help-19

[wooden python]

here is one

[mystic saffron]

So it has to contain derivatives?

Linear de is like when there r no power terms in it

[signal crown]

and the operator D here is :
$$D = \frac{d²}{dx²} + 8x \frac{d}{dx} -5 Id$$

[clever fjord]

Herels

[mystic saffron]

And no y times dy/DX kind of terms either

[mystic saffron]

Ohhh

Now I get it

So it's just operating in y

On

[signal crown]

yes

[mystic saffron]

Mmm

Ok one more question

What is this slide saying

[signal crown]

you can read

it is just defining what is a homogeneous differential equation

[mystic saffron]

Yes, but like

Can't u just

Operate of

f(t)

Operate on

[signal crown]

?

[mystic saffron]

To like make it vanish

Like

Lemme send an image

This

Or something like that

Cuz u can express f(t) in terms of y(t(

y(t)

[graceful chasm]

should be D(y)(t) btw not D(y(t))

[mystic saffron]

Whoa what?

[graceful chasm]

D(y) is a function

[graceful chasm]

we evaluate it at t

[signal crown]

when you apply an operator on y, you dont get 0 all the time, you can have a function f(t) on the left size

now if you want that f(t) disappear, good luck to find the good operator

[mystic saffron]

Yea but as long as we can find an operator

There's no way to distinguish

Bw homogeneous and non homogeneous

[signal crown]

If you can, but its not the goal here

[mystic saffron]

Is homogeneous and non homogeneous defined according to the D operator?

Or is it a generalised characteristic?

[signal crown]

No, for example :
y' - 3y = 0 is homogeneous
y'- 3y = cos(t) is not homogeneous

[mystic saffron]

Ohg

Ohh

y' here is dy/dx

[signal crown]

the goal is to solve a differential equation tho

[mystic saffron]

Right

?

[mystic saffron]

?

[signal crown]

yes

not always x on the bottom

[mystic saffron]

Yea but like not t

Right?

[signal crown]

wdym

[mystic saffron]

Like if y' is dy/dt then its all meaningless

[signal crown]

why

[mystic saffron]

Cuz then u can express cos(t) in terms of y

And then it will become homogeneous

[signal crown]

?

well let me rewrite it :
y'(t) -3y(t) = cos(t)

fine now ?

y is a function of t

[mystic saffron]

Ok but what is the derivative wrtm

?

If we take t

Then

This can happen:

[signal crown]

t or x, they are just variables
ok let me rewrite again

[mystic saffron]

So here, the two are both homogeneous

[signal crown]

y'(z) - 3y(z) = cos(z)

y a function of z

[mystic saffron]

t or z doesn't matter

Like

Listen

My question is

Can the derivative be with respect to the variable

z

[mystic saffron]

See this

[signal crown]

define your y here

y is a function of which variable

[mystic saffron]

y is any arbitrary function in t

[signal crown]

good

then you differentiate it in terms of t

[mystic saffron]

Yes

So then

What's the difference between homogeneous and non homogeneous

Like ok I'll write it better

Just a sec

[signal crown]

.

[signal crown]

.

[mystic saffron]

So the first two equations here are respectively homogeneous and non homogeneous

But why is (1) homogeneous and (3) not?

And 2 and 3 r the same

This is my core question

Can a non homogeneous differential equation be CONVERTED into a homogeneous one????

[signal crown]

i dont think so

[mystic saffron]

Then I'm lost

It should be convertible

[signal crown]

for an operator D, if you have
D(y) = 0 it is called a homogeneous differential equation
if D(y) = f, its not

if you send the f on the left, you have :
D(y) - f = 0, which is a different operator

[mystic saffron]

Yea it's a different operator

Call it D1

How does which operator it is matter?

The operator can be any

D(y)-f=0 is D1(y) = 0

[signal crown]

because the differential equation would be different, since your course defined a differential equation with an operator

[mystic saffron]

Oh

Yes

The equation will be different

[signal crown]

yea

[mystic saffron]

Holy shi

Thanks bro

Got it

Average noob error

Typical of me

[signal crown]

imma eat now

im hungry

[mystic saffron]

Aight thanks alot

[signal crown]

np

[mystic saffron]

Eat something delish

.close

[odd edge]

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[merry kestrel]

I wanted to prove if the order of group is 5, then it has to abelian.

[merry kestrel]

My goal is to check different verify the binary operations on set is always commutative

other than using cylcic group of prime order

[tall veldt]

this is pretty much it

[merry kestrel]

Yes, i wanted to see by enumerating cases

[low locust]

why do you hate yourself

[merry kestrel]

can I say the proof I have for |G|=4?

[merry kestrel]

It’s just because, we haven’t studied cyclic groups yet

This exercise comes before it

[tall veldt]

have you done lagrange?

