help-42

[calm coral]

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[young iron]

Someone pls verify answer

Answer blue underlined part has it as 1/5 rather than 2/5 what I have rest matches

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[errant oak]

How do you memorize the trigonometry formulas?

[thin tendon]

which ones?

some can be deduced

but the most complicated ones i would suggest the most easy way to memorize anything

put a paper with them written on it on the inside of your toilets typically on the door

if you have some time

you'll have them memorized pretty solidly

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[frozen flicker]

Can anyone tell me whats reciprocal in simple words

[eternal wagon]

The reciprocal in terms of writing is simply just 1/that number.
In terms of properties the reciprocal of x is the number that when multiplied by x, the equation equals 1

[frozen flicker]

Can u give an example?

[eternal wagon]

The reciprocal of 3 = 1/3

Because 3•1/3 = 1

[frozen flicker]

Ohhh okay thank youu

Does it only equal to 1 or

Oh nvm i get it thank u

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[twin apex]

The formula I'm getting for this is y=20+50x - is that correct?

[twin apex]

ty! ❤️

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[eternal bronze]

do I have to use calculator for this?

or is there a way to find out?

[trail glacier]

have you been taught binomial expansion

[eternal bronze]

yes

[trail glacier]

whats the formula

[eternal bronze]

summation k =0 to n (n choose k) x^n-k y^k

equals (x+y)^n

[trail glacier]

sorry i didnt look much originally and thought the powers of (1/3) were decreasing

i wonder if you can present this as the product of summations or something

[eternal bronze]

it's k

I had a problem with that too

[trail glacier]

i guess you can start by representing this series as a summation too

[eternal bronze]

yep

I got up to that part

sum k=0 to 100 (100 choose k) (1/3)^100+k 6^k

[trail glacier]

$\sum^{n}_{k=0} {n\choose k} x^{n+k} y^k$

yeah

[potent lotus]

dog.

[trail glacier]

hmm

n+k + E = n-k

[eternal bronze]

I got 1 using a calculator

[trail glacier]

E = n-k-n-k

E = 2(n-k)

[eternal bronze]

what's e?

[trail glacier]

im just trying to think of a way

to express this as two summations

[eternal bronze]

oh k

[trail glacier]

which can be expressed as binomial

2(k-n)

hmm

-2(n-k)

${n\choose k} x^{-2(n-k)}$

[potent lotus]

dog.

[trail glacier]

oh wait

thats not how product sum works

[eternal bronze]

I GOT IT

[trail glacier]

o

whatd u do

[eternal bronze]

lemme send work

[trail glacier]

alr

[eternal bronze]

made an invisible 1 pop up so it's in the binomial form

(1+2)^n times (1/3)^100

equals 1

[trail glacier]

,rotate

[eternal bronze]

(1/3)^k times (6)^k = 2^k

[trail glacier]

oh right

the first step in the working out is incorrect tho

those expressions arent equal

but you dont actually use that fact in your working out so its okay

[eternal bronze]

yh

[trail glacier]

also in the final working out dont just drop the summation notation

[eternal bronze]

I found that out

and got confued

[trail glacier]

you gotta show the whole process abt how you take the constant term out of the summation which is basically just factorising

alr good job

[eternal bronze]

ty

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[trail glacier]

np it was mainly u

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[calm coral]

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[green plaza]

My work so far

[night torrent]

,rccw

[night torrent]

,rccw

[green plaza]

,rice

[potent lotus]

2 roles found matching ce!

1.   Talk Announcements
2.   Advanced```
Please type the number corresponding to your selection, or type `c` now to cancel.

Role selection timed out.

Oct 1, 2022, 7:58 PM

[night torrent]

u r missing of a 1/2 factor

d/dx tan(1/2 x) =/= sec^2 (1/2 x)

,w derivative of tan(x/2)

[potent lotus]

Results provided by WolframAlpha

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Requested by Deep.#0001

[night torrent]

1/2

[green plaza]

It’s ln tho

Oh right

I see what u mean

[night torrent]

hmm

yes

,w derivative of ln(tan(x/2))

looks good

[potent lotus]

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[night torrent]

yes

[green plaza]

Shouldn’t it then be just 1/tan(1/2x) times 1/2sec^2x

[night torrent]

wait which Q are we talking about tho

[green plaza]

Where did cosec come from

The show that one

b)

[night torrent]

well you get this?

