help-23

[jade gust]

Not gonna spend time on this js need to know the steps I've already tried the problem to no avail because i started to js fuck around explorin maths while solving it but it's not a priority

[tall bough]

fr

[jade gust]

go away

why are you on roblox

[tall bough]

because im cool

[jade gust]

r u gon help me

die

[tall bough]

i just found it on google

u have googling skill issues hehe

[jade gust]

I know

I was js lookin at sum british further maths papers

cambridge or whatever

[tall bough]

https://www.nagwa.com/en/videos/915194638078/

mr tasman did i help u

[jade gust]

ur mon obese

[tall bough]

?

je parle pas francais

[jade gust]

ew

[tall bough]

u have grown ur learning moivre now

[jade gust]

that was a year ago

well

yesn't

[tall bough]

next step would be

fourier

[jade gust]

a bit last year and this year

dunno i'm js chillin in hs

somewhat

[tall bough]

hs too ez

when r u going to university

[jade gust]

i'm doing horrendous

[jade gust]

later this year

mayb

or i go military

like i said a year ago

i have my application on hold

[tall bough]

thats nice im also in the army

[jade gust]

fake

[tall bough]

no?

wanna see my rank badge

[jade gust]

no

oki

let's see it

r u in the dutch army

[tall bough]

no im not

[jade gust]

frig Euler's Formula 😡

i decided to apply binomial expansion LHS

cause i'm funny

[jade gust]

delete your account

[tall bough]

thats not how you talk to your superiors

100 JJ's

[jade gust]

i should be studyin my physigz

[tall bough]

yes do that instead of math

[jade gust]

wad

what can i do with

[jade gust]

uhh hello!!! @tall bough

[tall bough]

video was my help

[jade gust]

i do not accept your help

[tall bough]

u have nop watched the video?

[jade gust]

what happened to bewar

@dusk pebble

hello babez

[tall bough]

do not ping people !!!! read ze rules

[dusk pebble]

!!!!

[jade gust]

i'm illiterate

[dusk pebble]

hi abel

[jade gust]

halo

[tall bough]

that explains

[dusk pebble]

whats going on

[jade gust]

what do i do with this

[dusk pebble]

why we doing trig

[tall bough]

blud does not want to watch the video

[jade gust]

meow

i do not want to watch the video

i'm listening to hardstyle

https://www.youtube.com/watch?v=-XLHPPrRWSM

[tall bough]

then i would suggest as a good teacher

to watch the video

it is 6 minutes long

then 24/7 hardqtyle

you should be happy that im doing it for free!

[jade gust]

I've not been payin attention to my lectures

[tall bough]

sounds like skill issues fr

i owuld give u some good whopping and ull get A+

[jade gust]

that's so real

my institution is telling me to get lost if i don't meet their standards within this term

[dusk pebble]

ok but

[tall bough]

u know what a top g would do?

[dusk pebble]

whats wrong with expansing cos(5x) and sin(5x)

[jade gust]

wdym

why would i want to expand it

[dusk pebble]

since tan(5x) = sin()/cos()

[jade gust]

yes

[dusk pebble]

so if you can write out what the sin an dcos are then you have tan by default

[jade gust]

ok but what identity do i use

[dusk pebble]

de moivre's no?

[tall bough]

moivre

yes

[dusk pebble]

cos(nx) + isin(nx) = [cos(x)+isin(x)]^n

[jade gust]

then am i not working backwards

what i did was

[jade gust]

applied binomial expansion LHS

and

LHS/cos5theta=1+i tan 5 theta

solve for tan 5 theta

[jade gust]

funny

[dusk pebble]

that doesnt help that much tho

bc then you still have cos(5x)there

but pro tip

[dusk pebble]

cos(5theta) is the real part of the LHS, sin(5theta) the Im part

so group by powers of i and you have it no problem

[jade gust]

yas?