[merry kestrel]

It’s from the chapter 1, we have to use group axioms to verify

[merry kestrel]

Not yet

[tall veldt]

this is hell

[merry kestrel]

Let me tell, the G= |4| case

It’s seriously not that hard

suppose e,a,b belong to G

Identity commute with every element, so we only have to check ab, ba

since it’s closed under *

ab must be one of the elements in G

ab=a or ab=b is impossible, since e is the identity

ab=e will mean, set just contains 3 elements

so ab has to be the 4th element

Thus G= {e,a,b,ab}

This is will be our group G

similarly b*a can also only be equal to the 4th element

thus ab=ba

for all x in G

Does this makes sense?

@tall veldt @low locust

[low locust]

why

also what about stuff like a*(ab)

[merry kestrel]

Does this makes sense?

Let me edit

Wait

a*(ab)= eb=b, also aba=aab=b

[merry kestrel]

^

[low locust]

\* for *

how do you know aa=e

[merry kestrel]

I didn’t get it

[low locust]

(which is not true in one of the two groups of order 4)

[merry kestrel]

right

Is this proof incomplete?

@low locust

[merry kestrel]

?

here?

[low locust]

ok nvm

you start with the assumption that a,b are the elements which dont commute

[merry kestrel]

yes, ab!=ba

Our goal is to find there is no two elements which don’t commute right?

so if they don’t commute, a*b must be the 4th element

[low locust]

yes then its fine

[merry kestrel]

So, back to my question, can this reasoning easily extended to 5 ?

[low locust]

define "easily"

[merry kestrel]

Can you help me?

[low locust]

a similar type of argument should probably work but will take more effort

no thanks, I dont hate myself

[merry kestrel]

I definitely gained a lot of understanding from doing the cases from 1 to 4

hating or not hating themselves doing math proofs is subjective

[low locust]

5 will be more effort. because you might get that ab=c and ba=d. but then you have to fish for some contradiction that this cant work

[merry kestrel]

I’m already here

I’m here in this help channel to see somebody can help me with fishing

nvm. I’m closing the channel

Thanks for the help. have a great day!

.close

[odd edge]

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[merry narwhal]

So since it's talking about x^2

I only used binomial expansion up to x^2

[mystic saffron]

Can you rotate the screen and send a clearer pic?

Like a bit zoomed in

[merry narwhal]

Giving me (4-x^2)*[(135x^2-18x+1)(15x^3+6x+1)-(1)]

,rotate

[merry narwhal]

Which simplifies to: (42x^2-12x)(4-x^2)

Which eventually gives me 168x^2

Which is obvs wrong

[reef sandal]

You can use binomial theorem to find the constant terms of the bracketed polynomials

And then distribute -x^2

Atcually I don't even think you need binomial theorem per se

[merry narwhal]

Hmmm

That's what I did

[odd edge]

@merry narwhal Has your question been resolved?

[merry narwhal]

I kinda just wanna know where I went wrong

And if my logic was correct

<@&286206848099549185>

[odd edge]

@merry narwhal Has your question been resolved?

[odd edge]

@merry narwhal Has your question been resolved?

[odd edge]

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[shut mantle]

how do I do this

[mystic saffron]

plotting some points does the trick

compute all of those functions at like idk

x=-1,0,1

then because you know all of those functions are lines

just extend the line segment you would get

[shut mantle]

wdym

[mystic saffron]

what part did you not understand

[tepid yacht]

Or because it's all equations of a line, lines are in the form of y = mx + b, where b is the y intercept and m is the slope, the rise over run. You can mark the y intercept then apply the slope and then connect the dots

[sand night]

So

for the first one

your y intercept is -4

so you count down 4

now you know your slope is 1/3x and slope is rise over run

so count 1 line up, and then 3 over

and to get in the oher direction you also count down 1

@shut mantle

[tepid yacht]

https://www.youtube.com/watch?v=3YBF9pUvzAA&ab_channel=BrianMcLogan
Here's a video

[tepid yacht]

https://www.youtube.com/watch?v=-u55GD_sGLA&ab_channel=Mathispower4u
Here's this method

[sand night]

that method takes so much more time

than just learning that slope is rise over run

[shut mantle]

is this what u mean

[sand night]

yes

but

[tepid yacht]

Yes but plot the y intercept first

[sand night]

count from the orign

[tepid yacht]

And go from there

[sand night]

sorry

you count 4 down from the orgin

[shut mantle]

how would I do that

[tepid yacht]

Do you know what y intercept means?

[sand night]

you see how it says -4 at the end

So lets start with the basics

y=m x+b

y = y coordinate
m = slope
x = x coordinate
b = y intercept

So you are given the equation y= -1/3x-4

[shut mantle]

the line that's going straight

[sand night]

Your y intercept is where your line intersects at the y axis

[tepid yacht]

No

[shut mantle]

oops

[tepid yacht]

It's where it crosses the y axis

Where it crosses the y axis, that means the x coord is 0

[shut mantle]

is that the y intercept

[tepid yacht]

So for this, you should plot the y intecept first

[tepid yacht]

No

[sand night]

no the y intercept is -4

[tepid yacht]

lines are in the form of y = mx + b, where b is the y intercept and m is the slope

[shut mantle]

ohh

[sand night]

would you like to see the first one as an example

and then you do the others?

