help-10

[distant ravine]

So you're saying I can check if vectors are LI using either row with row ops / col with col ops, and I can find the matrix rep of T only by using col with col ops

[warm canopy]

But the mateix that represents T has to be the matrix whose columns are the vectors in the image

[warm canopy]

Indeed

[distant ravine]

Is there a reason for this?

[warm canopy]

For what in particular?

[distant ravine]

For having to use col to find the matrix rep of T

[warm canopy]

Yeah its just because of how matrices work lol

[distant ravine]

I just have a hard time remembering things if I don't fully understand the logic behind them. That's why I'm asking

[warm canopy]

You hit a vector in the standard basis by a mateix and you get a column of that matrix

[distant ravine]

I mean, I remember hearing something once like "if you put the vectors in columns, you're 'breaking' them"

something to do with basis

[warm canopy]

Not sure what breaking them means

[distant ravine]

Me neither lol

That's just the term the person used to describe it

[distant ravine]

What do you mean?

I think they meant that if you use row ops on vectors in rows, you can technically return to the original vector, but if you put it in col and then use row ops, you're changing the vectors or something

[warm canopy]

I gotta leave sorry, <@&286206848099549185> someone jump in please

[distant ravine]

Thanks for the help

[oblique sage]

[distant ravine]

👋

[oblique sage]

I have no idea what a matrix is

[distant ravine]

That's depressing

[oblique sage]

I’ve only taken calc ab

[distant ravine]

Why did you come here then lol

[oblique sage]

Because I was pinged

[distant ravine]

Well, I hope another helper comes...

[tardy epoch]

https://www.imdb.com/title/tt0133093/

[oblique sage]

Thank you Riemann

[distant ravine]

I'm never gonna pass linear algebra 😔

[tardy epoch]

https://pages.cs.wisc.edu/~matthewb/pages/notes/pdf/linearalgebra/Matrices.pdf

it doesn't really matter to most problems. just pick one and stick to it

[distant ravine]

Which site did you get this from? @tardy epoch

[tardy epoch]

i just googled "matrix as columns or rows of vectors"

[distant ravine]

Also, about Span: How do I check if a set of vectors spans a matrix?

[obtuse pebble]

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[solar cedar]

How to calculate how many squares with defined area fit into 64x64 area? For example, i need to fit 4 big squares with spaces of two pixels between them, so what size of squares would that be?

[dapper bloom]

Take the floor

Like if you have kxk squares, you would want to find m such that mk^2 = 64^2, so m=64^2 / k^2

But this value might not actually be an integer

So instead do m=floor(64^2 / k^2)

Oh wait I misread a little

^the work above explains how, given the size of the squares you can find how many (whole) squares will fit into a 4x4 area.

But you're also asking how you can find the dimensions of 4 squares fitting into a 64x64 area.

You'll basically use the same equation though, but now m=4 is given and we need to solve mk^2=64^2 for k.

None of this accounts for padding/gaps, for that I would just let k=m+p where m is the size of the rectangle and p is the amount of padding.

(So k is now the size of the rectangle+the padding)

[obtuse pebble]

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[obtuse pebble]

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[glossy ice]

Hello!

I am looking for a book(s?) with some pre-university math basics explained from scratch, but in a very detailed manner. Possibly with historical notes (for example, take a function. Why exactly this notation is used, where it came from, what other forms of notation are there, and so on).

I have a background in non-functional programming, so it would also be useful if the book covers something on functional programming too (or some examples of historical math applications in computers, or something), but it is not necessary 🙂

[versed cave]

That sounds super cool! But #book-recommendations might be a better place to post this

[glossy ice]

oh, thanks

.close

[obtuse pebble]

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[versed cave]

[obtuse pebble]

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[night holly]

For this question, I'm not quite sure how I should go about answering it. Though I could just google the answer (as it is a practice paper I sourced for revision), that wouldn't help me in an actual test if a similar question came up!

Can I have assistance with the working of this question?

[timid silo]

Do you know this rule

$cos^2(x)=1-sin^2(x)$

[warm shale]

Legolas

[night holly]

Unfortunately not, no

[timid silo]

Well do you know the Pythagorean theorem

[night holly]

Yes

[distant moth]

this has a direct formula doesnt it

[faint stag]

couldn't you also use identities?

[night holly]

oop-

[timid silo]

Yeah

There is an identity

But he doesn’t know it

[night holly]

What's the identity?

[heavy beacon]

sinx=Opp/hyp, cosx=adj/hyp

[night holly]

yes

[heavy beacon]

opp^2+adj^2=hyp^2

[night holly]

um

[heavy beacon]

a^2+b^2=c^2

[night holly]

yes pythagorean

[timid silo]

He’s deriving the identity

[heavy beacon]

Pythagorean theorem

right but i labelled them as opp and adjacent sides

[night holly]

ohhh ik Pythagorean

[heavy beacon]

to use SOHCAHTOA

[versed cave]

You can also find this identity with the equation of the unit circle ^^
The unit circle has equation x² + y² = 1,
Every point on the unit circle is in the form P(cos(θ), sin(θ)) and with a substitution:
cos²(θ) + sin²(θ) = 1

[night holly]

ah okay

that makes sense

[timid silo]

So divide both sides by cos^2x

What do you fe

Get

[night holly]

1= 1-sin^2(x) / cos^2(x)

[night holly]

1 = 1/cos^2(x) - tan x ?