[night torrent]

no

[green plaza]

Btw it’s ln as in log base e

[night torrent]

it should be 1/tan(1/2x) times 1/2sec^2 1/2 x

[night torrent]

yes in WA log is ln

[green plaza]

Yeah that’s what I’m saying so where did cosec come from

[night torrent]

dumb WA

okay so

we have

[night torrent]

this

do you get this?

,tex \trigangles

[night torrent]

1st

use both

so we have $\frac 1{2 \sin \left(\frac x2 \right) \cos \left(\frac x2 \right)}$

[night torrent]

thats

$2 \sin \left(\frac x2 \right) \cos \left(\frac x2 \right)$

[night torrent]

$2 \sin \left(\frac x2 \right) \cos \left(\frac x2 \right) = \sin x$

[green plaza]

Hmm sin 1/2x /2?

[green plaza]

Oh right

[night torrent]

so we have

$\frac 1{2 \sin \left(\frac x2 \right) \cos \left(\frac x2 \right)} = \frac 1 {\sin x}$

[night torrent]

[green plaza]

Oh and that’s where cosec comes from

Wait let me try it again using the sin 2x thing

[night torrent]

sure thing

[green plaza]

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[north frigate]

i just have a quick question. if, given a square matrix $A$ defined by $$a_{ij}=i+j$$, then that means that $$A^T$$ is defined by $$a_{ji} = i + j$$?

[potent lotus]

Pokerface.exe

[glass heart]

well by j+i but lets hope that you are working with commutative addition

[north frigate]

yes, i assume it is commutative

i think it gets the same final answer for each cell of A, but in a transposed manner, is that right?

[glass heart]

well the matrix is symmetric anyway

[north frigate]

if it was not symmetric, would it not hold the same values but transposed?

[glass heart]

symmetric means that it has the same values after transposing

[north frigate]

oh

i failed this subject twice, how could i remember that anyways lol

[glass heart]

A is symmetric iff A=A^T

[north frigate]

anyways

thanks for the explanation

cheers

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[whole panther]

I can do the multiplication but I'm curious as to why there's no inverse:

[flat gorge]

Didn't you read why?

it's out there. There exists no 2 x 2 matrix such that the product of the two can give you an identity matrix

that's why an inverse does not exist

[whole panther]

I was misinterpreting what I meant in the equation.

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[wary vessel]

hi! ive just tried this and marked it and the coordinates are not the same

would someone mind explaining what i am meant to do

[winter hazel]

,rccw

[winter hazel]

it

looks right tho

[wary vessel]

i rubbed it out

let me send the mark scheme co ordinates

(−2, −2), (1, 6), (4, −2) Plotted and joined

would this be right?

[winter hazel]

wait this feels weird

isnt this

f(x)-1

[pine schooner]

Right? Besides the point (1,6)

[wary vessel]

perhaps the mark scheme is wrong

[winter hazel]

yea

feels so weird

but yea

ur graph is defn right

[wary vessel]

what should it be/ how do i get to the answer

[winter hazel]

it

shld b urs

HAHAA

[wary vessel]

so the bit i rubbed out?

😭

[pine schooner]

Yeah

[winter hazel]

that bit u drew in pencil

that parts right

[wary vessel]

ah okay so u just add 2 to the y cordinates

[winter hazel]

ye

lol

yay

[wary vessel]

why do we add 2 to the y cordinate

[winter hazel]

um

its 2+ beside the f(x)

so for any f(x) we got before

weve to add an extra 2

so y increases by 2

[wary vessel]

i seeee

thank you for the help!

[winter hazel]

ayy

np

💕

[wary vessel]

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[strange lichen]

found the inverse matrix

dont know what to do from there

[ancient steppe]

Multiply the inverse matrix and the vector (1 -3); you should get (x y)

[strange lichen]

that worked, thank you

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[vivid mango]

Just want to verify here that I have done the work correctly for this problem, if not, some pointers of where I went wrong

[carmine sorrel]

why are x and z both odd?

[vivid mango]

The problem asks for them to be

number 1

[carmine sorrel]

ok, then x+z is not odd

[vivid mango]

oh yeah at the top, oops. but that didn't mess up my math, I don't think?

[carmine sorrel]

your math is mostly fine, you have some 'right idea, but wrong execution' equalities at the end.

2d is not equal to 2q, that basically says xy = y

you have yz = 2(2ac+a) = d = 2d, which already is equal to yx

[vivid mango]

oh that's an a

2ac + a

bad handwriting on that, sorry

[carmine sorrel]

and then, again, say 2d = 2a, so yz = yx = y by the end of all of these equalities. Which isn't true.

it's all the right idea, these things all multiply to even numbers, but you keep reusing letters that create equalities between things that aren't (necessarily) equal

[vivid mango]

So how would you reword what I've written then?

