help-17

[spiral turtle]

No problem, just I'm a little bit confused, so unless you're confident I'm hesitant to let you go at this point

Just want to make sure I understand the terminology (full vs partial) in use here

Before I potentially lead you astray

[polar vine]

Sure...

[spiral turtle]

Full functional dependency

A full functional dependency is a type of functional dependency where the dependent attributes are determined by the determinant attributes. For example, in the database of employees, the employee ID number fully determines the employee’s name, address, and other personal information.
Partial functional dependency

A partial dependency is a functional dependency where the dependent attributes are partially determined by the determinant attributes. For example, in a database of employees, the employee ID number may partially determine the employee’s address, but not the employee’s name or other personal information.

From some random website

Here a, b, and c are the determinant attributes. And d, e, f, g are the dependent attributes.

Well actually f seems to be both a determinant and a dependent attribute

[polar vine]

Sort of yeah

[spiral turtle]

f is determinant with respect to d, and is dependent with respect to some subset (perhaps not proper) of a, b, c?

The more I'm reading the more I am confused.

[polar vine]

Ah hold up this is aligns with my def

If there is no proper subset of set A which also determines B, then A={a1, a2, …, an}
 B is a FULL
functional dependency, otherwise, if there is proper subset of A determines B, then it is PARTIAL
For example, STUDENT_ID+AGE
 NAME is a partial FD, because STUDENT_ID alone is also
determines NAME, including AGE into the set A is unnecessary.
On the other hand, DEPT_ID
 DEPT_ADDRESS is a full FD.

[polar vine]

Yeah

[polar vine]

Seems so..

[spiral turtle]

It's actually directly contradictory to the one I posted

[polar vine]

For partial dependency it's different yeah.
Mb

[spiral turtle]

A partial FD is partial because it's not fully specified according to the definition I posted.

A partial FD is partial because it's over specified according to the definition I posted.

However, I would say "use the definition you were given, as this is what you will be tested on."

Thankfully, this was the definition that I originally inferred when I wrote my comments above.

I appreciate you sticking around!

[polar vine]

Cool Thank you very much!!

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[limber oak]

when should I use geometric mean?
I can understand arithmetic mean, but I have hard time understanding on geometric mean on it's real use

[worldly bluff]

I personally can't think of any real-life applications of the geometric mean, though I'm sure if you look it up there are plenty out there

It is present in inequalities, though

If you do olympiads or math problems related to inequalities, you'll see AM-GM a lot

[limber oak]

yeah..., I can see how it used on mathematical use. but can't really understand it in simple way for real world use...

[full ferry]

ive seen a video that explains the commonly used means and its real world uses before somewhere on youtube, cant find it though

[limber oak]

hmm...

[full ferry]

https://youtu.be/V1_4nNm8a6w?si=p97MPDDyuQdgR5UD

[signal granite]

Hello guys, I just joined the math group, nice to meet yall 😄

[full ferry]

i feel like ive seen another one... but this one works

[limber oak]

thx!

[spiral turtle]

Geometric means are useful when you're averaging over things that are exponential in nature. For instance, if you have two lights, and you want to pick a light that is midway between the brightness of the two, that's a job for geometric means, because perceived brightness is not additive but multiplicative.

In other words, 100 units of brightness looks roughly twice as bright as 10 units.

[bronze osprey]

one practical example is noise level, measured in decibels!

[spiral turtle]

Harmonic means are interesting as well, if you want to select a car that has halfway as good mpg as the two other cars, you would be wrong to use the arithmetic mean, and should use harmonic means instead.

[bronze osprey]

every 10 dB means that the sound becomes twice as loud

[spiral turtle]

(this is because the units of mpg are "backwards")

[bronze osprey]

so when you are working with multiplication like this, geometric means are the equivalents of the arithmetic mean

[limber oak]

hmm.... that is interesting 👀

[signal granite]

are electric or magnetic field also an example? because they depend on the inverse square law, if they are far then their strength is low, and if they are close they get really strong.

[bronze osprey]

so the average of 60 dB and 80 dB is 70 dB

which would be sqrt(1 * 4) = 2 times louder than 60 dB, as we expected

and not (1 + 4)/2 times louder

[bronze osprey]

absolutely

that's also an example, but it's not quite exponential

[limber oak]

thx all ❤️

[bronze osprey]

it's a good example of practical non-linear behaviour that is still neat

[bronze osprey]

no worries!

[bronze osprey]

yeah like lmao

[spiral turtle]

Oh man, I haaaaated problems like this one in school before I figured out how to think about them

[signal granite]

same

[bronze osprey]

oops I replied to the wrong one

this is the harmonic mean ofc

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[forest crypt]

please someone help me. this is like my third time asking. I still cant figure it the function for the part above the xaxis. i need to model the shape. I was thinking about cutting it as seen in pic 3 and just do piecewise off of that but i just cant do it can someone please help me find the f(x) im fking echausted

[forest crypt]

this almost worked but some parts dont work at all so can someone pls jst help me

[spiral turtle]

@forest crypt lagrangian polynomial + Chebyshev nodes

This should get you a single, albeit long, polynomial of high degree that closely interpolates your curve.

