help-27

[lone ravine]

Je suis desolée pour mon mauvais français

[olive snow]

Tbh when ppl speak french, i don't really watch the grammar or whatever, i assure you are speaking it well

You made two little mistakes (add/forget a letter) in both messages

Which change nothing to the meaning

[devout snow]

@restive river Has your question been resolved?

[restive river]

Idk how tbh

Should I do a synthesis analysis ?

[lone ravine]

You can use that f(x) = f(x/2)

[lone ravine]

I have no idea what this is

[restive river]

oh yeah

Nice idea

[devout snow]

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[restive river]

Can someone walk me through the steps on how to solve this

[stiff quartz]

Are you using quadratic formula or factorization to solve it?

[wicked turtle]

which one?

[restive river]

Like ik there's different ways to solve it since it's a quadratic ewuation

[split pivot]

Which

[restive river]

Either way works

[restive river]

12

[stiff quartz]

Which method do you prefer

[restive river]

Im not sure i haven't done much practice probably using the quadratic equation

[split pivot]

Discriminant will work as switz watch

So theres a formula for quadratic ecuations

Which is

[stiff quartz]

Ok, so first you will get a, b and c (the coefficients)

[split pivot]

Try making this using a,b,c

[stiff quartz]

x2 + 5x -24 = 0. Do you agree?

[split pivot]

Ohh shit right

[stiff quartz]

now we can get the a, b and c values

[restive river]

Should I make it become x²+5x-24=0

[stiff quartz]

yes

[split pivot]

You should firstly equal the equation to zero

[split pivot]

Yes

[stiff quartz]

a = 1, b = 5, c = -24

[restive river]

Ok and I plug it into

[split pivot]

Make him think man 🙂‍↔️

[restive river]

The quadratic equation

[stiff quartz]

yep

[restive river]

One sec

Oh I missed the plus minus

[split pivot]

-5+-sqrt

[restive river]

Hold ob

[split pivot]

Ye

[split pivot]

Now what you need to do

[stiff quartz]

reduce

[split pivot]

Now what do you think you should do now

[restive river]

Er idk the word but do I multiple the -4(1)(-24)

Multiply

[split pivot]

You could

I would recommend firstly doing

5^2

[restive river]

So 25

[split pivot]

Ye just write it as 25

And you can do the multiplications right away

[restive river]

Oka

96?

[split pivot]

Yep

Good

Now what do you have

[split pivot]

-5+-sqrt(25+96)

Take this 1 off out the denominator

[restive river]

Ok

Just 2 then

[split pivot]

Useless

Ye

Now just do the root

[restive river]

121

Like this?

[split pivot]

Sqrt of 121?

[restive river]

11

[split pivot]

👏

[split pivot]

Now what i do

Is it put two lines

And do one for + and one for -

[restive river]

So one is 5+11/2 and the other is 5-11/2?

-5*

[split pivot]

Ye

[split pivot]

Ducking great

https://media.discordapp.net/attachments/194772750957674497/1018378384323129414/182-shakethecat.gif

[restive river]

Do I leave my answer like that orr

😭🥺

[split pivot]

Ye

Ye

I mean if teacher will say that you should write

Sol: x1= -8; x2= 3

[split pivot]

But normally just leave it

[restive river]

OKIESSS

[split pivot]

Dont forget

In the next

(A-b)^2=a^2 -2ab+b^2

😉

[restive river]

What's this for 😭

[split pivot]

For (10-x)^2

[restive river]

Oh

Wait

If u don't mind

Can u walk me through that

💀💀💀😭

[split pivot]

Just put

10 where a is

And x where b

So

10^2-2 * 10 * b+b^2

[split pivot]

Wait

What

[restive river]

Idk

💀💀

[split pivot]

1. Where did you get 1

2. My bad your a is x and b is 10

[restive river]

Is x not 1 😭

[split pivot]

Your x is one line

[restive river]

Ope

[split pivot]

Why would it be one

Its x

You have to find it

😭

[split pivot]

Yes

Good

[restive river]

Bc im silly

[split pivot]

Now just do all ^ and multiplications

[split pivot]

Btw all this =-25

Dont forget

Youre doing the ecuation

Not just (x-10)^2

Nvm

[split pivot]

Gotta go take the shower

[restive river]

LOL okk

[split pivot]

Now just do a equation

Like the last

You can do it

[restive river]

Ok

I got it

[split pivot]

🫡

[restive river]

TAHKNK U SIR

.close

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[icy crag]

Since 0
is a possibility for oranges and for apples but not for both. we have
(9 + 1)(6 + 1)- 1 ways" Is the solution as described in the answer key, can anyone explain this to me please?

[verbal vector]

the easiest comparison for me is with factors of numbers

[icy crag]

I understand that 0 is not a possibility for both, however the formula that follows is new to me. What is the reasoning?

[verbal vector]

this

if we have a nukber

a^3 • b^2

how many factors are there?

the rule is

(3 + 1)(2 + 1) or 12

you either have the factor in or you dont

same idea with the fruit

[icy crag]

No, I still don't understand

[icy crag]

?