[carmine sorrel]

either use different letters, or just say that since 2ac+a is an integer (by properties/theorems you know) then yz = 2(2ac+a) is an even integer by definition.

You can consolidate it to yz = 2d, but then you shouldn't say yx = 2d, because that's the same number, and yz is not always equal to yx

[vivid mango]

So if I just changed one of those 2d's to 2e, the whole thing would work out correctly?

[carmine sorrel]

more or less.. there are still other issues.

[vivid mango]

What other issues are you seeing

[carmine sorrel]

read what this says and tell me if it makes sense

i know what you're trying to say, but this is another case of not saying what you were trying to say.

[vivid mango]

so whilst trying to explain it, I realized, that I can't grab the 2 and put it on d, because that would mean i'm saying ac + a = d in the second line, and the first one has it equal to 2ac + a... right?

[carmine sorrel]

yeah, the second line also says 4ac+2a = 2ac+a

[vivid mango]

oh wait

"thus 4 ac + 2a= 2(ac + a) = 2d"

that works, yeah?

[carmine sorrel]

yes

[vivid mango]

I just missed throwing that 2 in there... i immediately moved it over to the right side

[carmine sorrel]

I'd recommend rereading the whole thing a couple of times. even reading it out loud like your explaining the proof to your prof, and see if it makes sense.
If something is confusing, rewrite it. Use more words if needed. Not everything has to be an equation.

[vivid mango]

My main issue is that I missed where the professor started explaining proofs to the class. This is the first proof homework and it's tough for me to wrap my head around them

I've been on this problem for like 4 hours lol

[calm coral]

@vivid mango Has your question been resolved?

[vivid mango]

Alright I’m back! <@&286206848099549185> I have now completed question 1 with both cases. Feedback?

[vivid mango]

question 1

[torn gorge]

its wrote so small

[vivid mango]

https://cdn.discordapp.com/attachments/948770026914213909/1025904059682672733/image0.jpg

hmm

If you open it in a web browser by clicking it and clicking open original, it shows up a lot bigger

I tried to post the link, didn't realize it would just post the picture again lol

[torn gorge]

is the question "x and z odd the xy+zy even"?

[vivid mango]

yes

[torn gorge]

xy+zy=y(x+z) but x+z is even (odd+odd) then y*(even) is even

.close

is it sound good for you ?

[vivid mango]

No... I'm trying to verify if the proof I have written is written correctly. I'm trying to learn how to write proofs, this is my first ever writing of a proof

[torn gorge]

do i see well ? do you have a beard ?

[vivid mango]

What does that have to do with my math

[torn gorge]

i think you are younger

if it's you first proof

[vivid mango]

My age doesn't matter in this scenario, I've asked a question and you are harassing me instead of helping me

Thanks for trying. <@&268886789983436800> might want to take a look at this guy's behavior

[torn gorge]

however i think your proof is okay

[vivid mango]

.close

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[remote mural]

how is the contrapositive of any importance here

[torn gorge]

n(n+1) is every time even hence if n is even then n(n+1)-n=n^2 is even. if n is odd then n(n+1)-n=n^2 is odd

in particcular the last result prove (by contrapositive) n^2 even imply n even

[remote mural]

hmm

[craggy walrus]

since multiplication is repeated addition you are just adding an even number over and over which will always be even

[remote mural]

yeah i got it now

ty

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[remote mural]

how would i formally induct part a

[wintry glacier]

induct me daddy

[golden hearth]

you wanna prove n choose k = n-1 choose k + n-1 choose k-1 through induction? or the second part?

[wintry glacier]

no need for induction really

[torn gorge]

tough thing

[remote mural]

imma be real i have no idea where to start bruh

[golden hearth]

youre having trouble proving which statement exactly ?

[remote mural]

i know what strong induction is and i know what base cases and shit are but i just dont know this question in particular

with n choose k

[remote mural]

part a

idk where to start

oh wait

shit

i think i read it wrong

ok lemme try it first

ok yeah bruh im stuck

How would I conclude that n choose k is always an integer?

I understand why n!/k! where k<=n is an integer but not why the entire is

[calm coral]

@remote mural Has your question been resolved?

