help-13

[true wasp]

so 3x²

[silk gust]

mk

[true wasp]

Ok

[dire geode]

!noans

[cedar kiln]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[silk gust]

and rhs becomes 4(x^2-1)

[dire geode]

correct,

[true wasp]

yes

[silk gust]

so you have 4x^2-4=3x^2 -x+2

[true wasp]

Yes

[silk gust]

move everything to left side

what do you get

[true wasp]

x²+3x-2?

[silk gust]

close

[true wasp]

4x?

[silk gust]

you have a -x on the rhs

move it to the left

what does it become

[true wasp]

positive

[silk gust]

yea

+x right

[true wasp]

but i thought

[silk gust]

so the quadratic becomes x^2+x-2

[true wasp]

a+b should always he positive

[true wasp]

what

[silk gust]

whats that

[spring forum]

that's not necessarily true

[true wasp]

oh but my teacher said that

[true wasp]

How did it become 1/x?

[silk gust]

hm?

there is no 1/x

its a polynomial

[true wasp]

No like X is equal to 1 right

[silk gust]

if i didnt mess up, factor this and youre done

[true wasp]

OK

[silk gust]

wait your not you need to check for zeros in the denom

so basically reject 1 and -1

@true wasp if youre done js close this channel

[spring forum]

OP's class has started, so I don't think he'll be able to access this channel anymore.

.close

[cedar kiln]

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[sturdy escarp]

books says Logarithms
Inverse trigonometry
Polynomial
Exponential
Trigonometric

[sturdy escarp]

someone and an online source told me Logarithm
Inverse
Algebraic (or polynomial)
Trig
Exponential

so trig or exponential first?!?!

[supple grove]

the second is correct

[sinful bay]

What is this a list of?

[supple grove]

integration by parts, functions to take the derivative of

[dire geode]

what even is your question

[sturdy escarp]

alr so ig my book is just griefing then

[supple grove]

guess so

[sturdy escarp]

.close

[cedar kiln]

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[spring forum]

trig is definitely first, just wanted to add my opinion

[sturdy escarp]

alr bet

[frail yacht]

is there one "correct" answer for the order to learn those

wait actually is this an ibp rule thingy

[sinful bay]

Yeah

[frail yacht]

disregard, i misunderstood

[cedar kiln]

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[gaunt quartz]

helloo,, i'm looking for help regarding the concept of "tricky symbols" in math, as i dont really understand how i can deduce what specific operation do these "tricky symbols" mean at times.
i provided my textbook's description of this concept below.
ps: i'm a humanities student so i am not the smartest when it comes to math!!

[remote nacelle]

,rccw

[idle crystal]

most of the time its given

[remote nacelle]

these 2 "weird symbol" seem to be defined with operations you should be more familiar with.

[gaunt quartz]

how about for the example no. 2? i don't really get if the A❤️B is either multiplication or addition?

[silk gust]

it's both!

[idle crystal]

for example we can have this

[remote nacelle]

it's a mix of the two

[idle crystal]

also theyre not necessarily algebraic (like multiplication, or addition) it can be stuff like
A*B = 1 if their sum is even, 0 if their sum is odd

[gaunt quartz]

if it's like that, then how does 8❤️(4❤️5) work? would it act similarly to :

(4❤️5) = 8(4×5) ÷ 8(5+5) ??
im sorry i may seem a bit thick in the head when it comes to numbers

[idle crystal]

calculate inside the parenthesis separately

find 4❤️5 first

[remote nacelle]

no it’s more like

you have to put the result of 4❤️ 5 as the right side of 8 ❤️

[gaunt quartz]

so what does 8❤️ be?

[remote nacelle]

8 ❤️ is incomplete to compute it you need something as it’s right side. it’s (4x5)/(4+5)

[gaunt quartz]

(4×5)/(4+5) would be 2.22222+ wouldn't it?

[remote nacelle]

20/9 = 4 ❤️ 5

so now to complete the question you have to use the ❤️ définition on 8 ❤️ 2.222222…

[gaunt quartz]

hmm.. so we gotta replace A and B with 8 and 2.2222 ?
btw should we write it as 2.22 ? round it up?

[remote nacelle]

in this case i would assume they want an exact answer

maybe doing fractions 20/9 =2.222… would be best

[gaunt quartz]

fractions r about to make this more complicated omg (at least for me)

[remote nacelle]

you can approx by 2.22, but it won’t be exactly the right answer. imo try it out with fractions

[gaunt quartz]

so.. ([8×20/9]÷[8+20/9]) ?

it ends with 17.7777777778 in one of the operations

[remote nacelle]

to be fair computing this thing exactly is not most important thing it’s good fraction practice if you need it

i get 40/23 which is ish approximately 1.74 when computing it down

[cedar kiln]

@gaunt quartz Has your question been resolved?