[dusk pebble]

ya

easier to write out for specific n but ye

[jade gust]

wdym

[dusk pebble]

well

cos(2x) + i sin(2x) = [cos(x)+isin(x)]^2 = cos^2(x) + 2i sin(x)cos(x) - sin^2(x)

so cos(2x) = cos^2(x) - sin^2(x) since its the real part of the rhs

sin(2x) = 2sin(x)cos(x) since its the imaginary part

bc then it has i^1 in front

[tall bough]

beware has been doing too much math lately fr

[jade gust]

real

[dusk pebble]

😔 many such cases

[jade gust]

Imma fuck up this electrostatics/electromagnetism test tmr

[tall bough]

im

i like electricity

just apply maxwell equations and ur done

[flat frigate]

\({\displaystyle {\vec {E}}({\vec {r}})={\frac {1}{4\pi \varepsilon _{0}}}\sum _{i=1}^{N}{\frac {{\widehat {\mathcal {R}}}_{i}Q_{i}}{\left\|{\mathcal {\vec {R}}}_{i}\right\|^{2}}},}\)

[tall bough]

whyyy

[jade gust]

Why does no one express Coulomb constant as k_e

[tall bough]

because its ugly

[jade gust]

no

why's the norm so long

[jade gust]

thanks babez

[tall bough]

$\oint E dA = \frac{Q}{\epsilon_0} = \frac{4\pi r^2k Q}{r^2} = \frac{Q}{\epsilon_0} = 4\pi k Q = \frac{Q}{\epsilon_0}$

[flat frigate]

Fucktalogist

[tall bough]

see thats why

[jade gust]

ugly

[tall bough]

if u used 1/4pie instead u wouldnt get that

[dusk pebble]

contour integrals 😔

[tall bough]

whats that

is that complex analysis

[dusk pebble]

oint

my despised

[jade gust]

OSINT open source intelligence

[tall bough]

we no complex analyzing here

[jade gust]

beware get your doctorates

[tall bough]

he already hgas

[dusk pebble]

ill doctor ur mum dwai

[tall bough]

his thesis was about cheese numbers

[jade gust]

waw

Speed of light, Planck's constant, numerical eccentricity, euler's number, and coefficient of restitution in one 😱

[tall bough]

whats blud babbling about

[jade gust]

go play your roblos army RP

[tall bough]

am going to play honkai impact 3rd

[jade gust]

what happened to genshin

it just died

.close

[safe radish]

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[tall bough]

Havent played it fir 2 years

[tall bough]

.clise

[lean otter]

.close

[safe radish]

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[twilit torrent]

Is this taylor series

[twilit torrent]

don't see how though

e^(-Ts) \approx 1-Ts + ...

[vague frost]

well e^-Ts

can be rewritten as 1/(e^Ts)

[twilit torrent]

okay...

so what?

[vague frost]

whats the question in the problem ?

[twilit torrent]

I'm asking how do they approximate it

It looks like taylor approximation to me

not sure if it is though

and you just told me something trivial lol

[twilit torrent]

This is the question^

[vague frost]

well it looks to me like they used taylor

[twilit torrent]

could someone tell me what happened

[twilit torrent]

bro you're just repeating me at this point

please don't try to help if you don't know

you're flooding the channel

could someone pls show me how they got this approximation

it looks like a linear approximation in the left and quadratic approx on the right

is it?

<@&286206848099549185>

[plucky elk]

Yes

[twilit torrent]

can you show me how

I'm not getting the right side from left

what should i do?

[plucky elk]

Multiply top and bottom by e^(Ts)

[twilit torrent]

what is the objective of doing this?

[plucky elk]

To get this expression

[twilit torrent]

sorry i'm not following

after multiplying

am i supposed to make a substitution or something

can you type it out maybe?

,, \frac{1-e^{-Ts}}{s} \cdot \frac{e^{Ts}}{e^{Ts}}

[flat frigate]

hii_

[plucky elk]

Taylor expand numerator and denominator separately after simplifying

[twilit torrent]

,, \frac{e^{Ts} - 1}{e^{Ts} s}

[flat frigate]

hii_

[twilit torrent]

you mean linear approx?

anyway e^(Ts) would be like (1 + Ts + ...) - 1

[plucky elk]

Use whatever expansion you need to get the answer

[twilit torrent]

what would e^(Ts) * s be? do i just multiply taylor expansion of e^Ts and s

is that legal?