[timid silo]

tan^2x

[night holly]

ah

[timid silo]

And what is 1/cosx

[night holly]

sec^2(x)

[timid silo]

Ok

[night holly]

so

tan2x = sec2x - 1

so sec2x - tan2x
= sex2x - sec2x + 1

[heavy beacon]

that right

go go

[timid silo]

Oh yeah

Sorry the notation confused me

[night holly]

so it just is 1

ty

i learned quite a bit

[obtuse pebble]

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[quartz bloom]

problem 1.4.3 never had a question like this before

[tardy epoch]

can you type it out

[quartz bloom]

Find the value of $a^3b^7c^14$ given that $a^3b^2c=108$ and $a^2b^3c^5=240$

???

[warm shale]

byjos

[quartz bloom]

the c^14 is glitched but ok

[uneven palm]

Find the value of $a^3b^7c^{14}$ given that $a^3b^2c=108$ and $a^2b^3c^5=240$

[warm shale]

kihei

[uneven palm]

maybe try dividing them? I'm not too sure

[quartz bloom]

yeah i tried

didn’t work

[dapper bloom]

You could maybe try taking logs to give you linear equations in terms of a log

[tardy epoch]

you get new equations. use them

[dapper bloom]

Then let x=loga, y=logb, z=logc, solve for x,y,z.

[quartz bloom]

never done logarithms yet

learning that this year

[tardy epoch]

simplify $\frac{a^2b^3c^5}{a^3b^2c} = \frac{240}{108}$

[warm shale]

riemann

[quartz bloom]

how do i solve that

[dapper bloom]

They're just telling you to simplify it to get another equation that might be useful

[uneven palm]

do you know how to simplify exponents?

[quartz bloom]

don’t remember

[tardy epoch]

https://www.cuemath.com/algebra/exponent-rules/ Memorize these

[quartz bloom]

i have no idea what i’m looking at

[dapper bloom]

Rules of exponents

[uneven palm]

okay let's start simple, $\frac{a^2}{a^3}$ simplifies to $\frac{a * a}{a * a * a}$

[warm shale]

kihei

[quartz bloom]

oh yeah nvm i got it

[uneven palm]

now you can essentially "cross out" pairs of a/a

uh okay

[quartz bloom]

$\frac{bc^4}{a}=\frac{20}{9}$

?

oh

[uneven palm]

that's right

[dapper bloom]

=?

[quartz bloom]

idk

OH

[uneven palm]

this one lol

[warm shale]

byjos

[uneven palm]

yeah

[quartz bloom]

$$a=20$$ $$bc^4=9$$

[warm shale]

byjos

[dapper bloom]

Not necessarily

[quartz bloom]

bruh

[dapper bloom]

What if a=1 and bc^4=20/9?

[quartz bloom]

didn’t know that was an option

[dapper bloom]

Yeah yeah lol

Just have to be careful ig

[uneven palm]

is this even solvable?

how would you find $a^3b^7c^{14}$ with this info

[dapper bloom]

I think my log strategy works but it should be solvable without logs

[warm shale]

kihei

[tardy epoch]

brilliant

[quartz bloom]

this is the summer math packet for algebra 2

[dapper bloom]

Unless they cover logs before in this book but byjos prof skipped it planning to circle back later?

[quartz bloom]

ok so i jumped from geometry to accelerated algebra II

so i think i missed a lot

[tardy epoch]

all of this is in algebra 1

[dapper bloom]

You never took alg 1?

[quartz bloom]

i did

[dapper bloom]

Ah gotcha, just rusty then

[quartz bloom]

we never did log tho

[dapper bloom]

Yeah idk if log is always an alg 1 thing

[quartz bloom]

i don’t think it is

[dapper bloom]

These things depend on the school you take stuff at

[quartz bloom]

well i go to a private so

idk

[tardy epoch]

probably depends more on country

[dapper bloom]

You could maybe try to subtract the two equations and factor?

[quartz bloom]

idk how to do that with exponents

i forgor

[dapper bloom]

Then see if zero product property gets you anything?

[quartz bloom]

the what

[dapper bloom]

ig it would still give you something weird

Zero product property is the rule that says if fg=0 then either f or g is 0.

Idk if that would work here tho

[uneven palm]

I wonder what the "hint 122" is

[quartz bloom]

i have no idea what it means

nothing on the page number

[dapper bloom]

Not 240-108 either lol

[tardy epoch]

,calc 240-108

[warm shale]

Result:

132

[tardy epoch]

[quartz bloom]

no way

[uneven palm]

I found something: $\frac{(a^2b^3c^5)^3}{a^3b^2c} = \frac{(240)^3}{108}$

[warm shale]

kihei

[uneven palm]

I think you're just supposed to see that that nicely simplifies to a^3b^7c^14

kind of a weird question

[tardy epoch]

brilliant people

[dapper bloom]

Lmao

[quartz bloom]

i understand now why this class has a 90% dropout rate

[dapper bloom]

Algebra 2 is usually pretty reasonable some questions just aren't written very well lol

[quartz bloom]

*some textbooks

[dapper bloom]

You shouldn't have too many "magic" non-obvious steps like this at this level

[quartz bloom]

wait i think this worked

[uneven palm]

yeah it does work

[quartz bloom]

yooo

[uneven palm]

the sadder thing is I didn't even figure that out with my brain, it was google

pretty unintuitive of a question honestly

[quartz bloom]

well

🤷

me too

[uneven palm]

well simplifying that is something you should be able to do lol

multiply the power of 3 across to all the exponents

and then simplify that

[quartz bloom]

i don’t wanna do work rn

don’t feel like using my brain today

next ones are ez tho

[timid silo]

Oo

[obtuse pebble]

@quartz bloom Has your question been resolved?