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[gaunt quartz]

okayyy tysm everyone hehe

[cedar kiln]

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[soft path]

,tex
$
\text{Given } a,b,c \geq 0, a^2+b^2+c^2=3 ; \text{Prove:} \
\frac{1}{3} \leq \left( \frac{a}{3 - bc} \right)^2 + \left( \frac{b}{3 - ca} \right)^2 + \left( \frac{c}{3 - ab} \right)^2 \leq \frac{3}{4}
$

[wraith dagger]

Nerdyasianguy

[soft path]

I tried subsituting in 3 but don't know how to proceed

I know that the equality for the left side is when (a,b,c)~(0,0,√3)

And for the right side is when a=b=c=1

But idk how to deal with either

[upper laurel]

you mean right side

[soft path]

Oh yes, i'm never right

[ancient lodge]

$bc \leq \frac{b^2+c^2}{2}$ by AM GM

[wraith dagger]

Civil Service Pigeon

[ancient lodge]

Further hint: ||use this to rewrite 3-ab, 3-bc, 3-ac||

[cedar kiln]

@soft path Has your question been resolved?

[soft path]

So a²/(3-bc)² ≤ a²/(a²+3/2(b²+c²))²

[soft path]

.close

[cedar kiln]

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[feral dagger]

Help with 6th one

Is this a valid reason for the given set not being a vec space

! Help

[cedar kiln]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[limber dawn]

it looks good to me

[feral dagger]

Which axiom does it violate

Is it additive inverse, add iden, I can't pinpoint

[limber dawn]

ig it's whatever vector properties you used in your proof

like associativity of addition

it's more literally just a proof by contradiction ig. you assume it's a vector space, then show a contradiction, so it's not

so one of the assumptions you started with must be false

[feral dagger]

Okay so just contradicting the assumptions

[limber dawn]

yeah

[feral dagger]

Any tips on this book

Linear algebra done right

Trying to complete it

[limber dawn]

i haven't used it before, sorry :x

this problem seems nice to me

at least

[feral dagger]

Just lin alg in general tho

I'm kinda new

To this stuff

[limber dawn]

i guess whenever you get to thinking about matrices as "linear transformations", that's always a nice way to think about them imo

that's just one thing that comes to mind :p

i can't think of much else, i think it's an approachable topic

[feral dagger]

Thanks

How do i close this channel

[limber dawn]

you can do .close or .solved

and np!

[feral dagger]

Np!

[limber dawn]

you can ask more about lin alg and stuff whenever though

or even in #discussion

or #math-discussion

[feral dagger]

I thought that wasn't for questions

[limber dawn]

you can ask general questions to get people's opinions

but yeah it's not like a guaranteed way to get help on a specific quesiton

[feral dagger]

They seem to be talking about something else

[hallow pelican]

people wont notice you tho

🙁

[limber dawn]

it helps to phrase the question in a way that's interesting to them ig lol

[hallow pelican]

in general discussion doesnt want to be asked genuine questions

theyll just troll

[limber dawn]

it's like a casual chat

you can bring up the topic and get opinions

like in a busy bar

[feral dagger]

Alright thanks guys

[limber dawn]

most people will be drunk af (in this analogy) but still worth trying

[limber dawn]

good luck!

[feral dagger]

will come again for further questions

Once I complete this exercise

. Close

. Close

[limber dawn]

(no space)

[upper laurel]

if youre stuck trying to type this on a phone, try using the backspace key to get it right

it just needs to be .close or .solved

[feral dagger]

. close

[limber dawn]

almost 😂

[upper laurel]

here try this

[feral dagger]

Is this thing stuck

[upper laurel]

hiro you are on a phone

[feral dagger]

Yep

. close

[upper laurel]

hiro listen to me

stop typing

listen

[feral dagger]

Alright

👂

[upper laurel]

when you type ., theres a good chance the phone is adding a space afterwards

[feral dagger]

Oh

.close

[cedar kiln]

Channel closed

Closed by @feral dagger

Use .reopen if this was a mistake.

[limber dawn]

🎉

[upper laurel]

you can turn this off in the settings

search it up

[feral dagger]

Thanks man

[upper laurel]

its autocorrect

[cedar kiln]

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[feral dagger]

The closed under addition condition

Does it mean that if u, w belong to U then u+w must belong to U or that if u+w belongs to U then u, w must belong to U

Or is it both

[limber dawn]

i would say the box 1.34 says it pretty explicitly, it's the first one

not necessarily the second

[feral dagger]

So the reverse doesn't matter

[limber dawn]

it's not necessary yeah

[feral dagger]

Alrighg

.close

[cedar kiln]

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[cedar kiln]

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[crude crane]

.close

[wicked mantle]

Already closed

[cedar kiln]

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[spark mist]

i have found that n <= 4 will have an interger solution

but i cant verify that if n>4 there will be any solution

[soft path]

||It seems like Vieta Jumping, but I haven't solved it||

[spark mist]

it is infact vietta jump

[soft path]

I guess square both sides then write it as a quadratic

[spark mist]

i cant substitute a = (a*)^2

b=(b*)^2

and so on

if a,b,c,d is a square its easy to show that if n>4 there will be no sol

there will be actually a sol where a=b=c=d=0

but we cant have zero

[spark mist]

but a,b,c,d can be a non square integer

so i cant prove it

[cedar kiln]

@spark mist Has your question been resolved?

