help-17

[twin meteor]

ransik

[open sage]

there

sorry that was my mistake

[halcyon valley]

Soo

This becomes

Det(A^-1)det(b+i)

[open sage]

we can find out the determinant for A

[halcyon valley]

Agreed?

[open sage]

yes

[halcyon valley]

Yep

Det(A^-1) is?

[open sage]

1/det(A)

[halcyon valley]

Yes

And u have det(a)

[open sage]

yep

[halcyon valley]

Yep

Find b+I and apply det

Ull get

[open sage]

it's funny you know i've been working with internal product... diagonalization... subspaces and whatnot

this is the part about linear algebra

that confuses me most

its all these properties

[halcyon valley]

Lol i c

[open sage]

alright i'll work that out

thanks

[halcyon valley]

Anytime!

[vocal sleet]

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[untold crescent]

i need help trying to understand, how to sketch this function. so far i have the VA and y-intercept and also the local max

[untold crescent]

2 things i am not understanding right now are the inflection point and second root of f(x)

i have the general idea of how the graph is going to look

but i dont know what to do with those 2 points, inflection point and second root of f(x)

<@&286206848099549185>

[vocal sleet]

@untold crescent Has your question been resolved?

[untold crescent]

15 mins passed again, and no one to be seen

<@&286206848099549185>

[untold crescent]

maybe third time the charm?? <@&286206848099549185>

[sharp rain]

It is

Heyo @untold crescent

[untold crescent]

lets gooo

hiiiiii

[sharp rain]

Lemme read your question

[untold crescent]

okkk

[sharp rain]

It so long

[untold crescent]

lol

[sharp rain]

Hmm

Lot of details

[untold crescent]

yep

[untold crescent]

i made lines on how it should look like, but not in correct points

[sharp rain]

It looks something like this

[untold crescent]

ooo

[sharp rain]

Let's mention a few things

[untold crescent]

yes please

[sharp rain]

It approaches-1 at - infinity

Point of inflection about -2

[untold crescent]

what does this mean?

[sharp rain]

So concavity changes

Until -2 it's opening upwards

After that it's down ward

[untold crescent]

ooo

[sharp rain]

It cuts the x axis at -11/20

And 0

And shows a relative maxima at x= -0.25

[untold crescent]

how do you know where to plot the lines for from -1 to -4, do you just estimate it?

[sharp rain]

It goes to inifity

I can't possibly show that

[untold crescent]

one sec

[untold crescent]

ooooh

i am getting it

what about the postive side of x-axis? do we draw line there also

[sharp rain]

And it approaches - infinity at x=1

[sharp rain]

After 1 is a lot simpler

[untold crescent]

sorry i am still a bit confused, how do we know when the curve starts to bend

[sharp rain]

Follow g and j

[untold crescent]

cause we dont have horizatonal asymptote

[sharp rain]

We do

It's always supposed to be mouth opening upwards

And is supposed to approach 1 at infinity

No other curve can satisfy this condition

[untold crescent]

the dotted lines you drew?

[sharp rain]

Yes that's just supposed to show that at infinity the curve approaches 1

[untold crescent]

y=1?

oh is that what the limit mean,

[sharp rain]

Yes

[untold crescent]

so the dotted lines you drew, are refeering to the limit

[sharp rain]

Y=1

[untold crescent]

oooooh

omg

[sharp rain]

Yup

[untold crescent]

thank youuuu

[sharp rain]

You want me to draw this cleaner

[untold crescent]

i was about to end the help request, but you came just in time

[sharp rain]

??

[untold crescent]

yes please

[sharp rain]

Give me minute

[untold crescent]

i want to verify that I draw it correctly

[sharp rain]

Drawing on phone is hard

[untold crescent]

lol it is

[sharp rain]

Admittedly i am amazing at it as can seen by my obviously perfect curves :p

[untold crescent]

curve looks about perfect

[sharp rain]

https://tenor.com/view/toy-story-look-im-picasso-disney-mr-potato-head-gif-16632024

[untold crescent]

lmao

[untold crescent]

ooo, thank you so much

[sharp rain]

I free hand this shit

This is cool

[untold crescent]

lmao

[sharp rain]

I am not picasso

[untold crescent]

bro pulled up a

[sharp rain]

I am better

[untold crescent]

i forgot what its called

[sharp rain]

Lol

Anyways @untold crescent

Please check again

[untold crescent]

picasso student fr

[sharp rain]

See if I missed anything

I don't think I did though

Is that all for today?

[untold crescent]

everything looks good

thats all for today

thank you picasso

[sharp rain]

Your welcome

Have a good day

[untold crescent]

you too

.close

[vocal sleet]

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[fast stump]

i need help with a taylor series problem pls

[fast stump]

the top one

[reef sierra]

u messed up the indices

[vocal sleet]

@fast stump Has your question been resolved?

