help-36

[ember maple]

im lost im afraid

n pairs?

[desert mantle]

no

[ember maple]

lemme try again

[desert mantle]

do it for n=6

[ember maple]

n/2

?

[desert mantle]

yes

and what is the sum of each pair

[ember maple]

7

sorry i mean

14

[desert mantle]

no

7

for n=6

so in general for n?

[ember maple]

sorry give me a sc

by pair

do you mean that (1+6) and (6+1) is a pair

or just (1+6) is a pair

[desert mantle]

1 and 6 form a pair

sorry for the confusion I was imprecise

2 and 5 form a pair

3 and 4

[ember maple]

so (3+4) and (4+3) is considered the same right

so for n=6 i should get 3 pairs right

[desert mantle]

yes

n/2

like you said

[ember maple]

so in general

[desert mantle]

and they each sum to 7

[ember maple]

n/2(n+1)

[desert mantle]

yes

[ember maple]

so that series

[desert mantle]

(technically what we are doing only works for even n but the same is true for odd n)

[ember maple]

can be simplified to that formula

[desert mantle]

yes

[ember maple]

wait

lemme simplify that in my book and try to figure it out

if i cant lemme send where im stuck to u

bro thank you

i got the answer after that

thank you so much

i actyually learned something new

just 1 question

how did u transform the first series to teh second one

[desert mantle]

I just reordered the terms

and put a few brackets

[ember maple]

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

[ember maple]

isnt there 1 n?

[desert mantle]

1+2+3+4+5+6 = (1+6) + (2+5) + (3+4)

just reordered

first and last, then second and second-last, third and third-last etc

[ember maple]

ohhh

i see now

n is the last term

or 6 in this case

im actually stupid

thanks a lot tho

.close

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[boreal spruce]

Hi, I am going to prove the limit=1/4 by definition

But I stuck in the last step, could anyone give me some hints?

[tired walrus]

double check your algebra in the very first step. you fucked it up.

[boreal spruce]

Oh I am sorry. Rectified now. But I still dk what term is okay to drop out

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[heavy lichen]

Hello, is anyone familiar with drawing phase diagrams for a system of differential equations ?

[heavy lichen]

I have a question in the case of both eigenvalues being complex

[fluid sky]

u can just ask ur question here..

if somebody can help u they will

if ur problem is too advanced and u dont get a satisfactory result in these channels, u can try one of the advanced channels

[heavy lichen]

It’s concerning the actual drawing of the phase diagram

[heavy lichen]

Where can i find those ?

[fluid sky]

[fluid sky]

well theres the channel #odes-and-pdes

if u scroll down abit u can find the rest of the channels

sorry but i actually cant help u with differential equations 😦

not studied them myself

[heavy lichen]

I understand why we get these diagrams but our teacher didn’t put any values for the axes so it’s kinda confusing

[worldly vale]

for just sketching phase diagrams the actual numbers are too important just the general shape and behaviour is fine for your purposes

[heavy lichen]

Numbers ? What do you mean by that ?

For the case when both eigenvalues aren’t complex we get this which makes sense because the "y" axis is w and the "x" one is z

But in the first picture i sent he either forgot to write them down or we’re not dealing with quite the same diagrams ? I’m not sure

@worldly vale

[worldly vale]

you said your teacher didnt label the axes

[heavy lichen]

Yep

[worldly vale]

the numbers on the axes arent as important as just the general shape

[heavy lichen]

The axes are the variable tho

[worldly vale]

right i see

[heavy lichen]

Surely that’s important ?

[worldly vale]

well just pick a point and you'll be able to figure out which axis is which

[heavy lichen]

Do you know which one is which ?

I’m guessing o is the y axis ?

No r is the y axis ?

@worldly vale

But this is so weird

I think it might be a different way to look at it all together ?

Because r and o are the polar coordinates of our solutions

So maybe r and o aren’t what’s being represented on the axis ?

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[hard mist]

Given is a polar equation (of a circle), to draw the circle, both sides are mulitplied by r, the it is converted to cartesian form

[hard mist]

First step is multiplying by r on each side

But how to go from step 2 to 3?

The red arrow

[teal kayak]

send -2Rx to other side

[zenith sierra]

nvm

i misread the = sign

[hard mist]

Right, so now Ive got

$R^2+x^2+y^2+2Rx=R^2$

[soft zealot]

rainy

[teal kayak]

yeah then, $R^2+x^2+2Rx= {(x + R)}^2$

[soft zealot]

numbpy

[hard mist]

Yup, and whats that rule called in english?