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[spark mist]

.reopen

[cedar kiln]

✅

@spark mist Has your question been resolved?

[spark mist]

.close

[cedar kiln]

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[cedar kiln]

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[crimson sedge]

how do i solve this? im kinda stuck

[tropic oxide]

consider what it means that your quadratic has a linear factor at all @crimson sedge

[crimson sedge]

uhhh

im not sure what it means

[tropic oxide]

it means that the quadratic has a real root

and what can we say about it based on that?

[crimson sedge]

that it has real roots? 😭

idk what i should say

[tropic oxide]

there's a quantity you should know about that you can calculate for any quadratic to get some useful info out of it

it is commonly denoted with D or Δ

do you know what im talking about

[crimson sedge]

discriminant?

like b^2 - 4ac thing?

[tropic oxide]

yes the discriminant.

what can it tell us about the roots?

say it in general first.

[crimson sedge]

number of roots

0 two roots, = 0 one, <0 none

[tropic oxide]

ok, so knowing what this particular quadratic has at least one root, what must be true of its discriminant?

[crimson sedge]

D>=0

[tropic oxide]

ok so worth out D for your quadratic

(was away sorry)

[crimson sedge]

(176)^2 -4ac >=0

do i solve for ac?

and ill get the answer

[tropic oxide]

yes

[crimson sedge]

i can do that

thank you 🙂

.close

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[torn marsh]

could someone help me with e, i have already done a,b,c,d

[slender ginkgo]

can we get a,b,c,d

[tropic oxide]

show your sketch!

[torn marsh]

ok

[tropic oxide]

ok

so the graph will keep going down forever to the left of -1 or right of 2

now here is what i want you to do:

imagine a horizontal line (y=k) scanning this graph bottom to top. like sweeping across the plane.

at which height does it stop intersecting the curve?

[torn marsh]

hmm

y<-3 and y >27/16

[tropic oxide]

not quite. the curve keeps going down past what you have sketched, remember?

but yes the line stops touching the curve for k>27/16

[torn marsh]

so this q does not relate to

d

[mental trail]

it relates more to b

d is just to give you a better idea of what's happening, but you have to imagine what happens outside of your sketch zone

f is a polynomial, so once it starts decreasing for good past its stationary points, it's gonna keep decreasing

up until -infinity

[torn marsh]

so the answer is k< or equal to 27/16

[tropic oxide]

it does

[tropic oxide]

<=

[torn marsh]

<=

yes

[tropic oxide]

use <= if you cannot type the weak inequality sign

[torn marsh]

alright

[tropic oxide]

typing out < or equal to looks bad

[torn marsh]

got it

[torn marsh]

what is f?

[slender ginkgo]

Function

[torn marsh]

what about polynomial

[torn marsh]

i remember that

[tropic oxide]

polynomials are a special class of functions

[torn marsh]

very confusing to understtand tho

[slender ginkgo]

What is confusing abt it

[tropic oxide]

he was talking about f(x) as in your problem

[torn marsh]

the subscript

[tropic oxide]

you need names for each and every coefficient but the Latin alphabet does not have that many letters so you call them the same letter but with different subscripts.

a_0, a_1, a_2 are just three different variables that's it

[rapid mauve]

normally subscripts also separate related variables

eg: a here represents the coefficients of each term

so all of the a are coefficients

the subscript tells you which term it's a coefficient of

[cedar kiln]

@torn marsh Has your question been resolved?

[tropic oxide]

this is true but there's a risk of overthink

[rapid mauve]

that's fair

if that's the case, please ignore what i say for the time being

[cedar kiln]

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[torn marsh]

ok that makes sense

[torn marsh]

my other question is

how do we factorise x^3-x^2-x+3

or any cubic function

[rapid mauve]

is it a good idea to talk about the rational root theorem now

[iron wren]

You need to find one root first and long divide

[livid hound]

unfortunately: ||that doesn't have a good factorisation||

[torn marsh]

so for any cubic functions, to solve for for its x intercept

we need to use the root thereom?

[trail quiver]

synthetic division?

[livid hound]

rational theorem helps you find nice rational roots if they exist

[torn marsh]

is it a hard concept to grip because if it is, i wont bother

• its not requried for in my course

[worldly edge]

I usually put in simple values like 0,1,2,3,-1,-2,-3... Etc. i dont even know the rational root theorem lmao never needed but can you explain wtf it actually is?