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[sudden cloud]

Not the physucs

[frosty robin]

hi can someone help me just draw a free body diagram I want to make sure i have it set up nicely

there are 4 forces right ? two normal, one gravity and one for the hanging mass?

wait actually if the vertical hinge is my pivot point i dont count that force right

[frosty robin]

plz 😭 🙏

[vocal sleet]

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@frosty robin Has your question been resolved?

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[terse sparrow]

yeah

[sharp lynx]

It's not a yes or no question

[terse sparrow]

pls help me i hve watching video on youtube over and over still i have not understand the question

[vocal sleet]

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as this action is irreversible, and this channel may abruptly lock.

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[proper cosmos]

hello! i really need help in learning linear regression as I think it would be useful to understand why it gives its output

[proper cosmos]

and also using it to see how backpropagation works and stuff

so my question is why is the slope of a best fit line represented by cov(x,y)/var(x)

I know that both expressions get the spread of the data

I dont understand the cov(x,y) though

I know its supposed to get the average spread of both x and y

But why does multiplying them work?

why does cov(x,y)/var(x) represent the slope like y delta/x delta

<@&286206848099549185>

[hidden gyro]

do you know derivatives?

I am assuming you do

so first we define the error function as the sum of squares of the difference between the value the line gives, and the datapoints

let us say our data is x1,x2,x3,...,xn and y1,y2,y2,..,yn, and let us say that the mean of x and the mean of y, are both 0

and let us say our line is s*x = y

[proper cosmos]

yes

[proper cosmos]

I can understand this

Also another thing

[hidden gyro]

yes

[proper cosmos]

so we take the x and y of the points and calculate the error for both?

idk

[hidden gyro]

no, we calculate the error for y

[proper cosmos]

oh alright alright i understand noww

so the equation would be

sum (y(true)-y(pred))^2

Ye

wait

is that right?

[hidden gyro]

yes

that is right

[hidden gyro]

so this is sum(s*xi-yi)^2

[proper cosmos]

alright so our line is s*x = y and the avverage of all the datapoints x,y is 0,0

[proper cosmos]

wut

why is it s*xi?

[hidden gyro]

because predicted value of yi is s*xi

[proper cosmos]

Ohhh nvm i see i see

i thought it was true - prediction

and not prediction - true

[hidden gyro]

it is the same either way

(a-b)^2 = (b-a)^2

so you know that a function is minimised when the derivative is 0, right?

[hidden gyro]

what we do is we take the derivative of this

with respect to s

[proper cosmos]

no

[hidden gyro]

so d/ds (sum(s*xi-yi)^2) = 0

[hidden gyro]

extremised

[proper cosmos]

Wait i dont understand this part

i know the rest about derivatives

[hidden gyro]

minima?

[proper cosmos]

Yes

What is minima?

[hidden gyro]

ok

imagine you have a continuos differentiable function with a minimum valus

sry, i have to go now

[proper cosmos]

o its ok

ill try to learn what it is

[proper cosmos]

ok i can understand this noww

resent
and also using it to see how backpropagation works and stuff
so my question is why is the slope of a best fit line represented by cov(x,y)/var(x)
I know that both expressions get the spread of the data
I dont understand the cov(x,y) though
I know its supposed to get the average spread of both x and y
But why does multiplying them work?
why does cov(x,y)/var(x) represent the slope like y delta/x delta

<@&286206848099549185>

[hidden gyro]

am back

[hidden gyro]

yeh am coming to that

[hidden gyro]

so if we take the derivative of this with respect to s, and set it to 0

we sum(d/ds(s^2*(xi)^2-2s*xi*yi + (yi)^2) = 0

[proper cosmos]

😭

[hidden gyro]

this is the same as
sum(2s(xi)^2-2xi*yi) = 0

[hidden gyro]

what happened?

[proper cosmos]

i dont understand the d/ds

[hidden gyro]

derivative is represented by d/ds

do u understand now?

[proper cosmos]

can you make it f' to make it easier to understnad

is that ok

[hidden gyro]

yes

(sum((s*xi-yi)^2))' = 0

since (a+b)'=a'+b'

[proper cosmos]

so we basically find the derivative of each point?

[hidden gyro]

yes

[proper cosmos]

and that sum = 0

[hidden gyro]

yes

[proper cosmos]

well the error

i think

idk

sum squared error derivative

[hidden gyro]

yes

[hidden gyro]

so
sum(((s*xi-yi)^2)') = 0

sum((s^2*(xi)^2-2s*xi*yi + (yi)^2)') = 0

sum(2s*(xi)^2-2xi*yi) = 0

sum(s*(xi)^2)=sum(xi*yi)

s*sum(xi^2)=sum(xi*yi)

so we have

s = sum(xi*yi)/sum(xi^2)

= (sum(xi*yi)/n-1)/(sum(xi^2)/n-1)

= cov(x,y)/var(x)

[proper cosmos]

ok i see but why do we use the error and derivative to get this

i understand that we simplified the square basically

[hidden gyro]

because we want to minimise the error

and minimizing is usually done by setting derivative to 0

[proper cosmos]

Wait

so

wait im so confused how does derivative being 0 minimize the error

[hidden gyro]

did you understand the minima thing?