[tepid yacht]

Did you watch this video?

It would help

[sand night]

yes

[shut mantle]

and now you do the rise and run?

[sand night]

right there

so it 1/3

Rise one, run 3

[shut mantle]

alr

[sand night]

.

no

the slope isnt negative

[tepid yacht]

Basically what you did here, but you didn't have the proper starting point

[sand night]

its +

[shut mantle]

ah

[tepid yacht]

You went up 1 then over 3

[shut mantle]

okay

[sand night]

yes!!!

[shut mantle]

so am I finished

[sand night]

but that line is a little incomplete

so no\

[shut mantle]

oh

[tepid yacht]

Now use a ruler or a straight edge and connect the two dots

[sand night]

no you need atleast 3 points lol

[tepid yacht]

No you don't

3 points for parabola

2 for line

[sand night]

i would have atleast 3

[shut mantle]

the teacher said that yesterday

you cannot connect a line without 3 points

[shut mantle]

yes

[sand night]

ok

this time

[tepid yacht]

You can connect a line with 2 points

[sand night]

you can but

[tepid yacht]

3 is for a parabola

[sand night]

they are a beginner

[tepid yacht]

2 is the minimum for a line, 3 is the minimum for a parabola

[shut mantle]

okay now what do I do

[tepid yacht]

.

[sand night]

ok so this time instead of going up one

go down one

and left 3

[sand night]

basically what you did right here

[shut mantle]

for the x intercept ?

[tepid yacht]

No

1/3 is the slope, up one over 3

[shut mantle]

oh ok

ty for the help

[tepid yacht]

You can go down 1 left 3 as the same method

Because -1/-3 = 1/3

[shut mantle]

.close

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[prisma notch]

hello! i dont understand where the one came from and the statement "We can only cancel these factors if we limit our x-values so that they never cause a
0 in the canceled factors in the denominator."

[lavish osprey]

it basically means that we have to restrict the domain such that we don't include x = -2, x = -1, or x = 0

The idea is that your parent function couldn't handle those values because you'd have 0 in the denominator, making it undefined. Even though we simplified it, your simplified function inherits the parent function's domain

[prisma notch]

oh okay thank you but im confused on where the 1 came from?

[lavish osprey]

everything canceled out 🙂

similar to how $\frac{x^2}{x^2} = 1$

[clever fjord]

MellowDramaLlama

[prisma notch]

ohhh okay

thank you!

[lavish osprey]

yep np!

[prisma notch]

.close

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[thin anvil]

How is the numerator 69?

It should be 100?

I don't understand what happened here

I do see two negatives

Which means positive

But I'm confused about 69

[lavish osprey]

so we know that $sin(\theta_1) = -\frac{10}{13}$. Do you agree?

[clever fjord]

MellowDramaLlama

[thin anvil]

Yep

[lavish osprey]

Then $($sin(\theta_1))^2 = \left(-\frac{10}{13}\right)^2 = \frac{100}{169}$. Correct?

[clever fjord]

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

[thin anvil]

Yep

[lavish osprey]

ok good!

then we have $1 - \frac{100}{169}$. We need to find a common denominator to do subtraction so we notice that $1 = \frac{169}{169}$. Thus we have: $\\frac{169}{169} - \frac{100}{169} = \frac{169 - 100}{169} = \frac{69}{169}$

[clever fjord]

MellowDramaLlama

[thin anvil]

Oh

How can I forget this 😩

Thank you so much

[lavish osprey]

np! Just practice 🙂

[thin anvil]

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[signal rose]

Is the answer: 2

[lavish osprey]

The variable starts with the value 10

So 10+1=11

In their provided example

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[white minnow]

could somehow please help me get started on ii) ?

[white minnow]

I would post my work but I dont know where to start

do I need to use some identity?

I tried expanding but it seemed really long and it didnt seem like it was working

[lethal sundial]

Did you learn some stuff about a certain bilinear operator?

Like

The scalar product ? Maybe it's my French making the name weird

Because basically what that could help you with is

<u,u>=||u||²

It's simply applying that formula

And using the bilinearity property of the scalar product

[white minnow]

ah yes I get that u . u =||u||²

[lethal sundial]

You feel like it's okay to handle this?