[remote mural]

.close

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[remote mural]

if $P(x)$ is a polynomial with integral coefficients. And there exists distinct integers $a, b, c, d$ such that $P(a) = P(b) = P(c) = P(d)=5$.Prove that there does not exist integer k such that $P(k)=8$

[potent lotus]

pure maths>>>physics

[remote mural]

I do notice that $P(x)=(x-a)(x-b)(x-c)(x-d)R(x)+5$

[potent lotus]

pure maths>>>physics

[remote mural]

and as $P(k)=8$

[potent lotus]

pure maths>>>physics

[remote mural]

$(k-a)(k-b)(k-c)(k-d) R(k)=3$

[potent lotus]

pure maths>>>physics

[remote mural]

I have observed that 3 is a prime number too

the entire issue is that I don't know R(k) is integer or not

can someone give me a hint on how to proceed further?

ping me if someone answers

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[remote mural]

<@&286206848099549185>

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[unborn breach]

Excercise: Which function solves the differential equation?

ELI5: Where does the "-1" in front of e^2x come from? And why is is cos and sin (2x) and not just x?

[cloud topaz]

What have you done?

[unborn breach]

idk if it's readable, but following Khan Academy videoes lead me to this point.

[cloud topaz]

So your roots are 2+2i and 2-2i?

[unborn breach]

Negative, 2-i and 2+i

For clarification, this excercise is not homework, it's an earlier exam made public, which I am doing to prepare for my own exam tomorrow.

I'm hoping there will just be one or two real roots, but I must learn to find the complex solutions as well

[cloud topaz]

Ah I meant to write e^2x here no e^2

See if you understand this

@unborn breach

And when you solved the quadratic it shouldnt be over 4 but over 2

[unborn breach]

Oh yes I see that! That explains the 2x in cos and sin

But where does the negative come from in the front? -e^2x

[cloud topaz]

C and D can be anything

I’m this case C is -3 and D is -5

Then you factor out the negative

[unborn breach]

Oooh great thanks! That's helped a lot, I didnt see the factor part of it 😄 Then I do understand the formulas and the way to solve it! Great! Thought I was missing something formula-related with the -e^2x

Perfect! A ❤️ for you @cloud topaz

.close

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[cloud topaz]

np

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[jaunty sun]

My teacher wants us to use the squeeze theroem to solve this question, and Im confused on where to start.

[calm coral]

@jaunty sun Has your question been resolved?

[jaunty sun]

<@&286206848099549185>

[cursive vine]

I reckon that ur teacher wants u to use squeeze thm to prove lim(x to 0)sinx/x=1, then use the result to solve the two questions

[jaunty sun]

how would u use the squeeze thm to prove that?

thats what im confused on lol

[cursive vine]

U can google it
The proof is very typical and famous

https://math.stackexchange.com/questions/75130/how-to-prove-that-lim-limits-x-to0-frac-sin-xx-1

[jaunty sun]

thanks!

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[cerulean sage]

Can somebody think of a word problem for (+45) divided by (-5)?

[cerulean sage]

<@&286206848099549185>

[manic mist]

Maybe you can’t? Cause dividing can be worded as “split into __ groups”, and you can’t really split something into negative groups

Idk

[cerulean sage]

well, its textbook question so idk either

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[oak ridge]

hi can someone help me with this

i dont quite see how to construct a matrix

@ancient thistle hi

[ancient thistle]

hi

i am

[oak ridge]

HELLO

[ancient thistle]

in class

[oak ridge]

didnt expect u to reply

oh

ok i shall not disturb

[oak ridge]

u mean teaching a class

[ancient thistle]

[oak ridge]

TA-ing

yes

<@&286206848099549185>

would this work?

.close

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[alpine wadi]

Im struggling to do integration by parts

[alpine wadi]

im so stupid

integral from 0 to 1

of

x(1-x)^(1/3)

[remote mural]

I think it would be easier using u-sub

[plain panther]

first do the integration on the indefinite integral using the formula, then think about the definite integral later

[alpine wadi]

actually

i already did that

whats the trick for doing integration by parts twice

on an integral like

(x^2)e^(-x^2))

[remote mural]

Actually you can do it easier with only one u-sub lol

[alpine wadi]

sorry i meant x^2

[remote mural]

Basically $$\int_0^1 x ! \sqrt[3]{1-x} , \mathrm{d}x = -\int_0^1 ! x\sqrt[3]{x-1} , \mathrm{d}x$$

[potent lotus]

Seminaire

[alpine wadi]

yes

i already did that

im talking about integrating

[remote mural]

You already solved it?

