help-36

[pallid basin]

yes

when ur in like a higher math class they might make you simplify it further

but for now thats right

[clever lagoon]

how am I going to make that positive and negative

[pallid basin]

oh

de

dw

u dont

u just leave it

[clever lagoon]

it says it wrong

[pallid basin]

what.

[clever lagoon]

i swear

[pallid basin]

did it say the right and

ans

[pallid basin]

okay hold on

[clever lagoon]

dawg this shit gonna take up my whole page 😭

[pallid basin]

try like

0.92

[clever lagoon]

ah hell nah

For the square root?

[pallid basin]

just

trust

[clever lagoon]

wait

I got it right

im so damn smart

[pallid basin]

what was it

[pallid basin]

oh wait so true

[clever lagoon]

let me try to solve this next one on my own

easyy

its x=8 x=,8

-8

Now how is that and that in the same unit

[pallid basin]

its the same stuff

[pallid basin]

yeah

[clever lagoon]

easyyy]

waity

not perfect squaree

let me clutch up

give me a sec

[pallid basin]

what else does the problem say

[clever lagoon]

thats it

[pallid basin]

okay uh ig calculator

[clever lagoon]

brain smarts

[pallid basin]

so true

[clever lagoon]

GOD IM SO SMART

alright thanks for the help im going to got to bed now

[pallid basin]

no problem

[final saddle]

@clever lagoon Has your question been resolved?

[final saddle]

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[sand kayak]

I need help on this question im stuck pls help

[final saddle]

@sand kayak Has your question been resolved?

[sand kayak]

no

[vagrant vector]

Just set P(x)=21% and solve x?

[sand kayak]

would it be 53.315?

[vagrant vector]

round to nearest integer

lemme check

[sand kayak]

ok lmk

please

[vagrant vector]

nope

Wait sorry

It's P(x) = 21, not 21%

[sand kayak]

hmm yeah idk tbh im lost

[vagrant vector]

uh it's not hard

Lemme send working rq

[sand kayak]

okay

[vagrant vector]

X rounded is 36

K bye I got a class

[sand kayak]

okay well thanks i appreciate it

[final saddle]

@sand kayak Has your question been resolved?

[final saddle]

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[buoyant yarrow]

How do u graph f(x)g(x)

[manic lotus]

You need to figure out the functions for f(x) and g(x)
Is g(x) here implied to be converging at -1?

[buoyant yarrow]

i think its just an asymptote so not coverging

[buoyant yarrow]

how do u find the rule for g(x)

i think its (1/x^2 +2) -1

i think im wrong

[manic lotus]

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

[soft zealot]

(TR) Chrom

[buoyant yarrow]

how'd u work that out

[buoyant yarrow]

are u there?

if its too hard to explain, can u explain how to graph f(x)g(x)

if u want

[final saddle]

@buoyant yarrow Has your question been resolved?

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[sturdy lodge]

Hi

[sturdy lodge]

I need help

[final saddle]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[sturdy lodge]

Anyone?

[delicate remnant]

Which part

[tiny gorge]

this is hard to read, what's the length of the base?

[vagrant vector]

That's right what's the problem

[sturdy lodge]

This whole problem

Base is 36cm at the bottom

[vagrant vector]

u did a well

A is right

for the trapezium just use the trapezium formula

or derive it yourself

[delicate remnant]

1/2(summation of sides)×height

Ig

Parallel sides*

[vagrant vector]

mhm

[sturdy lodge]

I dont know how to use Pythagoras theorem

[vagrant vector]

It's right

[sturdy lodge]

Didn't understood that

[delicate remnant]

What grade is it

[vagrant vector]

basically short side²+other short side²=long side²

c is the hypotenuse

The longest side

[ashen dust]

a² + b² = c²

[sturdy lodge]

So it's the formula?

[vagrant vector]

ya

[sturdy lodge]

Then like why my teacher wrote AC²=AB²+BC²

[vagrant vector]

AC is the side called a normally

then AB is the side called b

And BC is the side called c

it's a better way of writing

It uses ABC as the points instead of the sides

[sturdy lodge]

Ohh but how come Ab is 8

And Ac 17

[vagrant vector]

wym

BC is just the longest side

[ashen dust]

your diagram dont even have ABC points

[vagrant vector]

17 is BC not AC

[sturdy lodge]

Hypotenuse?