[verbal vector]

uhhh

okay the fundamental theorem of counting says

if you have m ways to do one thing and n ways to do another

there’s m • n ways to do both

do you agree with me

[icy crag]

yes

[verbal vector]

okay

in this scenario

you can pick 0-9 oranges (10 options) and you can pick 0-6 apples (7 options)

so then 10 • 7 ways to pick the fruit

understand to here?

alright

last thing is that

there is a case where you pick neither of the fruits

so you have to subtract one

thus (9 + 1)(6 + 1) - 1

[icy crag]

ah, I thought the -1 was because you include zero in both cases, which can't be right since the requirement is at least 1

[verbal vector]

it is?

[icy crag]

I interpreted you saying neither as something else, apologies

thanks for the help

[verbal vector]

alright

[devout snow]

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[nova sage]

i have a question that is NOT about math

[nova sage]

however

you are all smart people

so

how does asexual reproduction work in angiosperms

actually nevetminf

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[feral ledge]

How would you solve this?

[timber pebble]

just look at it

should be exact at that point

[feral ledge]

How do you mean? I know you have to work out the gradient of line B

But I’m not sure how

[restive river]

It’s just the slope of the line - rise/run

[timber pebble]

you dont have to

just eyeball it

which one is closest

[feral ledge]

That’s what I need help with working out the gradient

[feral ledge]

How can you just eye ball the gradient?

[timber pebble]

which one appears most tangent

it should stay close to the function

it shouldnt come in at a wonky angle

or pull away too quickly

[feral ledge]

I don’t understand

I think your talking about the line

I’m talking about how you work out the gradient of line B

[timber pebble]

well youd need to function first

but its not intended

[feral ledge]

Well you need to do ur fuckin job and tell me the answer

[devout snow]

@feral ledge Has your question been resolved?

[devout snow]

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[fierce osprey]

me and my friends have been debating whether if the 1 at row 0 is to be isolated or to be grouped with the 1 at row 1, whats the case here

[fierce osprey]

( im new to kmapping and this confuses me )

( internet modules tell me that its to be isolated, while my friends have been telling me that i should be grouping it )

[smoky nimbus]

It's better to group it

So it reduces more

[fierce osprey]

but its still fine to isolate it?

[smoky nimbus]

It's not going to be the most reduced expression

[fierce osprey]

ah so its for the expression to be in its most simplified form?

[smoky nimbus]

Since you isolated it, you have x'yz but if you group it, you'll get yz

[smoky nimbus]

That's what a kmap is used for, to reduce to most simplified form

[fierce osprey]

how about in these cases

the lone 1 at column 01, row 1 is to be isolated right

[smoky nimbus]

Which?

[smoky nimbus]

Yes that's to be isolated

As a rule of thumb you want to make groupings in the size of 2^n

[fierce osprey]

alright alright

that would be all for now, thank you @smoky nimbus 🖖

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[serene dragon]

please help me find d(x+s)/dt

[devout snow]

@serene dragon Has your question been resolved?

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[hoary osprey]

so this is my answer how to determine the truth table

[hoary osprey]

the number 2 is wrong tho, my real answer is

r is false, s is false = false v false is false
q is true, so false <-> true is false but "~", so TRUE
r = false, so true -> false is false

so its false

how do i change the words into the symbols like on the number 4. T T F F T F F = False

idk what its called but i just call it symbols

[devout snow]

@hoary osprey Has your question been resolved?

[hoary osprey]

<@&286206848099549185>

[visual hazel]

apologies for my ignorance but whats your question here

[hoary osprey]

So here is my answers right

[visual hazel]

uh huh

[hoary osprey]

here are the examples and look at number 1 and 4

they have this kinds of symbols? im not sure what its called

T T F F T F F = False

How do i get the symbols of my answer

[visual hazel]

i see

[hoary osprey]

here are the questions

[visual hazel]

oh wow the book just kinda goes random with its truth value labelling

[hoary osprey]

yes it is

[visual hazel]

then just do however you want

make a truth table if you want

maybe something like this idk

[visual hazel]

^

[hoary osprey]

0 = false and 1 = true

here's a copy of a truth table

ohh i see

[visual hazel]

works too if you can understand it

[hoary osprey]

correct me if im wrong, my answer on number 1 should be TFFFTFFTTF

[visual hazel]

[hoary osprey]

cuz thats my answer on my truth table

[visual hazel]

yeah sure

usually i dont write the original and the negated together

but its whatever

[hoary osprey]

could you check my answer on number 1?

what would be your answer on number 1?

mine would be TFFFTFFTTF so its False

[visual hazel]

yeah its false

[hoary osprey]

I see

I get it now

I believe that’s all I need for now.

Thank you so much for your help, Shioshi.

Thank you so much for your time and help

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[junior totem]

i forgot what the addition method entails

[hollow pulsar]

if a = b and c = d
then a + c = b + d

[junior totem]

thank youu

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[humble glacier]

the C in the answer is 44 but i got 110

prolly had smth to do with the 2.5

[sullen island]

yeah the 2.5 shouldn't be there

$e^{\int 0.4 \dd{t}}$ ain't the same thing as $\int e^{0.4 t} \dd{t}$

[woven radish]

aPlatypus

[sullen island]

the second one is indeed e^0.4t / 0.4

[humble glacier]

oh wait

so it should just be e^0.4t

[sullen island]

yea

[humble glacier]

the e^0.4t/0.4 is wrong

[sullen island]

it is

[humble glacier]

thank you!