[alpine wadi]

( x^2 ) e^(-x^2)

yes

its 9/28

i just did by parts

how do i do

.stop

.close

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[urban ibex]

Hello can someone help me I’m confused on how I’m supposed to write an IA. I’m currently a junior in highschool

[urban ibex]

I’m currently in math applications

And I don’t understand the concept of an IA after reading up on it

[visual nimbus]

what does IA mean ?

[urban ibex]

Internal Assessment I think

[calm coral]

@urban ibex Has your question been resolved?

[urban ibex]

<@&286206848099549185>

[calm coral]

@urban ibex Has your question been resolved?

[tawny niche]

What??

What does that have to do with math lol

Looks like IA is a synonym for “exam”

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[wanton finch]

dk where to even begin

help appreciated

[calm coral]

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@wanton finch Has your question been resolved?

[hollow totem]

oof looks challenging

I know I've seen this problem before but I forget if I ever solved it

best I can do is start drawing lines and looking for congruent triangles and such idk

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[drifting rivet]

If $f$ is a polynomial, and $F$ a linear transformation, how are you to interpret $f \circ F$?

[potent lotus]

sam

[glass heart]

lets say $f=a_0+a_1x+\ldots+a_nx^n$

[potent lotus]

Denascite

[glass heart]

then $f\circ F = f(F) = a_0 I+ a_1 F + \ldots + a_n F^n$

[potent lotus]

Denascite

[glass heart]

where I is the identity

[drifting rivet]

and how should I think of it geometrically? Its not really transforming the polynomial f, is it?

My question stems from #algebraic-geometry

[glass heart]

not sure if there is a nice geometric view honestly. if you factor f you can think about each of the factors (F-lambda) as eliminating one of the eigenspaces of F

[drifting rivet]

I suppose its like a change of basis

But I dont understand how if we change basis in the two polynomials, but "reverse" this change in the point, that it can have the same intersection multiplicity

[calm coral]

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[outer pollen]

if x ∈ {2;7} U [8;9] then x ∈ N

[outer pollen]

is that true or false

[delicate olive]

8.5 is in the range of [8, 9]

[outer pollen]

so it's false?

[delicate olive]

Depends on the notation

If the problem uses precisely {} and [], then yes it's false

[outer pollen]

yeah it does use them presicely

and also

one other question

what if it was like the opposite

[delicate olive]

The intersection?

[outer pollen]

if x ∈ N then x ∈ {2;7} U [8;9]

no like this

[delicate olive]

Well what about 20

20 is a natural number, but it's not part of that set

[outer pollen]

so that's false too

[delicate olive]

Yes

[outer pollen]

alrightt

thank you

.close

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[steep mortar]

I need help with these few questions. Thanks.

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[steep mortar]

<@&286206848099549185>

[calm coral]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[steep mortar]

its been 45mins

Scroll up

[steep mortar]

ah okasy

So i dont understand these questions that i posted

[languid sphinx]

Try to make it as easy as possible for others to help. What don't you understand? What have you tried?

[steep mortar]

for 2) I thought if i just added 74 degrees to every new x axis it was close to, i'd get reference angle of 74

so like 180 + 74 = reference angle of 74

And yeah thats all i got for that

3. I think we just switch some values,
   cos^-1 (2/h) = θ
   sin^-1 (11/h) = θ

for 4, i think we graph then solve

5. no idea, maybe sketch out a triangle and solve

b) I could calculate it but they want in fraction form.

So i'd need to use a special triangle i think, etc.

[steep mortar]

Is this good?

<@&286206848099549185>

[calm coral]

@steep mortar Has your question been resolved?

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[stuck tiger]

hi im not really sure where to start or how to attempt this problem

[mellow crater]

try to imagine or sketch it, you'll see the solution immediately

[stuck tiger]

okay. would the form of the equation be in Ax +By+Cz=0 form?

something like that?

[mellow crater]

rather Ax +By+Cz+D=0 or using normal vector and a point A(x-x0)+B(y-y0)+C(z-z0) = 0

[stuck tiger]

okay thanks

[mellow crater]

you can use this, but you need to find a normal vector, can you

[stuck tiger]

no i wasn't taught how to find it yet. through cross product i believe

[mellow crater]

not really, can you tell me what's the projection of the point (1,-3,2) on the xz-plane?

hint, xz-plane is represented by y = 0

[stuck tiger]

im not sure. i only learned the scalar projection when its v onto w

not for a specific point on the plane

unless you have to find the mag of the vector?

[mellow crater]

y = 0 is a specific plane

maybe now?

