

so BE is half of BD

can you convert that to an equation and solve?

[lofty kelp]

im not sure if my answer is correct

[clear venture]

total noob question, why does 2x * x become 2x^2?

[tender portal]

because think of it as

having 2 x's multiplied together

and then mutliply that by 2

[clear venture]

oh

yeah

lol

thx

[tender portal]

when it says sketch the graph of f does it just means f(x)

[alpine sable]

Hmmm

[tender portal]

confusing times

[sly wasp]

Im confused

[alpine sable]

Imagine this complex shapes as something more elemental

i.e. the arrow (8), for example, it could be divided into a triangle and a, I suppose, square

[plucky crow]

for number 1 split it into a triangle and rectangle

14-7 will give you the height of the triangle.

using this concept you should be able to do the rest

alternatively a is a trapezium but thats besides the point lol

@alpine sable what seems to be the problem here

what dont you understand

about the question

[arctic umbra]

you simplify it 😭

10x-30 just simplify the expression

[plucky crow]

okay take me through your thought process

when attempting this question

what have you tried

what did you get stuck at

this was my thought process: simplify here means to expand the brackets, there is a 5 outside, and i know that because the whole thing inside the brackets is being multiplied by 5 i have to multiply everything inside the bracket by 5, 2 x 5 is 10, -6 x 5 is -30, so its 10x - 30

hopefully that helps you in the future

[alpine sable]

Help please

[glass lichen]

with what?

[alpine sable]

The question and also explaination

[glass lichen]

there are 5 questions

[alpine sable]

vertex and below

there confusing

[glass lichen]

ok well what's the vertex of a parabola?

[alpine sable]

?

[glass lichen]

no, the vertex is not a question mark

[alpine sable]

ok

[civic igloo]

I need help with an algebra word problem

[plucky crow]

i dont understand

if she withdrew 200

that means her account had 415

this is half of what she had right because she split it

so isnt it just 415 x 2

or is 215 her total

[civic igloo]

She had one part saved for her family and another for her expenses

[plucky crow]

oh i misread

but then yeah

does she still ahve

all the money

[civic igloo]

No she spent it on the iPhone

[plucky crow]

i mean

the money she saved for her family

is it still in her account

[civic igloo]

Yes

[plucky crow]

then it doesnt matter where she took 200 from

if she took 200

[civic igloo]

All the money except the 200 dollars she withdrew is in there

[plucky crow]

and her money now is her total - 200

then her salary is that + 200

so 415

assuming she still has the money for her family

[civic igloo]

Oh, Thanks for the help kind stranger

[silk terrace]

Anyone that is decent in desmos that can help me out? Trying to only draw the union of 2 inequalities 0<x<4 and 0<y<\sqrt(x)

So only the overlaps.

[noble sinew]

,w 0<x<4 and 0<y<sqrt(x)

[ocean seal]

Results provided by WolframAlpha

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

Requested by ScapeProf#9427

[silk terrace]

I am not liking wolframs as it is not making the edges dotted or piecewise. That is why I am using desmos.

[edgy trout]

How do you solve this system? Suppose A B C D are transfer functions that describe a system

r1 is reference 1, and r2 is reference 2. X is also a transfer function

I've always done this with one reference. have no clue what to do with the extra one

[alpine sable]

Hi can I get help with this question I don’t understand it

[jagged mesa]

Just question 1

[nocturne swift]

How long is it

[glass lichen]

,rotate

[ocean seal]

Something went wrong!

An unexpected error occurred while processing your command!
The error has been reported and should be fixed soon.
If the error persists, please contact our friendly support team at our support guild!