[teal kayak]

umm... it's just the formula for (a + b)^2

[hard mist]

Ah okay, in my language that rule has a special name 😁

Thanks.

c.lose

[teal kayak]

.close

[hard mist]

🤠

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[turbid nebula]

On my last exam i stubled upon this problem that just couldn't get through my head.
I will provide 2 problems.
One is to find Infimum and the other is to find supremum.

[teal kayak]

Try rewriting the set by dividing by n

for the first question

[turbid nebula]

3 + 1/n?

[teal kayak]

yes then you can prove that inf(A) = 3 + inf(1/n)

you already know the infimum of 1/n

[turbid nebula]

hmm i don't understand how

[teal kayak]

you don't even need to prove you should be able to see it intuitively

[teal kayak]

what is the definition of infimum you know?

[turbid nebula]

Give me a moment to phrase it in english

Infimum is the highest number closest to the lower boundary of the set

im not sure if that sounds okay

[teal kayak]

well, it sounds weird. Lemme put it in better words

[gritty solar]

Infimum

[teal kayak]

infimum is also known as greatest lower bound (glb)

so, (1) clearly it is a lower bound

(2) the is the greatest one, ie if there is any other lower bound then it should be smaller than the glb

.

Can you see then how 0 is the infimum for 1/n?

[turbid nebula]

because n goes to infinity and the higher the n is the closer it is to 0 but can never hit 0?

Dang math is actually getting fun now

[teal kayak]

I mean they sound similar but these are different concepts

[teal kayak]

This is the concept for limit

[turbid nebula]

Okay

Then i don't know

[teal kayak]

See, the point is that 0 is less than or equal to 1/n for each n

this is not hard to see as 1/n are positive numbers so ofc they are bigger than 0

ie 0 is a lower bound

but so is -1, -2, -234234, etc

so, you now need to prove that if l is any lower bound then l <= 0

making 0 the greatest lower bound or infimum

[turbid nebula]

It seems that what i had in mind was finding minimum instead on infimum, thank you

[teal kayak]

That's actually pretty close

the main advantage of infimum is that only

notice that 0 is NOT a minimum but it is an infimum

For even easily example consider, (0, 1)

[turbid nebula]

there is no minimum correct?

[teal kayak]

here, 0 is NOT the minimum cause 0 is not in the set but it seems almost like a minimum

The concept of an infimum encodes this 'like-a-minimum'

compared to that for [0, 1]

0 is the infimum as well as the minimum

[turbid nebula]

indeed

Then i assume the second problem goes to 6n^2+1

[teal kayak]

The supremum and infimum are real numbers, they shouldn't have n

use limit to see what happens as n -> infinity

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[turbid nebula]

Got it, thank you

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[dawn elk]

(f/g)(x) is same as f(x)/g(x)

so

(f/g)(4) = f(4)/g(4)

[nova trellis]

but you see, i can't figure out what f and g equal. i had a problem nearly identical to this a couple days ago and i couldnt figure out f and g, and the person attempting to help me made me look like an idiot

i know that g=4 though

oh wait f=x-1/x

oh wait, the answer IS f, because if i already know g=4 and it wants me to divide g from f, then multiply it by 4 then the answer is f=x-1/x

<@&286206848099549185>

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[cursive nexus]

a iii

[cursive nexus]

how do I start

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[tranquil pine]

Consant force + frictional force in the opposite direction = mass * acceleration

use this force balance equation

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[raven path]

Hi
I need to find the determinant of the matrix.
Unfortunately, my result is kinda wrong.
I have -11, but is should be -37.
Maybe it's some arithmetic mistake.
Here are my notes:

[stoic mural]

Row one column 3 of second matrix

Should be a plus1

Nvm

[raven path]

But it's 1 - 1

So should be 0

<@&286206848099549185>

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@raven path Has your question been resolved?

[raven path]

I found a mistake by myself
It was +24, it should be -24

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[potent yacht]

What's the difference between these two curves, figures a and d, if they both convey an inverse relation

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[potent yacht]

.reopen

[final saddle]

✅

[potent yacht]

<@&286206848099549185> ayo

[magic sparrow]

what do you mean what is the difference?

[potent yacht]

At constant momentum the force should be inversely proportional to the arm length

A and d are both inverse

What's the difference between these two curves if they both convey an inverse relation

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[dense pumice]

i'm thinking A

my strat was to first eliminate all the white marbles

actually wait that's probably wrong

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[whole pelican]

Need a little help with one question

[whole pelican]

Basically a ball is kicked

Following the trajectory of f(x) = - 4.9x^2 + 3.5x + 1

I'm asked when the ball stops and at what height it is

I know it stops at the summit

I have the derivative for the instant localisation of y but like

f'(x) = - 9.8x +3.5

I found the time not the height

0.357s

Any way I can actually find the height

Or do I need to use the original

Wait I'm stupid I need to use the original graph

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[lavish remnant]

I have a question on the binomial theorem

[tranquil pine]

ask

[lavish remnant]

basically I know that for an example like (x+3)^3

I would have the first term to the power of 3

and the second term 3 raised to zero

[tranquil pine]

3 raised to 0?