[vagrant vector]

yes

17 is the hypotenuse

[ashen dust]

8 is from (36-20)/2

[sturdy lodge]

Where did hypotenuse come here

[vagrant vector]

Uh

U see this right

AC is the hypotenuse

[sturdy lodge]

But it isn't a right triangle so what does hypotenuse have to do

[vagrant vector]

it is a right triangle

[sturdy lodge]

Then where is that angle

[vagrant vector]

Same height

oh

uh

I forgot to write

but I'll tell u it's a right angle

👍👍

[sturdy lodge]

Ohh thnx

[vagrant vector]

k gl

[sturdy lodge]

And I don't know

[vagrant vector]

what

[sturdy lodge]

Why they subtracted

[vagrant vector]

which part

[vagrant vector]

oh

[sturdy lodge]

36 from

20

And then divided 16 by 2

[vagrant vector]

So you're left with both sides

then try divide by 2 to find the side

[sturdy lodge]

What do u mean

[vagrant vector]

if u subtract 20 from 36

Cuz 36 is the bottom

you get left with both sides of the trapezium

which is where the right triangles are

[sturdy lodge]

20cm is connected vertically with two parallel lines and 36 covers the whole bottom right

[vagrant vector]

no

The lines aren't parallel

[sturdy lodge]

No I mean lines inside

[vagrant vector]

oh yes

yes

[vagrant vector]

.

[vagrant vector]

.

[sturdy lodge]

Ohh to see how much is left in the whole trapezium

We subtract

[vagrant vector]

yeah

So u get left with 2 of the right triangles

(their base)

[sturdy lodge]

Then we 14

16*

[vagrant vector]

Ya

Then there's 2 of them

And u need to find 1

[sturdy lodge]

What is base now

[vagrant vector]

So u divide by 2

[vagrant vector]

Uh wait

[ashen dust]

base is bottom part of the shape

[vagrant vector]

Greens are base

[sturdy lodge]

Ohh

[sturdy lodge]

Can u clarify the dividing part more

[vagrant vector]

U see u have 2 of the green parts right

[sturdy lodge]

Yea

[vagrant vector]

so u want just 1 to do your equation for pythagoras with

so what do u do

[delicate remnant]

Because it's a symmetrical structure u can divide it

[sturdy lodge]

Ohh

[vagrant vector]

Exactly

[sturdy lodge]

So both will be equal

[vagrant vector]

Yeah

[sturdy lodge]

But then again we can divide 8 by 2

[vagrant vector]

what for

[sturdy lodge]

Cuz why not simplify in the simplest way

[vagrant vector]

8 is 1

8 is 1 green part

16 is 2 green parts

U want to find 1 green part to do your Pythagoras theorem with

[sturdy lodge]

Ohh

[vagrant vector]

@ashen dust don't be rude smh

[sturdy lodge]

Now I got it

[ashen dust]

uhm no i just think its funny ;-;

sorry then

[sturdy lodge]

And the Pythagoras

Stuff

[vagrant vector]

That's just an equation

[sturdy lodge]

Yea so confusing

Kind of

[vagrant vector]

Yeah

it's ok as long as u get it

[sturdy lodge]

Can u make understand the Pythagoras

Theorem

[vagrant vector]

I can tell u what it does

[sturdy lodge]

Like that in a consise way

[vagrant vector]

Uhm

[sturdy lodge]

I never understand my teacher

[vagrant vector]

So basically

[sturdy lodge]

Yea

[vagrant vector]

u see this right

<ABC is a right angle

So

when AB is squared

[vagrant vector]

And added to BC²

[sturdy lodge]

This right

[vagrant vector]

No

[sturdy lodge]

Ohh

[vagrant vector]

U will get AC²

Where AC is the hypotenuse length

[sturdy lodge]

Ohh okay

Then

[vagrant vector]

In your question

U have the hypotenuse

So u want to find one of the other sides

so u take the hypotenuse length and square it

[sturdy lodge]

Yea there are two hypotenuse

[vagrant vector]

what??

[sturdy lodge]

Ohh

[vagrant vector]

I mean in 1 triangle

[vagrant vector]

So then u - the other side that u have ²

[sturdy lodge]

No I mean there are two right triangle

[vagrant vector]

yes

[sturdy lodge]

So two

[vagrant vector]

Both are the same

[sturdy lodge]

Hypotenuse

[vagrant vector]

So just choose 1

[sturdy lodge]

Ohhh

I got it

So like this is it

Are u here?

[vagrant vector]

Ya

[vagrant vector]

Like what

[sturdy lodge]

I mean the whole

Pythagoras

Stuff

[vagrant vector]

Ya

[sturdy lodge]

Okay

Now next

Problem

@vagrant vector

.close

[final saddle]

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[wind hawk]

Hey

[wind hawk]

Can someone explain the range and domain of functions

.close

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[barren orbit]

Need help checking the continuity of this limit

[barren orbit]

I was taught that the first step is to make sure that f(x) at the 0 is defined

However here it is undefined

So this function should be non-continuous right?

[minor nexus]

heres what it looks like on desmos, so i guess not

but i think it can be done by thinking about what happens as x is small

[final tangle]

ideas seem to be conflated here

[minor nexus]

if x is something like 0.01

your function is
0.01 ^ 1/0.01 = 0.01 ^ 100
Which is very close to zero

[final tangle]

continuity and limits are related,
the function not being defined at a certain value indicates some discontinuity there
but that doesn't necessarily mean the limit won't exist

[final saddle]

@barren orbit Has your question been resolved?