[proper cosmos]

so it takes the sum squared error, finds its derivative and then sets it to 0

[hidden gyro]

yes

[proper cosmos]

any how will the error relate to the original dataset

[hidden gyro]

we want the best fit line, right?

[proper cosmos]

Yes

[hidden gyro]

so the line with least error, right?

[proper cosmos]

Yes

[hidden gyro]

and to find the line with minimum error we take derivative of error and set it to 0

does this make sense?

[proper cosmos]

Well kinda but what would the error look like on a graph error is a function right?

[hidden gyro]

yes

error is a function of slope of the line

[proper cosmos]

Wait it is?

How

[hidden gyro]

here

error looks like a parabola with respect to slope

[proper cosmos]

i thought we were just subtracting the true with the predicted

[hidden gyro]

and then squaring it

and then adding it up

to get error

[proper cosmos]

What if we took the root of that sum?

[hidden gyro]

does this make sense?

[proper cosmos]

sqrt

[proper cosmos]

yes

[hidden gyro]

if we minimise the sqrt than we minimise the thing we are square root-ing

[proper cosmos]

ok but like i dont understand how it relates to sloope really

all i can see is that s*xi

the s represents the slope right

[hidden gyro]

yes

[proper cosmos]

but doesnt subtracting it ruin it?

[hidden gyro]

wdym?

[proper cosmos]

how would it relate to the slope then

[hidden gyro]

i dont get you?

[proper cosmos]

like s*xi - yi

[hidden gyro]

this is a linear function of slope?

[proper cosmos]

s*xi - yi is the slope?

[hidden gyro]

no, s is the slope

[proper cosmos]

and how does the error relate to thi

this*

[hidden gyro]

sum((s*xi-yi)^2) is the error

[proper cosmos]

but

how would it relate to the slope in the end

[hidden gyro]

i dont get you?

we have a formula for error involving slope and constants?

[proper cosmos]

ok you said we have to minimize the sum squared error

[proper cosmos]

yes i know

[hidden gyro]

so error is a function of slope

[proper cosmos]

ok how does minimizing the error give you the slope

[hidden gyro]

minimizing the error gives us the best fit line

[proper cosmos]

ok so f(s) = sum((s*xi-yi)^2)

[hidden gyro]

so the slope which minimizes error will be the slop of the best fit line

[proper cosmos]

Wwait

I think i understand it now

So basically we try to find the slope that gives us the least error

[hidden gyro]

yes

[proper cosmos]

how does finding the derivative and finding (a point i think) that has the derivative of 0

i mean 2 points

[hidden gyro]

one point

[proper cosmos]

is the 2 points yi and s*xi

oh

[hidden gyro]

oh i misunderstood you

when i said one point i meant (s,f(s)) with minimum f(s)

[proper cosmos]

Ahhh i see

[proper cosmos]

so as the slope changes we find the one where the derivative is 0 meaning that the error will be 0

right?

[hidden gyro]

no

[proper cosmos]

oof

[hidden gyro]

derivative 0 means error is minimised

[proper cosmos]

wait how?

[hidden gyro]

dyk maxima and minima?

[proper cosmos]

no

[hidden gyro]

oh

one sec

let us say you have this function

and you are looking for a point where the value is minimised

what will be the derivative?

(assuming differentiability)

[proper cosmos]

idk

[hidden gyro]

ok

[proper cosmos]

but i know its at the point that has the least y

[hidden gyro]

rn i am just going to explain you some intuition

[proper cosmos]

ok!

[hidden gyro]

let us say the point is (s,f(s)) and since the function is differentiable there are 3 possible derivatives, positive negative and 0

right?

r u there?

[proper cosmos]

yes

[hidden gyro]

ok

[proper cosmos]

one last thing what does differentiable mean?

[hidden gyro]

has a derivative

[proper cosmos]

oh ok ok

[hidden gyro]

so if the derivative is positive, we can go "slightly left" to decrease f(s) right?

[proper cosmos]

yes

[hidden gyro]

and if derivative is negative we can go "slightly right" to decrease f(s) right?

[proper cosmos]

what if its negative

yes

[hidden gyro]

so that means if f(s) is minimum derivative must be 0, right?

[proper cosmos]

wait yea because that means that its not at a mountain

and it doesnt have to increase or decrease its derivative slop

slope

[hidden gyro]

r u typing smthing?

[proper cosmos]

wait was i correct

[hidden gyro]

mostly

it can be at a mountain

but yes

[proper cosmos]

it can?

[hidden gyro]

yes

take -x^2 for example

this has derivative at x=0 as 0

but it is maximum there

[proper cosmos]

wait how do we find the derivative agian

[hidden gyro]

wdym?

yk derivatives right?

[proper cosmos]

yea i do

[hidden gyro]

so yk how to find derivtaive right?