If you are talking about explicitly the first term then yes. x^3 and 3^0

[lavish remnant]

and I would continue such as this: 1x^3 * 3^0 + 3x^2 * 3^1 + 3x^1 * 3^2 + 1x^0 * 3^3

[tranquil pine]

thats correct

Yes sounds good

[lavish remnant]

my question is what if the terms are sorted such that x is not in the front like (3-1/3x)^5 for example

would would I apply this method for this problem?

[dusty harbor]

$(3 - \frac{1}{3} x)^5$

[soft zealot]

heavy

[dusty harbor]

is what you mean

right

[tranquil pine]

then the first term is still 3^5 times (1/3x)^0 and so on

Yes it is the same idea

[lavish remnant]

yes

[dusty harbor]

please dont write 1/3x

[tranquil pine]

Refer to Pascal's triangle and binomial theorem if you want to know how to expand that

[dusty harbor]

write x/3

or (1/3)x

[lavish remnant]

so how would I do this?

[lavish remnant]

.

[dusty harbor]

like this

[lavish remnant]

do I put -(1/3)x^5 * 3^0?

[dusty harbor]

(-(1/3)x)^5 * 3^0

[lavish remnant]

oh I see

[tranquil pine]

well you could also see it as (-1/3x)^0

anyways, in the end you will have to alternate between plus and minus

Yeah for odd and even powers separately

Same reason why you have the expansion of (a-b)^2 be the way it is

(a-b)^5 = ... - ... + ... - ... + ... - ...

[tranquil flume]

What is lex doing here

You have a podcast to run

[dusty harbor]

after pursuing a PhD in machine learning and being a well respected researcher at MIT, lex fridman decided to self study calculus

[lavish remnant]

you are right

I barely did any math in my PhD

[dusty harbor]

damn programmers

[tranquil pine]

Wait are you actually a researcher in MIT? @lavish remnant

Interesting

Oh wait is it actually you, there is no way lol

[dusty harbor]

yes its him

you can see in the profile picture

[tranquil pine]

I mean yeah but that's like the first picture you can get online

[mellow cedar]

[pine root]

tf2 trolling

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[reef sinew]

What is the mean and standard deviation of these statistics?

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@reef sinew Has your question been resolved?

[reef sinew]

<@&286206848099549185>

[summer raptor]

Do you know how to find mean first? Given you have these frequencies

[reef sinew]

I only know how to find mean with the exact numbers not frequencies

[summer raptor]

the frequency is the exact number

what is the context of the frequency

[reef sinew]

So the question states “a waiter was times how long it took to server the customer.” (seconds) and then it was marked down how long they took

so the frequency is the amount of times a number falls in the range of the time

[summer raptor]

Okay so for mean, the first thing you want to do is find the midpoint of each time interval. So from 0-60 it would be 30, for 60-120 it would be 90, etc. Then find the sum of all these squared midpoints and divide by the sum of frequencies. You'll have to do a few calculations.

a squared midpoint would be like 30^2

You will need this mean to calculate the standard deviation, which is given by this formula:

[reef sinew]

ok yep I got it

thankyou

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[azure trellis]

hello

[azure trellis]

i was wondering how to do this 3D vector question

,rotate

[azure trellis]

so i have considered the formula for the dot product

ill post my working out

[shadow swan]

a.b=|a||b|cos(θ)

[azure trellis]

yeah i have considered that

but after simplifying everything i get a quartic

and none of the given solutions work on it

,rotate

[azure trellis]

,rotate

[azure trellis]

i was wondering if i had perhaps made a mistake in finding the magnitude of the vectors

[magic sparrow]

14a+35= |a||b|cos(theta)

[azure trellis]

yeah

and theta is 60 degrees

i got all of that

the issue is that i got a quartic that doesnt have the solutions given

unless i made a mistake in the working out I posted

[magic sparrow]

not that you should probably have to do this for your question but..

have you tried the quartic formula, like using a calculator and then checked a

[azure trellis]

i just did right now

the result is kind of interesting

so one of the real roots is 8.6043 ...

so when i input 8.6 into my quartic it becomes something like -69

[magic sparrow]

wait hold on

I think I see the issue

[azure trellis]

but when i input 8.6043 it becomes basically 0

[magic sparrow]

no stop I think I know the problem

they both form an angle of 60 degrees with the origin

not with eachother

so the angle between them is 0 degrees

that is the theta you should plug in

I think?