[barren orbit]

How do you get floors on desmos?

I cant find the function

[minor nexus]

type floor

[barren orbit]

Oh wait

[barren orbit]

I didn't say the limit doesn't exist

Because it probably does

But the question was to examine the continuity of the function at x = 0

[final tangle]

then what was

Need help checking the continuity of this limit
about

[barren orbit]

I was just double checking my answer

Sorry if I was annoying 😔

[final tangle]

well yeh, if a function isn't defined somewhere, it isn't continuous there

[barren orbit]

Alright so thanks then and i hope you have a great day 👍

[final saddle]

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[hallow cipher]

check this out I got this function that describes the time it takes for an object to land when thrown at the speed of 30m/s on the angle x assuming no wind, or anything like that. how can I find the angle that gives the highest total distance?

[hallow cipher]

also what does f'(x) imply?

.close

[final saddle]

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[floral shadow]

Did I do b right

If so how do I simplify tan^2 x +1=0

[solar glade]

,rcw 90

[lofty spade]

no sol. from that'

2 positive quantities cannot add up to 0

[still berry]

you made a calc mistake there (1-tan^2x+2) should be -tan^2x+3

[floral shadow]

can i find an asnwer with -tan^2x +3

[still berry]

yes you can

[floral shadow]

wait how

the answers say pi/3

2pi/3

and 0 and 180

[floral shadow]

these answres are from tanx=0

[still berry]

this will be simplified to tanx = sqrt3

so x will be pi/3 or 2pi/3

[floral shadow]

oh got it

[floral shadow]

isnt it a plus 3 tho so itll making it negative when swapped to the other side

and rooting 3 is impoosible

oh wait

you multiple it all by root -1

[still berry]

-tan^2x+3=0 can be written as tan^2x-3=0 (if u multiply both sides by -1)

[floral shadow]

yeah

i get it now ty

[final saddle]

@floral shadow Has your question been resolved?

[final saddle]

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[proper yoke]

does anyone know how to solve this? "deside X from the matrix ... if A = ..."

[final saddle]

@proper yoke Has your question been resolved?

[severe canyon]

You have $$A^T \left( X - B^T \right) = 7 \left( X - B^T \right)$$

[soft zealot]

Alberto Z.

[proper yoke]

Yes

Well the ^T is not just on the A

[severe canyon]

We can rearrange it into: $$ \left( A^T - 7I \right) \left( X - B^T \right) = 0$$

[soft zealot]

Alberto Z.

[proper yoke]

Okay but is it not easier to just multiply the A in the parentheses and then do ^T?

[severe canyon]

Yes it's the same

[proper yoke]

So we have AX - (AB)^T

On lhs

[severe canyon]

Yep

[proper yoke]

Okay so what do we do now?

Do we multiply the 7 on rhs?

X = (A -7I)^-1 - 7B^T + (AB)^T

Is this correct?

@severe canyon

[severe canyon]

I don't think so

[proper yoke]

Okay let me do it like you started

[proper yoke]

Where do we got from here?

[final saddle]

@proper yoke Has your question been resolved?

[final saddle]

@proper yoke Has your question been resolved?

[proper yoke]

.close

[final saddle]

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[half salmon]

!status

[final saddle]

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

[pure linden]

1

[half salmon]

If you set those linear equations equal to eachother what answer would you get out of it? Hint: where do they intersect?

[pure linden]

4,-4?

[final saddle]

@pure linden Has your question been resolved?

[craggy plank]

@pure linden Are you still there?

[final saddle]

@pure linden Has your question been resolved?

[vital crag]

no

the solution set is where the two lines intersect. count the squares

[final saddle]

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[honest egret]

What is the inverse of the function f (x) = 3(x + 5)2 – 4, such that x ≤ –5?

[honest egret]

I'm having issues knowing what to do

,help

[soft zealot]

A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!

[steady prairie]

hi

[soft zealot]

Victor Grignard

[steady prairie]

is this what you meant?

inverse of this?

[honest egret]

so yes

[steady prairie]

well , old method

oh well wait

$y=3(x+5)^2-4$

[soft zealot]

Victor Grignard

[steady prairie]

$y+4=3(x+5)^2$

[soft zealot]

Victor Grignard

[steady prairie]

$(y+4)/3=(x+5)^2$

[soft zealot]

Victor Grignard

[steady prairie]

root (y+4)/3 -5 =x

[honest egret]

how come you dont distribute it

[steady prairie]

so A option

[steady prairie]

like I didn't open the bracket?

you're asking that?