[white minnow]

I guess I know you would use that but im a bit stuck

[lethal sundial]

Just try to use them

[white minnow]

maybe with the step before that

[lethal sundial]

And see where it leads you

I see norms squared

I see a norm squared in the formula I mentioned

You are not stuck

[white minnow]

ohhh

so your going the other way

||u||² = u . u

like that

[lethal sundial]

It's an equality after all

[white minnow]

thank you I will try that

[lethal sundial]

If a=b doesn't imply b=a I'd be going 10 ft under my feet

[white minnow]

lol

[lethal sundial]

Okay though I really need to sleep I know someone's gonna be grumpy

[white minnow]

goodnight

[lethal sundial]

Good luck, you ll do it!

[white minnow]

thank you!

[odd edge]

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[hexed dove]

hello! is this the right server to ask about forces? e.g. push, friction, support, weight? if so, when a object increases in speed (thrust) does the friction to that object also increase?

[hexed dove]

In this case the object being a boat on the surface of water

[quartz oracle]

Yes, the water resistance should increase

[hexed dove]

okay, so is water resistance similar to air resistance in the sense that an object can reach terminal velocity where both the friction and thrust are in balance?

[quartz oracle]

When you’re travelling sideways, gravity is not in the direction you’re going, or against it

[hexed dove]

ok

[quartz oracle]

so in this case, the force that the water is fighting against is not gravity

[hexed dove]

yes

[quartz oracle]

by that point, I think the boat would be in danger of tumbling

so that might be why you don’t hear about it

[hexed dove]

I knew that, I'm just wondering about how the level of friction increases as the boat's thrust increases

[quartz oracle]

then under ideal conditions, I guess it would reach a sort of terminal velocity?

[hexed dove]

yes

yes, though I wouldn't think it would be very realistic

anyway thanks for the help, I'll close it down now

.close

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[quartz oracle]

you’re welcome

[hexed dove]

.reopen

[odd edge]

✅

[hexed dove]

maybe the water always has the same level of friction?

no matter the thrust of the object

nvm

.close

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[upper nexus]

Guys this is probably basic math for you guys but I need help getting the answers I’m not really good at finding the angles so I wanted to see if anyone could help me

[noble path]

Find the slope of Line A and B then use the atan function to get the angle between them $$|\atan{m_A}-\atan{m_B}|$$

[clever fjord]

Bring Back Beatrix

[upper nexus]

Okay so umm

Slope of Line A - m=2/3

Slope of line B - m= -4

Im not familiar with the atan function how do I plug this in

[noble path]

you have to use a calculator

,wa abs(atan(2/3)-atan(-4))

,w abs(atan(2/3)-atan(-4))

[clever fjord]

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[noble path]

its in radians so you have to multiply it by 180/pi

[upper nexus]

So 1.91 times 180/pi

[noble path]

,w 1.91*180/pi

[clever fjord]

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[upper nexus]

And it says to round to the nearest hundredth so does that mean the answer is 109.44

Or do I need to do something else

[noble path]

wait you would want to use the smaller angle intersection

so you have to subtract by 180

,w 180-19.435

[clever fjord]

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[noble path]

,w 180-109.435

[clever fjord]

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Requested by bringbackbeatrix

[upper nexus]

Ohhh damnn I would have gotten it wrong already again 😭

So is that the final result ?

70.565

Which rounded to the nearest hundredths is 70.57

[noble path]

yes but the question is still unclear as it doesnt said what part of angle intersection

[upper nexus]

Yeaa that photo shows everything they are asking

So if what u did is everything we need to do with what the question asked then I’m sure it’s correct right

[noble path]

wait are you sure line A has 2/3 not negative?

yeah its right

[upper nexus]

Line A has a positive slope right ?

[noble path]

for more exact write the full formula in calculator

[upper nexus]

How do I input it to the calc

[noble path]

`w 180-abs(atan(2/3)-atan(-4))*180/pi

,w 180-abs(atan(2/3)-atan(-4))*180/pi

[clever fjord]

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[noble path]

70.35 is the approximation to the nearest hundredths

[upper nexus]

Wait so the answers isn’t 70.57? It’s 70.35

[noble path]

yes its 70.35

[upper nexus]

And my slopes where correct right ?

[noble path]

its right

[upper nexus]

It’s cuz I only have one try left and honestly I searched up on google and got 70.53 so the numbers where switched

Okay thank you bro I really appreciate it

[noble path]

your welcome bro

[odd edge]

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[scenic shore]

Is it possible to simplify something like $\frac{A^3 B^2 cosh(Bx+C) {sinh}^2(Bx+C)}{\sqrt{1 + A^2 B^2 {sinh}^2(Bx+C)}}$?

[scenic shore]

Tough

[clever fjord]

Methylfluorophosphonylcholine

[odd edge]

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[quartz oracle]

Why would you need to do that

and what do you mean by “something like”?

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[sour basin]

I have to calculate the length of the green line.
My idea was that each triangle has an angle of 30°

[sour basin]

so the first triangles' green line should be tan30*6 right?

then the second triangle should be tan30*2sqrt3?