[timid silo]

I think i got it

[timid silo]

Yeah

I think now u know what to do

A is 3

And b is 2

C is 1

But why did they give a²b³c⁵=240

Hmm

Wait

I think there is more to this problem

Now we gonna group them such that we will have something common

So sus we dont have 5 as factor in a³b²c

Ok this approach is not working

[obtuse pebble]

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[turbid wren]

I just had my college algebra final and one of the questions stumped me a bit on rational exponents and when an answer becomes + or - for roots. I know that you can raise a rational exponent to its reciprocal to cancel it out, but I am unsure why the answer would only be positive in this instance. I tried formatting it as a quadratic and using the quadratic equation I got 2 answers, but I don’t know if I did that right.

[faint stag]

im pretty sure ur correct

either way works

[turbid wren]

hmm, I asked the professor and she said only the positive answer was valid, and when I input (-7776)^(2/5) in my calculator I get a domain error, so I guess that has lead to doubt. I know there are certain situations when you can take the square root of something without it being +- but I am unclear on when that is.

[faint stag]

ohhhhh

my bad]

yeah you cant square root a negative number

hold on

[fickle turret]

Oddly enough my mobile calculator gives 36

[faint stag]

yeah

the negative answer should still be correct

$(-7776)^{\frac{2}{5}} = (\sqrt[5]{-7776})^{2} = (-6)^2 = 36$

[warm shale]

irtiza

[fickle turret]

But the professor is probably right

[faint stag]

maybe the question asked you to give answers between a certain range?

what exactly was the question?

because if x defined a volume or a length, then it obviously cant be negative

but it really depends on what x was defining

[turbid wren]

There were no specific instructions, just the original equation at the top.

[faint stag]

yeah thats weird

[obtuse pebble]

@turbid wren Has your question been resolved?

[obtuse pebble]

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[wraith vapor]

I've been stuck on this optimization problem for a while now..I need help

"A school graduation class wants to hire buses and vans for a trip to jasper national park. each bus
holds 40 students and 3 teachers and cost $1200 to rent. each van holds 8 students and 1 teacher
and costs $100 to rent. the school has at least 400 students wanting to go, but at most 36 teachers.
what is the minimum transportation cost?"

[restive ridge]

show work

[wraith vapor]

?

[fickle turret]

Also what does "at most 36 teachers" mean?

[wooden cipher]

up to 36 but not 37 or more

[fickle turret]

So basically it means 36 here? The formulation is annoying though

[wooden cipher]

isnt it just cheaper to buy the bus

just buy 10 buses

[fickle turret]

5 Vans cost 500 dollars and they also contain 40 students

[wooden cipher]

oh oops

i was looking at teacher:student ratio

[fickle turret]

I think this exercise does not make any sense

[obtuse pebble]

@wraith vapor Has your question been resolved?

[obtuse pebble]

@wraith vapor Has your question been resolved?

[obtuse pebble]

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[mighty ether]

how do i do this problem? i thought i needed 3 points

[mighty ether]

to get a normal vector

should i just sub in some values for t? to get 3 points?

[obtuse pebble]

@mighty ether Has your question been resolved?

[flat rune]

but here you dont just have 2 points

[mighty ether]

i did this

[flat rune]

you have a line L and a pointA

[mighty ether]

yeah i was subbing in values for t

to get the points

[flat rune]

yes that works!

[mighty ether]

okay tysm

[flat rune]

if youre in doubt, you can check it by

just choosing 2 different points on the line L

[mighty ether]

and the dot product with the normal should be zero

right?

[obtuse pebble]

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[obtuse pebble]

@mighty ether Has your question been resolved?

[obtuse pebble]

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[placid forge]

If someone buys 4 tickets in a raffle with 100 tickets, what’s the chance you will lose? without replacement

[placid forge]

also would help if you can explain how to do it 👍

[zenith raft]

how does the raffle work exactly?

[placid forge]

also there is 2 prizes

[placid forge]

just tickets

there is 100 of them

they pull out 1

and there is 2 prizes to be won

[zenith raft]

so are 2 tickets pulled?

[placid forge]

yes

[royal basin]

does a loss in this case mean not getting either prize?

[placid forge]

yes

neither prizes

[royal basin]

and you have 4 tickets in the raffle

ok

[placid forge]

yep

[royal basin]

98/100 * 97/99 * 96/98 * 95/97

[placid forge]

oh so 152/165

and why do you do that may i ask?

cos i want to know for next time

or in tests

nvm i got it

.close

[obtuse pebble]

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[sterile wing]

Still unsolved.

Ans A

Help

[obtuse pebble]

@sterile wing Has your question been resolved?

[obtuse pebble]

@sterile wing Has your question been resolved?

[obtuse pebble]

@sterile wing Has your question been resolved?

[distant moth]

is this fiitjee monthly exam?

[sterile wing]

Nope

[tardy epoch]

Use https://en.wikipedia.org/wiki/Leibniz_integral_rule#General_form:_differentiation_under_the_integral_sign

[sterile wing]

Didn't work bro we discussed it earlier as well

[tardy epoch]

show what you tried

[obtuse pebble]

@sterile wing Has your question been resolved?

[tardy epoch]

so did you not try using it?