[forest crypt]

i rlly tried everything ig my brain is too friend rn to figure otu what im doing wrong ik this is bitchy and its fine if not possible but could u help me just slightly to find at least the first step of how to do it

cuz im just so tired istg

[spiral turtle]

If you give me the min and max of the domain of the curve (the min x and max x where you want the curve to go to) I can give you the chebyshev nodes. Then you can tell me what point is on the curve at that node, and I can give you back the polynomial

[forest crypt]

x min is 0 x max is 48.7

[spiral turtle]

Ok one moment

I'm going to use 17 nodes because that is how many you have currently. But because your curve has a large slope right up to the edge, it might need more.

[forest crypt]

just tell me whatever will help you help me and ill get it done

i really need all the help because i just cant get this alone atp

[spiral turtle]

[0.10387292407674523, 0.9295459143385062, 2.5527743516167156, 4.9182811402082685, 7.945511786280757, 11.531377584452155, 15.553766179891879, 19.875699957965466, 24.350000652455734, 28.824301324727404, 33.14623503690183, 37.16862352500594, 40.75448917806046, 43.7817196461766, 46.1472262300324, 47.7704544427675, 48.59612719632533]

Can you get me the points at these x coordinates?

They do not need to be exact

Just let me know where you actually sample from in your list of points

@forest crypt

Sorry about the delay, I am on my phone on my bed being insomnia man, and I couldn't find an online tool to generate these points, so I had to log into my computer remotely via my phone and write a short python script to do it.

[forest crypt]

lord bless u fr, if it makes u fele better im a crying mess rn

[forest crypt]

give me a. moment

[forest crypt]

i mean as seen in the tbale i just estimated them

[spiral turtle]

Which is fine

[forest crypt]

sorru im dumb rn so instead of x values on the table i insert what u gave me right?

[spiral turtle]

Yes exactly

And let me know the y values corresponding to the x values

[forest crypt]

ok give me a momenr pls

[spiral turtle]

Take your time

[forest crypt]

this is wrong, right?

[spiral turtle]

19 and 37 are written wrong

[forest crypt]

shit

[spiral turtle]

You forgot the decimal

[forest crypt]

yea

the y axis is the same as last time tho

uhm let me see if i cando smth

[spiral turtle]

You don't need to put these points into desmos unless it helps you find the y points

[forest crypt]

im sorry im a mes si can figure it out

cant

its fine you dont havr to help me

[spiral turtle]

Well, I can't actually get the y coordinates from the image or else I might.

Well, once you get them, you can plug the points into this: https://www.dcode.fr/lagrange-interpolating-polynomial

[forest crypt]

im plugging the x values but idk how to get the y values

its just giving y =0

i mean y max is 18.7 i think

thats akll i know

[forest crypt]

ok so once i get the y values , i insert them here and i should get the f(x)?

wait i might be able to do it

nvm i give up

im sorry

i justgot this but i dont think its corret

oh its just copying ir wtf

nvm

thanks nevertheless ig

[spiral turtle]

I'm sorry you were having trouble

Best of luck

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[true gale]

im not sure how i should go about solving an exercize like this, I tried detemening the possible ranges, but it is getting me nowhere. I assume that some numbers will have a circular like pattern, but I dont see how that helps me determine what happens for all numbers < -3/2, I also wrote a program that can take a number and give you the awnser for x iterations, but i still dont see how to find a behaviour(s) that is true for numbers <-3/2

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[alpine zealot]

anyone know how to prove 8b

[paper depot]

prove each half of the ineq separately

[alpine zealot]

u mean a/b<a+c/b+d and a+c/b+d<c/d?

[sharp shell]

Yeah thats what he means

[alpine zealot]

bet

i just solved a/b<a+c/b+d and got a/b<c/d

could that just be it

[foggy rune]

cb > ad
to prove $\frac{c}{d} > \frac{a+c}{b+d}$:
$cb+cd > ad + cd$ which means:
$c(b+d) > d(a+c)$
$\frac{c}{d} > \frac{a+c}{b+d}$

[twin meteor]

1013

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[nocturne trout]

what is happening here?

[nocturne trout]

what is happening here?

[knotty pulsar]

helo

help me solve the differential equation

[rapid anvil]

This channel is taken

[knotty pulsar]

what do you mean

[rapid anvil]

Someone else has asked a question in this channel

Please use a different one

#help-9 perhaps

[rapid anvil]

Looks like they divided through by $\frac{\pi h^2}{4}$

[twin meteor]

user95040

[rapid anvil]

Then swapped the right and left side

@nocturne trout

[nocturne trout]

divide both sides by pih^2/4?

[rapid anvil]

Sorry

I mean multiply by 4

Then divide by $\pi h^2$

[twin meteor]

user95040

[nocturne trout]

multiply both sides by 4

hm

[rapid anvil]

Ok like denote dV/dt as V' and dh/dt as h'

We have V' = (pi h^2)/4 h', multiply by 4 to get 4V' = pi h^2 h' then divide by pi h^2 to get 4V'/pi h^2 = h'

Then pull V' out of the fraction so we have 4/(pi h^2) V' = h'

Flip lhs and rhs

[nocturne trout]

I got it, thanks!

[rapid anvil]

So h' = 4/(pi h^2) V' as required

No worries

[nocturne trout]

/done

/end

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.close

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[rapid anvil]

Use that - Good luck with your studies!

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[buoyant veldt]

what does the lim thing mean again

essentially how do i solve this?

[paper depot]

simplify the expression until plugging in x=-2 no longer results in a division by zero, then do that

[buoyant veldt]

factorise numerator

then sub in x=-2

righty

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[paper depot]

yes essentially

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[hushed nexus]

If there is an event in the sample space, doesnt it mean that it has some probability of happening?