Exception

aiohttp.client_exceptions.ClientPayloadError: Response payload is not completed

[tender portal]

<@&268886789983436800> can you mute or ban @alpine sable , inappropriate spamming of question channels

[glossy island]

👍

[nocturne swift]

lol

[abstract fossil]

is this 51

since they are congruent

[glass lichen]

yes, opposite angles are equal

[abstract fossil]

how do i solve this

[slow pendant]

Use triangle law

[abstract fossil]

its asking to find the missing measures

so z is 39

and y is 51

wha

it would have to be 180

what does that mean

ok

but what do i figure out

with the knowledge that the sum is 180

is it 73

whats that symbol next to 107

y is 51

so x is 56

whats the symbol next to 107

i dont

is it a u or something

[gusty oyster]

If we are given sets of vector and we are supposed to find whether they are linearly independent or not
How do we write them in matrix form?

For example sets of vectors are (1,2),(3,4)

Should we solve for
1 3
2 4

Or

1 2
3 4 ?

Could anyone please confirm I have seen both version on google

Oh

[glass lichen]

(0,0)=a(1,2)+b(3,4)

0=a+3b
0=2a+4b
so you get a row of 1,3 and then 2,4

then augmented with 0,0 column vector

[gusty oyster]

Uh this is confusing cause my teacher has used second method as well

[glass lichen]

$\begin{bmatrix} 1&3&0 \ 2&4&0\end{bmatrix}$

[ocean seal]

moshill1

[gusty oyster]

Um

So

In the book

In the sol manual

They used the other method

1 2
3 4

[alpine sable]

I just need help with turning it into an equation

[merry hornet]

If i have 10% chance of winning a certain case and i open that case 10 times. what are the odds for me to win one of the cases?

[charred flint]

don't open cases

[merry hornet]

lmfao thats hypothetical

[tawny lion]

@tender portal input 1 into both, if it creates same value it's continues

derive both, then input 1, if it creates the same value it's differentiable

[tender portal]

there's an additional variable k tho?

I know how to do it when it's just x

[coral pagoda]

Okay, so two things must happen, both $\lim_{x\to 1} f(x)$ and $\lim_{x\to 1} f'(x)$ must exist

[ocean seal]

dackid

[tender portal]

Yes

[abstract sundial]

@coral pagoda HEY IS THIS RIGHT

[tawny lion]

no

[coral pagoda]

So we see that f(1)=1 and $\lim_{x\to 1^+}f(x)=1+k+p$

[tawny lion]

you can see on the graph

[ocean seal]

dackid

[tender portal]

Yep

[coral pagoda]

So in order for the limit to exist, set them equal to each other

[abstract sundial]

@tawny lion I SUBSITUTED IN THE VALUES FOR X

[coral pagoda]

So we see that k=-p

[merry hornet]

<@&286206848099549185>

[tender portal]

Got that

this is where im stuck rn

[coral pagoda]

Okay great, now we need the derivatives to agree at x=1

[alpine sable]

is the equation correct?

[tawny lion]

bro, -(-2^2) -8(-2) - 13
-4 + 16 - 13
f(-2) = -1

[coral pagoda]

We see that $\lim_{x\to 1^-}f'(x)=-1$ and $\lim_{x\to 1^+}f'(x)=2+k$

[celest gorge]

@ me please

<@&286206848099549185>

[ocean seal]

dackid

[coral pagoda]

Still there @tender portal ?

[abstract sundial]

DAMN

[tender portal]

Yes

[merry hornet]

dackid can you answer ma question real quick? its simple

[tender portal]

Wait I'm trying to understand that step

[coral pagoda]

In order for it to be differentiable at x=1, the derivatives must agree at x=1

[celest gorge]

if its simple then just do it

[merry hornet]

idunno how

but its probs simple to him

koz he big brain

[tender portal]

Oh ok got it got it

[coral pagoda]

So now set them equal to each other. We have $-1=2+k\Rightarrow k=-3$, and since $k=-p$ we see $p=3$

[ocean seal]

dackid

[tender portal]

Ok

[coral pagoda]

So the quadratic in the piecewise should be $x^2-3x+3$

[ocean seal]

dackid

[tender portal]

Would that be the only possible solution

[coral pagoda]

Give me a reason why it wouldn't be

[tender portal]

I tried graphing just x^2 and it is continuous but it's not differentiable because there's a cusp

[abstract sundial]