[azure trellis]

wait how would that look on a diagram

if you don't mind could you draw it out

[magic sparrow]

well it would look like the vectors are parallel

in 3D space

it would look like you have two parallel vectors

[azure trellis]

ah

then wouldn't there be no angle

between them

because they are parallel

[magic sparrow]

yes

the angle between them is 0

they both form an angle of 60 degrees with the origin

meaning they both have the same angle from the origin

meaning they are both going the same exact direction

[azure trellis]

ah

thats really confusing

ill try with 0 for theta

okay that didn't work

[magic sparrow]

lol dang I thought I figured it out

one second

I'll try working on it

[azure trellis]

thanks

[magic sparrow]

I recommend since the question tells you that it wants the positive value of a

b isn't an answer

and from that

d isn't either

so I'd just plug and check a and c

[azure trellis]

thats what i did

[magic sparrow]

and?

[azure trellis]

a is the answer

[magic sparrow]

perfect

what's the issue then

[azure trellis]

epic

[magic sparrow]

lol

[azure trellis]

i was just wondering if my equation was wrong

but it wasn't

[magic sparrow]

geez I don't even know, it looks proper to me

[azure trellis]

so everything is good

[magic sparrow]

actually

I suppose your formula was wrong?

just the cos(theta) part though

because theta wasn't 60

it was 0

[azure trellis]

yeah

but apart from that everything is good

thanks for the help

.close

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[vocal locust]

given five xy coordinate points how do you make a bestfit line or a trendline?

[vocal locust]

<@&286206848099549185>

[half summit]

lmk if you don't understand somethingg

in your case n = 5

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[lofty kindle]

ok so suppose ep>0
|x-3||x-2|<ep

so i said suppose delta=1 then
0<|x-2|<1
-1<|x-3|<0

this is where i am stuck

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@lofty kindle Has your question been resolved?

[tranquil pine]

Do you recall the epsilon-definition of a limit? In your case, for every $\varepsilon > 0$ you need to find a $\delta > 0$ such that for every $x$ with $|x-2|<\delta$ we have $|x^2-5x+6| < \varepsilon$.

[soft zealot]

Landau08

[tranquil pine]

Naturally, when someone gives you smaller and smaller values of $\varepsilon$ you will need to make $\delta$ smaller as well to satisfy $|x^2-5x+6| < \varepsilon$ for all x in a $\delta$-environment around 2. You are probably stuck, because your choice of $\delta$ does not depend on $\varepsilon$.

[soft zealot]

Landau08

[final saddle]

@lofty kindle Has your question been resolved?

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[final saddle]

@novel marsh Has your question been resolved?

[final saddle]

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Channel closed

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[tranquil pine]

.reopen

$a=\frac{(m_1-m_2\mu-m_3)g}{m_1+m_2+m_3}$

[soft zealot]

Landau08

[tranquil pine]

.close

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[sonic crystal]

How do I simplify this?

[sonic crystal]

Not quite sure where to start

Maybe with the exponents ?

[woven tide]

How do I find the angle inside the triangle? This is geometry

[grim badger]

#❓how-to-get-help

[final saddle]

@sonic crystal Has your question been resolved?

[final saddle]

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[fallen violet]

Help

[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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[tranquil pine]

i already explained this to you for like 20mins

[fallen violet]

Bruh

[fallen violet]

1

[tranquil pine]

i told you how to do it and told me random numbers to guess the answer...

[fallen violet]

No

[tranquil pine]

#help-38 message

[fallen violet]

Well I’m finding someone else that can help

.close

[final saddle]

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[twilit basalt]

hey, anyone know what is meant when its said that "and arithmetic is modulo 2" ?

[twilit basalt]

prof didnt rly explain it too well and cant rly find anything online

[worldly vale]

think like how you add times on a clock

but there are only two hours

1+1=0

[twilit basalt]

cuz 2 mod 2 is 0 right

[worldly vale]

yes

just take mod after any calculation

[twilit basalt]

ok so ig ill try to see if 3. is a vector space.

we have vector $<1,2,3,1> and <2,2,2,2>$ as an example.

[soft zealot]

alep

[twilit basalt]

so when adding them, would i do smthg like:

$1+2 = 3 \rightarrow 3 \text{ mod } 2 = 0$

and then go on from there?

[desert mantle]

3 mod 2 = 1

[soft zealot]

alep

[twilit basalt]

sorry yes im stupid

what about for scalar multiplication?

or does the arithmetic modular concept only apply to addition

[desert mantle]

their notation isnt great but all entries of the vectors should be from H

so writing 2 or 3 inside a vector doesnt make sense cause those arent in H

[twilit basalt]

oh yes

i didnt get that

[worldly vale]

scalar multiplication can only be by 0 or 1 also

[desert mantle]

everything is just 0s and 1s

[twilit basalt]

is it even possible to make a vector that satisfies x + y = z * w with only 1s and 0s?