[honest egret]

yes

[steady prairie]

because I want it to equal to x

and i'm increasing the degree of x

by opening that

[honest egret]

alr ok

its either c or d right?

[steady prairie]

I don't think so

otherwise the roots would've existed as conjugates of each other

its A

[honest egret]

why

[steady prairie]

$x^2-(9+5i)x+(25i+20)$

[soft zealot]

Victor Grignard

[steady prairie]

sum of roots = -b/a

product of roots = c/a

[abstract walrus]

Its D

[steady prairie]

in the quadratic represented by

[abstract walrus]

If 4-5i is a root

Its implied that

4+5i must also be a root

[steady prairie]

$ax^2+bx+c$

[soft zealot]

Victor Grignard

[honest egret]

why is it d then

[steady prairie]

in this

[abstract walrus]

Bwcauzs

Sum of roots

-b/a

4+5i +4-5i +5

13

So -13

If in A ther was +5ix it would also be correct

[honest egret]

because they cancel each other out?

[abstract walrus]

Since they dont need tk be conjugates if there are complex coefficients

No

[steady prairie]

oh wait , silly mistake

[abstract walrus]

If a equation has real coefficients

Then complex roots are in conjigates

[steady prairie]

just said that about conjugates

[abstract walrus]

So we get D

But if in the first option

There was a +5ix

Instead of -5

[steady prairie]

ik

ye

[abstract walrus]

Then thats correct

[steady prairie]

silly me

[honest egret]

okay

would it be 1

i.e C

.close

[final saddle]

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[final saddle]

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[jovial folio]

i can only figure out (x-3)^2 + (y+1)^2

idk how to do the horizontal strech by 3 and about the y-axis

[steady prairie]

the equation is of an ellipse

but the horizontal stretch thing

I don't get it

[jovial folio]

oh

yeah

usually u dont encouter that so idk

/do you know how to find a^2 and b^2

[steady prairie]

I think that's called the semi major axes

a is 4

[jovial folio]

would a still be 4

[steady prairie]

measured from 3 to 7

[jovial folio]

if its transformed? with the stretches

[steady prairie]

oh wait

[jovial folio]

and about the y axis

[steady prairie]

that's the original circle

[jovial folio]

it kinda tricks u up

giving the circle

[steady prairie]

no

[jovial folio]

yeah

[steady prairie]

I think it means 3 in each side

3 units each side

do you have the answer?

[jovial folio]

nope

[steady prairie]

so according to me , its 3 units each side horizontally and 2 units vertically

[jovial folio]

(x-3)^2/9 + (y-1)^2/b^2 = 1

this is what i got

a = 9 because horizontal stretch by 3

y - 1 because shifted up 2

[steady prairie]

nono

[jovial folio]

idk what to do about the y axis tho

[steady prairie]

a is 7

4+3

[jovial folio]

ok

[steady prairie]

and b is 4+2

6

so the equation will (x-3)^2/49 + (y+1)^2/36 =1

[jovial folio]

hm

i see

thanks

[steady prairie]

DO check it if you can

because it's what I've interpreted from the statement

[jovial folio]

@steady prairie did u do the about the y axis?

that it asked for

cuz idk how to do that

usually u just multiple by -1

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@jovial folio Has your question been resolved?

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[red field]

any ideas?

[red field]

nvm i just realizied that the answer is 4 cuz there are infinitly of these

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[tranquil pine]

Can someone help me on #28 here? I just recently closed a channel on this and I still don't get it. I now know cis = cosine theta + i sin theta but that still doesn't really help. I know we're supposed to be converting to (r, theta) form but I'm not sure how

[loud sundial]

imma just use $\cos \alpha +i \sin \alpha$ and $\cos \beta+i \sin \beta$ for convenience

[soft zealot]

Civil Service Pigeon

[loud sundial]

since I assume the problem is with the trig parts

what do you get immediately upon multiplying these

[tranquil pine]

im not sure

why are you multiplhying them?

[loud sundial]

let $z_1=r_1 \text{cis} \alpha$ and $z_2=r_2 \text{cis} \beta$

[soft zealot]

Civil Service Pigeon

[loud sundial]

then you have $z_1=r_1 (\cos \alpha +i \sin \alpha)$ and similar for $z_2$

[soft zealot]

Civil Service Pigeon

[loud sundial]

so that gives you $$z_1 z_2 =r_1 r_2 (\cos \alpha +i \sin \alpha)(\cos \beta +i \sin \beta)$$

[soft zealot]

Civil Service Pigeon

[loud sundial]

which is why I asked you to multiply out $$(\cos \alpha +i \sin \alpha)(\cos \beta +i \sin \beta)$$

[soft zealot]

Civil Service Pigeon

[loud sundial]

Don't overcomplicate it out - ||it's the same as multiplying out smthn like (x+5)(x+7)||