@tawny lion I got for F(-2)=5

[coral pagoda]

Okay, so that one's wrong

[tender portal]

Yeah I got nothing else haha

thank you

[coral pagoda]

Using the approach I used, try to give me a reason why it would be any different

[tender portal]

Hmmm if p was a different value the function wouldn't meet because it would shift along the y axis

[coral pagoda]

True, but we did not guess the value of p

[tender portal]

Yes that's true

I guess there can be no other values because then the derivatives would not be equal to each other

at x=1

we calculated limits from both sides of 1

[coral pagoda]

or k, we solved them by setting $\lim_{x\to 1^-}f(x)=\lim_{x\to 1^+} f(x)$ and $\lim_{x\to 1^-} f'(x)=\lim_{x\to 1^+} f'(x)$

[ocean seal]

dackid

[tender portal]

Yep

airtight

[coral pagoda]

Because the limit only exists when the left and right hand limits are the same

[tender portal]

Yep

[abstract sundial]

@coral pagoda can u help me after

[tender portal]

no its -1

[coral pagoda]

And there were no other possible solutions

[tender portal]

Yep

[hardy geyser]

2^2 times 2^2 is 2^4 yes?

[coral pagoda]

Yep!

[hardy geyser]

Ty

[tender portal]

Yes

This one I don't even know where to start

[abstract sundial]

HOW

[tawny lion]

bro

[tender portal]

plug -2 into your original equation

[tawny lion]

join voice

join mathematics

[abstract sundial]

Can we do it in like 20 mins I'm in class right now @tawny lion

[abstract sundial]

I did

[tawny lion]

ok

let me identify the mistake, one sec

i think you are inputting -2 into -x^2 and getting 4

@abstract sundial alright look

the function is -x^2 - 8x -13

-(x^2) -(8)(x) - 13
-(-2^2) or -(-2 * -2) which is -(4)
-4 -(8)(x)
-4 -(8 * -2)
-4 -(-16)
this is equal to 12
you still have -13

12 - 13 = -1

[abstract sundial]

I thought I was supposed to do -2(x^2)

[coral pagoda]

First, given $g(x)=\frac{f(x)}{f(x)-3}$, solve for f(x).

[ocean seal]

dackid

[tawny lion]

no, you input -2 into x

you can also check yourself based on the graph

when you see on x axis that it is -2, y is -1

[tender portal]

Oh did I start wrong, I just set g(x) = 3 from the information given and then set that equal to the f(x)/f(x)-3

[coral pagoda]

Well, you can, but this just makes what you're about to do more clear

[tender portal]

Ok

[alpine sable]

can someone help me with a problem

Angle 1 and angle _ are supplementary angles. Just enter the number. There is more than one answer

<@&286206848099549185> ^

[abstract sundial]

Oh

[coral pagoda]

Do not ping helpers until it has been at least 15 minutes since you have asked for help

[alpine sable]

o alright mb

[edgy sand]

anybody familiar with this?

[tender portal]

I can't isolate f(x) the best I can do is f(x) = g(x) * (f(x)-3)

I got into a hot mess trying to further

[coral pagoda]

Ffs! Everyone who is not Zach move somewhere else!

[abstract sundial]

@tawny lion I put in -6 and still got -1

[coral pagoda]

Well this gives $f(x)=g(x)f(x)-3g(x)\Rightarrow 3g(x)=g(x)f(x)-f(x)$

[ocean seal]

dackid

[tender portal]

Oh

[coral pagoda]

And we can now factor f(x)

[tender portal]

Yep oops I put too many brackets confused myself

[coral pagoda]

So we have $3g(x)=f(x)(g(x)-1)\Rightarrow f(x)=\frac{3g(x)}{g(x)-1}$

[ocean seal]

dackid

[tender portal]

Yep got that

Now I can plug in the numbers

[coral pagoda]

Okay, to find the tangent line we need the form y=mx+b where m is f'(4)

[tender portal]

Right

[coral pagoda]

And what is f(4)?