[calm pecan]

huh

[dark kiln]

no

[calm pecan]

you sure there isnt an error in the marking

that seems reasonable

[dark kiln]

like you have events A B C mututally disjoint

that's the sample space

then B | C is event

and A & B is event

but also ~A & ~B & ~C is event

[calm pecan]

hm sure

[dark kiln]

A & B has no chance

[hushed nexus]

well the reasoning says that the answer is debatable upon cuz one of the testing agency says its A other says its B

[dark kiln]

your answer is right

i just don;t understand the explanation

[calm pecan]

if this is from the marks app or something similar id disregard it since there's lots of errors there sadly

[hushed nexus]

but i am sure t can only be A

[calm pecan]

your answer appears fine

[dark kiln]

yeah i'm confused, nvm

[hushed nexus]

Well, they used gemoratrical probhability to dissprove it

[calm pecan]

huh

show me

[hushed nexus]

so i want to know what is the errror in using gemotrical probability then?like I kind of understand that prrof too

i will send one sec

[calm pecan]

im waiting

[calm pecan]

the what

[hushed nexus]

i will go with A as its more official of an anwer, but is this way of dissproving with geometrical probabiliy okay?

[calm pecan]

whats the wire shit

also yeah of course nta is right here, for once lmao

[hushed nexus]

they considered an example

[calm pecan]

you just think of $P(E)$ as $\frac{n(E)}{n(S)}$ and there isnt much room for doubt

[twin meteor]

Percy

[calm pecan]

i dont understand this schpiel at all

[calm pecan]

also maam portion hua?

[hushed nexus]

so like there is still a point at 0.5, and thats why there is still a probability of it occuring?

[hushed nexus]

huh?

[dark kiln]

wtf is nta

[calm pecan]

testing agency

for those of us who like to suffer

[hushed nexus]

thats a testing agency in India (official) who take jee and neet exams

[calm pecan]

uh, syllabus lol

'portion'

i should be studying since i havent done shit but im just helping people here for warmups

[hushed nexus]

oh, syllabus completed, i am giving random year tests

[calm pecan]

yeah i mean as far as i understand you're defining the sample space as [0,1] and that definitely does have 0.5 in there

[calm pecan]

owfoiqwef jealous

[hushed nexus]

that's what i think too, might ask my teacher when i can tho

[calm pecan]

im so bad at my math lol + coord nahi padhi

[calm pecan]

yeah definitely

it's weird

again, if it's marks, might be worth just disregarding it

[hushed nexus]

coordination toh maine bhi dhang ki nahi ki, bas chale aisi ati hai TT

[calm pecan]

there's a pyq from this year (which makes it not really a pyq) but basically there's some circuit which could be either NAND or NOR and there's both in the options :D

and har source pe same options and same answer

i mean i checked mathongo marks and esaral

toh yeah somebody makes a mistake and saare just copy it

[hushed nexus]

yup nta ke bohot lafde hote hai and trusting online source is out of question

[calm pecan]

yeah i need to get it functional at least, but just 6 ish days and id rather work my way through phy-chem backlog 😭

wait can i add you

[hushed nexus]

so for now, i got with nta cuz uska jo maan kare woh wo karta hai

[calm pecan]

you're getting the rants

:D

[hushed nexus]

yh yh you can 🙂

[calm pecan]

yeah prolly the best for now if you want a percentile lmao

[hushed nexus]

yes

[calm pecan]

maybe leave it on just in case someone else has something

if you have another question later though just close this before

[hushed nexus]

. close

.close

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[stiff fossil]

How do you differienate Sigma notation in Calculus

[stiff fossil]

to find the gradient

[paper depot]

can you show exactly what function you're looking at

sigma notation means addition and so generally you just take the derivative of each term, but do show it still

[stiff fossil]

ye I know

[green crow]

It's as she said. Differentiate each term

[stiff fossil]

oh thank you

[green crow]

Another way, x³ is a constant wrt to the sigma, so u can pull it out of the sigma

[stiff fossil]

oh, ok

thanks

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[ionic dew]

i need help in phsyics math question

[atomic jasper]

!da2a

[vocal sleet]

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/

[ionic dew]

ok so im stuck in a phsyics question

can i state the question?

[queen root]

yes

[ionic dew]

an inclined plane with 65 degrees to the horizontal is in a park. The ramp is 5m long. A ball of mass 57kg rolls down the incline, assuming theres no friction, cakculate the net force

[atomic jasper]

did you make a drawing?

[drowsy hatch]

is that the complete question

[ionic dew]

yes

[ionic dew]

yes

[atomic jasper]

!show

[vocal sleet]

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

[ionic dew]

i already calculated the weight force, magnitude of normal force

the question is asking to calculate net force

[leaden ingot]

to calculate net force, you first calculate net force on horizontal axis, then net force on vertical axis

[ionic dew]

wdym? do i add the forces together?

[calm pecan]

yes

[leaden ingot]

... not exactly "adding"

it would be true if it's vector

but i mean, come on, we care about the value (and the direction, but we'll get into that later)

[ionic dew]

so i calculated the mg cos 65 and it was 236.1N
weight is 558.6N

[drowsy hatch]

no friction btw

[ionic dew]

normal force is 236.1N, weight force is 558.6N, acceleration down the slope is acceleration is 8.88ms-2

so to find net force? what do i do?