[livid hound]

concept isnt that complex

[torn marsh]

ok ill listen

[rapid mauve]

if a polynomial has rational roots, they must all be factors of p/q, where p is the leading coefficient and q is the constant term

[crimson delta]

rational root theorem tells you which easy values to guess. so that you dont have to guess completely randomly

[worldly edge]

Oh

Well idts this polynomial has rational roots then

One idea might be to use the depressed cubic formula that i learnt tp flex on my friends

Oh its not a depressed cubic

[rapid mauve]

idt this one has a nice factorization either

[worldly edge]

You might need to transform it by writing x'=x-b/3a

[torn marsh]

what level is rational root thereoum

[worldly edge]

That is implied as the polynomial doesnt have a rational root

[rapid mauve]

fair yeah

[worldly edge]

I never learnt it formally

You can learn it in any point of ur life tho

[torn marsh]

I see

so

we dont need to use the rational root thereoum in solving quadratics

[livid hound]

rrt is usually introduced around when you're introduced to cubic+ polynomials

there are better alternatives when factorising quadratics which is why it isn't used for that

[torn marsh]

or in the form of ax^n + bx....+c where n is greater than 0 but not equal to 3

[rapid mauve]

for quadratics you can complete the square and use the quadratic formula

[rapid mauve]

well i mean, if the equation is degree 1 (n = 1), it's a simple linear equation anyway

no need for any fancy factoring or theorem, just solve for x or y

[torn marsh]

i mean what about for example

[rapid mauve]

if n = 2, it's a quadratic. see above

[torn marsh]

n=6

or n=5

[rapid mauve]

then you long divide

but tbh

if you can find a root by long dividing, most likely you can find it faster via the RRT

if all of the roots are complex, welp

but if n is odd, at least one root must be real, so

[torn marsh]

do u mean

this

[rapid mauve]

yes, but for polynomials

[torn marsh]

ah

because what i did was i sketched a cubic function

but it had the wrong x intercept

but im just wondering if i would get marked down for that

[rapid mauve]

maybe yes, depending on examiner

[torn marsh]

nvm i remember my examiner saying we dont need to solve for x in cubic f

[rapid mauve]

well at least you know how to now (a bit)

[torn marsh]

.close

[cedar kiln]

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[cedar kiln]

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[pseudo merlin]

why do they give us x(0) = 3

[pseudo merlin]

whats it there for

[slender ginkgo]

What’s ‘it’?

[pseudo merlin]

nvm i see

how would i start for this q?

[slender ginkgo]

Construct the de first

From the question

What do u know abt dP/dt

[pseudo merlin]

dP/dt = sqrt(p)

[tropic oxide]

it's the initial condition that the DE comes with

[slender ginkgo]

Not yet

[pseudo merlin]

oh

[slender ginkgo]

Missing one thing

[pseudo merlin]

wat?

[upper ruin]

proportional

Not equal

[pseudo merlin]

umm i kind of forgot what proportional and stuff means

[slender ginkgo]

D:

[pseudo merlin]

:(

[upper ruin]

Two things are (directly) proportional if their ratio is constant

[pseudo merlin]

how do we make the ratio constant

[upper ruin]

Huh?

[pseudo merlin]

oh..

uhh

sooo wat do i do

[slender ginkgo]

Use this

[pseudo merlin]

idk wat to do with that

[gentle echo]

erm find the constants first which should be easy and then just integrate

[gentle echo]

and you have the initial condition x(0) which will give you the integration constant when used

[slender ginkgo]

we havent event contructed the de 🥀

[gentle echo]

its literally given

💔

[flat mica]

ugh

constant of proportionality is so ugly

[slender ginkgo]

):

[flat mica]

why not say constant of proportion?

synonymous

[gentle echo]

proportionality constant too...

[flat mica]

proportion constant

[gentle echo]

nooooooo

😭

[flat mica]

anyway thats my bah humbug comment of the mornng, carry on

[gentle echo]

@pseudo merlin aee you aware of what you need to do?

[slender ginkgo]

@pseudo merlin

[gentle echo]

oj wait

its a different quedtion

😠 1 question per channel man its confusing

as thr others have said

we're told that the rate of change proportional to sqrt of population at that time

so in words just $p'\propto\sqrt{p}$

[pseudo merlin]

hi gyutys

[wraith dagger]

parabolicinsanity

[pseudo merlin]

sorohh

so i just put any letter i want

ok i will put G

[gentle echo]

k is the normal 🥀

[pseudo merlin]

dP/dt = Gsqrt(p)

[slender ginkgo]

i think ${\dot{p}}$ is more appropriate than ${p'}$

[wraith dagger]

k

[gentle echo]

yes but that feels to physics-y

:3

[pseudo merlin]

guys im doing physics

today i learnt that

a baryon is 3 quarks

ahhahahah

[slender ginkgo]

not particle physics gng 🥀

[pseudo merlin]

oh

[gentle echo]

thats dlc content

[pseudo merlin]

whats dlc

[gentle echo]

finish the main storyline first

[pseudo merlin]

what

[gentle echo]

now you have the differential equation

just em

integrate

[pseudo merlin]

ok brb

[gentle echo]

🤷

its a seperable de so should be straight forward

[pseudo merlin]

wsait..

what am isuppoosed to be finding..

[gentle echo]

the

[gentle echo]

P(t) function

isolate P and make it dependent on t

[pseudo merlin]

wait why P

oh

im fiunding p function

ok

[gentle echo]

done!1!!!