[devout snow]

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[fathom harness]

From point A, which lies outside the circle (O), draw two tangents AB and AC to the circle (O) (B and C are the points of tangency). The ray AO intersects the chord BC at point H, and draw the diameter BK of the circle (O).

Prove that ∠ACD = ∠HKB.

Given data:
• OA is perpendicular to BC, and OA is parallel to KC.
• AK intersects the circle (O) at point D.
• Triangle ABK is similar to triangle ADB.
• Triangle BDK is a right triangle.

[devout snow]

@fathom harness Has your question been resolved?

[fathom harness]

<@&286206848099549185>

😭😭😭

[dapper fable]

abk is similar to adb helps solve it

[fathom harness]

Can you explain it

My teacher said that the tip is proving 4 blueish angle is equal

[dapper fable]

nvm i was on something

[fathom harness]

<@&286206848099549185>

[fathom harness]

<@&286206848099549185>

<@&286206848099549185>

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[obsidian nebula]

can someone explain how did our equation 2/s^2+4 got simplified to tan inverse

[violet wind]

It didn't get simplified, they took the integral

[devout snow]

@obsidian nebula Has your question been resolved?

[obsidian nebula]

we will take 2 from nominator and 1/2 out from the denominator in equation which will leave us with 1/s^2+2 to integrate right?

[violet wind]

nope

can't pick and choose which part of the denominator you want to pull out a 2 from

[obsidian nebula]

ya exactly

[violet wind]

do you know how to integrate 1/(x^2+1)

[obsidian nebula]

ya thats tan inverse x

[violet wind]

ok

use s = 2u then

[obsidian nebula]

oh

i need to substitute

ok makes sense now

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[main oasis]

Translation:
Let x be the result of the following operation (image above, line 1). Decide if the following statements are true or false.

• x is less than 1000
• x is not an integer
• x is an odd number

How do you solve thin type of question? I have no idea where to begin.

[supple knot]

Try writing every term in parentheses as a single fraction

1+1/2=3/2

1+1/3=?

[main oasis]

4/3

I'll see what I can come up with

After doing that nearly everything cancelled out and I got x = 1006, so I guess it's solved

Thanks for the hint

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[hexed berry]

Guys...

[hexed berry]

If I have something like 2*(x+1)^2

Yeah, I get 2x+2 * (x+1)

NOW.

Do I multiply 2*(x+1) or

(2x+2)*(x+1)

????

[small urchin]

The second

[hexed berry]

Ah yes?

[hexed berry]

What's the reason behind it tho?

[trail eagle]

There's parentheses there in any case, not writing them is what's confusing you

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

[hexed berry]

Wait so

Parentheses never leave after you multiply?

WHAAAAAT???

[trail eagle]

They leave when it's unambiguous, but as you've written it above 2x + 2 * (x+1), the order of operations would stick with 2x+ (2*(x+1)) if you don't have parentheses. That is not the same as 2 (x+1)(x+1)

[hexed berry]

FUCK.

[hexed berry]

Now my exercise is correct.

FUCK yeah!

[hexed berry]

What do you mean when it's ambiguous

Any rule master?

[trail eagle]

As a rule of thumb, if you're multiplying by a single constant, no parentheses. If you're mulitplying other things, keep the parentheses. It'll be clear if you don't need them

So 2(x+1) = (2)(x+1), but we don't need the parentheses for 2
(x+1) * (x+1) we need them since order of operations would induce the wrong interperetation if we just write x+1 * (x+1)

[hexed berry]

Why tho?

I don't get it, fuck.

Why is (x+1) not the same as x+1(*(x+1)

[trail eagle]

It's the order of operations.
In x + 1 * (x + 1), the "correct" way this is parsed is that we start with multiplications, and then move onto addition.
So in other words x + 1 * (x + 1) = x + (1 * (x + 1)) = x + (x+1) = 2x + 1

(x+1) * (x+1) is parsed as you would expect as
(x+1) * (x+1) = x^2 + x + x + 1 = x^2 + 2x + 1, which as you can see isn't the same as above.

When in doubt, just put more parentheses to ensure the operation you're writing actually corresponds to what you mean

[hexed berry]

Well, I was doing this exercise so

Gotta find second derivative, y'know

yeah, and when I added parentheses it started to work.

Then again @trail eagle

when am I supposed to leave the parentheses?

what do they affect?

[devout snow]

@hexed berry Has your question been resolved?

[devout snow]

@hexed berry Has your question been resolved?

[royal radish]

whats your question

[hexed berry]

Based pfp, a man or woman of culture I must say.

[hexed berry]

When do we remove parentheses?

[royal radish]

thank you

[royal radish]

whats the orignal question

i really dont wanna

read all of that

text wall

[hexed berry]

This.

Second derivative, you see.

[royal radish]

do u know how to find the first

@hexed berry ?

[hexed berry]

Of course

[royal radish]

what is it

[hexed berry]

F'(x)*g(x)-g'(x)*f(x)

[royal radish]

what

why are you using the quotient rule

[hexed berry]

Because we gotta use quotient rule?

[royal radish]

you can bring

the denominator

to the top

and just make the exponent -1

than just do the power rule along with the chain rule

[royal radish]

does that make sense

[hexed berry]

Yeah but like

my dumb cirno intelligence

won't let me try that during test

you smart me cirno

[royal radish]

what

you basically have to do this

unless u want a crazy long quotient rule

but they probably wont even accept that

[hexed berry]

Yeah

Next time gonna do that then.