[tranquil pine]

one sec lemme write this out

or type it out lol

$(\cos(\alpha) \cdot \cos(\beta)) + (\cos(\alpha) \cdot i sin(\beta)) + (i \sin(\alpha) \cdot \cos(\beta)) + (i \sin(\alpha) \cdot i \sin(\beta))$

[soft zealot]

BlazeStorm81

[tranquil pine]

ts so complex lmao

[loud sundial]

imma just rewrite that a bit

$[\cos \alpha \cos \beta -\sin \alpha \sin \beta]+i[\cos \alpha \sin \beta+\sin \alpha \cos \beta]$

[soft zealot]

Civil Service Pigeon

[loud sundial]

Now you can apply your ||trig addition identities||

[tranquil pine]

lemme see which trig identity suits this

[tranquil pine]

Sum/Difference Indentities?

[loud sundial]

yeah

[tranquil pine]

so is this $\cos(\alpha+\beta) + i \cos(\beta+\alpha)$

?

[soft zealot]

BlazeStorm81

[loud sundial]

close but no cigar

check the second term again

[tranquil pine]

oh

so is this $\cos(\alpha+\beta) + i \sin(\beta+\alpha)$

[soft zealot]

BlazeStorm81

[tranquil pine]

i think thats the correct version

[loud sundial]

✅

[tranquil pine]

okay awesome whats the next step

[loud sundial]

so now we've shown that given this

we have that $z_1 z_2 =r_1 r_2 \text{ cis} (\alpha+\beta)$

[soft zealot]

Civil Service Pigeon

[loud sundial]

all of these are just a direct application of this

[tranquil pine]

so is the answer then just $8 \cdot cis(\frac{\pi}{2}+\frac{\pi}{4})$

[soft zealot]

BlazeStorm81

[loud sundial]

yup

[tranquil pine]

wow okay

thank you for helping out

i think i get it now

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[loud sundial]

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[uneven light]

can someone walk me thru this idk where to start

[minor nexus]

i think it is asking you to find y, so we can untangle it by first integrating to find dy/dx, then integrating again to find y

||dont forget +C||

[uneven light]

so set it up like this first

[minor nexus]

yep perfect

[uneven light]

where does the y'(0) come in tho

i'm confused about that

and y(0) = 1

[minor nexus]

well, when you first integrate, you get something, +c

y'(x) = dy/dx

so you can find out what c is with that information

[uneven light]

i see

so when i get that integral that will be y'

and then for x i put 0

[minor nexus]

yep

[uneven light]

thius look good so far?

[minor nexus]

yep, i like that

[uneven light]

is this my answer or is there something more i need to do?

do i need to integrate asgain

[minor nexus]

we need to find y in terms of x

so yeah

[uneven light]

gotcha

y(0) = 1 sooo let me plug it in

[minor nexus]

not 100% agreed with your integration

i think you factorised -2 out of the integrql, but didnt do it for the other term

[uneven light]

wat

would the 2 just become x

not 2x

idk i forget

[minor nexus]

i wouldnt recommend factorising from line 2

you can integrate directly

[uneven light]

kay

so it would just be 2e^-x + 2x

[minor nexus]

||+c||

[uneven light]

yes ofc but otherwise those numbers are right?

[minor nexus]

yep, youre correct, good job

[minor nexus]

yep, i think youre good

well done

[uneven light]

tysm for the help

been stuck on this question for a little bit

so its a relief

i appreciate you

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[minor nexus]

no problem

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[tranquil pine]

can someone explain me how iz z^2 in x^2 and y^2 in the brackets?

[silver hare]

ok expand the top line

[tranquil pine]

moment

[silver hare]

?

[tranquil pine]

I dont get how the author wrote this problem for moment inertia

I dont understand either

[silver hare]

so whats ur question

[tranquil pine]

how is z^2 in x^2 and y^2 bracket

I dont get it

its +z^2

I marked with blue line the issue im stuck with

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[gritty temple]

how can you tell with this one using the right hand rule

i cant tell since the curl seems to go in two different directions

(vector caclulus question)

[magic sparrow]

You can compute the cross product directly I think

it is confusing me aswell, it seems the normal in Q1/2 is in the opposite direction as in Q3/4

[gritty temple]

yeah its strange unlike anything ive seen before

[magic sparrow]

Maybe it isn't even asking you about the normal vector yet

in a right-hand coordinate system the z-axis points out of the page

maybe part (i) isn't even about the vector field yet

Can you show the other parts

[gritty temple]

sure

im only on part ii)

[magic sparrow]

This isn't a test right?

[gritty temple]

what do u mean

its homework questions

[magic sparrow]

Just asked because of the points (3) and stuff

[gritty temple]

ah

[magic sparrow]

Well anyways for part (i) I think it's just outward

[gritty temple]

what's the explaination for that?