[pseudo merlin]

OMG

WEMBARASSING

EMBARSSING

WAIT

[gentle echo]

why

anyways

you'd be done

[gentle echo]

c and G are

either experimentally determined

[pseudo merlin]

wow I DIS IRR

I DIDEI ITT

[gentle echo]

or somethinf

[pseudo merlin]

um

why is there answser differnt tto mine

[gentle echo]

why did you

remove c

[pseudo merlin]

oh

ok just imagine that 2 is c

[gentle echo]

c not 2 🥀

[pseudo merlin]

why is there asnwer different

their

[gentle echo]

G looks more like a 6 too

erm

it doesn't matter

[pseudo merlin]

why

[gentle echo]

because

the solutions depend on

G and C

[pseudo merlin]

oh ok

[gentle echo]

but you see that theres a quadratic solution? thats all that matters for a differential equation

[pseudo merlin]

oh

so if i get a completely different asnwer

how will i know im right

wait lket me try anoither

[gentle echo]

just differentiate, honestly

[pseudo merlin]

they got this

[pseudo merlin]

oh

[plucky merlin]

I will note, the sign in front of c, doesn't matter, it can be either plus or minus

[pseudo merlin]

oh ok

[gentle echo]

thats for directly proportional to the population not its sqrt

[plucky merlin]

Constants multiplied to c, like 6c, can just be written as c, since it's still just a constant

[pseudo merlin]

I don’t get it

[gentle echo]

and like

[pseudo merlin]

Am I wrong

[gentle echo]

is this a different problem?

[plucky merlin]

I think its a different question

[pseudo merlin]

No the same

[gentle echo]

buh

what

[upper ruin]

Impossible

[gentle echo]

it said the population is proportional to the sqrt 💔

it IS a different problem 😭

[pseudo merlin]

wat is it..

[gentle echo]

anyways

the c can just be subtituted as

e^c=A

[pseudo merlin]

ohh wait i was doing anotyher one

but i didnt send the

question

oops..

[gentle echo]

no problemo

:3

[pseudo merlin]

wait soo

am i wrong or no

[gentle echo]

like i said, it just all depends on the constanrs

[pseudo merlin]

for this one

[gentle echo]

so no

[pseudo merlin]

ok good

thanks!!!!

ima sleep now

[gentle echo]

okay thug

[pseudo merlin]

wow

did u just call me a thug

[gentle echo]

yes :3

[pseudo merlin]

wow im kind of sad

fhanks a lot

im gonna have a bad sleep now

.close

[cedar kiln]

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[gentle echo]

🥀

[cedar kiln]

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[mighty shuttle]

A 2 by 2 matrix $\begin{bmatrix} a&b\c&d \end{bmatrix}$ is said to be orthogonal if $a^2+b^2=c^2+d^2=1$ and $ab+cd=0$.Prove the set of all orthogonal 2 by 2 matrics forms a group

[wraith dagger]

wai

[mighty shuttle]

So I'm thinking

I have to do is show ad-bc≠0

[tropic oxide]

is this your first time seeing the words 'orthogonal matrix'

[mighty shuttle]

no

[tropic oxide]

ok do you know what an orthogonal matrix is otherwise

like the definition of that word

[mighty shuttle]

Yeah , det is 1

[tropic oxide]

mmmm nope.

[mighty shuttle]

det is ±1 right

[tropic oxide]

still not the defn

[mighty shuttle]

isn't that a valid defn

[tropic oxide]

no

there exist matrices which fit your desc but are not orthogonal

[mighty shuttle]

let the matrix be A. then AA^T =I

[tropic oxide]

yes THAT'S the defn (modulo minor shit)

so if you want to show that all these matrices are invertible you can and should use that

[mighty shuttle]

Okay, I thought that would only come in handy later

nvm, see how it helps

so that makes proving it's orthogonal easy

from that it follows that |A|≠0 and thus every element is invertible

[crimson delta]

please no det

AA^T=I literally shows invertibility

[mighty shuttle]

right

[cedar kiln]

@mighty shuttle Has your question been resolved?

[mighty shuttle]

done

thnks

.close

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[faint plinth]

hello if im dividing exponents and the bottom exponent is negative would it just stay negative? for example: x^7/8*2x^-10 would it be 7-(-10)? or just 7-10?

[dire thorn]

$\frac{x^7}{8}\cdot 2x^{-10}$

[wraith dagger]

purururuuriuruin

[dire thorn]

This??

$\frac{x^7}{8 \cdot 2x^{-10}}$

[faint plinth]

x to the power of 7 over 8 times 2x to the power of -10

[wraith dagger]

purururuuriuruin

[faint plinth]

yeah that

would it be like 7-10 or would it be 7-(-10)

[dire thorn]

$\frac{1}{x^{-10}} = x^{10}$

[wraith dagger]

purururuuriuruin

[dire thorn]

$\frac{x^7}{8 \cdot 2x^{-10}} = \frac{x^7}{8 \cdot 2} \cdot \frac{1}{x^{-10}}$

[wraith dagger]

purururuuriuruin

[dire thorn]

It is 7-(-10)

[faint plinth]

no im asking if it would be that

cause you know how if dividing exponents you subtract them so in that case would it be 7-10 so that its -3? or like 7--10 so that it turns to a positive 17

[dire thorn]

Yes you subtract the bottom one from the top. The bottom number is -10, the top number is 7, -10 substracted from 7 is 7-(-10)=17

You can also see it is x^17 from the last 2 images

$\frac{x^7}{8 \cdot 2x^{-10}} = \frac{x^7}{8 \cdot 2} \cdot \frac{1}{x^{-10}} = \frac{x^7}{8 \cdot 2} \cdot x^{10} = \frac{x^7\cdot x^{10}}{8 \cdot 2} = \frac{x^{17}}{8 \cdot 2}$

[wraith dagger]

purururuuriuruin

[cedar kiln]

@faint plinth Has your question been resolved?