[twilit torrent]

what's the taylor expansion of s?

isn't it just like 1 or something

so just taylor expansion of e^(Ts) then right?

[plucky elk]

Yes

[twilit torrent]

hmm i think i'm doing something wrong then

idk how to find the taylor expansion of s

it's s

,, \frac{(1+Ts + \frac{(Ts)^2}{2} + \ldots) -1}{(1+Ts + \frac{(Ts)^2}{2} + \ldots) s}

@plucky elk

this is bad?

[plucky elk]

You're almost there

[twilit torrent]

what is wrong?

I have gotten to T/ (1+Ts)

I'm missing the T/2

[flat frigate]

hii_

[twilit torrent]

@plucky elk

:V please just tell me where i'm doing wrong

I have to use this result for proving other stuffs

and i can't proceed without this result

@thin bridge could you help me with this question pls?

I guess i'm almost done here

Need help with finishing touches

[plucky elk]

You didn't simplify

1-1=?

[twilit torrent]

I did

[plucky elk]

That's silly. You can always come back to prove this later

[twilit torrent]

(Ts + (Ts)^2/2 + ...)/ s + Ts + (Ts)^2/2

[plucky elk]

Use algebra to simplify more

[twilit torrent]

that is true but i am doing control system review for my test tomorrow

and i wanted to know how this approximation was made

[plucky elk]

So?

[twilit torrent]

Just wanted to know in case i need to use that result

because i do make use of the result right after

I don't want to memorize it

[plucky elk]

My point still stands

[twilit torrent]

Uhh i already did but i had T/ (1+Ts)

unless i'm blind

[twilit torrent]

I took the linear terms from here because they don't seem to use quadratic terms on the left

@plucky elk ?

smh

,, \frac{Ts + \frac{T^2s^2}{2}}{s + Ts^2} = \frac{T (1 + Ts/2)}{(1+Ts)}

[flat frigate]

hii_

[safe radish]

@twilit torrent Has your question been resolved?

[plucky elk]

Yea so the linear terms give you the first approximation

[twilit torrent]

That's the part i don't see

how is T(1+Ts/2)/ (1+Ts) the same as T/(1+T/2 s)

[plucky elk]

Your denominator looks wrong

[plucky elk]

s cancels. What do you get after that

[twilit torrent]

what

how is my denominator wrong

[plucky elk]

.

[twilit torrent]

how can i even cancel

why is my denominator wrong in the first place

[plucky elk]

Factor out s from the numerator and denominator

[twilit torrent]

anyway s cancels and you should get (T + T^2s/2)/ (1+ Ts+ ...)

[plucky elk]

s / s = ?

[twilit torrent]

It's literally not coming out the way

it comes on paper lol

You tell me

What

assume we get rid of the quadratic term on the top which should've been T + (T^2s/2) but doesn't matter

we get T / 1+ Ts

not T/ (1+ T/2 s)

[twilit torrent]

which is literally what i said like 40 minutes back lol

[safe radish]

@twilit torrent Has your question been resolved?

[safe radish]

@twilit torrent Has your question been resolved?

[safe radish]

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[reef grail]

how do u do part b

[late crypt]

i think f'(x)>0 should be satisfied

[reef grail]

ah ok

I was confused about whether it was the first or second derivative

what does f''(x) > 0 mean

that the function is increasing by a greater value each time?

[safe radish]

@reef grail Has your question been resolved?

[gusty jackal]

Correct.

The slope is constantly rising.