[proper cosmos]

Yes nvm

because if we find the derivative for the point x = 0

itll just return 0

since y is 0

i mean the slope

mb

i mean the slope is 0

[hidden gyro]

anyway

since we are llokinf for a point where f(s) is minimised

f'(s) has to be 0, right?

[proper cosmos]

yes

Wait but

wait nvm nvm

OHH i get it

but would that also mean

that at the minimum

wait so

x*slope = 0

[hidden gyro]

just slope 0

[proper cosmos]

that would be the minimum right?

[proper cosmos]

Yes

[hidden gyro]

from here

[proper cosmos]

OHHHHHHH so we are finding the derivative of the function of the slope that equals 0

[hidden gyro]

yes

[proper cosmos]

such that s,f(s) find the minimum f(s)

[hidden gyro]

yes

[proper cosmos]

which makes s * minimum slope(0) = f(s)

[hidden gyro]

?

i dont get you

[proper cosmos]

wait

[proper cosmos]

we are finding a slope that is 0 right?

[hidden gyro]

slope of f(s) is 0, not s is 0

[proper cosmos]

yes yes thats what i mean

[hidden gyro]

yes

[proper cosmos]

so s*m(slope of f(s) which is 0) = f(s)

[hidden gyro]

no?

[proper cosmos]

but i thought on a grid its s,f(s)

[hidden gyro]

yes

[proper cosmos]

and x times the slope gives y

[hidden gyro]

no

x*s = y

on the grid it is (x,s*x)

[proper cosmos]

wait so that means

that means f(s)

[hidden gyro]

is the errir

[proper cosmos]

is

the slope(representing x) times the slope of fs = f(s)

[proper cosmos]

m*s

[hidden gyro]

no

[proper cosmos]

why not

[proper cosmos]

i thought f(s) is y

[hidden gyro]

no

f(s) is the error

[proper cosmos]

but why does it represent y

[hidden gyro]

it doesnt?

[proper cosmos]

oh

so what does

s,f(s) mean

[hidden gyro]

it means the points (s,f(s)) on the graph of slope vs error

[proper cosmos]

i dont understand 😭

[hidden gyro]

do you understand this?

[proper cosmos]

we are trying to find the slope that matchs with the minimum error

and the minimum error is 0 right?

[hidden gyro]

not neccessarily

you see ' in it

that means derivative is 0

[proper cosmos]

so it means

[proper cosmos]

that the thing multiplying by s is 0

[hidden gyro]

no?

the derivative of the error is 0

[proper cosmos]

what does it mean then?

[proper cosmos]

ok what gets the derivative of the error to 0?

[hidden gyro]

by minimizing the errot

do you get ne?

[proper cosmos]

and how do we minimize the error?

[hidden gyro]

by setting the derivative of error 0

[proper cosmos]

ok but what do you do with the derivate after that

well i mean

once you solve for the thing that matches with the derivative 0

well how do you solve for it

[hidden gyro]

here

[proper cosmos]

ok but doesnt that mean that at that point multiplying by the derivative will give you the minimum f(s)

[hidden gyro]

no? at that points f(s) is minimum

r u there?

[proper cosmos]

yes

[hidden gyro]

did you get this?

[proper cosmos]

so the slope of f(s) is 0?

[hidden gyro]

yes

[proper cosmos]

then whats being multiplied by the slope to get f(s)??

[hidden gyro]

we dont do that?

[proper cosmos]

nothing?

[proper cosmos]

but the slope of a line is

[hidden gyro]

f(s) is not a linear function of s

[hidden gyro]

f(s) is not a line

f(s) is the error

s*x is the line

[proper cosmos]

but then why does it look like a line

i mean not look

but like

[hidden gyro]

f(s) looks like a parabola

[proper cosmos]

why does it seem like s would be on the x axis and error on the y axis

[hidden gyro]

no issue with that

[proper cosmos]

but wouldnt that make s * slope of f(s) = f(s)

[hidden gyro]

no

f(s) is not a linear

[proper cosmos]

Ohhh

[proper cosmos]

so

what does that mean

For the thing

[hidden gyro]

it means we find out the minimum of f(s) to get the s for the best fit line

[proper cosmos]

and that also means that we can find the s that correalates to the minimum of f(s)

right?

[hidden gyro]

yes

[proper cosmos]

so we do that by setting the slope of the non linear equation of f(s) to 0

[hidden gyro]

yes

do you get it now

[proper cosmos]

So

[proper cosmos]

Once we do that we solve for s right?

which represents the slope right?

[hidden gyro]

yes

[hidden gyro]

yes

[proper cosmos]

so we solve for the slope and distrubute the square and then solve for the derivative of it and we then seperate the sllope and it givves sum xi*yi/sumxi^2 = slope

[hidden gyro]

yes

[proper cosmos]

so by minimizing the error we get the slope that matchs for that right

so we get the least error

also wouldnt that mean it could get stuck at local minimums

i understand it now

[hidden gyro]

nice

[proper cosmos]

yipeee

i finally understand it

[hidden gyro]

nice

[vocal sleet]

@proper cosmos Has your question been resolved?