[magic sparrow]

because it's a right hand coordinate system

[gritty temple]

yeah okay i get that then just the normal hand position

i thought it was asking about the curl hand position thing

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[paper lodge]

I need help with this problem. The way I setup is 40u''+94u'+120u=0 and u(0) = 5/12 ft, u'(0) = 4 ft/s. Is that wrong? Im missing the answer

[paper lodge]

<@&286206848099549185>

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[stiff belfry]

it is wrong

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[bright adder]

Hello, I am trying to understand how to interpret eigenvalues. I did my work via matlab and was quite confused by the results i got.

[royal gust]

Why were you confused by your results?

[bright adder]

The results of the last row, decreases after the 5th year, and then increases at year 10. Also I'm trying to understand steady state of eigenvalues and eigenvectors, and while doing so I don't know if my explanation or understanding is correct based on the results

I'm wondering if I'm doing this correctly. Year 3 = A^3 * S, Year 5 = A^5 * S, Year 10 = A^10 * S right?

[royal gust]

Ye

[bright adder]

the eigenvalues i got were lambda = 1, 0.57192, 0.77807 through Matlab. And now I am struggling to interpret the eigenvectors and what the values are supposed to mean.

[final saddle]

@bright adder Has your question been resolved?

[bright adder]

<@&286206848099549185>

I guess my question is: How do you interpret the value that has decreased and then increased exponentially?

[royal gust]

Consider the eigenvalue 1.
It comes with an eigenvector. I'll just call that v, right now.

This vector satisfies the following:
Av = 1v

This tells us something pretty important:
If you take anything in span(v), then A doesn't change it. This is a steady state.

[bright adder]

Lambda = 1; eigenvector doesn't change. Does the eigenvalue always have to be 1 for a steady state?

And is steady state the same as a stable eigenvector?

[royal gust]

Well, let's look at the eigenvalue 0.57.
This has an eigenvector, I'll now refer to this as v.

This vector satisfies the following:
Av = 0.57v

When A acts on this vector, the vector returns in the same direction, but decayed

I suppose in the context of this question, the three companies will fail, if their market share forms a vector in span(v)

[bright adder]

Would that also mean the samething for the eigenvalue of 0.778

[royal gust]

Indeed. They'll fail, but a bit slower.

[bright adder]

So like in this context, eigenvalue specifically helps determine value of their shares over time?

[royal gust]

If A doesn't change v's direction, v is an eigenvector of A.
A can still change v's magnitude. The factor by which v's magnitude is changed is v's eigenvalue.

In this case, eigenvalue represents an increase/decrease to all three shares

[bright adder]

if i'm understanding correctly, eigenvalue = rate of increase/decrease of the shares right?

and then if the eigenvalue is 1, it's steady

Is it the same as saying stable?

[royal gust]

It all comes together with:
Av = (lambda)v

Hopefully you've seen this equation before

If v is an eigenvector of A, then A acts like a constant multiplier to v.

I suspect the question is just looking for the eigenvector with eigenvalue 1

Because that's when the market has no movement

[bright adder]

so then the eigenvector kind of predicts how the shares will redistribute overtime to the three companies right?

[royal gust]

If you plug an eigenvector into A, then you'll get back the exact same vector, except multipled by some constant

In a sense, this is the "easiest to understand" action A can possibly take

[bright adder]

ty for the help

sorry i've been struggling with this for the last few days and every explanation still confuses me

If I understand this, the eigenvector has a specific value associated which is the eigenvalue. When eigenvector multiplied by A, then it will be equal to some constant * eigenvector.

[royal gust]

Yeah, exactly

Worth noting that most vectors get "turned" by A. Eigenvectors are special because they maintain their direction after A.

It's worth thinking of a few simple examples, I'll throw one at you:
Consider the linear transformation in R2 that flips vectors vertically. For example, (1,1) becomes (1,-1)

What are some eigenvectors of this?

[bright adder]

gimme one second to write this down

eigenvalues = -1.41, 1.41; eigenvectors = (2.41, 2.41) for lambda = 1.41

[royal gust]

All this transformation does is flip vectors vertically. It just multiplies the second component by -1

Are any vectors unchanged by this action?

[bright adder]

No?

[royal gust]

Consider (1,0)

If I flip that vertically, then I get back (1,0)

So (1,0) is an eigenvector, and it has an eigenvalue 1.

[bright adder]

So instead of 1 row with 2 columns, the flip becomes 2 rows 1 column right?

[royal gust]

,w vector (1,0)

[soft zealot]

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[royal gust]

I mean geometrically, over the x-axis

,w vector (1,-1) and (1,1)

[soft zealot]

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[royal gust]

So yellow would turn into blue, after our transformation

[bright adder]

And A tells you how that is done while the eigenvalue tells you whether or not it's longer or shorter than the span?