[stuck tiger]

I'm not really understanding right now but thank you for the help

.close

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[potent lagoon]

dude you keep asking the same question

[manic void]

What is soloution

I need soloution

[mortal orbit]

If you find any coterminal angle with -100° that we will note a°, then a° + n*360° is another coterminal angle, with n any integer

[manic void]

Can you solve it step by step?

[mortal orbit]

I think it's easy enough

a coterminal angle with -100° is ANY angle of the form -100° + n*360°, with n ANY integer (except 0 of course)

[manic void]

So the answer can be infinite

[mortal orbit]

So, to get a coterminal angle... you plug any integer you want for n

the number of answers is infinite, but ALL the answers are finite because n is finite

[mortal orbit]

so plug in any integer for this formula (1, 2, 3, -1, etc....)

not 0 because otherwise we don't have an angle different than -100°

[manic void]

Oh thanks bro,

Be blessed by

.close

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[clever whale]

How would i solve this

[calm coral]

Please don't occupy multiple help channels.

[stoic compass]

umm

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[remote mural]

how would i simplify (3i * pi + 3/2)/ pi ^2 + 1/4

[stoic compass]

well

I realize the bottom is a difference of squares

dk if it helps

[remote mural]

what?

its not a difference though

its addition

[stoic compass]

oh rihgt

mb

[leaden thunder]

$\frac{3i \pi + 3/2}{\pi ^2 + 1/4}$

is this what you're simplifying?

[stoic compass]

no

[remote mural]

uh 1/4 is on the bottom

as well

denominator*

[remote mural]

huh

im the one asking the question thouhg

[stoic compass]

mb

[potent lotus]

riemann

[remote mural]

yup

[stoic compass]

I won't help then gl guys

[remote mural]

thats what im simplifying

[leaden thunder]

use this identity

$a^2 + b^2 = (a+ib)(a-ib)$

[potent lotus]

riemann

[remote mural]

what

yeah i simplified a + 1b and a - 1b

to get pi^2 + 1/4

it was originally (pi + 1/2i)(pi - 1/2i)

[leaden thunder]

write it back that way

then use $a(b+c) = ab + ac$ in the numerator

[potent lotus]

riemann

[leaden thunder]

Something should cancel

[remote mural]

yeah but the reason why i did it in the first place

was to eliminate i from the denominator

[remote mural]

when i cancel them i get back to my original equation i was supposed to solve

which is 3i/pi + 1/2i

[leaden thunder]

that's as simplified as it gets

what are you solving for

[remote mural]

eliminating i from the

denominator

[leaden thunder]

then just use $\frac{1}{i} = -i$

[potent lotus]

riemann

[remote mural]

then i get pi * i

for the denominator

i have to multiply by it's conjugate

i think thats what its called

[leaden thunder]

can you just show the full instructions

you keep adding new instructions

[remote mural]

wdym

my original equation was 3i/pi + 1/2i

[leaden thunder]

that's not a question

that's just a formula

[remote mural]

i need to eliminate i from pi + 1/2

so i multiply by its conjugate

[remote mural]

i literallyu have no idea

what you mean

[leaden thunder]

take a picture or screenshot of the problem

[remote mural]

i have to write it in complex form

[leaden thunder]

don't type it out

[leaden thunder]

and the instructions?

[remote mural]

write it in compelx form

[leaden thunder]

.

[leaden thunder]

.

[remote mural]

?????

im literally saying

the exact instructions

i have no idea why you need a screenshot

it says "write in complex form"

which is a + bi

[remote mural]

looks like my man cant comprehend discord text

can only understand computer generated screenshots

crazy

[leaden thunder]

insulting the only person willing to help you ?

crazy

[remote mural]

willing?

thats crazy

am i wrong?

the fact that you cant solve a question with instructions quoted directly from the problem

is enough for me to insult you

you dont even give me a decent reason

????

wtf

shut up

[remote mural]

bro who even are you

out of all the help chats you somehow ended up here

[steep mortar]

brodie your heated, you need to relax

doesnt matter whos in the right or wrong you shouldnt allow others to make you react.

[remote mural]

i expected something helpful after waiting a while and he responds with "i need a screenshot of the instructions"

💀

thats complete bs

[steep mortar]

lol i understand but still bro

these people dont get paid or nothing

we're lucky to get help

[remote mural]

i understand that

this is

just a huge

stretch

something as simple as "write in complex form"

needs to be screenshotted

which is just

bs

its not about that

@remote mural make a valid argument before going off on me bro

its about knowing exactly how to help u

[remote mural]

????

bro

what?

why are you guys

so confusing

i thought this was a server for math

it is

[steep mortar]

@remote mural What your saying is right but thats not the problem

[remote mural]

but we cant read your mind

[remote mural]

????

you make no sense

he needing a screenshot for "write in complex form"

has nothing to do with my preferred learning env

how did you even connect those two bro

????