[desert mantle]

well play around a bit

[twilit basalt]

ah yes we can have <1,0,0,0>

and <0,1,0,0>

[desert mantle]

no

[twilit basalt]

yes

my brain isnt

[desert mantle]

1+0 is not the same as 0*0

[twilit basalt]

working

yea so i dont think any vector would satisfy the property he gave

unless im missing smthg

[desert mantle]

what about all zeros

[twilit basalt]

can we have two identical vectors?

[desert mantle]

I'm not sure what you mean. I thought you only want examples of vectors in U for now

[twilit basalt]

well to see if its a vector space, we'd wanna know if it can satisfy two properties

one of them being that

Adding any two vectors in U produces a vector in U.

[desert mantle]

oh you wanna check if this is a subspace

[twilit basalt]

yes

so i was asking whether we could add two identical vectors to check the property

[desert mantle]

there are three things you have to check for subspaces

dont skip the first one

space is not empty

[twilit basalt]

what are the three? the prof gave us two only

ok so the space is not empty is the one that applies to 3 im guessing

but how do we know its empty?

[desert mantle]

give an example of a vector in U

to show its nonempty

[twilit basalt]

for this one?

all 0s

[desert mantle]

ok

good so first property done

now addition

lets take two arbitrary vectors in U

lets call them u=<x1,y1,z1,w1> and v=<x2,y2,z2,w2>

what is their sum

[twilit basalt]

<(x1 + x2) mod 2, (y1 + y2) mod 2 ....>

[desert mantle]

yes but we dont really wanna bother with writing the mod and just do it implicitly

good what equality do you now have to check for that vector

[twilit basalt]

equality?

😅

sorry im rly bad w just working w unknown variables

but if we add then we'd have

[desert mantle]

we have to check that the sum u+v still satisfies the defining equation of U

[twilit basalt]

<(x1+x2), (y1 + y2)..>

[desert mantle]

namely that the sum of the first two entries is equal to the product of the last two entries

what is the sum of the first two entries of u+v

[twilit basalt]

(x1 + x2), (y1 + y2) ?

[desert mantle]

the sum of the first two entries

[twilit basalt]

(x1 + x2) + (y1 + y2) ?

[desert mantle]

yes

[twilit basalt]

sorry forgot to replace the comma

[desert mantle]

what is the product of the last two entries

[twilit basalt]

(z1 + z2) * (w1 + w2)

[desert mantle]

yes

can you multiply that out?

[twilit basalt]

$z1w1 + z1w2 + z2w1 + z2w2$

[soft zealot]

alep

[desert mantle]

ok we now have to check whether this is equal to x1+x2+y1+y2

[twilit basalt]

it doesnt

[desert mantle]

because u is in U, what do we know about x1+y1

[twilit basalt]

i think

[twilit basalt]

not sure honestly

no clue

[desert mantle]

u is in U and therefore satisfies the defining equation of U

so x1+y1 = z1*w1

[twilit basalt]

how so?

how do we know for sure that u is in U

[desert mantle]

.

thats how we chose u in the first place

[twilit basalt]

ah ok i see

so we just assume that u is in U?

is that why u said to arbitrarily choose vectors in u

[desert mantle]

we want to check whether U is closed under addition

for that we have to check whether the sum of two vectors in U is again in U

so we take two vectors in U and compute their sum and check whether it is in U

[twilit basalt]

ah yes ok i see

so thats the 2nd property satifisfied

[desert mantle]

no

[twilit basalt]

nice

😢

[desert mantle]

we have to check whether $x_1+x_2+y_1+y_2 = z_1w_1+z_1w_2+z_2w_1+z_2w_2$

[soft zealot]

Denascite

[twilit basalt]

i see

[desert mantle]

we know that u is in U and therefore x_1+y_1 = z_1*w_1

we also know that v is in U and therefore x_2+y_2 = z_2*w_2

what can we do with that information

[twilit basalt]

hmm

uh

we can conclude that the 2nd property isnt satisfied 😭

[desert mantle]

not so fast

why do you think it is not satisfied

[twilit basalt]

lets see

lemme look at the definition again

ok ill paste it here for reference

Adding any two vectors in U produces a vector in U.

yea i still have no clue

[desert mantle]

what do you get if you plug the two equations up there into this one

[twilit basalt]

$z_1 * w_1 + z_2 * w_2 = ...$

the rest

[desert mantle]

ok

can you simplify that

[soft zealot]

alep

[twilit basalt]

$z_1 * w_1 + z_2 * w_2 = z_1w_1+z_1w_2+z_2w_1+z_2w_2$

[soft zealot]

alep

[twilit basalt]

simplify this ?