[drowsy hatch]

forces are vectors right

[ionic dew]

i think so

[drowsy hatch]

so they have to undergo vector addition

for that break all the forces into its components

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@ionic dew Has your question been resolved?

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[calm pecan]

just give me hints

[calm pecan]

i tried doing some vector analysis shit, but it really doesnt amount to anything
all i know is that the triangle is equilateral so all angles are 60

and the area can be given by $\frac12 QR^2 \sin(60^\circ)$

[twin meteor]

Percy

[calm pecan]

other than that im out of ideas

ping me

[atomic jasper]

make a drawing

[calm pecan]

vector analysis gives me like $|\vec{PQ} \times \vec{PR}| = 2\sqrt{3} \vec{PQ} \cdot \vec{PR}$, but as i said, i don't think that amounts to anything

oh for fucks suck

[twin meteor]

Percy

[calm pecan]

what am i supposed to be seeing

[atomic jasper]

thats what the drawing is for

if there is something to see

(usually there is)

[calm pecan]

i did some geogebra (the angle isnt exact but its good enough)

nothing jumps out at me

im shit at geometry though so i dunno

[hushed nexus]

Try drawing on paper and marking the angles

[calm pecan]

i doubt it's euclidean geometry though, i mean, the closest thing this course has is analytic geometry and linear algebra

[calm pecan]

;-; you sure there's a point? software is usually much better than me

[atomic jasper]

paper is faster usually

[calm pecan]

yeah but nothing jumped out at me when i did that so i did the software and now im clueless but with confidence

[hushed nexus]

Try doing it on paper, it will help

[calm pecan]

;-; alrighty

lets see if it does

alrighttttt how do i draw this

ugh

[atomic jasper]

dont worry too much about it being exact

its just a sketch

[calm pecan]

i had just a sketch 😭

okay let's say i have a sketch

(i have like 4)

and geogebra

what now

ykw ill come back here i cant do this shit rn

.close

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[rain sinew]

does anyone know how to answer this?

[rain sinew]

its vectors

[paper depot]

,rccw

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@rain sinew Has your question been resolved?

[rain sinew]

i have the answer but idk how to get to it

[drowsy hatch]

use section formula

[rain sinew]

what’s that

[drowsy hatch]

formula that gives us a point which divides a given line segment in given ratio

[rain sinew]

oh? what’s the formula?

[drowsy hatch]

or a given vector in a given ratio ( which is needed here )

[drowsy hatch]

its easy you can just watch a 5 min video on youtube

[rain sinew]

this was my working out

but it ended up being wrong

i equated both equations cus they equaled to each other

[drowsy hatch]

idk much

all i know about this is the section formula may help

i dont really like vectors to begin with

[rain sinew]

same

oh it’s fine i got it

i just did it my way lol

.close

[vocal sleet]

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[honest mirage]

does Clairaut's Theorem count for any combination of derivatives?

[honest mirage]

I cant make partials here, but does d/dtheta* d^2f/dr^2 = d^2f/dr^2 d/dtheta

or any combination of those

essentially when there isnt any symmetry and both arent sqaured or something similar

[flat whale]

you can just treat $f_r = g(r, \th)$

[twin meteor]

riemann

[vocal sleet]

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[rapid flume]

So they are asking the reading of the voltmeter. In the solution they have mentioned current flow through 10 ohm is zero.What's the reason behind that? (I'm at 11th..hoping some easy explanation)

[worldly gale]

The current flows from both 5V cell and 30V cell, but in opposite direction

So it will cancel out

[rapid flume]

Makes sense!..but how would you know if they are equal?🤔

[worldly gale]

we will have to calculate that

but here its mentioned in the question itself

Because we need to calculate the potential difference between the points a and b

[rapid flume]

Can you please elaborate?

[worldly gale]

The question asks us to calculate the reading of voltmeter right?

[rapid flume]

Yeah

[worldly gale]

and what does a voltmeter calculate?

[rapid flume]

But my qestion is why I1 and I2 are equal

[worldly gale]

I1 and I2 are not equal

[rapid flume]

The voltage difference..i got that point

[rapid flume]

Then how will they cancel out?

[worldly gale]

I1 AND I2 ARE NOT CANCELLING OUT

[rapid flume]

You mentioned that earlier

[worldly gale]

I1 flows in the loop with the 5ihm and 4 ohm resistor, not the 10 ohm one

[worldly gale]

I didn't say that I1 and I2 will cancel out

And I2 flows in the loop with the 2 5 ohm resistors

[rapid flume]

Oh I can understand now..thank you

[dark kiln]

there's no circuit that includes 5V

i don;t get it whatever

ok i see, there is current in 5V

[rapid flume]

How!?

[dark kiln]

right, there isn't but it's for some other reason

idk what i'm looking at

[rapid flume]

Oh what's that?

[dark kiln]

i don't know lol

[rapid flume]

It's okay

Its clear to me now

The I1 that coming from the loop1 is going back to loop1..so no current is going through the 5V (according to KCL)..same with I2..hence there is no current in 5V💁‍♂️

[vocal sleet]

@rapid flume Has your question been resolved?

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[jolly mortar]

since my channel closed..

[oak magnet]

Make a sign table

[jolly mortar]

like the number line

?

<---------(-3/4)-----(-2/3)------0------------------------------6>

[oak magnet]

How do you know which part is the solution interval ?