[royal gust]

A is the transformation itself. We could find a matrix for it, but it's easy enough to describe without a matrix representation, I think

(1,0) is an eigenvector. When you take (1,0) and flip it over the x-axis, it stays exactly where it is.

Because it doesn't grow or shrink, the eigenvalue is 1.

Are there any other eigenvectors?

[bright adder]

No

[royal gust]

Note that anything on the x-axis counts as an eigenvector

[bright adder]

is it because it's in the same direction?

[royal gust]

But we normally group them and refer to them with their span

So (1,0) refers to all of these

,w vector (0,1) and (0,-1)

[soft zealot]

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[royal gust]

So if we plug blue in, we get yellow back. Blue and yellow are "in the same direction", just opposite. This is an eigenvector too.

(0,1) is an eigenvector with eigenvalue -1

[bright adder]

ty i think im starting to understand now

i just need to digest the info a little more

i appreciate the time you took to help me 😄

[royal gust]

Np. Feel free to ask if you have anything else!

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[rotund glen]

am i able to say yes?

for that last part

i got these graphs

so i can see it gradually getting closer

<@&286206848099549185>

[tiny gorge]

the error will go to zero as n->infinity, but i assume you need to prove this

[rotund glen]

how would i go about doing that @tiny gorge ?

we have these notes

[tiny gorge]

offhand i'd think that uniform continuity and a bound on the derivative of sine would be helpful

[rotund glen]

shit okay

do you think the question was asking for a formal proof?

i am not sure how to go about the proof tbbh

[tiny gorge]

dunno, what kind of class is this?

[rotund glen]

numerical analysis

i think based on the question tbh, its asking us to look at the matlab graphs n see how the trend would continue

which we can say it will go to zero

but feel free to disagree ofc

[tiny gorge]

do they ask you to do other proofs in this class? if not then yea, i'd guess they just want you to try making plots for various values of n and see from the graphs that the approximation error is going to zero

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[hybrid tide]

MN is equal to half the length of XZ

[hybrid tide]

?

[craggy plank]

!status

[final saddle]

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.
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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

[hybrid tide]

2

[craggy plank]

May I check out your progress real quick?

[craggy plank]

Which is longer? MN or XZ?

@hybrid tide

[hybrid tide]

XZ MN is half the length of XZ

[craggy plank]

Could you explain your first equation?

Translate it in English

Like
x=2y
x has twice numbers of apples than y do

[hybrid tide]

U have to use the midsegment theorem here

[craggy plank]

Ik

But I suggest you think twice about your first equation

[hybrid tide]

But isn't MN supposed to be 1/2 of XZ?

[craggy plank]

yes it is

That’s why I told you to look at your equation and translate it

[hybrid tide]

I don't get what u mean by translate

[craggy plank]

There’s a small but fatal mistake

Well

What you wrote in the equation is XZ is 1/2 of MN

[hybrid tide]

MN is 2x+1

XZ is 5x-4

1/2(2x+1)=(5x-4)

I don't get what I'm doing wrong

[craggy plank]

1/2(MN)=XZ?

Lemme translate it for you

When you divide MN into two parts, you’ll get XZ

[hybrid tide]

Yes

[craggy plank]

What you want is
XZ is twice longer than MN

[hybrid tide]

Yes

[craggy plank]

The first one is what you wrote

[hybrid tide]

I'm listening

[craggy plank]

Have you found your mistakes?

[hybrid tide]

Nope 😂

[craggy plank]

..

[hybrid tide]

Oh

Alr I get it

Thx 🙏

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[warm python]

$a_n=\frac{\left(2n+1\right)}{\sum_{i=1}^nn^2}$, find $\sum_{i=1}^{20}a_i$

[soft zealot]

Why am. I here

[warm python]

so I'm guessing I expand and simply use partial fractions to decompose the second part?

or is there a better way>

which would be

[ocean lintel]

You can pfd that, sure
Assuming it's sum of the i^2

[warm python]

yeah

but is there any better way

[ocean lintel]

Then probably express it using the harmonic sequence

[ocean lintel]

Not that I can think of rn

[scarlet sequoia]

this really just looks like 'do you know the formula for sum(k^2)'

and 'do you know how to pfd'

and finally 'do you know telescoping'

[ocean lintel]

Oh yeah you do get some telescoping

[warm python]

so $\sum_{n=1}^{20}\frac{12}{\left(n+1\right)\left(2n+1\right)}+\frac{6}{\left(\left(n\right)\right)\left(n+1\right)\left(2n+1\right)}$

[soft zealot]

Why am. I here

[warm python]

ah, ok. This is. going to take a while, but I think I can do it from here. Thanks

.lcose

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[magic sparrow]

.lcose

.lreopen

.llosec

[magic sparrow]

.lcoose

.laceolse

[ocean lintel]

We're all children aren't we

[scarlet sequoia]

when you get 16 year old, the only thing that ages is your body

[magic sparrow]

@dry light @robust mulch Let us know when you get there

[robust mulch]

i am older than you

[ocean lintel]

You should see my father
16 is a bit much

[magic sparrow]

are u

gookman is 20?!??