[vocal sleet]

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[fading marsh]

ماهي دافعة ارخميدس

[vast shale]

?

what the hell

[vocal sleet]

@fading marsh Has your question been resolved?

[vocal sleet]

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[vocal sleet]

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[zinc hill]

can someone check this pls

[vocal sleet]

@zinc hill Has your question been resolved?

[vocal sleet]

@zinc hill Has your question been resolved?

[zinc hill]

can someone check 5 and 6 specifically cause i think the last two r right ?

[proper cosmos]

uh

[zinc hill]

uh

[silk kindle]

Hello, I think it's all correct

[vocal sleet]

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[undone pier]

quick question to check my understanding: when you express a matrix in its own eigenvector basis, the results are always diagonal?

[vast shale]

plz help

[gaunt sparrow]

!occupied

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[twilit ocean]

Let $\frac{we^u-2v+w^2}{uv^2-w}=1$. Find $\frac{\partial u}{\partial v}$

[twin meteor]

hskthca

[twilit ocean]

isn't the solution just multiplying both sides by the denominator, putting everything to LHS then letting F(v, w, u(v,w)) = 0? then du/dv = -F_v/F_u?

why is wolframalpha giving a really complicated answer?

[tidal dock]

did you provide that that fraction =1 ?

[twilit ocean]

wdym?

oh yes

in wolframalph

somehow, using this method WA provides the same answer for dw/du, but not du/dv

[tidal dock]

show what you gave to it

[twilit ocean]

so via this you'd realistically expect no more than a few terms in both the numerator and the denominator in the derivative

[tidal dock]

hm, weird

[twilit ocean]

i got du/dv =

$\frac{2+2w}{we^u-v^2}$

[twin meteor]

hskthca

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[cobalt arch]

how does the sin/cos/tan change through the angles q and t or in general

[full summit]

sohcahtoa

[cobalt arch]

yes but how do they change

since sin q and sin t will be different

[full summit]

sin is opp/hyp

so sin q opp would be 35 hyp is 37

opp/hyp = 35/37

sin t opp would be 12 hyp would be 37

opp/hyp = 12/37

[cobalt arch]

ok thank you

.close

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[tulip parcel]

ok guys i have an intersting case i wanna present and ask quesitons about. Basically statistics territory

[tulip parcel]

They have to write 10 letters each day. More than 1 mistake and need to rewrite. More than 2 rewrites a day and they get a warning. More than 3 consectuive warning days during the same week and they get fired

Assuming that the number of errors per letter can be described by independent random variables identically distributed with parameter 𝜆=1.0 Poisson, calculate the probability that the secretary will be fired at the end of the 4th week at the latest.

So we basically divide this into 4 parts

Part one.Probability that a letter has more than 1 mistake

As the task said we are supposed to use the poisson here apparently

i would just be interested in knowing why exactly poisson works here

second part is what is the probability that she makes more than 2 mistakes in a day

and my question would be why we use the binomial here

<@&286206848099549185>

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@tulip parcel Has your question been resolved?

[tribal dawn]

poisson is just binomial with large n and small p, so they could be demonstrating their similarity, don't completely know

[tulip parcel]

ah ok makes sense since a letter has a lot of words i guess and the probability to make an error is relatively small

[tribal dawn]

it is a little weird to me bc n is pretty small so i don't quite know why they'd use poisson

[tulip parcel]

nope 10 is not the n here

she writes 10 letters a day

but each letter individually

only allowed max 1 mistake

so i assume the letter has many words

[tribal dawn]

oh gotcha

[tulip parcel]

Guess that's why they set the lamda as 1 (which is n * p). to make it easier

[tribal dawn]

yep

[tulip parcel]

would you know why use the binomial in the second one?

[tribal dawn]

it's weird if n is that large and p is that small, but technically binomial works too

it's just that poisson is easier for big n and small p

poisson is an approximation of binomial 🙂

[tulip parcel]

ah ok guess it is a variation that works better in these conditions

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[winter tide]

do i have reading comprehension disabilities?

if ur 350 ft away from the hot air balloon, isn't it from the point its at in the sky?

cuz ur not 350 ft away from where the hot air balloon began

i keep struggling with these stupid questions cuz i cant draw my traingles right

[vast shale]

I think you're right

[winter tide]

if im observing the hot airballoon from that point, im using binoculars and looking at it at an angle not straight to the floor??

😭

[thin jay]

well generaly away means the perpendicular height

these types of questions also come in 10th class board exam

in India

so yeah

[vast shale]

It's the horizontal distance.