[jolly mortar]

if its less tham 0-

[oak magnet]

So which interval ?

[jolly mortar]

i thoight

i choose a number betwen

to see if iti fits

when i plug in that number

[oak magnet]

Have you already seen someting like this ?

[jolly mortar]

no

[oak magnet]

May i explain it ?

[jolly mortar]

ok

[oak magnet]

So see your product of term ?

Each line will be for one of them

So you start by (4x+3)

It is 0 when x = -3/4

For x -6 =0 <=> x = 6

For 6x+4 = 0 <=> x = -2/3

Ok

Once you have the zero for all

You put them on the top of the table in the same way you would put on the real line

[oak magnet]

As you did here

So far so good ?

[jolly mortar]

es

[oak magnet]

So now you draw a vertical line below each of x value you found

As in the picture

[jolly mortar]

IM SORRRYY im confused a bit

[oak magnet]

By what ? Tell me

And don't be sorry

[jolly mortar]

the sign chart, i think i jave saw it but like i forgot the main rules

[oak magnet]

Main rules are you find the zeros of all terms in the product

And then for each line there will be a term of your product

And then you put on this line, the sign of your term depending the real line you have above the chart

[jolly mortar]

yes

can you make one out

[oak magnet]

Sure

[jolly mortar]

what do the circles reprwsent

[oak magnet]

Where the term of the line is 0

Thoses are 0

Ideally

And so now whats missing are the signs in the empty case

[jolly mortar]

now i get the 0s

how can u tell if they output will be - or +

[oak magnet]

Do the sign of the three term and put it in line

Since 4x + 3 is increasing

[jolly mortar]

so the number line i made

[oak magnet]

It will be - and +

[jolly mortar]

examlke

can u give an example

[oak magnet]

Well for the first line you have the term 4x+3

So the sign on the line will be - + + +

Cuz it is increasing

Going from negative to positive at the 0 point

Which is when x = -3/4

[jolly mortar]

how do u know this

[oak magnet]

Thats a linear function

[jolly mortar]

im really confused i just do the number line

i just want to know a number -3/4 ane -2/3

[oak magnet]

Well, sum both and divide by 2

Thats the number in the middle

[jolly mortar]

hmm

i got 0.125

[vocal sleet]

@jolly mortar Has your question been resolved?

[jolly mortar]

well!

<@&286206848099549185>

ok cus]

my prof say that this is the ansser

but isnt the ineq

including

also how did he get -2

isnt it -5

[oak magnet]

Root of the polynomial

[jolly mortar]

cus the bottom factored is

[oak magnet]

On the denominator

[jolly mortar]

(x-5)(x+2)

OHHHH

HIU2FBWOIGVOIWELVB

why i forgot i have toswiytch the signs

bbut still

wouldnt u have to use brackets

[-2,5]

instead of the parenthesius

[vocal sleet]

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[oak magnet]

It include the value

But you can't else you divide by 0

[vocal sleet]

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[tacit orchid]

what would be my null hypothesis here and my h1? i can't seem to get them and i dln't know if i've done this question correctly

[vocal sleet]

@tacit orchid Has your question been resolved?

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[gentle jewel]

Hi there, I have this problem and I have been stuck for a while on it. It is sparx maths and am in year ten. I have tried watching the video, done that method and it doesn't seem to work. If somebody could walk me through this that would be greatly appreciated

[vocal sleet]

@gentle jewel Has your question been resolved?

[gentle jewel]

Gtg now

.closs

.close

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[fervent matrix]

yo wassup guys, what do they mean by question 1? isnt that just where i multiply the rows and columns ?

[fervent matrix]

so it'll be 2x1?

[lone linden]

They want the dimensions

[lone linden]

so yes this

Note that you're not rlly "multiplying" the rows and columns

the x doesn't mean multiplication here

[fervent matrix]

i am on q2

yes

it is the format

rowsxcolumns

what do they mean I is identity matrix

[half solar]

help

[vocal sleet]

@fervent matrix Has your question been resolved?

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[fervent matrix]

is question 4's answer 44?

[dusty marlin]

@fervent matrix !noclopen

!noclopen

[vocal sleet]

Please don't repeatedly close and claim a new channel with the exact same question. This erases all previous progress made towards your problem and is confusing for helpers, making it more difficult to help you. Please be patient, even if your channel has not received much attention.

[fervent matrix]

bro its a new question

just a different problem

tf

[dusty marlin]

…oh

[fervent matrix]

i asked about q1 before

now i am on q4

[dusty marlin]

My bad

[fervent matrix]

no problemo man

[dusty marlin]

I can’t help you with the problem, however. I haven’t started Linear Algebra yet

[fervent matrix]

crazy bre

its matrices

or matrixes

[sweet phoenix]

by double do u mean 2A

if so its not 44

its actually 0, a singular matrix

[vocal sleet]

@fervent matrix Has your question been resolved?

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[coral orchid]

how

[polar nymph]

Algum brasileiro?

Boa Noite!

[hollow sundial]

you're given a side length and angle in a right triangle

that means you can solve for all sides

[vocal sleet]

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

[barren ether]

👍

[vocal sleet]

@coral orchid Has your question been resolved?