[desert mantle]

yes

[twilit basalt]

you'd just divide by $z_1 * w_1 + z_2 * w_2$

i think

[soft zealot]

alep

[twilit basalt]

both sides

[desert mantle]

no

not divide

[twilit basalt]

uuhhh

trying to think

$z_1 * w_1 + z_2 * w_2 = z_1w_1 + z_2w_1 + z_1w_2 + z_2w_2$

[soft zealot]

alep

[twilit basalt]

no

havent done math in a while im sorry

[desert mantle]

we subtract z1w1 +z2w2 on both sides

what do we get

[twilit basalt]

$z_1 * w_1 + z_2 * w_2 = z_1w_1+z_1w_2+z_2w_1+z_2w_2$

[soft zealot]

alep

[twilit basalt]

just putting it here

for referenc

didnt simplify yet

$z_1 * w_1 + z_2 * w_2 + z_1 w_1 + z_2 w_2 = +z_1w_2+z_2w_1$

[soft zealot]

alep

[twilit basalt]

i think?

[desert mantle]

no

[twilit basalt]

ah

yea no clue then.. havent done the most basic math in a while

[desert mantle]

yes I noticed

you really need to work on your basics

this is impossible to do without them

[twilit basalt]

true

thanks for the help anyways

:D

[desert mantle]

so, when we subtract on both sides we get 0=z1w2+z2w1

this means this has to be true for all choices of u and v

but eg if we choose u=<0,0,1,0> and v=<0,0,0,1> then it is not true, the RHS is equal to 1

and as we notice, indeed u+v = <0,0,1,1> is not in U

we could have just given that counterexample from the start but sometimes it's not easy to find counterexamples so it's good to try to prove something to then know how you should choose specific values

[twilit basalt]

icic

yea that makes more sense

also , sidenote, when doing this arithmetic modulo 2 thing, does that only apply w addition or w scalar multiplication too

[desert mantle]

also with scalar multiplication

but because the only elements are 0 and 1 there isn't really any modular action happening there

[twilit basalt]

so for example <1,2> multiplied by constant 2

[desert mantle]

cause you never get bigger than 2 anyway

[twilit basalt]

we do 2 * 1 mod 2

and 2*2 mod 2

so <0,0>

?

[desert mantle]

yes

[twilit basalt]

alright, got it

thanks for the help again, much appreciated

:D

[desert mantle]

youre welcome

[twilit basalt]

.close

[final saddle]

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[gritty glen]

Need some help

[tranquil pine]

what part are u stuck with

[gritty glen]

Number 2.

[tranquil pine]

what have u tried

[gritty glen]

Im getting

{1….8}

As my union

[tranquil pine]

nope

oh

yes as ur union

whats the complement of that

[gritty glen]

Gimme a sec

{9,10}??

[tranquil pine]

yes

[gritty glen]

Can you check some of my questions

[tranquil pine]

sure which

[tranquil pine]

why is the last one not onto

[gritty glen]

Integer y in the codomain has no integer x

This one as well

[tranquil pine]

what integer cant you map in your codomain?

[gritty glen]

F(x)=0

[tranquil pine]

oh ic

its N not R

[gritty glen]

Is that right??

[tranquil pine]

this one im not so sure

what does it mean by bitstring

[gritty glen]

Are you sure on this one

[tranquil pine]

yeah these are all correct

[gritty glen]

Do you know binary??

[tranquil pine]

yes

[gritty glen]

Bits and bytes

[tranquil pine]

but what is meant by bitstring of the set

is it a 1 if the element is in the universal set?

or ?

[gritty glen]

Lemme check the book

Bitstring is a binary representation of a set

[tranquil pine]

well how did you get ur solution for the bitstring of A?

I would have wrote like 11011001

[gritty glen]

The ith bit from the right represents presence or absence of the ith element

1 and 3 are correct right

And the middle one is {9,10}

[tranquil pine]

ok then ur solution is wrong

[gritty glen]

Hmm k

[tranquil pine]

3 is wrong

[gritty glen]

How?

[tranquil pine]

is A intersect D is the empty set

how is 6 an element of D

[gritty glen]

Wait its {7,5}?

[tranquil pine]

no

[gritty glen]

It has 2 elements

[tranquil pine]

yes.

What does A intersect D = empty set eliminate as answer choices?

[gritty glen]

Js a sec

It would eliminate {7,5}

[tranquil pine]

no

A intersect D = null set means what in english?