[quartz oracle]

or tan 30 * tan 30 * 6

[toxic rose]

this looks like a pythagorean spiral

[sour basin]

yeah but I did this 12 times and added the length

but my solution is not correct

[toxic rose]

pythagorean spirals generally start with an isosceles unit right triangle

but i dont think thats the case here

[sour basin]

I tried to add all those values

what did i do wrong

[toxic rose]

it is not necesarry the angle is 30 deg!

[solemn jay]

Sum of a GP!!!

[toxic rose]

sorry what?

[tired hollow]

May be useless but, maybe the deg isn't constant

[sour basin]

if its not constant than the whole excercise is stupid? no?

I think ed is right but what is my q? ^^

@solemn jay can you give me a hint on how to get q?

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[sinful stone]

I'm getting confused by terminology here. What does it mean when a sequence {a_n} is bounded? What defines bounded or bound? As if it is being contained in an area..?

[sinful stone]

In terms of Calculus; Sequences

[shy smelt]

It means it there exists some bounds it will always be between

[sinful stone]

boundaries they mean?

[shy smelt]

Yeah, a sequence a_n is bounded if there exist x, y such that x < a_n < y for all n

<= or < doesn't really matter I think

[low locust]

it doesnt

[sinful stone]

aha, I see.
So if a sequence {a_n} is bounded below by a lower bound X, does this mean that a_n is always greater than X?

[low locust]

yes

[sinful stone]

Because it can be imagined as if X is the floor and a_n is the paper airplane (im just trying to get some sense here lol)

and being "bounded above" would be the ceiling

ok lol

[low locust]

yes

[sinful stone]

But if every value of n in a_n is equal to X... how do you know if it is an upper bound or a lower bound? Weird scenario but just a q

would you say that the sequence is bounded at all?

(Or perhaps a_n would just = X in that case)

[low locust]

sure

like Jelle said, it doesnt matter whether the definition has < or <=

but if you are not happy with that, you can just say a_n < X+1

and a_n > X-1

[sinful stone]

yeah that works

thanks so far ❤️ i'll ask more later probs

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[sinful stone]

.reopen

[odd edge]

✅

[sinful stone]

does n always have to be positive?

in a_n

[low locust]

well sequences usually are like that

well, non-negative

a_0 is also very common

[sinful stone]

i wouldn't get an exam question talking about negative sequences that go toward n -> -infinity?

[low locust]

but technically it doesn't have to

you could also start with a_{-17}

it would just be weird

I mean I dont know your teacher

but would it really make that much of a difference?

[sinful stone]

i dont know, i just feel weird with negative sequences.

textbook is mainly mentioning positive n, so I'm not going to delve deeper into negative sequences just yet

[low locust]

its really just a sign switch in the index

$a_1, a_2, a_3, \ldots$ vs $a_{-1}, a_{-2}, a_{-3}, \ldots$

[clever fjord]

Denascite

[low locust]

sure it looks weird but it means the same thing

[sinful stone]

actually yeah its not that complicated

works out, tysm <3<3

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[open heath]

The springs of 1500kg car compress 5.0mm when its 68kg driver enters the driver’s seat. If the car goes over a bump, what will the frequency of the vibrations be?

[open heath]

So far, i’ve brainstormed a bit on how to interpret this..

[fallow elm]

need help on these

[copper quarry]

#❓how-to-get-help

[fallow elm]

how

im lost

[copper quarry]

how can you be lost

look at the channel

[fallow elm]

isn't this help channel?

[copper quarry]

its someone else's

[fallow elm]

😭

[copper quarry]

you need to get your own

[open heath]

😂

[copper quarry]

#❓how-to-get-help

[open heath]

So far, i’m thinking whether this 5mm can model the amplitude of we consider it as a wave

But to relate it to frequency, which is the speed/wavelength

The frequency can be derived by the period, but we don’t know that..

However the wavelength..

[clever fjord]

Dyssrupt

[fallow tapir]

where k is the spring's constant

[open heath]

How do we derive this formula?

I looks like something from CM

[clever fjord]

Dyssrupt

Dyssrupt

Dyssrupt

Dyssrupt

Dyssrupt

Dyssrupt

[fallow tapir]

which gives us this.

[open heath]

Omega is the angular freq?

[fallow tapir]

yes

[open heath]

Ok. Still it is worrying that my book doesn’t refer to this SHM equation..

Thanks though.

So k = 1568*(~10)/0.05

20*15680 = 313600

Actually there was no need for that

K/m = 200

sqrt(200)/2pi

That is 2.251

Is that correct?

Ah. I think it is the change in force

68*10/0.05

13600

I messed up a few calculations.. anyways i wrote it down instead

13600 as k, so sqrt(k/m) = sqrt(13600/1568)

= ~8.67

But this is omega^2

So omega = sqrt 8.67

= 2.945…

Omega = 2pi(freq)

So f = 2.945/(2pi) = 0.4687

Hz

Is this correct?