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[pseudo root]

Hello i need some help with a math problem, its very easy math (not to me i feel dumb) but there is an issue it is in swedish... here is the picture. basically it shows what happens when you dilute medicine. Its according to that triange. ÖS means wished substance (styrka) , volume (ML) means ammount of substance and läkemedel (VS) means active substance. I need help because acording to the triange VS devided ML should be the ÖL but in the last picture it shows 2mg/ml but 100/100 is 1? im so confused :(

[sweet phoenix]

what i think it means is the 100mg substance is diluted

the volume stays the same

but the concentration has changed

idk i dont do chemistry sorry

[vocal sleet]

@pseudo root Has your question been resolved?

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[vast shale]

Could i ask a boolean algebra question?

[vast shale]

Im trying to understand how the first line is equivalent to the second line

[edgy gulch]

A XOR B = ( NOT(A) AND B ) OR ( A AND NOT(B) )

[edgy gulch]

.

[vast shale]

?

I’m sorry man

[edgy gulch]

that + with a circle around it

it means exclusive or correct?

[vast shale]

Yea

[edgy gulch]

do you know the definition of exclusive or?

how to write it in AND and OR statements?

[vast shale]

1 0 =1

0 1 = 1

We learned based off 2 input truth tables

[edgy gulch]

ok great you gave me its truth table

can you write it in AND and OR statements?

[vast shale]

Hmm

its clicking

[edgy gulch]

or do you know kmaps?

[vast shale]

I do know kmaps

[edgy gulch]

ok great

so the truth table of exclusive or is

0 0 0
0 1 1
1 0 1
1 1 0

[vast shale]

this is based off of 2 inputs right ?

[edgy gulch]

yea

[vast shale]

that might be where im getting cofused

when we are dealing with more than two inputs

[edgy gulch]

doesnt matter

[vast shale]

How does the truth table logic apply

ok

[vast shale]

I get this

[edgy gulch]

can you fill the kmap with it?

[vast shale]

yes

Can i ask you this question before we proceed with that

[edgy gulch]

yes

[vast shale]

lets say we have three inputs a b c the truth table still is the same ?

nothing changes

?

or output i mean is the same

[edgy gulch]

you mean if we have like A XOR B XOR C?

[vast shale]

right

I think

[edgy gulch]

then we just deal with A XOR B first

(A XOR B) XOR C

[vast shale]

Ok

now going back to the orginal question

I dont even know how to ask where im confused

[edgy gulch]

well do you have the kmap filled

[vast shale]

one sec

Hopefully i did that right

[edgy gulch]

ok good

now can you write its minimum expression?

[vast shale]

would it be just A ?

[edgy gulch]

no..

[edgy gulch]

look at where the 1s are

[vast shale]

ones are at 1 0 and 0 1 = a + b ?

[edgy gulch]

one is at A = 0 and B = 1

so that expression should be

$\overline{A}B$

[twin meteor]

Shioshi

[edgy gulch]

correct?

[vast shale]

ok

ok

Im seeing that

[edgy gulch]

now what about the one at A = 1 and B = 0?

[vast shale]

A!B

[edgy gulch]

and then what should you put in between these two terms?

AND or OR?

[vast shale]

or ?

[edgy gulch]

yes

so now are you convinced that

$A \oplus B = \overline{A}B + A\overline{B}$

[twin meteor]

Shioshi

[edgy gulch]

?

[vast shale]

I see it

[edgy gulch]

now lets go back to your question

you have

$(\overline{A} + B) \oplus AB$

[twin meteor]

Shioshi

[edgy gulch]

(ignoring the other not cause its not relevant)

[vast shale]

Forsure

[edgy gulch]

now can you rewrite the XOR in your question to AND and OR?

[edgy gulch]

using the result we just got

[vast shale]

So just so i dont confuse my self

!(!A + B) AB + (!A + B) !(AB)?

[edgy gulch]

yep

which is your second line isnt it

[vast shale]

Did my professor do A!B + !AB ?

[edgy gulch]

yeah

but order doesnt matter

A or B is the same with B or A

[vast shale]

right based off the truth table

ok

so what is the point of the kmap ?

[edgy gulch]

to write the XOR expression in terms of AND and ORs

[vast shale]

the kmap ?

[edgy gulch]

yes

[vast shale]

thats amazing

ok I got it now

Thanks so much for your help

and patience

I really appreciate it

.close

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[cosmic oasis]

how would i do this?

[cosmic oasis]

i derived it but it didnt really work out

[gaunt sparrow]

$\frac{d}{dt} P \ne 1$, its just $\frac{dP}{dt}$, which is your original DE...

[twin meteor]

Azyrashacorki

[gaunt sparrow]

So in particular, $\frac{d}{dt} (\frac{7}{10} - \frac{5}{10}P) \ne -\frac{5}{10}$

[twin meteor]

Azyrashacorki

[gaunt sparrow]

It should be $-\frac{5}{10} \frac{dP}{dt}$

[twin meteor]

Azyrashacorki

[cosmic oasis]

ohh

how would you incorporate p(2) = 3 into the equation?