[tender portal]

9/2

[coral pagoda]

Good, so we know (4,9/2) is a point on our line

[tender portal]

Yep

[coral pagoda]

So we have $\frac{9}{2}=5(4)+b$

[ocean seal]

dackid

[coral pagoda]

Now solve for b

[tender portal]

-15 1/2

[coral pagoda]

Yes, but let's keep it in improper form -31/2

[brisk steppe]

Woah, I got -31/2

Oh,

[tender portal]

Alright

[coral pagoda]

So we see that $y=5x-\frac{31}{2}$

[ocean seal]

dackid

[coral pagoda]

And that's part a

[tender portal]

Yep

[brisk steppe]

Ok.

[tender portal]

Wait how did we get the slope as 5?

[alpine sable]

any1 with access to mathscinet.ams.org can help me with a paper please?

[native temple]

how?

[tender portal]

jesus flooded w questions lol

[coral pagoda]

Move somewhere else please

[tender portal]

nvm I got it

[native temple]

oh it's in use dackid?

[lofty kelp]

lol

[tender portal]

yeah it was in the problem

oops

[coral pagoda]

Yep

[abstract sundial]

CAN I GET HELP @coral pagoda

[lofty kelp]

channel was clear

[native temple]

no

[tender portal]

oh we were working on part b of the question

[coral pagoda]

It sure as hell isn't

[abstract sundial]

I WAS NOT TALKING TO YOU @native temple

[native temple]

wair it isn't?

[tender portal]

no we're still working on it

[coral pagoda]

I am talking to all of you. Go somewhere else please

[lofty kelp]

ok

[coral pagoda]

Can you reshare the screenshot Zach

[jovial knoll]

guys

for question 11

[nocturne swift]

woAH

WOah

[coral pagoda]

Quick reminder, we have [ f(x)=\frac{3g(x)}{g(x)-1}]

[ocean seal]

dackid

[nocturne swift]

Albert Einstein u r smart u should be able to help these people

[tender portal]

Yep

[coral pagoda]

I swear to God, go away!

[jovial knoll]

wait the pic is loading

[tender portal]

Im trying to use that to solve it right now

[coral pagoda]

So we know f is not continuous when g=1

[jovial knoll]

do they just want me to put the equation for the volume of the sphere over the volume of the cylinder? is that it?

for #11

[tender portal]

Let me think about that for a sec

[coral pagoda]

Read it and go somewhere else

[jovial knoll]

me?

[tender portal]

Alright yes because it becomes undefined

[coral pagoda]

Yes you

[jovial knoll]

oh sorry

[native temple]

wait?

how does this make sense

[tender portal]

a function's not continuous if the limits don't meet, should I use that for this problem?

[coral pagoda]

The problem is we know nothing about x=3

[tender portal]

Yeah

The problem skips that

we have the numbers on both sides of it though

f(2) = 3/2

and f(4) = 9/2

the problem says f'(2) = 3

[alpine sable]

Can someone check this

Derivatives

We are reviewing for my exam next week

[coral pagoda]

Honestly Zach, I'm not sure

[tender portal]

I'm currently just assuming it is because the numbers seem to work out in some respect

[coral pagoda]

That's not a good reason

[tender portal]

Yeah true

[alpine sable]

No one knows derivatives here ?

Or someone does

[coral pagoda]

Read

[tender portal]

We're kinda tryna work out a problem rn

[coral pagoda]

I'm a bit stuck, because the Intermediate Value theorem suggests it may be possible that f(x) is discontinuous at x=3

[tender portal]

Hm

[coral pagoda]

At minimum, we know g(x) must be discontinuous somewhere in the interval (2,4)

[tender portal]

Yes

because the denominator of the equation we came for f(x) came up with changes from -2 to 2 right?