[hexed berry]

Thank you diamond

Based pfp ans based brain

Based face too probably

[royal radish]

no problem 👍

[hexed berry]

What do you think about your pfp

[royal radish]

what

[hexed berry]

Yeah what do you think about your prp

btw sent you a fr

[royal radish]

what do you mean

what do i think

about my pfp

lol

if i didnt like it, it wouldnt be my pfp

[devout snow]

@hexed berry Has your question been resolved?

[hexed berry]

No like

wdyt about girls that

[royal radish]

how has your question

not been resolved

[hexed berry]

paint their nail like Emilia

Yeah my bad

[royal radish]

bruh i got no idea what emilias nails look like 😭

[hexed berry]

.close

[devout snow]

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[royal radish]

i just know the character

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[humble fulcrum]

Are there any good strategies in integrating functions like 1/(x^4 + 1), cscx, 1/x^5 + 1) etc

[versed juniper]

umm like what exactly id use different methods for each of those integrals

[fossil locust]

integration is a case-by-case process

[versed juniper]

yep adding a single thing to an integral can make its ideal approach entirely different

[fossil locust]

also like the integral of 1/(x^5 + 1) is nasty

[humble fulcrum]

Thing is, there is no clear technique that you can use in integrating those kinds

[fossil locust]

csc x is not hard

[versed juniper]

oh so you are asking about the little tricks you can use to make them easier?

[humble fulcrum]

Kind of

[fossil locust]

https://www.youtube.com/watch?v=av4EqKInHcU

[versed juniper]

you know all about u sub, trig sub, that kind of stuff?

[humble fulcrum]

Yea

[versed juniper]

what about a "fancy one"

[royal radish]

Is that seriously the integral

That’s wild

Good thing integral sheets exist for a reason

[versed juniper]

you u sub after

[humble fulcrum]

Yea that's doable, but like how do u know what to manipulate it into

The only thing ik is u have to do lots of trials and errors

[versed juniper]

ill just say it how i heard it

you learn to "smell" it

when you do a lot of integrals you just look at it and feel like you know what goes next

what we can do now for you is show you a lot of different tricks to manipulate the integral into something more familiar

we cant really "teach" you exactly what to use because integrals are built on a case-by-case basis

[fossil locust]

yeah it's impossible to really come up with methods on your own

all you can do is look at other questions you've done and try to see if you can apply the same methods

[restive river]

The integral of sec(x) has a pretty interesting history. It has a whole Wikipedia page.

[tame gulch]

I realise this is unhelpful for OP, but for the trig ones like $\int csc(x) dx$, my teacher just told us to memorise them

[woven radish]

luna-maia

[royal radish]

Than who invented u sub if it’s impossible 🧐

[versed juniper]

there can only be so many methods discovered before it's just renaming an old one 😭

[humble fulcrum]

Well those other questions, thing is those have an obvious technique u can use

[royal radish]

I lokey be praying sometimes that I can invent the math my self on tests

But nothing is impossible

Who knows

[fossil locust]

Newton and Leibniz I'd say

u-sub is just the chain rule in reverse

[vital dagger]

Reverse chain rule

[humble fulcrum]

While these kinds u have to do lots of manipulations to find an equal expression that is doable

[fossil locust]

starting out with $f'(g(x)) \cdot g'(x)$, you can integrate that

[woven radish]

southlander!

[versed juniper]

welcome to math

[fossil locust]

https://math.stackexchange.com/questions/325950/integral-of-cscx

also there can be many different forms for the same integral

[humble fulcrum]

Yea but in the first place, how did they find an equal expression for it that is integrable

Was it trial and error

[vital dagger]

MIT integration bee math tricks just search something along those lines on yt

[vital dagger]

I assume it's just Riemann summ and they find some cool e function?

[humble fulcrum]

e

for instance this https://math.stackexchange.com/questions/333611/evaluating-int-frac1x41-dx

how did they find an equivalent expression for it

trial and error?

[fossil locust]

just use partial fractions

[humble fulcrum]

is it factorable?

[fossil locust]

yes

https://math.stackexchange.com/a/333620/1245737

there is a note below the answer, point 1

[humble fulcrum]

was this a known factor?

how did one find this out

[fossil locust]

add 2x^2 and subtract -2x^2

then complete the square and then difference of two sqaures

[humble fulcrum]

ah

well i wanna know how do you come up with those

[vital dagger]

...you just do

[fossil locust]

it's hard to come up with it by yourself

[vital dagger]

Like honestly idk what to tell you

[fossil locust]

maths is a very very old field
chances are whatever you do, it was probably done by some guy hundreds of years ago

especially at a pre-research level, so like all of undergrad and before at least

[humble fulcrum]

uh what so those guys already know what to do already?

[vital dagger]

No I said that they just do know how to come up with these solutions

They have the knowledge to advance and they know how to use it

And they do, so in a sense yes they know how to do it, if the question was posed differently

[humble fulcrum]

so no trial and error?

[vital dagger]

Not sure what you even mean by trial and error

Keep changing the functions until it looks integrateable?