[gaunt sparrow]

Well you know that $\frac{dP}{dt} = \frac{1}{10}(7-5P)$

[twin meteor]

Azyrashacorki

[cosmic oasis]

yes

[gaunt sparrow]

So that means that $\frac{d^2P}{dt^2} = -\frac{5}{10} \cdot \frac{1}{10} (7-5P)$

[twin meteor]

Azyrashacorki

[gaunt sparrow]

For t=2 this gives P=3

[cosmic oasis]

huh so how would u get the answer 2/5 out of that

[gaunt sparrow]

Well you plug in P=3

[cosmic oasis]

ah

yeah i understand now tysm

.close

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[vocal sleet]

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[uneven quarry]

hi um

[uneven quarry]

i accidentally typed ,iam dying in #discussion

how do i become alive again?

i've been dead for a full day lol

[heavy yoke]

there are 3 ways to manage the studying role:

• select "hide the discussion channels" in id:customize
• use the bot in #info
• type ,iamnot studying (or just ,iamnot dying) in #bots

[uneven quarry]

ah

,iamnot dying

[twin meteor]

Removed the studying! role from you.

[uneven quarry]

that worked :3

i maybe should've tried that

i tried ,iam alive

thank you!

[heavy yoke]

it is really just string-matching because dying is a substring of studying!

[uneven quarry]

i just realized that 🪦

,iam udying

[twin meteor]

Gave you the studying! selfrole.

[uneven quarry]

ah even that worked

you're right

,iamnot ying

[twin meteor]

Removed the studying! role from you.

[uneven quarry]

that also worked :p

i definitely learned something

tyvm!

,close

.clothes

.clo

.close

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[vocal sleet]

@gloomy estuary Has your question been resolved?

[vocal sleet]

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[little yoke]

HELLOOOOO, I'm so damn confused here. I already solved this yesterday but I need validation what and which is right😭😭😭

For number 1, what exactly is the unknown? I wrote it down that hypotenus is the unknown, but someone mentioned to me that the unknown is angle.

Another thing, let's say it's actually looking for the angle and I do solve it. Couldn't I look for the hypotenus then to check whether it's correct or not? And of course, if I do look for the sin and cos value, they have to be the same final answer.

[little yoke]

. close

Already talked Abt it w my teacher, what I did was just right 👌

.close

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[vocal sleet]

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[oblique tree]

hello, may I ask how do I know the derivative of sin, tan, sec?

[mint badge]

as in like
how it's derived?

how people found out what the derivatives of sin is?

or just

what the derivatives are

[oblique tree]

yes

[oblique tree]

this

[novel cliff]

I mean, first principle right?

[mint badge]

no but u cant do that

because u need lhopitals for that

[oblique tree]

for example, what's the derivative of sin? it's cosin, right?

[mint badge]

and there's some

contradiction or smth

where

you use one to get one

lhopital to get first principles and vice versa or smth

[outer warren]

you don't need lhop for first principles

[heavy yoke]

people can derive the derivatives from first principles, just not using l'hopital's rule

[mint badge]

ye u do

look

sinh/h as h -> 0

[outer warren]

that's not lhop

[mint badge]

identity?

[oblique tree]

lhop?

[heavy yoke]

there is a proof of that using the squeeze theorem which does not rely on l'hopital's rule

[outer warren]

that identity can be justified from sandwich theorem

[mint badge]

lhopita'ls rule

[novel cliff]

yeah squeeze theorem, failed to recall the name

[mint badge]

mk

[silk osprey]

🤔

why does everyone keep saying you need lhopitals rule for first principles lmao

[novel cliff]

I mean I can just pull out textbook right now lol, but mainly just first principle

[silk osprey]

defeats the purpose of it

[heavy yoke]

proofs of derivatives of sin(x) and cos(x):
https://www.youtube.com/watch?v=HVvCbnrUxek
limits used in the proofs:
https://www.youtube.com/watch?v=5xitzTutKqM
https://www.youtube.com/watch?v=Ojtwh8XDF8M

[oblique tree]

What about tan?

[novel cliff]

anyways, you figure out sine and cosine, and the rest is just identities

[heavy yoke]

quotient rule

[novel cliff]

well tanx=sinx/cosx

quotient rule

[oblique tree]

is it cot?

[mint badge]

nop

[oblique tree]

ooh

[novel cliff]

cotx=cosx/sinx

[oblique tree]

I'm confused lmaooo

[heavy yoke]

we know that tan(x) = sin(x)/cos(x). once we know the derivatives of sin(x) and cos(x) we can use the quotient rule to find the derivative of tan(x).

[oblique tree]

i see

btw, do yall got any tips for studying formulas for exams?

like memorizing the process

cs chain rule is so damn long

[novel cliff]

chain rule aint that bad

chain the outside, chain the inside is what I say

or you can add a "multiply" if you wish

"chain the outside, chain the inside, then multiply"

for example you have (2x^2+5x+7)^4

chain the outside: 4(2x^2+5x+7)^3

chain the inside: (4x+5)

multiply

4(4x+5)(2x^2+5x+7)^3

there is your derivitive

[oblique tree]

did u use foil?

bro look TT

[novel cliff]

tell me what foil is?

[oblique tree]

oh i meant foil method

howd u get the 4x+5

[novel cliff]

never heard of that in my life

4x+5?

derivitive of 2x^2+5x+7

is 4x+5

[oblique tree]

how

[novel cliff]

wdym how?

[oblique tree]

hpw did u derive

can u do like step by step

[novel cliff]

derivitive of 2x^2 is 4x

derivitive of 5x is 5

derivitive of 7 is 0

add them all up

4x+5

[oblique tree]

Oohhh

i seee

[novel cliff]

you know the power rule of derivitives?

right?