[gritty glen]

Its an empty set

[tranquil pine]

not quite

what does intersect do fundamentally?

[gritty glen]

Finds the common

[tranquil pine]

yes

so A intersect D = null set

means?

[gritty glen]

Finding common?

[tranquil pine]

null set means an empty set

[gritty glen]

Yes

[tranquil pine]

so what commons do they have?

(none)

[gritty glen]

Oh how would write that

[tranquil pine]

A and D dont share elements

[tranquil pine]

huh

[gritty glen]

Its A u C

[tranquil pine]

what

[gritty glen]

How would d be involved

Wait nvm

Looking at the wrong question smh

[tranquil pine]

Its $D \cap A = \emptyset$

[soft zealot]

hibyehibye

[tranquil pine]

so what answer choices does that eliminate?

[gritty glen]

A thru D

[tranquil pine]

urm no

what elements must NOT BE in D

[tranquil pine]

based on thus

this

[gritty glen]

Nothing

Empty set

[tranquil pine]

okay so A intersect D = empty set

means every element in A ISNT IN D

so what elements arent in D?

[gritty glen]

1,3,4,5,6

[tranquil pine]

yes and ur answer choice has a 6

meaning its wrong

[tranquil pine]

what numbers are we left with

[gritty glen]

^^^

[tranquil pine]

no

1,2,3,4,5,6 are not in D

What numbers are left

[gritty glen]

7,8,

9,10

[tranquil pine]

theres more

yes

7,8,9,10 we are left with

can it be 8?

[gritty glen]

No

[tranquil pine]

ok we are left with 7,9,10

[gritty glen]

Yea

[tranquil pine]

we can eliminate one of them based on the first statement

D is a subset of B union C

which one can we eliminate?

and why

[gritty glen]

10?

[tranquil pine]

why

[gritty glen]

Because it is included in the set

[tranquil pine]

huh

is 10 a subset of B union C?

is 9 a subset of B union C

[gritty glen]

No its 7

[tranquil pine]

is 7 a subset of B union C

[tranquil pine]

why

first tell me what B union C is

[gritty glen]

{6,8}

[tranquil pine]

no

what is $B \cup C$

[soft zealot]

hibyehibye

[gritty glen]

Why is it not 6,8

[tranquil pine]

do you know what U is?

[gritty glen]

Set

[tranquil pine]

no

union

[gritty glen]

Union

[tranquil pine]

it joins two sets

[gritty glen]

Yea those 2. Circle thing

And the thing between

[tranquil pine]

so what is B U C

[gritty glen]

6?

And 8

[tranquil pine]

no

thats intersect

union is joining

i have to gtg u can probably close and reopen this channel

andnsomeone can help u

[gritty glen]

Alr no problem

Thanks for helping

[final saddle]

@gritty glen Has your question been resolved?

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[chilly anchor]

We consider the next 5 births that will take place in the hospital.

What is the probability that there will be more girls than boys?

[chilly anchor]

It is a simple problem and yet, I can't calculate this

[tranquil pine]

the probability that there will be more girls than boys is the same as the probability of more boys than girls

[chilly anchor]

yes which is 0.5

[tranquil pine]

no

[chilly anchor]

the solution is 16/32

[tranquil pine]

so the answer is (1 - "probability that there are same boys as girls")/2

oh 5 births so yeah there aint no way that there are same boys as girls so its (1/2)

whats the problem

[chilly anchor]

The exact calcul

Like the answer is obvious, but I don't know how to get it with math

[tranquil pine]

P(more girls) = P(more boys)

[chilly anchor]

yes

[tranquil pine]

P(more girls) + P(more boys) + P(same) = 1

P(same) = 0

2 * P(more girls) = 1

P(more girls) = 1/2

[chilly anchor]

omg this is basic math, what am i becoming

thx

.end

.close

[final saddle]

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[final saddle]

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[gritty glen]

Need help plz

[dry light]

Are those vectors

Recall that $u \cdot v = |u| |v| \cos(\theta)$

[soft zealot]

Umbraleviathan

[gritty glen]

Yes

@dry light

[dry light]

You know cos(θ) = 0.6

Let u = <a,2> and v = <2,a>

Then u • v = 4a

[silk saddle]

wow are we doing physics here

[silk saddle]

too much help

[dry light]

Banned

You can find |v| and |u|

[silk saddle]

just find the modulus of the vectors each

yeah its not too difficult

and then take the dot product

[gritty glen]

Wdym modulus

[dry light]

Magnitude

Another word

For it

[gritty glen]

This is for linear alg

Lol

I got 3.27

[silk saddle]

Yeah

[gritty glen]

Buts that not what the answer is

[silk saddle]

!show

[final saddle]