[humble fulcrum]

yes

[vital dagger]

Well they do that I guess

[humble fulcrum]

well that's very hard then

rip

[vital dagger]

Or they could also just imagine a function that's integrateable, then try to find a way to make it look similar

That's basically ODEs

[humble fulcrum]

well ig that's it

anyways thanks

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[analog badge]

Can anyone help me with time series ?

[analog badge]

I have this tables

what model should i choose based on this ?

My goal is to forecast microsoft stock prices

btw my english is not the best

The automatic model and ARIMA(1,1,1) with drift have the lower AICc , but in the other hand they have one of the highest RMSE , how can this happen ?

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[solar brook]

Can someone help? I'm trying to calculate the Daylight Factor (DF) at point X, but my result is consistently at least 2.5% too high. I need it to be below 5% to align with logical expectations

[solar brook]

Window Dimensions: 2 meters wide and 2 meters high.
Reference Point (X): 0.8 meters high and 1 meter away from the window.
Obstructing Building: 6.2 meters tall and 6 meters away.
Calculating the Obstruction Angle:

𝜃=tan−1(6.2−0.8/6+1)≈39.8∘
Calculate Ratios:

𝐻−𝐻𝑥/𝐷+𝐷𝑥= 6.2−0.8/6+1≈0.77

𝑊/𝐷+𝐷𝑥= 2/7≈0.29

Using BRE Tables:

Finding the intersection of these ratios to get the SC value. Assuming SC value of 0.05

ERC: 𝐸𝑅𝐶=𝑆𝐶×brightness or reflectance = 0.05x0.1 = 0.005
IRC: Using BRE tables to find the IRC value. assuming IRC value = 0.02

𝐷𝐹= 𝑆𝐶+𝐸𝑅𝐶+𝐼𝑅𝐶= 0.05+0.005+0.02= 0.075
Converting percentage : 𝐷𝐹=0.075×100= 7.5%

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[slate obsidian]

Im not sure where im going wrong here. I need to use stokes' theorem
the four points are on the plane z=1/3 y
a parametrization of this is r(u,v)=u i + v j + 1/3 v k
curl (F)= 10y i +2z j +4y k, which in terms of u and v is 10v i + 2/3v j +4v k
the two derivatives of r(u,v) are i and j+1/3k, the cross product of these is -1/3 j+k
the dot product of curl(F) and this cross product is 10/9 v
integrating from 0 to 3 with respect to v and then 0 to 3 with respect to u gives 15

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[supple knot]

The dot product of curl(F) and |r_u(u,v) cross r_v(u,v)|sounds wrong

The k component is 4v * 1 and that's already larger than 10/9*v

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[keen bramble]

How do you integrate this problem?

[keen bramble]

I have been watching Organic Chemistry tutors video on how to integrate these types of problems, and he does not have an example like this in the video. He has something similar, but I dont know how to integrate a problem like this.

<@&286206848099549185> '

[solar goblet]

just separate the fraction?

$\int\frac{7x^2-9x+3}{x^2}\dd x=\int7\dd x-\int\frac9x\dd x+\int\frac3{x^2}\dd x$

[keen bramble]

ok did this. Im confused on what to do for the 3/x^2 though? do you just leave it since there is no x on the top?

and afterwards is that the answer plus c?

[solar goblet]

what have you done

i cant believe youve done this

[keen bramble]

bruh

[amber edge]

you can integrate it like u integrate any other x^n you add one to the power and divide by the power

except the power is -2

[keen bramble]

is that not what I did

[solar goblet]

no thats not what you did

[keen bramble]

😦

one sec

ok is this better?

I forgot the 9^2 and 3^2

[amber edge]

Ok so id start by saying its better to simplify your x terms before you integrate

wait im reading the wrong thing oops

[amber edge]

so the first issue is you've accidentally done 7x^2/x^2 = 7x so when you integrated you got 7x^2/2 which would be correct if you were integrating 7x but you're integrating 7

[keen bramble]

its 7x^3 in the original. my handwriting just bad

[amber edge]

oh

then yeah thats correct

but the 9/x term is a special case

9/x = 9x^-1

if you add one to the power you get 9x^0

it actually integrates to 9ln(x)

so that one you just have to know

[keen bramble]

does that apply to the 3/x^2 too?

[amber edge]

not quite

3/x^2 = 3x^-2

if you add 1 to -2 you get -1

which is fine

you can do it normally

$\int \frac{3}{x^2} \dd x = \int 3x^{-2} \dd x = \frac{3x^{-2 + 1}}{-2+1} + c$

[woven radish]

I can't believe you've done this

[amber edge]

ill get it right eventually

thats how you do that integral

so you should get $$ \int \frac{3}{x^2} \dd x = \frac{3x^{-1}}{-1} = -\frac{3}{x}$$ using negative powers

[woven radish]

I can't believe you've done this

[amber edge]

if that makes sense

im not good at explaining stuff sometimes

[keen bramble]

I got it now. Thanks for the help

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[strange knot]

Two textbooks are selected at random from a shelf containing three statistics texts, two
mathematics texts and three engineering texts. Denoting the number of books selected
in each subject by S, M and E respectively, find (a) the joint distribution of S and M

[strange knot]

this is my jpdf

it doesnt add up to one

when i look it up online

(x=2, y=2) has a value which i dotn think is possible

and (x=0, y=2) has a different value than mine which i think is wrong

[tall knoll]

what are x and y?