[oblique tree]

[oblique tree]

yess

I js get lost easily when the function is diff from the examples TT

[novel cliff]

alright good

lol no worries

ok your example

cos-1(5x-9)

remind me again what the derivitive of cos-1 is....

um I can figure out here

[oblique tree]

thats long as helll

[novel cliff]

y=cos-1x
cosy=x
-sinyy'=1
y'=1/-siny
y'=1/-sqrt(1-cos^2y)
y'=-1/sqrt(1-x^2)

there found it

[oblique tree]

btw, our prof told us to "Let u" first

thats why theres a u on my solution paper

[novel cliff]

oh yeah, the let u, I used to do that

now I just do the chain inside chain outside thing

now your example

lets see

[oblique tree]

u=5x-9
u'=5

[novel cliff]

cos-1(5x-9)

[oblique tree]

when i see " ' " means its the derivative right

[novel cliff]

yeah

it is pronounced "prime" if you want to know

y'=y prime= dy/dx

[oblique tree]

and when theres no variable beside the constant, their derivative is 0, right?

[oblique tree]

yea i know xD

[novel cliff]

yes

now to solve your question with my method

cos-1(5x-9)

chain outside: -1/sqrt(1-(5x-9)^2)

chain inside: 5

multiply

-5/sqrt[1-(5x-9)^2]

done

[oblique tree]

thats a shortcut

wow

btw, can i solve these on scientific calculator?

[novel cliff]

um, not sure, never used a calculator for these anyways

[oblique tree]

oh okay okay

[novel cliff]

• if you are to be quizzed on it, chances are you will have to show your work

[oblique tree]

yeah........welp- our quiz will start at 2:00

[novel cliff]

prob not the same time here

[oblique tree]

I live in PH XD

[novel cliff]

my time is currently midnight XD, gl on your quiz

[oblique tree]

is there any tips u wanna share me?

[novel cliff]

what are yall tested on?

any chance you know?

[oblique tree]

wym

basic cal quiz

[novel cliff]

in canada, we are always told like which section of the textbook we are quizzed on

[oblique tree]

and theres no formulas provided..

[novel cliff]

we are provided formulas but I dont need em

[oblique tree]

ive got notes

dang

formulas r not allowed too lol

Im cooked

[novel cliff]

no dont be

I mean there arent a lot right?

what are there?

[oblique tree]

its 70 items

[novel cliff]

logarithm, exponential, trig, that is basically it right?

[oblique tree]

oh

its

continuity functions, derivatives part 1 and 2

[novel cliff]

go into more specifics

[oblique tree]

wait

[velvet shell]

like the definition of coninuity?

[oblique tree]

it only says derivatives, so basically its continuity functions ans derivatives

[novel cliff]

continuity functions..... polynomials?

[oblique tree]

Its graphing

removanle discontinuity
jump discontinuity
infinite discontinuity

DUDEEEE

whole finals is the coverage

[velvet shell]

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

Have u gone over this ?

Continuity at points?

[oblique tree]

yes

but its supposed to be x ->c

its easy

[twin meteor]

穴熊

[oblique tree]

derivatives is too complicated for me tho

[velvet shell]

What type of derivative?

[oblique tree]

inverse trigonometric functions

[velvet shell]

And I'm assuming polynomial, exponential, and trig as well?

[novel cliff]

inverse trig is not that bad either, you just have to know your identities and derivitives of regular ones well

lets say you dont remember what the derivitive of y=tan-1x

[novel cliff]

well what you do is:

tany=x

derivitive of tan is sec^2

y'sec^2y=1

y'=1/sec^2y

now if you recall

sec^2=r^2/x^2

[oblique tree]

whats r

[novel cliff]

radius of a unit circle

this is how I remember trig ratios

sin=y/r

cos=x/r

tan=y/x

cot=x/y

sec=r/x

csc=r/y

[oblique tree]

i see ill try doing that

[novel cliff]

now one thing important to know

since x y and r form a right triangle

x^2+y^2=r^2

there is a formula

sec^2=1+tan^2

if you dont remember this, then look at this

r^2/x^2=x^2/x^2+y^2/x^2

so therefore

y'=1/sec^2y=1/(1+tan^2y)=1/(1+x^2)

and there you have it

dy/dx of tan-1x is 1/(x^2+1)

[oblique tree]

I understans nowww

d*

thankuuu

i appreciate ur help!

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[hybrid mantle]

logarithmic differentiation

[hybrid mantle]

i worked all the way up to

$\frac{dy}{dx} = y (\frac{x}{x^2-4} + \frac{1}{4x+2})$

[twin meteor]

suds

[hybrid mantle]

which is correct

what is this last line

that confuses me a lot

[heavy yoke]

you just replace y with the known formula for y

[hybrid mantle]

ohh i seeee

[river kettle]

They convert the square root and square root to indices

[hybrid mantle]

okay

that is all

thank you

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[hybrid mantle]

.reopen

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✅

[hybrid mantle]

wait would it be wrong if i didnt replace y with the known value?

[heavy yoke]

not necessarily wrong, but for situations where y is an explicit function of x we prefer to have a formula for the derivative which only depends on x

[hybrid mantle]

yeah

like i'd lose marks

thank you

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Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[hardy sun]

I'm having trouble with this question, like I don't really know how to begin this

[paper depot]

probably easier is to attempt to prove |z+w|^2 ≤ (|z|+|w|)^2

see if you can manipulate that ineq somehow to distill it to something more easily provable

[hardy sun]

Ohhh, okk I will try that

I got to this so far,