[remote mural]

dude

i understand that

sometimes

a stretch is a stretch

you cannot deny how stupid this argument is

man do u hear yourself

[remote mural]

do you?

im actually losing brain cells talking to you

u cant lose none

there we go

are you underaged?

yes i am

you shouldn't be on discord little buddy

you shouldnt cause u clearly dont know how to talk to people

[remote mural]

huh

[steep mortar]

This is actually very entertaining lol

[remote mural]

especially people u need help from

do you hear yourself bro

you're defenidng a guy who needs a screenshot containing text that says

"write in complex form""

do you hear yourself

right now

that guy is a very smart helper and wouldve helped you if ud have given him thr chance

[steep mortar]

Thats my point, you reacted instead of responded

[remote mural]

i can tell that he probably has knowledge about maths

[leaden thunder]

<@&268886789983436800> this is not a good use of a help channel

[remote mural]

LOL

mods

please look at how stupid

this argument is

i dont care if i get muted or banned

but this is just

ridiculous

god

[candid crane]

Help me out here ...

If you agree that the argument is stupid, why are you continuing it?

[remote mural]

i would've stopped

if lennyt didnt come

what

bro

i wasnt talking

for like 5 minutes

[candid crane]

And yet you keep talking.

What are you trying to achieve here?

[remote mural]

it seems that there is pride involved

because i honestly just really dont want to "admit" that im in the wrong in front of ridiculousness

[candid crane]

Okay, so I think this can be fixed with a few hours mute to calm down. Then your silence will not be indicating that you "admit" anything.

[remote mural]

ok thanks

[candid crane]

.close

[calm coral]

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[wise lotus]

how would i find the mean and period

[calm coral]

@wise lotus Has your question been resolved?

[wise lotus]

<@&286206848099549185>

[calm coral]

@wise lotus Has your question been resolved?

[calm coral]

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[pastel vale]

how would i solve this equation

[strange lichen]

i would let sqrt(x) = another variable like "k"

then make the equation in terms of that other variable

then solve as a quadratic

once u have the solutions for the other variable, set it equal to sqrt x

then solve for x

[pastel vale]

ok thanks

.close

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[oak ridge]

hi can someone tell me why this is inconsistent

[cursive vine]

if y+z-2x≠0, clearly, by Guass elimination, the system has no solution, hence inconsistent.

[oak ridge]

why did the question say "the system is consistent iff y + z - 2x = 0"

oh wait that means y z and x are restricted to being only 0

is that right?

wot

[cursive vine]

Yes

[oak ridge]

ohh

so if theyre only 0

they cant be R^3

okay i get it

tysm

.close

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[remote mural]

Where do I go from here

[frank gull]

what are you trying to do?

what's the original problem?

[remote mural]

I'm trying to find x

[frank gull]

all I see is 1 +/- sqrt(7). Did you find those with the quadratic formula? What was the original problem?

[remote mural]

Nevermind that's my answer I think

Thank u

[calm coral]

@remote mural Has your question been resolved?

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[slim quail]

plz

no clue where to start

[frank gull]

geez I haven't seen that mudkip meme in forever.

[slim quail]

ye

[frank gull]

good times

okay so what have you tried thus far?

oh wait it said you haven't started

lol

[slim quail]

had to jump available to even get help lol

[frank gull]

okay so do you know that the function passing through the x axis gives the roots?

[slim quail]

yes

[frank gull]

so that basically means that these will be your building blocks for your function

[slim quail]

ok

[frank gull]

so on the left side, where does your function cross the x axis? At what values of x?

[slim quail]

11, 0, and 5

[frank gull]

perfect

so that means that we have a function that equals 0 at these points

[slim quail]

ight

[frank gull]

in other words (x - 11) is one factor. You see why? Since 11-11 = 0

[slim quail]

ok

[frank gull]

can you give me the other two?

[slim quail]

0-0=0 and 5-5=0?

[frank gull]

perfect

so what would that be in terms with x?

[slim quail]

?

[slim quail]

so x=0?

[frank gull]

yep!

so (x - 0)

see?

[slim quail]

so how would I find the fuction given that x=0?