[sterile wing]

Wait I forgot to send it

Let me

It didn't work the last time

Got stuck here after applying the modified leibnitz

[sterile wing]

, rccw

[obtuse pebble]

@sterile wing Has your question been resolved?

[humble quest]

why does f'(0) exist?

[obtuse pebble]

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[rare star]

Hello can someone help me solve 4sin(4x)=-8sin(2x) ?

[humble quest]

what did u try

[rare star]

Tbh just plugging in values

But that seems highly inefficient

[humble quest]

first of all

simplify the constants

and let t = 2x

[warm shale]

Hellboy

Hellboy

[humble quest]

aight

u take it from here

[rare star]

If I divide boths sides by 2sint

it should be cost = -1

right?

[humble quest]

whatchu think?

[rare star]

which occurs when t=pi ?

I think it is right

[humble quest]

good luck

[rare star]

thank you

[obtuse pebble]

@rare star Has your question been resolved?

[obtuse pebble]

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[worn yacht]

could someone please teach me how to do complex antiderivatives?

[tardy epoch]

Stop misusing help channels

Go find a book

[worn yacht]

like $1/(1+u^2$ $du$=$tan^-1 u+C$

[royal basin]

[warm shale]

kangaroo rat

[royal basin]

still

[worn yacht]

lol

[tardy epoch]

#latex-testing

[royal basin]

did you mean $\int \frac{1}{1+ u^2}\dd{u} = \arctan(u)+C$?

[warm shale]

Ann

[tardy epoch]

So complex

Use Cauchy's integral formula

[royal basin]

this particular one is worth committing to memory
also it is not clear what you consider to be "complex" and hence your request is unsatisfiable really

[worn yacht]

wait you explained this yesterday...

[royal basin]

what

[worn yacht]

didn't you?

[royal basin]

this was me retyping what you said

[worn yacht]

nvm

[worn yacht]

yes

how do i do antiderivatives like this?

[worn yacht]

is this still misusing?

should i close the channel?

[worn yacht]

could u please help?

[trail musk]

I thought you were talking about complex analysis for a sec there

[worn yacht]

oh

[worn yacht]

how would you do something at this level?

[trail musk]

Like doing calculus on complex numbers. Best to avoid using the word complex if you're not actually working with complex numbers

But yeah these are a category of integrals that require trig subs

Trigonometric integrals

I guess is what you're getting at

[royal basin]

you learn the basic ones such as powers, trig, inverse trig etc.
you learn methods such as substitution and integration by parts
you practice applying them over and over to different integrals

[trail musk]

Where you have squares plus or minus one

Things that look like that

[worn yacht]

i dint realize i needed to learn this

[royal basin]

"i didn't realize that to learn the hard stuff i need to get the basics down"

[worn yacht]

lol

ok thanks everyone

.close

[obtuse pebble]

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[thin pine]

https://gyazo.com/cf6637a821752dc785e3d182f2c1ced2

[thin pine]

this is false because for not every vector can you multiply it by 1 and get that vector, right?
Proof: Since there exists an x in V s.t. 1x != x, this is not a vector space

.close

[obtuse pebble]

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[trail musk]

Consider what happens when a1 is 0

[obtuse pebble]

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[haughty stratus]

why is f(x) = cos x

[haughty stratus]

an even function

since

cosx doesnt equal cos(-x)

e.g.

cos60 =/ cos(-60)

how?

cos 60 = 1/2

cos -60 would be idek

wdym by go backwards?

ah

so its just based on circle trig

ic

[past fog]

@haughty stratus question

this might help

[haughty stratus]

ok

[past fog]

cos is even right?

give me an example of a function that isn’t even

[haughty stratus]

f(x)= ^3

oops

[past fog]

(Simply so you do this yourself)

[haughty stratus]

f(x) = x^3

[past fog]

no let’s do trig

To keep it simple

[haughty stratus]

oh

[past fog]

One that’s odd

[haughty stratus]

f(x)= sinx?

donut just said that one

[past fog]

okay and is tan even or odd?

[haughty stratus]

would be even right

[past fog]

nope

odd

[haughty stratus]

damn

i can understand if the function is = x

but when you add trig it gets weird

[past fog]

okay so even vs odd functions basically just (graphically) look a certain way as well

sin starts at the midline right?

then either goes up or down right?

[haughty stratus]

x axis?

[past fog]

well yes the standard graphs midline is x axis

But what I’m saying is, the midline of the amplitude of the graph

[haughty stratus]

hh

[past fog]

maybe my explanation isn’t going to help here

[haughty stratus]

if the question says "a is a constant" what does that mean?

a can be anything?

f(a^2) where a is a constant, a=/0

[past fog]

what’s a constant

Is x a constant? Is + a constant? Is 4 a constant?

[obtuse pebble]

@haughty stratus Has your question been resolved?

[obtuse pebble]

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[proven zephyr]

found this question on a past exam paper

[proven zephyr]

i found the formula to find the 700th doll

$(\frac{54}{40.5})^x * 40.5$

[warm shale]

MarveI

[proven zephyr]

how to calculate it without calculator

cuz i think it's not allowed

[grizzled shore]

what is this equal to

what are you solving

[proven zephyr]

(54/40.5)^700 * 40.5

= 1.1603 * 10^89

[grizzled shore]

let's see

[proven zephyr]

54/40.5 = 4/3 btw

[grizzled shore]

108/81 = 36/27 = (4/3)^700 * 40.5

wait what

oh it's 12

man im dumb

so 1.25^700 * 40.5

[proven zephyr]

yes

wait no

[grizzled shore]

oh

[proven zephyr]

1.33

[grizzled shore]

1.33^700

yeah

im curious too now

[proven zephyr]

idk how they expect students to find the answers manually

[obtuse pebble]

@proven zephyr Has your question been resolved?