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[strange knot]

x is random varible for math tb and y in random variable for stats textbook

[misty crest]

you found out

[tall knoll]

the question says M and S are those random variables but alright

show me the calculations you did to get those numbers

[strange knot]

okay here i called M as X and S as Y

if you needed (M = 1, S = 1) = 2/8 * 3/7

[tall knoll]

now we reach the crux of the problem. That calculation is missing something

that assumes that you pick a math textbook and then a stats textbook; that's not the only way to select one of each

[strange knot]

i mean

even if you picked the stats book first

its

3/8 * 2/7

[tall knoll]

indeed it is

[strange knot]

yeah...

[tall knoll]

so you can get 1 math and 1 stats book by picking a math then a stats OR a stats then a math

how does one normally handle OR when computing probabilities?

[strange knot]

addition?

[tall knoll]

quite so

[strange knot]

yes.

thank you got it

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[lucid mason]

can some1 help with b)

i think im tired but i keep getting it wrong

ik -5pi/12 is -75 degrees = -45 - 30

so

tan(-pi/4 - pi/6)

and then u start the identity

[halcyon otter]

use addition formula for tangent

since u already have tan(-pi/4 - pi/6)

[lucid mason]

why

45 + 30 gives positive 75 tho

[halcyon otter]

denominator is +

[lucid mason]

or do i just add a negative at the very end?

[river knot]

^ this

[lucid mason]

but

[halcyon otter]

it’s 1+

[river knot]

it’s always opposite the sign of the operator in numerator

[lucid mason]

so how do i do with plus?

tan(pi/4 + pi/6) ?

thats just weird tho bc it gives positive 5pi/12

[lucid mason]

oh

OH

ohhh

i made a mistake i think then

[lucid mason]

if u mean only here

[halcyon otter]

yes

that’s all

[safe knoll]

if ur confused u can also write
tan(-5pi/12) as tan(7pi/12) which is just tan(pi/3+pi/4)

and then u dont have 2 negatives and u wont be confused

[lucid mason]

tyy

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[sand quarry]

For (3) I concluded that this is only possible if
$$ \int_{-\infty}^{\infty}x(t)\left[\cos(\omega t)\sin(\alpha \omega) - \sin(\omega t)\cos(\alpha\omega)\right] = 0 $$
if you take $\alpha = \frac{k\pi}{2\omega}$ for some integer $k$ then you're left with an even multiple. But is my thinking correct overall?

[woven radish]

Aero

[sand quarry]

To be clear, the notation above is describing [x(t) \xrightarrow{\mathscr{F}} X(j\omega)]
where $j = \sqrt{-1}$

[woven radish]

Aero

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@sand quarry Has your question been resolved?

[wheat bough]

yes

i believe so

[sand quarry]

Issue is: kpi/2omega doesn't make much sense in my mind

alpha is meant to be a constant I presume

but we are making it depend on omega

[sand quarry]

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[simple canyon]

given this system,
1)they ask us to find the rank of this system
2)and then determine the principal matrix and the principal equations and the principal var of these ystem
3) Rouché-Fonténé Theorem to give the neccessery and sufficient condition on and b for the system to be consistent (specify the determinant bordering the principal determinannt)
4) solve the system if it consistent,

for the rank i wanna use REF

so what i know is that to find the principal matrix i need to find the rank of the matrix, and then those equations will be the equation of my matrix (independent equations)
and then put them as principal equations

for Rouché-Fonténé Theoreme, based on my understand it's say that:
if the rank of (A) = rank(A |b ) < n the system is consistent, it's have infinite solutions
if rank(A) = rank(A |b) = n it's the system is consistent and have only one solution
if rank(A) < rank(A|b) the system is unconsistent and don't have solution
and then for question 4 i believe the system is consistent based on the value of a and b, so i just reply with that value and solve the system

do i'm doing anything wrong?

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[simple canyon]

<@&286206848099549185>

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[wispy geyser]

am i right with D here?

[vital dagger]

It's wrong

Show your workings like you did the last

[wispy geyser]

im srry i mistyped i meant D there

[vital dagger]

You chose B though

[wispy geyser]

damn man its on paper for this

[vital dagger]

😭😂

[wispy geyser]

its random

i picked b there then typed it on mistake

[vital dagger]

It's D that's correct

[wispy geyser]

i would send a pic but i genuinely cant here 😭

thank you again

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[half cargo]

Question: If two nxn matrices A and B over a field F have all four of the following being equal to each other, must A be similar to B?
Characteristic polynomial of A
Characteristic polynomial of B
Minimal polynomial of A
Minimal polynomial of B
Prove why or give a counter example.

My thoughts: I think the answer is yes bc I really can't think of a counterexample. I found 4x4 matrices that both had characteristic polynomial x^4 and minimal polynomial x^2 that had different JCF so weren't similar but then I realised the characteristic polynomial had to be equal to the minimal polynomial so that wasn't a counterexample.

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@half cargo Has your question been resolved?

[pulsar dock]

If the characteristic polynomial for a matrix equals the minimal polynomial that tells you a lot about the kind of Jordan blocks you have as you already saw. Namely that each eigenvalue can only have a single jordan block

[half cargo]

I think that because you get eigenvalues and algebraic multiplicities from the characteristic polynomial and the size of the largest Jordan block corresponding to an eigenvalue from the minimal polynomial

That means that they must have the same JCF and are therefore similar?