[winter tide]

i dont understand 😞

[onyx schooner]

I see one mistake btw

[vast shale]

Since it's saying the distance from the ground

Not the actual distance from the balloon when it's up

[onyx schooner]

You changed the sides

Why

[winter tide]

^

[vast shale]

I think the right one is the solution

[winter tide]

i just think i have reading comprehension issues

the right one is the solution yea

[onyx schooner]

Oh okay

Yeah right one is right

There's no problem with it

[onyx schooner]

Yeah it is in the sky honestly

[winter tide]

yeaaa idk i think the wording is just stupid 😭

[onyx schooner]

No like it's fine if you're wondering that

[vast shale]

That it's the horizontal distance is usually mentioned

But I don't see much problem with it

[onyx schooner]

But the thing is if it was in the sky then it will still not change anything to the problem, the problem will still be valid

[winter tide]

heres to hoping i dont get anhy weirdly worded questions like that on my exam 🙏

[onyx schooner]

Trigonometry works everywhere (some exceptions are there but lets not talk about it)

[winter tide]

oh while im here

[vast shale]

I just consider them as mere points

[winter tide]

for question 12

did i solve that right or no

and 14

[onyx schooner]

,w x²-x-1=0

[twin meteor]

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Requested by arnabpal

[vast shale]

cos(x) = 1/2 - root5/2 or 1/2+ root5/2

[onyx schooner]

Not it is not

[vast shale]

what did you do after this?

[onyx schooner]

That would be cos inverse

Firstly

[winter tide]

i just left it like that 😭

[vast shale]

ah

[onyx schooner]

Okay so see you have done everything right

[olive igloo]

,w tan(x)^2 - tan(x) - 2 = 0

[twin meteor]

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[onyx schooner]

Now you have
$\cos{x}=\frac{1 \pm \sqrt{5}}{2}$

[winter tide]

yea thats what i have

is that wrong

[twin meteor]

Arnab

[onyx schooner]

You should have this first

[winter tide]

yea i have that

[onyx schooner]

No you have x=cos(1±√5)/2

That's one mistake and it's not the principal solution

[winter tide]

so this?

[onyx schooner]

Yeah

[winter tide]

ok

how ab 14

[onyx schooner]

And another thing

It's not the principal solution

[vast shale]

is this right?

[winter tide]

yes(?)

[onyx schooner]

This one is partially right

[onyx schooner]

,w y²-y-2=0

[twin meteor]

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[onyx schooner]

tanx=-1
tanx=2

Two solutions would be there

Again you have made the same mistake

[vast shale]

what about the answers after pi?

[onyx schooner]

This is partially correct

[vast shale]

mhm

we need full precision though

[onyx schooner]

Because of this

It is not the general solution

[onyx schooner]

It is a solution of that Question

[winter tide]

so this?

[onyx schooner]

Yeah

But again it is not the general solution

Yeah but that doesn't contribute

Hm?

[vast shale]

jk

[onyx schooner]

Like if you have cos(x)=1
You can't say that x=0°
You have to say that
x=2πn±0 where n belongs to a natural number

[winter tide]

what do u get when the cards are being dealt in increasing order

[onyx schooner]

Like. The increasing order is mentioned in the question
A<2<3<4<......<J<A<K

[winter tide]

yes

[onyx schooner]

Use that

Bruh my battery is going 6% now 🥲

[winter tide]

use what

[onyx schooner]

Like you what the answer or the process

[winter tide]

both

i got an answer but im not sure if its right

[onyx schooner]

Honestly I haven't reached probability yet my co-ordinate geometry is going on I can help you with algebra but I haven't still done the probability course so sorry for that

[winter tide]

its ok

i'll ask in a diff channel

[onyx schooner]

And for the trigonometry question your solutions wound be
For Q 12
x=2πn±arccos((1±√5)/2)
For Q14
x=πn+arctan(-1) and πn+arctan(2)

[winter tide]

do u think i have to write pin for it to be right

[onyx schooner]

Pin?

[onyx schooner]

You need to add ±2πn in the cos inverse function

[onyx schooner]

And here is the proof of that thing if you want

[winter tide]

ok ty

.close

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[open sage]

In R3 the subspaces S and T are defined

a) Find a basis for S intersection T

so firstly i've determined S to be LI and T is also clearly LI so i won't bother

which meeans the provided spans (span = gen) are basis vectors for the subspaces

[gaunt sparrow]

What do you think S and T look like as subspaces of R^3?