[proven zephyr]

meh

ima just close this

.close

[obtuse pebble]

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[obtuse pebble]

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[odd arch]

Question

[odd arch]

solution

this is related to permutation, i've got the solution but i need an explanation

[obtuse pebble]

@odd arch Has your question been resolved?

[odd arch]

<@&286206848099549185>

[sudden fox]

Hmmmmmm

Okay so basically what's happening

I was thinking of a solution and it would go something like this:

• You can either choose one O to put in your string of 4 letters, then choose 3 other non-O letters to fill in the rest, and also make sure not to choose duplicate
• Or, you can choose two O to put in your string of 4 letters, then choose 2 other non-O letters to fill in the rest, and also make sure not to choose duplicate

solving the first one

• 4P3 = 4! / 3! = 4, there are 4 ways to place the lonely O

• then there are 7P3 = 7!/4! = 210 ways to place the other non-duplicate letters

• since they are two dependent things, 4 * 210 = 840 ways

• 4P2 = 4! / 2! = 12, there are 12 ways to place the two Os

• then there are 7P2= 7!/5! = 42 ways to place the other non-duplicate letters

• since they are two dependent things, 42 * 12 = 504

then add both: 840 + 540 = 1344

yay i solved another counting problem, yummy 😋

[odd arch]

yeahh congratulation hahaha

thank you so much btw

[sudden fox]

np np

[odd arch]

.close

[obtuse pebble]

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[soft dagger]

Using hough line transform, the points are expressed on the form

r = x*cos(theta) + y*sin(theta)

src: https://en.wikipedia.org/wiki/Hough_transform#Detecting_lines

Yet, I create a line using python:

theta = np.arange(0.0, 180, 0.25)*np.pi/180.0
x = np.arange(0.0, 90.0, .125)
#Line:
y0 = x*1.0 + 10  # i.e. slope of 0.25*pi

I create four points from this line

# Wrong interesection
hough00 = x[0] * np.cos(theta) + y0[0]*np.sin(theta)
hough01 = x[10] * np.cos(theta) + y0[10]*np.sin(theta)
hough02 = x[20] * np.cos(theta) + y0[20]*np.sin(theta)
hough03 = x[30] * np.cos(theta) + y0[30]*np.sin(theta)

This gives me an incorrect angle. However, flipping the x term

# Correct intersection
hough00 = -x[0] * np.cos(theta) + y0[0]*np.sin(theta)
hough01 = -x[10] * np.cos(theta) + y0[10]*np.sin(theta)
hough02 = -x[20] * np.cos(theta) + y0[20]*np.sin(theta)
hough03 = -x[30] * np.cos(theta) + y0[30]*np.sin(theta)

Gives me the correct one shown in the figure.

Does the hough transform not use the same origin if cosine and sine terms are positive?
For instance, I know opencv and other algorithms might flip the sine term because they work with a flipped y in the frame

[soft dagger]

Using both terms as positive I get the following intersection, which is wrong

[obtuse pebble]

@soft dagger Has your question been resolved?

[obtuse pebble]

@soft dagger Has your question been resolved?

[soft dagger]

.close

[obtuse pebble]

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[hoary venture]

what does a solution converging mean? i have a function with two coefficients alpha and beta

[timid silo]

Send the entire problem plz

[hoary venture]

it's just a supply and demand function

alpha and beta are assumed to be positive

[novel knoll]

Means the sequence {s_t} will converge (say g_t=1/t converges to 0 for example)

[hoary venture]

in other questions i've just used economics to deduce the possible values

ye so supply = demand

must alpha be >1?

idk the mathematical proof

[novel knoll]

What is p_t?

[hoary venture]

pt-1 price in the previous period

pt is current price

so you solve for pt

in terms of pt-1

[novel knoll]

What?

Are you given a relation between p_t and p_{t-1}?

[hoary venture]

no

well not explicitly

[novel knoll]

What

[hoary venture]

idk

do you want the whole question?

[novel knoll]

Obviously

Why are you posting half questions

[novel knoll]

And have you done 1 and 2?

[hoary venture]

yea

[novel knoll]

Which is what?

[novel knoll]

And here it says s_t=alpha p_t which is much different from what you posted here?

[hoary venture]

huh

did i post the wrong question

nice one will

bruh sorry i have a bunch of worksheets open

[hoary venture]

i got this one to be Pt = 135 - betaPt-1 / alpha+5

i am so confused

[novel knoll]

What?

[novel knoll]

Where does any of that come from from this?

Where is beta from? Where is 135 from? Where is 5 from?

[hoary venture]

alpha??

i literally don't know

[novel knoll]

Sounds like you are mixing up different excercises

[novel knoll]

Either find where you have done the questions to this or start over from 1

[hoary venture]

beta is a coefficient multiplied onto the price in the previous period

[novel knoll]

Not in what you posted here, no

I don’t see beta anywhere

[novel knoll]

Can you tell me where you see beta?

[hoary venture]

this is the question i'm trying to solve, idk why i copy pasted a different picture

[novel knoll]

So why is your answer

Anything with beta?

Agree beta is nowhere to be found in this question?

[hoary venture]

because it was the answer to this

[hoary venture]

ye ofc

[novel knoll]

And why do you post answer to that?