Or am I mistaken

Like they have to have the same eigenvalues and block structure?

[pulsar dock]

Thats the big picture idea, but Im not sure how precise you are expected to be

[half cargo]

Yeah I have no idea how to make it more precise haha

[pulsar dock]

If every eigenvalue can only have 1 jordan block, thats a very strong restriction

[half cargo]

Yeah very true

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[vital dagger]

Why'd you delete

[naive owl]

oh ok let me reopen

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[pale sapphire]

im very lost on the second part

[tribal herald]

because 2/7 x + 3/7 y = 3/2 x + 4y you get that y = -17/50x

and so you can plug that into the constraint to find the x value at which a critical point occurs

[pale sapphire]

how did you get the fractions

[tribal herald]

divide Fx by 7

and Fy by 2

you're just solving Fx and Fy for lambda

so you can equate them

[pale sapphire]

is it kinda similar to finding the critical points where you have to zero out a variable?

[tribal herald]

wdym by that

[pale sapphire]

ok nvm lol

[tribal herald]

it's similar to optimization in calc 1 right

[pale sapphire]

i dont remember that lol

[tribal herald]

ah i see

it's way too tricky to optimize two variables at once

so the better idea is to get your variables in terms of one

[pale sapphire]

gotcha

[tribal herald]

lagrange multipliers guarantees you whatever relationship comes out of Fx, Fy and F_lambda will give you a critical point

often times you want to solve F_x and F_y for lambda so you can relate them together

[pale sapphire]

ok that makes sense actually thank you

i think ill be back for more questions

[tribal herald]

👍

[pale sapphire]

so i divide 2x+3y by 7

and 3x+8y by 2?

[tribal herald]

yeah

[pale sapphire]

ok cool

[tribal herald]

the better way to htink is you can say you're solving for lambda

[pale sapphire]

what happens to the other symbol

[tribal herald]

that would get divded aswell right

because that's the whole equation

[pale sapphire]

does it cancel out?

[tribal herald]

the 7 divided by 7 would

not the lambda

that's a variable

[pale sapphire]

how come its not there when its solved or in the simplied part

these are solutions to a review so this is the profs work

[tribal herald]

the work is a little misleading sort of

[pale sapphire]

yeah it really is

it sucks

and he makes typos

[tribal herald]

so first you have $2x + 3y -7\lambda = 0$

right

[woven radish]

dolphn

[tribal herald]

your goal is to solve this for lambda

[pale sapphire]

that the wishbone sign right?

[tribal herald]

yeah

[pale sapphire]

ok

[tribal herald]

$2x + 3y = 7\lambda$

[woven radish]

dolphn

[tribal herald]

divide by 7

then 2/7 x + 3/7 y = lambda right

[pale sapphire]

yeah that makes sense

[tribal herald]

so you'd want to do the same for Fy

[pale sapphire]

im confused as to why the thing is inside the equation

[tribal herald]

lambda?

[pale sapphire]

yeah

[tribal herald]

ah i see

the method of lagrange multipliers introduces lambda

to find the lagrangian, you use your objective and constraint functions

if you have one constraint, the lagrangian F is equal to $F(x,y,\lambda) = O(x,y) - \lambda C(x,y)$

[woven radish]

dolphn

[tribal herald]

where O is your objective function and C is your constraint

in this case O is given to you straight up right

f(x,y) = x^2 +3xy + 4y^2

[pale sapphire]

ok i got what the equation is

[tribal herald]

so the lagrangian introduces this lambda

and we want to look at Fx = 0, Fy = 0, and F_lambda = 0

and relate them together

the best way to do this in most cases is to solve F_x = 0 for lambda

like we did above

and we can also solve Fy = 0 for lambda

[pale sapphire]

im sorry im so lost

[tribal herald]

it's all good

does it make sense how we construct F

let's just like imagine we started from the beginning

[pale sapphire]

yes

[tribal herald]

okay awesome

now the method of lagrange multipliers specifically tells us we want to look at Fx = 0, Fy = 0, and F_lambda = 0

[pale sapphire]

yes

[tribal herald]

so we take our partials and we write those equations down

now we want to somehow relate these equations to eachother

the best way most of the time is to solve Fx for lambda, like we did above

which gave us 2/7x + 3/7y = lambda

[pale sapphire]

yes okay

that makes sense

[tribal herald]

now we can also solve Fy for lambda right

[pale sapphire]

yeah its 3/2 x+4y

[tribal herald]

3/2x + 4y = lambda right

[pale sapphire]

yeah

[tribal herald]

that implies taht 2/7x + 3/7y = 3/2x + 4y

[pale sapphire]

theyre equaling each other

yeah

[tribal herald]

because they both equal lambda

yep

now this tells you that y = -17/50x

you could ahve chosen to solve for x aswell

you just want it nice and simple for when you substitute back in

[pale sapphire]

well im trying to figure out how -17/50 got there

[tribal herald]

ah i see

[pale sapphire]

ill show you the og

im looking at the solutions to see how its solved

[tribal herald]

they're just using 2/7x + 3/7y = 3/2x + 4y and solving for y

that's why we wanted to solve Fx and Fy for lambda

so we got a new equation that we can work with

[pale sapphire]

yeah but im confused what they plugged in to get -50/17

or the other way around lol

[tribal herald]

they're just re-arragining 2/7x + 3/7y = 3/2x + 4y

like subtract 2/7x from both sides

subtract 3/7y from both sides

[pale sapphire]

wouldnt that just make it negative on the other side?