[cedar kiln]

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[crimson sedge]

where does the 20 come from? it appeared out of nowhere

[topaz crow]

think about why 180=4p+9f+4c
then try rearranging the formula into wanted form

[crimson sedge]

oh i get it

i wasnt thinking of 180

yea

thanks :)

.close

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[silver tusk]

What is the first term of the product of ( 3x 2 − 2x ) ( 6x 3 − 2x 4 + 3x ) when it is written in standard form?

[silver tusk]

is it talking abt mutiplying the first terms or like the highest degree when u mutiply it

[loud gyro]

highest degree

[silver tusk]

ok thank u

[loud gyro]

thats the standard form, you write from highest to lowest degree in that order

[silver tusk]

.close

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[verbal turret]

Why is the mantle of a cone is πrs

[cedar kiln]

@verbal turret Has your question been resolved?

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[keen hound]

uhh help

[mighty shuttle]

this is basically parametric differentiation

@keen hound you here?

Let's try something simpler
$\pdv{ \phi(x+y,x-y)}{x}$

[wraith dagger]

wai

[keen hound]

yeah

[keen hound]

ok

i tried setting cx - az = u and ay - bz = v

[mighty shuttle]

cool

[keen hound]

and i got

del phi/del x = Uc

del phi/ del y = Vc

del phi/del z = -(Ua + Vb)

where U = del phi/del u

and V = del phi/del v

@mighty shuttle

[mighty shuttle]

yeah, just a minute

[keen hound]

wait it is cy- bz

im blind

[mighty shuttle]

uh, quick question, this is supposed to be an equation of two variables, right, unless I'm tripping ( otherwise all vars are independent)

right, it is

[keen hound]

No

it's x, y, z

@mighty shuttle

[mighty shuttle]

so f(x,y,z)

[keen hound]

yep

as in it depends on x,y,z

but there are only two inputs

[limber marsh]

what is phi

[keen hound]

a function

[limber marsh]

there have to be restrictions on phi

[keen hound]

like?

[limber marsh]

like as written it seems as though the equation isn’t true

[mighty shuttle]

ah, right parametric

[limber marsh]

if phi(x,y)=0 for all (x,y) for example then the thing that’s written is false

[keen hound]

im so demotivated rn i dont even want to attempt the next two problems 😭

[mighty shuttle]

Let $cx-az=t;cy-bz=u$
\
$\phi(t,u)$=0
\
Differentiating both sides
\
$\pdv{\phi(t,u)}{t} \cdot ( \pdv{t}{x} + \pdv{t}{y}+ \pdv{t}{z})=0$
\

ugh

epic LaTeX fail

This follows from the multi var chain rule

[keen hound]

mhm

[wraith dagger]

wai

[mighty shuttle]

@limber marsh do correct me if I'm wrong pls

is this the entire problem though

[keen hound]

ywa

[limber marsh]

who gave you this problem

[keen hound]

yes

[keen hound]

It's in my reference material

Higher engineering mathematics

[limber marsh]

see this message. engineers are bad at writing problems so every problem is a podasip (prove or disprove and salvage if possible)

[keen hound]

I'll just leave it be and ask my prof

[limber marsh]

it would be a good exercise for you to try this

you can also ask your prof but they’ll be impressed if you come prepared

[keen hound]

Try what

[limber marsh]

try finding conditions on phi that make the statement true

a good hint is to look at wai’s comment

[mighty shuttle]

Now we aso see that $c = \pdv{t}{x}$ for instance that will help you finish this

[wraith dagger]

wai

[limber marsh]

where are you getting this

oh

yeah

i mean that’s fine

but you actually just don’t solve the problem from this

(because the statement as written is false)

[keen hound]

I'll get back to you

In like ten minutes after trying some stuff

Yeah i cant figure anything out

[nova snow]

engineer boy

[keen hound]

while we're at it, can we do this

this is a disgustingly lengthy problem

HOW is one supposed to get the third derivative

@mighty shuttle @limber marsh

[mighty shuttle]

uh, I don't see anythhing but the regular method

[keen hound]

yeah but it's soo long

[mighty shuttle]

I know

[glossy elm]

water beam

[nova snow]

come vc

[raven shard]

use r_x and r_y instead of writing everything out fully in terms of x and y

[cedar kiln]

@keen hound Has your question been resolved?

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[cedar kiln]

Channel closed

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[ruby topaz]

.close

[cedar kiln]

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[silk plover]

help pls

[silk plover]

we need to find range

[dusty wren]

What step are you on?