[fallow tapir]

can you try writing all this on paper

?

or maybe tex it

[fallow tapir]

,rotate

[fallow tapir]

what's 68.1?

also 1 mm = 10^(-3) m

[open heath]

68*10

I’d rather use 10 than 9.81

0.005

Dang

So chuck another 0

136000

angular freq becomes 9.313

Dividing by 2pi gives 1.482 Hz

[fallow tapir]

seems correct.

unless I am dumb.

[odd edge]

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[spiral mesa]

Hello, is it possible for a radius to be decimal?

[nimble blaze]

yes

[umbral socket]

Hi, is cosh2x = cosh^2 x +sinh^2 x?

[quartz oracle]

yes, you can check this by using the definition of cosh and sinh in terms of exp(x)

[umbral socket]

what does exp(x) mean

[quartz oracle]

e^x

[umbral socket]

oh ok I'll try reading the proof of it. Thanks a lot

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@spiral mesa Has your question been resolved?

[spiral mesa]

hello again, can the center of the radius be decimal?

[nimble blaze]

#help-19 message

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[dawn mason]

hello, for this question, does it mean that the linear transformation doesnt exist? since i only have 2 linearly independent vectors in R3 space

[lyric moat]

can you explain why it won't exist?
To solve this you would need to use the linearity property

[dawn mason]

i dont know i used the stacking method and its not a square matrix so i cant find the inverse

[lyric moat]

yeah, you cannot always find the transformation matrix if transformation of n linearly independent vector is not given where n is the dimension, but here you just need to add the first two then divide by two

[lyric moat]

T(v1)+T(v2) = T(v1+v2)

[dawn mason]

so this case it would be (4 4 4)?

is it correct to say it is T(2 2 2) = (4 4 4)?

[lyric moat]

yes

given that the transformation is linear

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[warm hawk]

Hi guys, how am I supposted to read the following.

$$
\exp(\ln(x))=x \quad \text{for} \quad x \in Dm(\ln)=]0, \infty[=Vm(\exp)
$$

[clever fjord]

SimonWin

[warm hawk]

subject is inverse function

ln(x) and exp(x) is inverse functions

I get the exp(ln(x))= x

And I get the $\forall x \in Dm(\ln)$

[clever fjord]

SimonWin

[warm hawk]

And I get why it's ]0, infty[ because you can't obviously take ln(0) and below doesnt exist

But why is it equal to Vm(exp)

?

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[spare willow]

\

[spare willow]

^^ solution

for part c, on the last step, why does the summation not include a summation for n cubed

like

(n+1)^3 isnt just 3n^2 + 3n + 1

[low locust]

you have those on the left and on the right

so they cancel

only (n+1)^3 survives

[odd edge]

@spare willow Has your question been resolved?

[spare willow]

why does it survive

[low locust]

on the left you have 1^3+2^3+...+n^3+(n+1)^3

[spare willow]

oh wait

[low locust]

on the right you have 1^3+2^3+...+n^3

[spare willow]

That makes sense

Thanks a bunch

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[tawny lagoon]

hello

can someone explain why it become 169/8

cause i get somthn diff

[nimble blaze]

distribute the 2

[tawny lagoon]

what do you mean by distribute

[nimble blaze]

p(q-r) = ?

[tawny lagoon]

oh

i see what i did wrong

.close

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[serene anvil]

y = abs(x^2 + 2)

[serene anvil]

y = abs(x^2 - 2) why here 2 equation need to make wile in 1st one as it is we write ie positive why can't it have down facing equation

[wooden python]

|x^2 + 2| = -(x^2 + 2) when x^2 + 2 < 0.

[viscid flint]

,w graph |x² - 2| from -3 to 3

[clever fjord]

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[serene anvil]

oh understood so still there are two equation we consider when it will be negative input and when its positive we use normal one

but in |x^2 + 2| we don't need to specifically use them as its always positive output

@wooden python am i right?

[wooden python]

yes

[serene anvil]

thanks @wooden python

server looks busy today

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[lucid tendon]

i understand the degrees but without converting to find the quadrant is confusing

[low thorn]

you can think that pi is 180 degree and from there u can have rough estimate

in which quadrant ur angle is going to lie

[wooden python]

divide each one by pi/2 and round up.

[lucid tendon]

pi/8 is around 22 degrees so it will be quadrant 1

[low thorn]

hm

[nimble hull]

well you're not supposed to convert to degrees first

an easier way to think of it is that since it's less than pi/2 (90 degrees) it must be in first quadrant

anything between 0 and pi/2 is 1st quadrant

what angles are 2nd quadrant then?

in radians

[low thorn]

if u aren't bounded by time then just imagine all major degrees and their quadrant

making it easier for you

[lucid tendon]

if the numerator is larger then it is likely to be in quadrant 2-4?