[open sage]

planes

so we'd need the line

[gaunt sparrow]

So SnT should be the intersection of those planes

[open sage]

that intersects them both

and we know that line

must go through 0

so.. i'm trying to think about it but

it would look something like

all linear combinations of S's vectors = all linear combinations of T's vectors?

something like that

[gaunt sparrow]

I think you can easily find a normal vector to both those planes

[open sage]

uhh

i think we'd seen a method where

you write each basis vector as a column of a matrix

multiply each of those by a scalar

and equal them

so like

Ac=Bd

A,B the basis matrices

c,d any R scalar

[gaunt sparrow]

Yeah I think this would essentially boil down to writing the planes S and T as

$S(s_1,t_1) = s_1 \vec{u_s} + t_1 \vec{v_s}$
and $T(s_2, t_2) = s_2\vec{u_t} + t_2 \vec{v_t}$

[twin meteor]

Azyrashacorki

[gaunt sparrow]

And solving for the s1, t1, s2, t2 that make them equal

In any case the normal vectors approach is faster, but you do whichever works with what you've learned

[open sage]

see the thing is

technically i know how to find the normal vectors

like that was part of my second linear alg exam

but i failed the first one

and we were taught to solve it a certain way

i asked my prof though and she said as long as we got a correct result with a process that made sense

we could solve it any way we wanted

which is cool becuase not all professors are like that

[open sage]

so... the normal vectors...

would be the orthogonal complement

[gaunt sparrow]

That's nice of them honestly

[open sage]

to the subspace

right?

[gaunt sparrow]

Yeah

[open sage]

okay yeah i can do that

and i assume common internal product?

ie dot product

[gaunt sparrow]

cross product rather

[open sage]

oh yeah

my bad

anyways one i have the normal vectors for each basis

they should be orthogonal to each other

[gaunt sparrow]

Not necessarily

[open sage]

oh

[gaunt sparrow]

The planes don't have to intersect orthogonally

But, remember that their intersection line lies in both planes

And both normal vectors are orthogonal to anything in the plane

[open sage]

sometimes visualizing it makes it easier for me

these are our two subspaces

that line is what we're trying to find

[gaunt sparrow]

If you plot the normal vectors, you should be noticing something with the intersection

[open sage]

yeah im not quite sure how to do that in geogebra

okay i've plotted the line

as well as the normal vectors

each in its correspondin colors

oh

the... intersection vector

is normal to both normal vectors?

[gaunt sparrow]

Indeed

[open sage]

interesting

so this is really an internal product problem

[gaunt sparrow]

The intersection lies in both planes, and both normal vectors are orthogonal to their respective planes.
In particular, they themselves must span a plane that is orthogonal to the intersection!

So then all you need is a vector perpendicular to both normal vectors

[open sage]

.

just use <v,u> = 0

[gaunt sparrow]

I mean you can also just cross product again

[open sage]

yeah well that’s essentially what regular internal product is, right?

[gaunt sparrow]

<v,u> usually the inner product, which standardly corresponds to the dot product

[open sage]

okay hold on

i may be mixing up a few things here

it’s my understanding two vectors are orthogonal when <v,u> = 0

by cross product, do you mean the whole i j k thing?

[gaunt sparrow]

Yes

[open sage]

oh okay

yeah sorry i was mixing that up

[gaunt sparrow]

The cross product of two vectors gives you a vector orthogonal to both of those you started with

[open sage]

it’s confusing cause we haven’t really used cross product in linear alg

yeah i remember the hand thingy

so i could either do cross product

or

<v1,u>=0
<v2,u>=0

i mean cross product is probably faster

just making sure

[open sage]

v1,v2 the basis vectors

and then i’d just solve for u

[gaunt sparrow]

Okok from the beginning

[open sage]

yep wasn’t part of linear alg funnily enough

it was part of “entry” mathematics

[gaunt sparrow]

Yeah that's how you'd do it otherwise

You'll get equations to solve for the coordinates of u

[open sage]

yep

probably a bit longer though

[gaunt sparrow]

You also might run into a choice at some point since there are two vectors that are orthogonal to both of them

Just pick whichever it doesn't really matter

[open sage]

well yeah but those vectors are LD

so it's either 1

or -1

[open sage]

like, between each other

[gaunt sparrow]

Yeahyeah exactly

[open sage]

they're linear combinations of each other

[gaunt sparrow]

They're opposites

[open sage]

i'm just worried about using cross product because we might stumble into problems where

we're not in R3

and i haven't used cross product outside of R3

[gaunt sparrow]

True. It's safer to use the inner product then

[open sage]

like in entry math we had what was called "line and plane"

which was... as the name would suggest

lines and planes in R3

and the operations between them

so since you were always in R3 you'd just use internal product

[vocal sleet]

@open sage Has your question been resolved?

[open sage]

yup. thanks for the help

[vocal sleet]

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[queen mountain]

Hello I need help with some algebra 1 I didn’t take it my freshman year and now idk what I’m doing

[visual forge]

ask a question

[queen mountain]

Ima take a photo of it

[fallow gull]

Ooo this

so I would start with simplifying the expression

do u know how to do that

[queen mountain]

Honestly no im not good at math

I’m taking this class again and I js can’t understand it

[fallow gull]

okay well let’s start with like

smth basic

do u know anything abt like terms

[queen mountain]

I think I do

[fallow gull]

if I ask u to simplify 4x-7-2x

what would be ur answer

[queen mountain]

Uhh

I’m gonna be honest I have no idea

[fallow gull]

okay so

we’d start with combining 4x and -2x

or basically add them together

bc they’re like terms

they both have the variable x

right

[loud walrus]

Imagine x = potato

[queen mountain]

Yes

[fallow gull]

so

simplifying 4x-7-2x

it would be

2x-7

you combine or add together 4x and -2x

[queen mountain]

Where do you get the 7 from

[fallow gull]

it was in the original problem I gave out lol

[fallow gull]

^^

an example problem

[queen mountain]

Oh I thought we were talking about my problem lol

[fallow gull]

nono I’m just using it as an example

[queen mountain]

I understand

[fallow gull]

ye

so

[fallow gull]

the same concept also applies to here

the problem also contains distribution

do u know how to distribute??