1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[silk plover]

2 , i know i have to use cos ( a+b) but it will be too messy i want a cleaner sol

[dusty wren]

You'll see that most stuff cancels out after using cos(a-b) and cos(a+b), not too messy

[silk plover]

1/root 2 stuff

cancels

[dusk goblet]

🤔

[silk plover]

let me try

long way

okay

[dusk goblet]

wdym by long way

just note that cos(pi/2 + x) = -sin(x)

[silk plover]

i thought there might be shorter ways to do it

[dusk goblet]

try to think about how you can use this

[silk plover]

oh wait

[dusty wren]

Btw, welcome to mathcord

[silk plover]

how about using cos A + cos b = 2cos (a+b/2) cos a-b/2

and cos a - cos b = -2sin (a+b/2) sin (a-b/2)

[silk plover]

cool ppl here

[dusk goblet]

sure

[dusk goblet]

i like this though

[silk plover]

log with base root 5 ( 3+ root 2 ( cos x - sin x )

got this

its for sure done now

because

cosx - sinx belong to [-root2 , root 2]

now multiply by root 2 that was outside

[-2,2]

now add the 3

[1,5]

log root 5 now remaining

hmm , is ans [0.2]????

[heavy thorn]

hello. im new

[dusty wren]

Welcome to mathcord!
Unfortunately, this channel is occupied by someone else- if you want to get help you can open your own channel (see #❓how-to-get-help ). For off topic discussion you can check out the discussion channels

[heavy thorn]

okay, thanks

[cedar kiln]

@silk plover Has your question been resolved?

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[faint plinth]

if x^2 + 25 was x^2 - 25 would it also be rewritten? something like (x+5)(x-5)?

[prisma pike]

Yesh

In general $a^2-b^2=(a+b)(a-b)$

[wraith dagger]

denzio321

[faint plinth]

difference of two squares

[prisma pike]

Mhm

[cedar kiln]

@faint plinth Has your question been resolved?

[upper ruin]

Nope, x² + ...² can't be factored

In the next years you'll probably see it actually can, but in a different math world (aka the complex numbers set)

So, for now, just know that it can't be factored over the real numbers

[cedar kiln]

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[coral cobalt]

this might be really easy but how the frick do i solve this

[coral cobalt]

ive forgotten all about shapes and angles 🥀

im so fucking stupid

.close

[cedar kiln]

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[flint cape]

https://tenor.com/view/me-atrapaste-es-cine-its-cinema-cinema-esto-es-cine-gif-12869046600151364058

[coral cobalt]

dont worry im not that dumb usually

[pastel vault]

hey Conquestor

[coral cobalt]

i blame this on having studied only algebra and calc for the past few months

[coral cobalt]

hi south

[subtle halo]

Hey

[storm zealot]

I think area of parallelogram is base into height

[coral cobalt]

yeah

i closed it cuz i solved it

thanks gng

[pastel vault]

it's resolved already

[cedar kiln]

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[paper karma]

Trigonometry time

[paper karma]

cosecA-CotA=..........
[proove it as tan(A/2)

[flat mica]

might be easier to prove it the other way and then work backwards at the end

[paper karma]

i understand that emoji
mine is to study
ur is to make me solve

[paper karma]

just do it however

[flat mica]

excuse me?

[paper karma]

i mean make me do it

[flat mica]

!noans

[cedar kiln]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[paper karma]

what u have to do is make me do it

[flat mica]

bruh I'm not your dom

[paper karma]

whatever
then do ur duty sir

[flint cape]

On tonight's episode of "How to tell someone to do your homework without telling someone to do your homework"...

[paper karma]

i hope i wont be rude i didnt mean it like that

[paper karma]

im practising and not doing homework bruh

[flint cape]

Try and rewrite both sides of this, and see if they match up

[paper karma]

if i dont want to i could skip

[flint cape]

You see, the joke is, I don't care if it's not your homework - the premise is the same: you're all-but-asking someone to do this for you

[paper karma]

hmmmmm u r not wrong also
Im pretty weak at Trigonometry😭

[flint cape]

In response to the [?], rewrite the left hand side using the cosec and cot definitions and try to get this into some simplified experssion

Similarly do the same with the right hand side (look up half-angle-identities)

[flint cape]

For the record, weakness is not an excuse for subordination

[paper karma]

i mean thats the answer there are multiple option so ive to derive it so i dont think it would be any good to change RHS

[paper karma]

i didnt mean to ask for subordination but was asking for a suggestion so i can do it myself

[flint cape]

Well I mean I did explain how to approach this

[flint cape]

So did gfauxpas, for that matter

[paper karma]

ohk

so
(C-S^2)/(SC)

so i can get s(A/2) in denominator multiplying 2 in numerator

🥺

.close

[cedar kiln]

Channel closed

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[nova snow]

LMAO

[paper karma]

.reopen

[cedar kiln]

✅

[dusty wren]

Smooth

[paper karma]

.close

[cedar kiln]

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[flint bobcat]

how do i do quadratics

[supple grove]

how do you solve quadratics?

or graph them

[flint bobcat]

solve

[slender ginkgo]

Any problem in particular?