[nimble hull]

not always

something like 121pi/1000 would be in quadrant 1

[wooden python]

if the numerator is larger than the denominator, then your angle is larger than pi.

honestly imo you're making this shit more complicated for yourself by trying to think about what's more "likely" or not.

[nimble hull]

that's if you ignore the pi in the fraction

in pi/2 the numerator is greater than the denominator but pi/2 is less than pi

[lucid tendon]

im sending in a picture it might take a while

so focus on the pi/x in order to find quadrants?

[nimble hull]

if the angle is greater than pi what quadrants could it be in?

[lucid tendon]

quadrant 3

[nimble hull]

or...?

[lucid tendon]

quadrant 4

[nimble hull]

yep

so which one is 10pi/9 in?

[lucid tendon]

what is the angle in this equation?

[lucid tendon]

i think its quadrant 3

[nimble hull]

yes

because it's in between pi and 3pi/2 (180 and 270 degrees)

quadrant 4 is for angles between 3pi/2 and 2pi (270 and 360 degrees)

this could help

[lucid tendon]

is it the same rule but backward when the fraction is negative?

[nimble hull]

if the fraction is negative you could add 2pi to get an equivalent angle

[lucid tendon]

ohh,i think I get it now thank you

have nice day

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[mystic saffron]

How do I solve this question?

"Hamilton wants to listen to three songs of different genres in his Spotify list. The list consists of 20 songs of which 13 are
pop songs and 7 are jazz songs. In how many ways can he choose to listen to two pop songs and one jazz song
if the order of the songs doesn't matter."

[mystic saffron]

Yeah

So yiu understand you need

• Two pop songs out of the 13 available
• One Jazz song out of 7 available

Right?

[mystic saffron]

yeah

And also that the order doesnt matter

and 20 in total

[mystic saffron]

yes

Yeah

[mystic saffron]

Just select 2 out of 13 and multply with selection of 1 out of 7

13C2 x 7C1

Did you understand this?

[mystic saffron]

I have been taught permutation and combinations but I don't really know when to use one or the other

Hmm yeah

So when the arrangement/order matters, you use Permutation

When the arrangement/order doesnt matter you use combination

Oh I see

Both of them are just SELECTING some number of things from a Larger set of things

Oh

I have 13 jazz songs, i require Any two
How many ways can i select two jazz songs? 13C2

I think I understand now

Yeah

@mystic saffronThank you dude. I appreciate your kindness.

[mystic saffron]

No worries

[lavish osprey]

Just a small piece of advice, often when you’re first starting out problems consider a small example that won’t be too big to fill out possibilities then count them up. For example, if you were to let numbers be the pop songs and reduce to 5, then do letters for the jazz songs and reduce to 3, then choose 1 jazz and 2 pop, you’d get the following result

If you can take your problem and find a smaller example it helps with understanding the combo formulas

[odd edge]

@mystic saffron Has your question been resolved?

[mystic saffron]

Thank you. I will try it out.

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[rigid quiver]

In a tournament each participant had exactly one game against each of the other participants. No game ended in a tie. It was observed that
For any two participants there is a third participant who defeated them
both.
a) Show that the tournament cannot have six participants in total.
b) Show that the number of participants in the tournament can be 7.

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@rigid quiver Has your question been resolved?

[rigid quiver]

<@&286206848099549185>

<@&286206848099549185>

Someone? lol

[rigid quiver]

<@&286206848099549185>

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@rigid quiver Has your question been resolved?

[rigid quiver]

<@&286206848099549185>

[steel moss]

Oh dear

[blazing pecan]

I know I've seen a youtube video on this problem before, I just don't remember where it was lol

[rigid quiver]

Damn

I would appreciate if you tell me how to do it

[blazing pecan]

I don't remember that either 😔

[rigid quiver]

Damn

Sad

[blazing pecan]

I mean part (b) should be easy, you just have to find any configuration of 7 people that works. I can get out some paper and see if I can't figure out part (a)

[rigid quiver]

ok

[shy flume]

Bro what is that problem

A) find the answer using contradiction method

Ig u gotta assume A and B are a pair and they r defeated by a third player X etc

[rigid quiver]

Yes ok, but how does that prove anything?

I tried to do that

And Im whit nothing

<@&286206848099549185>

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[delicate mountain]

Is this correct ?

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[versed junco]

how do i do this?

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[mystic saffron]

Wouldnt it be A?

Cause the way the arrows are lined up in the picture

I may be wrong

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[umbral stag]

im not sure how to do this problem. i tried to factor the 2 out of the function parameter but im not sure if I can even do that

[merry finch]

you dontk now that f is linear in that sense

$\int_0^{0.5} 2f(t), dt = 2\int_0^{0.5}f(t), dt$

[clever fjord]

Frosst

[merry finch]

but not when the 2 is inside

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[cursive totem]

why the video use the transitivity of congruence? the Chinese remainder theorem not works if a1,a2,...an, are the same numbers?