or you divide 2/7

and 3/7

[tribal herald]

3/2 x - 2/7x = 21/14 x - 4/14 x = 17/14 x

and 4y - 3/7y = 28/7 y - 3/7y = 25/7 y

[pale sapphire]

ok that makes sense'

how do you get rid of x then

[tribal herald]

our goal is to get a relationship between y and x so we can substitute into F_lambda

that's where we get rid of an extra variable, in the F_lambda

we can't do that right now until we simplify this equation more

[pale sapphire]

so lambda is 17/14x?

like substitute lambda into 17/14x

[tribal herald]

vice versa

we know that F_lambda is 7x + 2y = 30

but htis is really annoying because it has two variables right

so we want to find a way to make it into only one variable

[pale sapphire]

oh my lord

this is so messy lol

im tryna get some boba lol why do it gotta be s complicating

[tribal herald]

from our work above we know that 0 = 17/14x + 25/7 y right

so true...

optimzation is always messy

so -25/7 y = 17/14 x

so -50y = 17x

so y = -17/50 x

[pale sapphire]

did you multiply by 1/2?

how did you get to 50?

[tribal herald]

multiplied this line by 14

14 /7 = 2 so 2 * -25 = -50

[pale sapphire]

i think im brainfarting

is there a way you can show me on a paper on how you did it

[tribal herald]

yeah

[pale sapphire]

thank you

[tribal herald]

$(14) \frac{-25}{7} y = (14)\frac{17}{14}x$

[woven radish]

dolphn

[tribal herald]

$(2) (-25) y = 17x$

[woven radish]

dolphn

[tribal herald]

because 14 / 7 = 2

[pale sapphire]

yeah

this makes a lot more sense now

[tribal herald]

awesome

so y = -17/50 x

right

[pale sapphire]

yes

omg

[tribal herald]

now we have gotten something REALLY convienent to substitute into F_lambda

[pale sapphire]

youre amazing

[tribal herald]

just plug in -17/50 x for y

so 7x - 34/50x = 30

solve for x

[pale sapphire]

its crystal clear now

thank you

do you think i can dm you if i need help again

cuz you actually help me understand the concept

[tribal herald]

sure

i dont know how long ill be on for but yeah

most of these will be the exact same approach

it's just the derivatives might look uglier etc

[pale sapphire]

yeah that makes sense

ill apply this to my other ones

[devout snow]

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[devout snow]

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[primal jolt]

We're given the col space of A in R3x3

we're given Y0 and asked to find alpha such that AX=Y0 has a solution

did i solve this correctly?

the solution would have to be included in the col space of A, right?

[devout snow]

@primal jolt Has your question been resolved?

[primal jolt]

I'd also like to know if I solved b correctly

b) Find all solutions of the system AX=(1 1 0)^T

[devout snow]

@primal jolt Has your question been resolved?

[primal jolt]

.close

[devout snow]

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[devout snow]

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[void knot]

if y1,y2,y3 are known particular solutions to a nonhomogeneous diff equa, define y(x) = k_1 y_1(x) + k_2 y_2(x) + k_3 y_3(x), then If k1+k2+k3=1, then y is also a solution to the original differential equ?

[devout snow]

@void knot Has your question been resolved?

[sage burrow]

plugin y in your diff equa and look if it is fulfilled.

[devout snow]

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[spiral cape]

please assist. What can I do besides turning it into polar coordinates?

[restive river]

pray

(im not helper) 🙏

[devout snow]

@spiral cape Has your question been resolved?

[devout snow]

@spiral cape Has your question been resolved?

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[shrewd kettle]

Determine with the help of these points an approximation to cos(127 deg - 53 deg) and sin(53 deg+53deg)

[shrewd kettle]

Is the question formatted wrong because the answer is in decimals and I dont think theres a way too do that with just the image?

[cyan surge]

It's a unit circle.
So your coordinates would be (cos53, sin53) [blue one] and (cos127, sin127) [red one]
Now use cos(127-53) = cos127cos53 + sin127sin53

[shrewd kettle]

yeah I understand that you use this . but since the question is asking with the points but I dont see how they are relevant

[cyan surge]

Do you know that the x-coordinate represents cos and y coordinate represents sin on unit circle?

[shrewd kettle]

x axis and y axis

on a circle

like in this case cos 53 is 0.6

[cyan surge]

Yes

Similarly you get sin 53, cos 127 and sin 127

[shrewd kettle]

i mean like is the image even relevant to solve it

[cyan surge]

How'd you get coordinates and angles without this image?

[shrewd kettle]

I mean cant you just use the formula on this without an image

[cyan surge]

if you use the formula,
You get something like this as LHS; cos127cos53+sin127sin53.
You wouldn't know the value of cos127, cos53, sin127 and sin53 without this image.

[shrewd kettle]

ah. i think i get it

sleep deprivation is real. you get the values of them then multiply them at the end

[cyan surge]

If you do directly cos(127-53), you get cos(74) on RHS.
which is equivalent to sin(18).
You could use sine table but you're required to use trigonometric formulas here.

[cyan surge]

Yes

[shrewd kettle]

idk why i thought the values would change

thanks anyway