[tropic oxide]

https://www.youtube.com/watch?v=-KWsS2FZVTA&list=PLzr_MlWyOdDt87OAJCKpZtxUmYv8r1dCV

[flint bobcat]

thanks

[slender ginkgo]

Split cases

If absolute

[tropic oxide]

an entire playlist for you

[flint bobcat]

ok

[ember heath]

do u have a problem with the modulus or the quadratic

[cedar kiln]

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[fallow drift]

can someone help im confused what to do ext

[limber dawn]

first just get the position of the tip of his shadow

x(t)

then take the derivative to get velocity

[fallow drift]

sorry im so confused

X = distance I assume?

[clever venture]

the distance function

[fallow drift]

like yk s(t)

[limber dawn]

yes

[clever venture]

based on time t, what is the x position?

[fallow drift]

okok

[limber dawn]

x(t) means x as a function of t

you can treat the position of the man as some variable that you know, idk what to call it

x_man

or you can even use other variables if you prefer, like angle

[fallow drift]

Ye

okay

Like this right

s(t) was what you were asking?

[limber dawn]

yeah exactly

[fallow drift]

so like

we’re given the derivative..

Not x(t)

It’s not that hard to find x(t) right

But if it was more complicated

What’s the proper way of finding x(t)

[limber dawn]

we don't need to write things in terms of t

we could, but, we don't have to

[fallow drift]

Ig rlly

Oh

[limber dawn]

so like we could use s(t) = 0 + 5.5t or something

[fallow drift]

what should I do now?

[limber dawn]

but here, all we need to do is write the position of the tip of the shadow (call it x ig) in terms of s

[fallow drift]

Oh

how 😭

[limber dawn]

we don't need to know the form of s(t) itself

[fallow drift]

I still not rlly get

[limber dawn]

ig one way to view this is, just start with geometry first

[fallow drift]

What the point of similar triangle is

[limber dawn]

the bottom of the triangle is x

[fallow drift]

oh what

[limber dawn]

then s is the distance between the left two vertical lines

[fallow drift]

OHH

ohhhhħ

[limber dawn]

✅

[fallow drift]

How do we know

Which yellow were asked for

[limber dawn]

the left vertical line is the light pole

the middle line is the man

yellow

oh

[fallow drift]

ya

ok kinda makes sense

[limber dawn]

we want x because that gives the position of the shadow

the other yellow gives the position of the shadow from the man (middle line), but the man is moving too

so we don't want that one bc it has a different rate of change

[fallow drift]

Is this right

[limber dawn]

so we just want to do geometry first, see how s and x are related

[fallow drift]

Help

im so laggy

Sorry

[limber dawn]

don't assume s is 45 tho

because s will be changing in time

we want the full relation between s and x, for any s, not just s = 45

[fallow drift]

Wait I wrote

[limber dawn]

that way we can relate change in s to change in x

[fallow drift]

45-x

X-45

[limber dawn]

right

but replace 45 with s

[fallow drift]

Huhhhhhhhhhhhh

[limber dawn]

bc of what i just said

s will be changing

the question is asking about rates of change

[fallow drift]

Do we rlly need to tho

If I put s =45

Ill be solving for at that specific point right

[limber dawn]

yeah

then you'll get x at that time

[fallow drift]

Okay

[limber dawn]

but then you still have to find speed

[fallow drift]

Oh

umm

[limber dawn]

speed is where rates of change come in

[fallow drift]

okay

Lemme

Solve rq

Do I isolate for

X

[limber dawn]

sure yes

mainly just an equation that relates x and s is important

if you isolate x that is helpful too

[fallow drift]

Okay

I at

Wait

S or X?

Which one is better

[limber dawn]

x

because then you can just take the derivative

dx/dt

and that will be the answer

[fallow drift]

Oh

What

[limber dawn]

they ask for a speed

in the question

so yeah that's what speed is

a derivative

i assume this is a calculus class right?

[fallow drift]

okok

[fallow drift]

Ye

Uhh whats s

[limber dawn]

i realized the answer is pretty simple so you may be able to visualize it instead

but if this is for calculus it's worth doing the math anyway

[limber dawn]

s is the position of the man (from the pole which we can say is 0)

x is the position of the shadow (from the pole again)

[fallow drift]

Can you show me that way too

[fallow drift]

Okay

[limber dawn]

i guess the 2 ways are similar, but there's a shortcut. i can explain it right after we do the math bc it'll be clear from it

ok so for now

$\frac{x}{15.5} = \frac{x - 45}{6.3}$

[wraith dagger]

back to ginger

[limber dawn]

you had this

just replace 45 with s

$\frac{x}{15.5} = \frac{x - s}{6.3}$

[wraith dagger]

back to ginger

[limber dawn]

now isolate x like you mentioned

tell me what you get

[fallow drift]

Hip

yup

Here

Does s = s(t)

[limber dawn]

correct ^

you can just write "s" for short

but s is a variable, and variables can vary (in time)

ok so you got

6.3x = 15.5x - 15.5s

solve for x now

isolate it

and just solve

oh wait you did sorry

i'm blind

ok so the pole is 15.5 instead of 15 ft so i get 9.2 instead of 8.7 but yes

$x = \frac{15.5}{9.2} s$