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[nova summit]

I made an error after while I was trying to create the proper derivative for the washer method, since I can't have an x variable within the derivative

I don't understand if I am supposed to solve 4-x^2 for y, or if I am supposed to do something else

if i'm doing this cirrectly, y= 4 is the top graph, and 4=x^2 is the bottom graph

and within the washer method i'm supposed to put (top)^2 - (bottom)^2 as the definite derivative.

,help

[clever fjord]

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!

[nova summit]

nevermind, but what i'm basically asking is

what is supposed to go here?

i know for sure that it isn't supposed to be a whole number lol

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[nova summit]

<@&286206848099549185>

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.close

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[fair egret]

Can someone help me understand why is x2=0?

[ashen ingot]

think of 0 as the zero vector

and append it to A

or whatever that matrix is called

[mortal trench]

ok think about it this way

this is still a system of eqns

0 x1 + 0 x2 + 1 x3 = 0

0 x1 + 1 x2 + 0 x3 = 0

...

[fair egret]

o so we dont know about x1

is that why it is 1?

"The reason why (1, 0, 0) can be an eigenvector in this case is because we often normalize eigenvectors for simplicity. If x1 is arbitrary and x2 = x3 = 0, we can choose x1 = 1 without loss of generality. This gives us the vector (1, 0, 0)."
from ai

got it

thanks

.close

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[cosmic solar]

I need help with physics based math with two parts. The question is: "A tectonic plate moves at 4cm/year, how far would it move in one second. Then, what's its speed in kilometers per million years"

[fervent hawk]

what have you tried?

[cosmic solar]

I haven't been taught how to solve this kind of thing before so nothing at the moment, I've looked up how to solve it but not gotten any concise answers.

[fervent hawk]

i see

so, first we know it moves 4cm a year

[cosmic solar]

For the assignment it gives me the answer but I predict that I'll do more of this in physics so I want to understand it

[fervent hawk]

so, when we are talking about moving in secs, it will be really slow, right?

[cosmic solar]

Correct

Extremely

[fervent hawk]

so the number will be really small

now, 4cm a year

what is a year?

in terms of seconds

[cosmic solar]

I don't know off the top of my head

Quite a bit

[fervent hawk]

it's okay

we go through step by step

[cosmic solar]

3.154e+7

[fervent hawk]

ohhh ok

how did you get that number

[cosmic solar]

Google, I haven't been taught that kind of math either

[fervent hawk]

it's okay, we can go through it now

[cosmic solar]

For context: I'm a Junior in highschool who is enrolled in CiHS and we are starting a college level physics class

I'm not super advanced in math

[fervent hawk]

i see, sounds wonderful

[fervent hawk]

no worries!

[cosmic solar]

so the e+7 part = 10⁷?

So it's 3.154x10⁷

[fervent hawk]

let's list out some time values

[cosmic solar]

Okay

[sand night]

Use dimensional analysis

Oh ur helping him sorry

[fervent hawk]

year >> day >> hour >> mins >> seconds

[fervent hawk]

we can count bit by bit with these

e.g.

1year=365.2422days
1day=24hours
.
.
.

let's list them out

now that we have all the numbers

we just multiply them together

[fervent hawk]

to get this number

which i assume that your prof/teacher would like you to find it yourself with × than google i guess

[cosmic solar]

So 24 hours=1440 minutes

[fervent hawk]

good

[cosmic solar]

1440 minutes = 86,400 seconds

[fervent hawk]

yea

,calc 86400*365.2422

[clever fjord]

Result:

3.155692608e+7

[cosmic solar]

Oh a calculator bot

[fervent hawk]

i see, it's a bit off, since we used 365.2422 instead of 365

anyways

now that we know

[cosmic solar]

So it's a bit of a process then, to find the seconds

Per year

[fervent hawk]

yep

1year=31556926seconds

next part is fun

I'll need some time to type

[cosmic solar]

Converting this to distance?

[fervent hawk]

yea, but you'll also have to manipulate the units too

[cosmic solar]

Great

[fervent hawk]

$1$year=$31556926$second

$\frac{1}{31556926}=\frac{\text{year}}{\text{second}}$

$\frac{4\text{cm}}{\text{year}}\cdot\frac{\text{year}}{\text{second}}=\frac{4\text{cm}}{\text{year}}\cdot\frac1{31556926}$

so

we have

4cm/31556926

which is around

,calc 4/31556926

[clever fjord]

Result:

1.2675505846165e-7

[cosmic solar]

OH

Yeah this is beginning to make more sense

I see

[fervent hawk]

and i guess you know the e-7 means
×10^{-7}

[cosmic solar]

And we'd round up, correct?

Or

[fervent hawk]

it depends on what your prof/teacher wants

[cosmic solar]

Ah okay

I see now though

So it'd be 1.3x10^{-7}

[fervent hawk]

yea

or

for writing

we use ()

instead of {}