You just said that was the wrong question

[hoary venture]

man i was confused and worked out the wrong answer

[novel knoll]

So I ask again, have you done 1) and 2) to this? If so what is the answer

[hoary venture]

my brain is so frazzled

i'm doing them now 😭

sorry

Pt = 12 - 5Pt-1 / alpha + 2?

is the general solution

the particular solution is in the form X = C / 1-b which when i google nothing similar comes up?? is my lecturer making up shit idk

[novel knoll]

Oh wait

[novel knoll]

Yes when you fix parenthesis

[hoary venture]

and then factorise left side and divide?

[hoary venture]

whats wrong with the brackets?

[novel knoll]

1+1/2 reads at 1+(1/2)=1.5

And not (1+1)/2=1

[hoary venture]

oh

[novel knoll]

Is the problem when you type in discord

[hoary venture]

ye

[hoary venture]

is this okay?

typing it is pretty poor ik

[novel knoll]

Yep

[hoary venture]

so surely alpha must be >-2? because equilibrium price must always be positive

but thats just econ logic and not maths

i dont know what the proof here is

[novel knoll]

Well you are told alpha is positive already

[hoary venture]

so > 0?

[obtuse pebble]

@hoary venture Has your question been resolved?

[hoary venture]

i get what converging means in this context, but how do i arrive at that answer?

[obtuse pebble]

@hoary venture Has your question been resolved?

[obtuse pebble]

@hoary venture Has your question been resolved?

[obtuse pebble]

@hoary venture Has your question been resolved?

[trail musk]

@W¡ll#0777

[hoary venture]

Hello sir

[obtuse pebble]

@hoary venture Has your question been resolved?

[limber quartz]

$p_t = \frac{12 - 5p_{t-1}}{\alpha + 2}$

Oh

[warm shale]

Disorganized

[limber quartz]

What is the initial condition in this problem?

[obtuse pebble]

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[obtuse pebble]

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[tribal garnet]

this makes a linear pair right?

[tribal garnet]

.close

[obtuse pebble]

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[obtuse pebble]

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[hoary venture]

Everything was in the sc

[hoary venture]

This

[obtuse pebble]

@hoary venture Has your question been resolved?

[obtuse pebble]

@hoary venture Has your question been resolved?

[obtuse pebble]

@hoary venture Has your question been resolved?

[obtuse pebble]

@hoary venture Has your question been resolved?

[hoary venture]

[warm canopy]

Advice, open a new help channel, post the question again and summarise how far you've gotten so that people dont have to follow the breadcrumbs to see where you're at

[hoary venture]

Okay thanks

.close

[obtuse pebble]

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[cunning citrus]

wait i didnt get it lol sorry for opening again but
i used $y=\tan\left(\frac{360t}{24}\right)x$
but how do i get it so that the x intercept is 3.5

[warm shale]

harvard

[cunning citrus]

https://www.desmos.com/calculator/chf9skmfb0

im tryna draw all the lines in the blue part

its the indian

flag

there should be 24

[fierce lagoon]

What are you trying to do

You know there's a polygon maker in desmos right

[cunning citrus]

im trying to put 24 lines inside the circle

and they have even gaps

[cunning citrus]

but how do i use the polygon maker to make this

[fierce lagoon]

it should be polygon()

In the Parentheses, you list out the points

So like

polygon((2,3), (3,4), (-2, 6)) for example

[cunning citrus]

but the lines arent a polygon

[warm canopy]

replace x with (x-3.5)

you also need to change to degrees mode like i said

[obtuse pebble]

@cunning citrus Has your question been resolved?

[cunning citrus]

how

[cunning citrus]

alr

oh

IT WORKS

ur so smart

now I can do the rest

thanks

[warm canopy]

Nice one

[obtuse pebble]

@cunning citrus Has your question been resolved?

[obtuse pebble]

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[obtuse pebble]

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[thin pine]

https://gyazo.com/108fd94f8c641db9146d4687bcc63bce

[thin pine]

im confused how to start

its basically giving you conditions for a vector?

right

and its saying is that a subspace

so i know a and c satisify zero vector but

e doesnt

but i dont know how to check the other two conditions

[warm canopy]

take $a = (a_1,a_2,a_3)$ and $b = (b_1,b_2,b_3)$ in your "subspace"

and see whether $a+b$ and $\lambda a$ are also in the "subspace"

[warm shale]

ΣAC

ΣAC

[thin pine]

wdym

tho

[obtuse pebble]

@thin pine Has your question been resolved?

[warm canopy]

you're gonna have to give me more than just "wdym" after I've explained exactly what you need to do

[tardy epoch]

wdym tho

[visual wasp]

xd

[thin pine]

ok

so like

how do you see each of the examples

cause to me it reminds me of like a null space or something

but like an easier way would maybe be a vector

so like a. is two vectors

[warm canopy]

what the hell are you on about lol

[thin pine]

nono

one vector

[warm shale]

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

[tardy epoch]

https://giphy.com/gifs/the-simpsons-scared-homer-simpson-jUwpNzg9IcyrK

[thin pine]

$\begin{pmatrix}
3 \
-1 \
1
\end{pmatrix}$

[warm shale]

! matthewzz

[thin pine]

that would be a

[warm canopy]

don't start choosing specific vectors, you'll be here for literally forever

[thin pine]

wdym

https://gyazo.com/108fd94f8c641db9146d4687bcc63bce

[warm canopy]

it doesnt really matter what these sets look like

[thin pine]

they are vector subspaces of r3 right?