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

[dry light]

Yeah you just take the magnitude of the vectors

[dry light]

That's what |u| means

[gritty glen]

4a / (sqrt(a^2 + 4) * sqrt(4 + a^2)) = 0.6

[dry light]

Magnitude of u

[gritty glen]

this is my equation

[dry light]

You do realize that $\sqrt{a^2 + 4} \sqrt{4 + a^2} = a^2 + 4$

[soft zealot]

Umbraleviathan

[gritty glen]

Yes

[dry light]

$$4a = 0.6a^2 + 2.4$$

[soft zealot]

Umbraleviathan

[dry light]

It's just a quadratic at this point

[gritty glen]

Got 2/3 and 6

So 2/3 doesn’t work right as a solution

[dry light]

It's not an option

It probably does work but your answer choices doesnt have it

It does have the other

[gritty glen]

Could you check if this is correct

[ivory grove]

yes it is

[gritty glen]

Ty

[final saddle]

@gritty glen Has your question been resolved?

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[tranquil pine]

How do I find the derivative of 9/x using the formula?
I get to (9/x+h - 9/x ) / h

[tranquil pine]

But how can i simplify that?

I mean the formula lim h->0 (f(x+h) - f(x)) / h

[rain compass]

$\frac{\frac{9}{x+h}-\frac{9}{x}}{h}$?

[soft zealot]

maximo

[rain compass]

how can you add the fractions on top?

[tranquil pine]

put each term over common denominator x(x+h)?

[rain compass]

yes

[tranquil pine]

-9h/(x^2+xh) / h

[rain compass]

yes. do you know how to divide fractions?

[tranquil pine]

-9h/(x^2+xh)h
Factor out h
-9/(x^2+xh)
Sub h=0
-9/x^2

[rain compass]

yes

[tranquil pine]

great. thx

[final saddle]

@tranquil pine Has your question been resolved?

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[stoic mural]

Not familiar with the notation

Yeah I am hearing that in university right now but we use different notation

[rain compass]

consider (-.99)^2 and (-.98)^2

you'll notice as you get closer to -1 from the right, you approach 1 from the left

(-.99)^2 = .9801

(-.98)^2 = .9604

as you approach -1 from the right

x^2 approaches 1 from the left

no

im saying as you approach -1 from the right

so -.97

-.98

-.99

x^2 tends to 1 from the left

.9604

.9801

...

1-.99 = .01

1-.98 = .02

1-.97 = .03

as you approach 1 from the left, 1-x approaches 0 from the right

[final saddle]

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[sterile violet]

So I have to simplify K until it gives me 12 which is the answer given

knowing that N is different from 1

and that I have done this

I have simplified as much as I could, I put everything in base 5

except for that "7" I got

and all of the 5s have square root of "n-1" but i don't know how to use that in my favor

so I'm stuck at that point

[supple mantle]

Hmm

Is that x in between 35 and 5 a multiplication or is it the symbol "x"?

[sterile violet]

it's a multiplication

not an unknown term

I got confused by that too

but it's just the multiplication symbol

the only incognita is "n"

have you figured it out @supple mantle ?

I'll keep trying

So I separated the addition and worked in them sepparately, I advanced a bit but still no result

ok it's not "1" It's 5, I'm dumb

so it's 5 + 7 times something

so if the answer is 12

then that "something" gotta be 1

I gotta make the 5 term

a 1

5 elevated 0

so I got to make it 0

how am I going to do that? xD

[supple mantle]

Well

5^1 means what?

[sterile violet]

5

[supple mantle]

Okay

[sterile violet]

Idk why I put 1 xD

sorry

[supple mantle]

5^-1 means what?

[sterile violet]

1/5

[supple mantle]

Or 5/(5^2)

Now 5^0?

[sterile violet]

that's 1

[sterile violet]

this 1/5

[sterile violet]

this 1

[supple mantle]

Yep

So 5^0 * 7 + 5?

Wait

[sterile violet]

hmmm

that's 12

so I gotta make the exponent of the 5

a 0

and idk how to do that

hmmm the term above

[supple mantle]

Hmm

[sterile violet]

a 0

si the term above, a 0

[supple mantle]

Don't complicate yourself

First

The denominator is a $5^{\frac{-n-1}{n-1}}$ right?

[soft zealot]

VulcanOne

[sterile violet]

ammm

it's 5 elevated

n+1 / n-1

[supple mantle]

Yep

That's in the denominator

But we can use exponent properties

[sterile violet]

when passed above

[supple mantle]

And make that go up

[sterile violet]

yeah it would be

what you wrote

[supple mantle]

Yep

Now that term is throughout the whole expression

Which means it is multiplied by it

Right?