[scarlet sequoia]

oh I never said the rest stops aging before that

[ocean lintel]

Who's gookman

[magic sparrow]

@robust mulch

[robust mulch]

gookman

[scarlet sequoia]

i said sup_years(the rest aging) <= 16

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[covert folio]

hi

[magic sparrow]

Hello

!status

[final saddle]

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

[covert folio]

how do i do part b?

i dont know where to begin

[magic sparrow]

use properties of square roots that you know

rationalize denominators

make common denominators

[covert folio]

so i make it 1 big fraction first?

by multiplying the denominators together?

[magic sparrow]

do all kinds of simplification

[covert folio]

.close

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[lime cloak]

Hi, i wonder where i made mistake

[lime cloak]

The text of the exercise is "determine the derivatives of the following functions"

On the left is solution in book

[desert mantle]

they made a mistake

[lime cloak]

That's relief then

Thanks

. close

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[tranquil pine]

im just confused of

x < 0 and x <= -2 intersects

so

how am i supposed to make it

do i take the lowest one

e.g x <=-2, x> -2

[craggy plank]

[tranquil pine]

??

u need translate?

[craggy plank]

I’m just watching

Ignore me

[tranquil pine]

help me :(

[craggy plank]

No, I’m just here to spectate

[tranquil pine]

why

[craggy plank]

I’ve solved a lot of problems today

Kinda need some rest 😄

[tranquil pine]

same

i solve a lot everyday

ok u can rest here

;)

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[lavish crescent]

how do i solve question 1 (a)?

[tranquil pine]

what have you tried

[lavish crescent]

supplementary relationships

so cos 140 = sin40

i think

oh wait nvm i got it

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[lilac estuary]

Consider the inner product space R^3 where vector addition and scalar multiplicationa re defined in the usual way and the inner product on R^3 × R^3is the standard dot product.
Let S : R^3 → R^3 describe an orthogonal reflection in the plane P, where P is
described by the Cartesian equation z = 0.

(a) Find the matrix AS that represents S with respect to the standard ordered basis
{e1, e2, e3} of R^3

[lilac estuary]

I know I have to find the effect of S on e1, e2 and e3 and then the entries of my matrix will be the transformed standard vectors but I have no clue on what the effect is

[junior token]

have you tried drawing a picture of the reflection?

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@lilac estuary Has your question been resolved?

[lilac estuary]

I hace no clue on how to do it tbf

[junior token]

this is what it does, right

[lilac estuary]

how did you get that?

orthogonal reflcetion in the plan P where P is described by z=0

[junior token]

because z = 0 is the plane containing the x basis vector and the y basis vector

[lilac estuary]

yes so how come the z is reflected if the prthgonal reflection is in the x and y plane

[junior token]

the xy plane is the mirror

the things on the mirror aren’t reflected

but everything else is

[lilac estuary]

alright I get it

it's an orthogonal reflection with respect to P

therefore As=(e1,e2,-e3) with ei the standard basis of R^3

i=1,2,3

[junior token]

Yes

[lilac estuary]

ty

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[sour torrent]

I’m really struggling with this

[sour torrent]

I am doing old exams so I have the solution but it does not make much sense to me

Any explanation is appreciated

[next onyx]

pythagoras right?

[sour torrent]

No

This is multi variable Calc so I’m doing triple integrals but the integral boundaries are the main issue

[scarlet sequoia]

this is spheric coordinates

r = sqrt(x^2+y^2+z^2)

x = rcos(theta)cos(phi)

y = rcos(theta)sin(phi)

z = rsin(theta)

theta goes from 0 to 2pi

phi goes from 0 to pi

[lyric summit]

spherical coords must be applied with modification of one of angles, you will need to use arc cosine

[sour torrent]

Here is the solution btw

[lyric summit]

yoru solution is based on cylindrical, bu ti wud use spherical

precisely

[sour torrent]

I’m not gonna lie I’m kinda lost

[lyric summit]

that can be useful:

[sour torrent]

Okay that makes sense

I get it a bit more

[lyric summit]

-pi/2 < phi< arc cos ( sqr ( a^2 - b^2 ) )

but i said, i wud use spherical coords

[sour torrent]

Can you explain how you would do this step by step?

[lyric summit]

hmm eng is not my native one, it is hard fo rme to use beauty words to descrieb it, i just can see it at once

theta angle is walkign around from 0 to 2pi

that is, i wud say flat angle

if you stand on z axis and you look at the flor

you can see circle

btw, i wud change y < b into z < b

since voluem wil be the same

and phi angle

i stay on vertz of x axs

and then i see this photo i gave you here