[coral pagoda]

No, that is now why

[tender portal]

oh

[coral pagoda]

g(2)=-1 and g(4)=3. If the function were to be coninuous on [2,4], then there exists a c in [2,4] where g(c)=1

[abstract sundial]

YOU DONE YET @coral pagoda

[coral pagoda]

However, there is no value of x which g(x)=1, so we have discontinuity within this interval

[abstract sundial]

WHY IS THIS KID TAKING SO LONG WITH THE HELPER PAY MORE ATTENTION IN CLASS

[coral pagoda]

Moon, ask someone else. You're starting to piss me off right now

[abstract sundial]

WHAT THE FUCK

[abstract fossil]

damn

disrespect

[abstract sundial]

THIS IS THE ONLY CHANNEL

[lofty kelp]

patience

[abstract sundial]

THERE IS NO OTHER CHANNEL TO GET HELP

[abstract fossil]

im waiting too

but im not yelling

[lofty kelp]

patience

[coral pagoda]

There are 9 other channels to get general help and you can ask in the topic specific math channels

[tender portal]

no given value or no value at all?

[coral pagoda]

No value where g(x)=1. After all, look at our function f(x)

[tender portal]

Oh right

[jovial knoll]

he is correct

none of them answer

all are dead

[tender portal]

So we know there's a point of discontinuity but we don't know if it's exactly at x = 3

[coral pagoda]

Now this does suggest it is discontinuous at x=3, but that there is a point in which it is discontinuous between the interval 2 and 4

Exactly

[tender portal]

Ah

So the best we can say is that between the interval of (2,4) there is a point of discontinuity

[coral pagoda]

It's really hard to tell if we can deduce any more than that

So... it's possible 🤷

[tender portal]

Haha alright

Fingers crossed there's nothing as vague on the actual test

[coral pagoda]

Wait hold on

It says that f(x) is differentiable for ALL real numbers

[tender portal]

so there can't be a point of discontinuity?

because then it wouldn't be differentiable?

[coral pagoda]

differentiability implies continuity and $g(x)\neq 1$

[ocean seal]

dackid

[tender portal]

one of the theorems in our textbook

[coral pagoda]

Yep

This is true

[tender portal]

Then how can our previous function have a denominator of 0

[coral pagoda]

I feel this problem is poorly worded, since we already know if it were continuous, then $f(x)=3$ would happen in the interval (2,4) by the intermediate value theorem

[ocean seal]

dackid

[tender portal]

Oh alright

[coral pagoda]

Talk to your teacher, there are definitely some issues

[tender portal]

Alright I will

He's a little confusing at times

[lofty kelp]

may I acquire assistance when available please ?

[tender portal]

I think we're done

Thanks as always dackid

[edgy sand]

can someone help me with this one?

any <@&286206848099549185> ?

[robust phoenix]

y=-3,5 right ?

[candid torrent]

@robust phoenix be a bit careful of your wording

y does not have multiple values here

these lines intersect at a single point so it only has 1 solution

[velvet pelican]

@edgy sand what is the issue?

[robust phoenix]

it has no solutions

[candid torrent]

alright

[alpine sable]

Tryna find the amount of adults that attended currently, but I’m lost as to what to do next

[vernal igloo]

Is this technically a correct way of simplifying this?
https://gyazo.com/5e29dfaf58ae8ea33291be724f3807fb?token=6f90448093f1c9f4635b80b038fed434

[shell widget]

@vernal igloo $\frac{2^{-3}}{2^{2}} = \frac{1}{2^{3} \cdot 2^{2}} = \frac{1}{2^{5}} = 2^{-5}$

[ocean seal]

Sup?

[alpine sable]

Can someone help me with these two last problems

[vernal igloo]

what? no?

[obsidian crane]

For b you multiply A's answer with 7.48

[alpine sable]

oh

Lemme try

@obsidian crane ty

[junior python]

What's the difference between Evitable discontinuity and finite jump discontinuity?

Function context

[keen wasp]

anyone know why the answer is B and not A

[spare hill]

wtf im confused as well now

i think i got the reason. gimme a minute to jot it down

nvm... sorry

[pseudo summit]

Guys

Why some functions are written as F(x) and others P(x)?