[warm canopy]

yes

[thin pine]

ok well if we ignore the vec

[warm canopy]

you need to do this, see if a+b and lambda*a still satisfy the relations that are defining these sets

[thin pine]

ohhh

so you get something like

a1 + b2 = 3(a2 + b2) & a3+b3 = -(a2+b2)

then distribute the constants

wait am i on the right track

[warm canopy]

yeah thats one of the things to check

[thin pine]

then the lamda for the other

and you get the same thing

can i write a formal proof and you see if it looks good?

[warm canopy]

yeah and you said you already checked the zero vectors

sure

[thin pine]

also does e) pass the closed under adittion

[warm canopy]

you tell me

[thin pine]

no

[warm canopy]

no you won't tell me? or no it doesnt pass

[thin pine]

$\text{I get that } a_1 + 2a_2 - 3a_3 = 1-b_1 -2b_2 + 3b_3$

[warm shale]

! matthewzz

[thin pine]

i get that it wont pass

[warm canopy]

tip: you don't need to check addition for e because you already know the zero vector doesnt belong in there

[thin pine]

yea i know

but i want to see if i can check

[warm canopy]

it does not pass

[thin pine]

as if i didnt check the zero vec property

[warm canopy]

you would get 2 rather than 1

[thin pine]

wdym

you plug in a+b for all of the a's and b's

how would you get an extra constant

[warm canopy]

youd check the value of (a1+b1)+2(a2+b2)-3(a3+b3)

gather all the a's and all the b's

you'll get 1+1

because a and b are in the set

[thin pine]

ohhhh

you basically group it back to a1 +...+ a3 + b1 + ... b3 = 1 + 1

!= 2

[warm canopy]

!= 2

?

what u doin

[tardy epoch]

a1 +...+ a3 + b1 + ... b3 = 1 + 1 != 2

[warm canopy]

itd be a1+2a2-3a3+b1+2b2-3b3 = 1 + 1 = 2

!= 1

[thin pine]

oops

ya ok

thanks

.close

[obtuse pebble]

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[obtuse pebble]

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[cyan pagoda]

what is an inflection point

[obtuse pebble]

@hidden bronze Has your question been resolved?

[obtuse pebble]

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[boreal oasis]

Ive gotten stuck on this a few times, i tried to count and add with the graph

[boreal oasis]

but ive just ogtten stuck

[turbid sail]

Before I help you what’s your favourite tft comp?

[kindred oasis]

How did you find 42?

[turbid sail]

The definite integral from 0 to 6 would be from x=0 to x=6 just so you’re clear

[boreal oasis]

i like ragewin a lot

but ive seen revel canoneer op

[turbid sail]

Valid response

[boreal oasis]

6+1/2(6)(6)+(3)(6)

thats how i found 42

[kindred oasis]

Why did you add 6 at the beginning?

[boreal oasis]

for the intial ppint

[turbid sail]

Just count the squares

[kindred oasis]

That has nothing to do with the area though

[boreal oasis]

it doesnt ?

[kindred oasis]

Right?

[boreal oasis]

i thought it does

[kindred oasis]

It's just where the function starts

[turbid sail]

It has nothing to do with any calculus it just wants you to get comfortable with definite integrals the actual problem deals with counting area geometrically with squares and triangles which you are very familiar with

[kindred oasis]

1/2(6)(6) is the triangle area, and (3)(6) is the rectangle area. If you sum them you get the area you're trying to find

[turbid sail]

From 0-6 there are 3 squares which are 1x3 and 2 squares cut in half (triangles) which are 3/2 respectively. So 9+2(3/2)=12

[boreal oasis]

oh i see

[fickle swan]

GUDETAMAAAAAA

SO CUTEEE

[boreal oasis]

so what do you think for the other ones ?

henlo

[turbid sail]

Oh wait

I didn’t read

[boreal oasis]

yeah

so what about the others ?

the same thing ?

[turbid sail]

Yeah

[boreal oasis]

what do you suggest the numbers

for the 15 0

[kindred oasis]

Try to calculate it by dividing it in shapes you can calculate the area of

[boreal oasis]

oki

i shall do that

thank you

.close

[obtuse pebble]

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[turbid sail]

This question is somewhat weird because you’ll have to approximate the ones somewhat but for the top tile I would say it is ((3)(2))/2

[obtuse pebble]

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[obtuse pebble]

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[feral sentinel]

hi, can someone tell me what would the logic statement be for this?

like something => something

i wanna try to prove by contradiction or contraposition

but i cant seem to even write out the logic statement to do so

is it that
two consecutive positive integers are co prime => gcd is 1?

[compact shadow]

Because

(1)(x+1)+(-1)x=1

gcd(x,y)=min{|ux+vy|: u and v are integers}

[feral sentinel]

wait hold on

[compact shadow]

Need a proof of this?

[feral sentinel]

i wanna try it myself hah

[compact shadow]

Good

[feral sentinel]

i need help with the logic statement thou

just that

[feral sentinel]

is this right?