[queen mountain]

No I don’t

I’m sorry if I seem helpless

[fallow gull]

It’s okay

ur just learning this

distribution is when u like, multiply multiple terms if that makes sense

for example

4(x+2)

if I ask u to distribute, what would ur answer be

[queen mountain]

Well I would think I have to multiply 4x2 so 8

8x

[low meteor]

No its four times x

[fallow gull]

8x??

[low meteor]

Plus 4 times 2

So 4x + 8

Hope that makes some sense

What would -3(2x-1) be?

@queen mountain

[queen mountain]

I honestly have no idea

[low meteor]

Divide the whole operation in two parts like I did earlier

Multiply 2x by -3

This produces- ?

You following, bud?

[queen mountain]

Yes im trying to calculate the problem

-6?

Or -6x

[low meteor]

Yeah

-6x

Then how about we multiply -1 by -3

?

[queen mountain]

-3

[low meteor]

No

Its 3

Positive 3

[queen mountain]

Is it cause it’s negative times a negative?

[low meteor]

Yea

Neg times neg is a positive number

[queen mountain]

Okay

[low meteor]

What would the overall answer be then?

[queen mountain]

-6x right

[low meteor]

-6x + 3

There were two parts, remember?

[fallow gull]

If it helps u visualize better Chris

[queen mountain]

I’m really trying hard to understand this but math js makes my head hurt a lot

[low meteor]

🙂

Math is like -

the most beautiful thing

What are you even saying

[fallow gull]

This is only the beginning lol, but trust, it’ll be a lot easier once u understand the basics

do u get how like terms and distribution works tho, right??

[queen mountain]

Idk that I can’t understand it even when taught and it js seems all clustered up

[fallow gull]

or do u want to practice a bit more

[queen mountain]

I sorta understand it

[fallow gull]

both concepts??

[queen mountain]

Were they the ones we just did?

If so then yes

[low meteor]

Why dont you give your problem a shot now?

[fallow gull]

yes

https://cdn.discordapp.com/attachments/903463353417072641/1309389720975052870/IMG_7932.jpg?ex=674167b4&is=67401634&hm=72d1bdb5ca64e1bceca7c0ac5d14362387ef9f7259fed12ab01f565477c53c44&

Putting this here so I don’t have to scroll

[queen mountain]

😭

[low meteor]

Lol

[queen mountain]

Ok let’s try this

[low meteor]

-(6x+3) is basicslly -1 (6x+3)

Can you apply the distributive law here?

[fallow gull]

oh yes, watch out for this whenever u see a negative sign next to anything with parentheses

[queen mountain]

So I would do -1 x 6x ?

[fallow gull]

mhm

and what else

[low meteor]

Yes and then -1 x 3 also

[queen mountain]

Ok then I add them when I finish that?

[low meteor]

Yeah

[queen mountain]

Ok so -6x plus 3x?

[low meteor]

-1 times 3 is -3

[queen mountain]

Oh okay

[low meteor]

It would be -6x -3

[queen mountain]

So do I add them now?

[low meteor]

Yeah

[queen mountain]

-3?

[fallow gull]

-6x - 3 right

If u wanna visualize the steps

[queen mountain]

Omg this is js piling up

I just don’t understand I’m sorry

[low meteor]

Dont give up yet

[queen mountain]

I don’t want to but me trying to actually learn this is difficult

[low meteor]

It will be whole lotta simpler once you add up the like terms

[low meteor]

Come on man this aint that bad 🗿

[queen mountain]

Probably for you

I’m so bad at math it’s my only class without an A

[low meteor]

2x^2 and -6x^2 are like terms

Do you get this?

[queen mountain]

I think I do cause they have x in them

[fallow gull]

yes, but also, it’s x^2

which is different from just x

ppl sometimes mistake adding x and x^2 together when combining like terms

[queen mountain]

Okay so where do I go from here

I have the like terms now what

[low meteor]

Add them up

[fallow gull]

add all ur like terms together

[low meteor]

What do you get by adding 2x^2 and -6x^2

[fallow gull]

any terms with x^2 add together, any terms with x add together, and any terms that r just numbers add together

[queen mountain]

-4x^2

[fallow gull]

YUHHHHH

[queen mountain]

😭

[fallow gull]

okay any other like terms that should be added together??

[queen mountain]

I don’t think so

[fallow gull]

r u sure

[queen mountain]

am I missing something?