[frank gull]

well a function is at 0 at it's roots. We're finding the roots currently

we're doing it one step at a time

[slim quail]

ok

[frank gull]

so how would you express 5 in terms of x and 0?

[slim quail]

would that be the cords?

[frank gull]

(x - 5)

[slim quail]

oh ok

[frank gull]

now we can put this together to get our fucntion

f(x) = (x -0)(x - 5)(x + 11)

[slim quail]

okmthank you so much

[frank gull]

the last thing is the sign

[slim quail]

that makes it so much easier

[frank gull]

when you have a function, pay attention to how it trends as x goes towards the right

[slim quail]

ok

[frank gull]

in our case, it's heading down towards - infinity, see why?

[slim quail]

yes

as x approaches neg inf, y approaches neg inf

[frank gull]

so then we need to put a -1 in the front

and then we get a representation here, like this:

[slim quail]

ok

[frank gull]

so that's one way to do these problems!

[slim quail]

ok, i do have one more question

i also dont know exactly where to start here

also, what define if the x is + or - in the parentheses?

.close

[calm coral]

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[remote mural]

jfcjyfyfitf

[remote mural]

.close

[calm coral]

Channel closed

Closed by @haughty quiver

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[coral osprey]

Thank you very cool

[calm coral]

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[keen maple]

;-; im giving up

[keen maple]

im def failing tomorrows exam ;-;

so i know that it got factored

but my brain doesnt know how

or at least where did the 20 come from

and the -6

[dull wagon]

identify common factors in both expressions

[keen maple]

first is (1-2x)^2

then 5x+3)^3

but idk how this happened

[dull wagon]

oh for that, they swapped the order of terms

a + b = b + a

[keen maple]

still confused

[dull wagon]

they started with something in the form
= A + B
A simplifies to a
B simplies to b
but they wrote in the order
= b + a
instead of = a + b

[keen maple]

naw i ment this

i get the simplify part

[dull wagon]

so is what they did here what you had issue with?

[keen maple]

yeh im confused how they factored it in ;-;

[dull wagon]

huh, your still unclear about whether your issue is with this or the following step

[keen maple]

oh wait nvm

i get it now

sorry

im really tired rn

ty

.close

[calm coral]

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[upper cosmos]

Need some help unpacking how it went from step one to step two 😅

[ocean cypress]

just expanding the binomial

[steel mason]

just expand

[ocean cypress]

(x+y)^2 = x^2 + 2xy + y^2

where x = theta hat - E(theta hat)
and y = E(theta hat) - theta hat

[upper cosmos]

Ah, that makes sense, thanks for quick help ♥

.close

[calm coral]

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[spring fjord]

What

[manic ermine]

?

[spring fjord]

Question number 5

[uneven gale]

good question

[alpine stone]

You need to take arccos

[spring fjord]

No idea what that is

[alpine stone]

cos^(-1)

[spring fjord]

Oh, but why cosine

This is cross product, shouldn't it be cos for dot and sin for cross

[alpine stone]

Because A * B = |A| |B| cos(theta)

Oh cross product?

[manic ermine]

sinx=sin(pi-x)

So 180-60

[alpine stone]

Ah mb

[spring fjord]

Damn they gotta add unnecessary steps

I will verify the answer

Yeah it's 120 thanks

[manic ermine]

Np

[spring fjord]

.close

[calm coral]

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[calm coral]

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[karmic ridge]

are there 4! ways for 5! ways to order 4 distinct vehicles across 5 parking spots

[karmic ridge]

anyone?

i was thinking 5! bc one of the options will be no car

[leaden thunder]

the question is pretty awfully stated

can you just show the original problem

[karmic ridge]

ur probably right

[karmic ridge]

there is no original problem

lets see if i can state it better

[leaden thunder]

you just made up this probleM?

[karmic ridge]

i mean its related to smth im doing

How many ways are there to park 4 different vehicles on 5 consecutive parking spots?

is it 4! or 5!

[leaden thunder]

it's more than 4! because that's how many ways there are to park them in 4 consecutive parking spots

so if you have 1 extra spot, you have a whole new set of ways

[karmic ridge]

so 5!

?

[leaden thunder]

how did you get 5!?

[karmic ridge]

bc its 5 options, the fifth being no car

[leaden thunder]

sounds good

[karmic ridge]

cool

.close

[calm coral]

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[calm coral]

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[calm coral]

Please don't occupy multiple help channels.

[remote mural]

.close

[calm coral]

Channel closed

Closed by @plush radish

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[clever thorn]

Can someone help me?