[spare hill]

just to emphasize that theyre different and allow us to reference them individually

theyre basically names

if we call all of them F(x), it would be akin to us all being named Bob. we wouldnt know who or what we're talking about

and that in itself eliminates the whole point of names or references like that

[keen wasp]

what did u have in mind

[spare hill]

y' = 2x^(-3) = 2xy^2 -> x^(-2) = y^2 which before simplification shows that it misrepresents or fails to represent completely the negative axis

i'm not sure tho

i hated stuff like +/- and verification like that, so im not qualified to find the specific step in the process that justifies it

[keen wasp]

<@&286206848099549185> Sorry for tag, but could u please help me out

[coral pagoda]

Okay, we can do the computation real quick

[keen wasp]

you get y = -1/x^2 after integrating

but idk why x cant be neg

[coral pagoda]

[ \dv{y}{x}=2xy^2\Rightarrow \frac{1}{y^2}dy=2x] integrating both sides gives [ -\frac{1}{y}=x^2+C\Rightarrow [y=-\frac{1}{x^2+C}]

[ocean seal]

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

[coral pagoda]

Now let's plug in the point (1,-1) to find C. So [ -1=-\frac{1}{1+C}\Rightarrow -1-C=-1\Rightarrow C=0]

[ocean seal]

dackid

[coral pagoda]

So the particular solution is $y=-\frac{1}{x^2}$

[ocean seal]

dackid

[keen wasp]

yeah i got there

[coral pagoda]

When looking at differential equations, we want to find an open interval in which the solution is true

So we have two possibilities $x\in (-\infty,0)$ or $x\in (0,\infty)$.
So... choose one

[ocean seal]

dackid

[spare hill]

how did you know that there's two possibilities and how did u identify them?

[coral pagoda]

The only point of discontinuity is 0

[keen wasp]

OHHHH

[spare hill]

ohh

discontinuity i see

oh fuckkk

[knotty sleet]

Can it not be discontinuous

[coral pagoda]

So it's the two intervals that are made by disconnecting 0

[keen wasp]

wait

\yeah

[spare hill]

how did u notice it's discontinuous?

[knotty sleet]

Why can't it be discontinuous

[keen wasp]

why cant it go from neg infinity to finity with a hole

[spare hill]

graph? or intuitively?

[knotty sleet]

Can't divide by zero

[keen wasp]

because 1/x^2 has a hole or asymptote idek at x = 0

[spare hill]

oh... right

[knotty sleet]

Also asymptote in graph

[spare hill]

ah

that too

[coral pagoda]

When looking at a differential equation, we are looking for an interval where the solution holds

$(-\infty,0)\cup (0,\infty)$ is NOT an interval

[ocean seal]

dackid

[keen wasp]

why not

[knotty sleet]

Is that just the convention

[north jasper]

Can someone please help me on a math question

it’s Algebra 1

[keen wasp]

ask in a diff channel

[north jasper]

Oop

Which channel then

[keen wasp]

q1

[coral pagoda]

Kind of

[alpine sable]

What's the difference between f(x) = ax + b and y = ax + b?

[ionic jewel]

nothing

[coral pagoda]

One tells you more about the function than the other

[ionic jewel]

f is the name of the function in the first one

[coral pagoda]

But yeah, it is the same function

[ionic jewel]

f takes an argument of x

you can have f(x,y) = x+y as an example

[spare hill]

but in that case, you can still simplify it

[alpine sable]

Mkay

[spare hill]

and say z = f(x,y) = x+y

[ionic jewel]

fine

f(x,y,z) = x/y+z

[coral pagoda]

You're gonna see functions a lot more in the future. So keep em handy

[spare hill]

i think of z as the casual name for it

[knotty sleet]

Do you know where I can read more about this? A quick Google search on 'do solutions to differential equations have to be continuous' didn't seem to give anything useful

[keen wasp]

yeah i would like to know some more i dont really grasp why

[coral pagoda]

I think it has to do with "existence of solutions." i did not understand the concept very well when I took the class since I wasn't as mathematically competent as I am now.

[keen wasp]

ok thanks for your help 🙂