[night moth]

yes

[feral sentinel]

ohh

thank u guys

[feral sentinel]

oh also i didnt wanna tag u for like more trivialish questions lol

[compact shadow]

Sure

[feral sentinel]

like ill tag for more interesting questions

[compact shadow]

I just came by like answering all other questions

Appreciated

[feral sentinel]

are u a senior in college or smth

or junior

[compact shadow]

Graduate student

[feral sentinel]

ohhh

ur so good at math lol

its like

u type something out

withint seconds

and i need to take a few minutes to process it

[compact shadow]

Should be like that… otherwise half of my learning time was wasted for nothing 😂

[feral sentinel]

that is

very true

XD

i still got a long way to go before getting gd at math

[compact shadow]

👍

[feral sentinel]

thx

.close

[obtuse pebble]

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[obtuse pebble]

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[lost cargo]

back with another question. I have an important entrance exam tomorrow and my school basically taught me the bare minimum for math in high school so could someone just point me in the direction of what topic this question falls under and the answer to it since there's no answer key. I need to figure out what it is first

[floral garnet]

It's calculus

Or u can say integration

With limits

[lost cargo]

ah yeah I could tell it was calculus but wasn't really sure what part of calculus it was I'll take a look at it now tho ty!!

[floral garnet]

Ok do u need any help with the solution

[lost cargo]

yeah if you could tell me what the correct answer is and how you reached it that would be really great

[floral garnet]

Ok

Ans is A

-x³-x + 2

So do u know to integrate??

[lost cargo]

no unfortunately not I'm really new to this

[floral garnet]

Hmm

U need to learn some formulas

[lost cargo]

I have the general idea of what limits are but I'm not familiar with integration or differentiation I've just heard of both of them

[floral garnet]

U need to learn it first

[lost cargo]

I have a formula sheet but I don't really understand what I'm looking at because I have no idea what the parts mean

[floral garnet]

Yeah that

[lost cargo]

yep I'm going to start studying them today

tysm for the reply as well!

[floral garnet]

First learn the differentiation then Integration

Good luck with that

👍

[lost cargo]

ty!!

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[obtuse pebble]

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[polar harbor]

How do I work out the roots of this quadratic expresssion

2x2 + 12x + 10 = 0

[night moth]

You can use the quadratic formula but i think in your case factorisation would be easier

[timid silo]

ez

just factor

[night moth]

Do you know how to factorise a quadratic function?

Yep

[polar harbor]

Of course

[night moth]

Then factor it

Then you will get 2 sepaarte linear equations of x then solve for x

You will get 2 values

[polar harbor]

But I don't how to find the two values that are in common for +10 and +12x

[night moth]

Ooh so thats where youre stuck

[polar harbor]

Yeah

[visual wasp]

it has 2 roots max

[night moth]

You would have to split 12 x into 10x and 2x

[visual wasp]

maybe u could try to find one that seems "easy" with trying numbers

try for x = 0, 1, -1

[night moth]

Since 10 times 2 is 20

[visual wasp]

when u find one its done

[night moth]

That is u reliable

Unreliable*

[visual wasp]

if the root is -1, then u have an easy factorization by (x+1)

[night moth]

Factorisation is better

[visual wasp]

yeah

i looked at this znd instant knew that -1 was a root

then u factorize by X+1

and you have the other one :)

[night moth]

How you have to split the middle term really only comes through practice

[polar harbor]

But doesn't it have to be in common with 10

[night moth]

Wdym

10x is common with 10

2x with 2x^2

[polar harbor]

Oh ok I thought you have to find the two separate values for 10 and if it is in common with 12x

But in this case do you have to solve for bx first in ax^2 + bx + c = 0

[night moth]

2x^2 + 12x + 10 = 2x^2 + 2x + 10x + 10
= 2x(x + 1) + 10(x+1)
= (2x + 10)(x+1)

[visual wasp]

i still think that look for and easy root is better

[proven zephyr]

it's unreliable

[night moth]

Yes

It only works for really simple functions

[polar harbor]

Like 2(x + 5)(x + 1)

[visual wasp]

yeah but here it is

so why dont do this if it is way easier

[visual wasp]

perfect

[vestal moss]

meow

[visual wasp]

meow

[night moth]

Well thats just preference then

I feel like factorisation is better always

[proven zephyr]

he's also factoring

[visual wasp]

mmh yeah if u prefer it, then yeah

im doing it also

[proven zephyr]

both are a way of factoring

[visual wasp]

but quicker because of the easy pattern

[proven zephyr]

but unreliable for harder problems

[visual wasp]

i mean as long as factorization as u use is useful, mine is useful too

[proven zephyr]

ok

[visual wasp]

for harder problems u have other methods

[proven zephyr]

i didnt say it's not useful

[polar harbor]

What do I do with the 2

[visual wasp]

not talking to u dw

[polar harbor]

Out of the bracket

[proven zephyr]

ok

[visual wasp]

divide by 2

if u want

to see that its not a root

[proven zephyr]

i'd say just leave it as it is

[visual wasp]

yeah

[polar harbor]

Ok because it would equal to 0

[visual wasp]

yeah

[proven zephyr]

yes

[visual wasp]

0/2 = 0

[night moth]

Remember that the whole thing is equated to 0

[night moth]

This

[polar harbor]

Alright thanks guys

.close

[obtuse pebble]

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• Show your work, and if possible, explain where you are stuck.
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[dusk estuary]

.

[pastel scaffold]

how do i do 13 iii

and b

[misty terrace]

uwu rotate

[pastel scaffold]

answer to the ai, and ii are 1.55 and 1.27

i know the answer to iii but idk how the sheet got it

[timid silo]

consider the triangle ABD. Length AB is 6, and angle BAD is 15

find BD using trig

[pastel scaffold]

sorry i didn't word it right

i am fine with i and ii

just need help with iii

[timid silo]

the height difference of A and C is equal to the sum of the difference A and B with B and C

ie add i and ii