[reef grail]

Ah

thank you

[gusty jackal]

Wait not constantly

But yeah the slope is rising

[reef grail]

.close

[safe radish]

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[dense epoch]

Can someone help with this

[dense epoch]

I tried subtracting and dividing but it didn’t work

[timber crescent]

assuming the growth of the plant is linear we can use the general form y = mx + c

[timber crescent]

try substituting the values of x and y into that and you'll get simultaneous equations which you can solve for the value of m and c

x would be the number of days and y would be the height in this case

[dense epoch]

19=m(5)+c

[timber crescent]

yea

use another pair of x and y

you'll get another equauon

[dense epoch]

28=m(8)+c

[timber crescent]

yea can you solve for m and c now

[dense epoch]

Oki

Thank you

[timber crescent]

np

[dense epoch]

Do yk how to do this one

[timber crescent]

we find both the total number of males and females

let x = total number of males

180/x = 2/9

solve for x

and total number of females can be found from the total employees

what do u think should be done now

[dense epoch]

1,350-810

?

[timber crescent]

yea

i meant after that, do u have any ideas to continue

[dense epoch]

540x5/9

[timber crescent]

yes, go on

[dense epoch]

+180x2/9

and that number over the total amount of employees?

[timber crescent]

that's correct

[dense epoch]

Ok thank you have a good night/day/evening !🩷

[timber crescent]

np, u too

[safe radish]

@dense epoch Has your question been resolved?

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[limber drift]

Ignore my grade.

I need like some sort if video to help me relearn how to do those

i doubt anybody is willing to teach me...

If i knew what kind of trig this is i could just search yt

but i dont so it meaningless to scroll through yt trying to find it.

.close

[safe radish]

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[fast jungle]

Uh

The picture is not very clear

[limber drift]

dont worry about it

i gave up

[fast jungle]

Why

[limber drift]

ill wing is some how

[fast jungle]

aight

[safe radish]

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[novel magnet]

A projectile would have the greatest velocity as it gets released from the cannon right?

[novel magnet]

if no other force other than gravity acted on it

like

if a ball is thrown from a cannon

then the only force acted on it would be the gravity force?

[stoic dune]

If you let it drop for a long time, the velocity could get larger

[novel magnet]

really?

[stoic dune]

Depends what the terminal velocity is, I suppose

[novel magnet]

ok hold on

[dull sequoia]

that would require there to be resistance

those dont exist in physics

[stoic dune]

Oh yeah what was I thinking

[dull sequoia]

[novel magnet]

@stoic dune thats the diagram

so would it still have the greatest velocity before it lands?

[stoic dune]

If resistance is not a thing that exists, then yes.

[novel magnet]

hmmm

weird

how come tho?

cus doesn't the velocity start dropping after it leaves the cannon?

[stoic dune]

If resistance is a thing that exists, then yes

"air resistance" is doing a lot of work on this question

[dull sequoia]

well actually

he said velocity

[stoic dune]

Also yeah, the ball is going up so it gets slower

[dull sequoia]

not speed...

in which case, it depends where "positive" velocity is facing

[novel magnet]

air resistance is negligible

[stoic dune]

I have assumed you mean speed when you say velocity

[novel magnet]

well

[stoic dune]

But I suppose if the ball is going down, that could be a negative velocity, too

[novel magnet]

"where does the projectile have the greatest velocity?"

[dull sequoia]

it really depends where positive velocity is defined

[stoic dune]

Okay so I think they're trying to get you to recognize that "lower ball = more potential energy absorbed = faster ball*

But yeah, velocity is a sus word there

[dull sequoia]

unless it tells you what the initial velocity is

if it tells you that then there'll be a sense of direction

[novel magnet]

no initial velocity

i hate physics ffs

[dull sequoia]

is this the exact diagram they've drawn

[novel magnet]

@dull sequoia

[dull sequoia]

ok show the rest of the question

[novel magnet]

umm

hold on

[novel magnet]

ive already calculated the value

@dull sequoia for number 2 of the first pic

[dull sequoia]

it's still ambiguous dammit

but im gonna say at the beginning

[obtuse plover]

Assuming this is the projectile path, the ball would be fastest right before it hits ground no?

[dull sequoia]

but that's speed

😢

[novel magnet]

lmaooo

[dull sequoia]

although if u define down to the floor as positive velocity

then you put this contraption very high

it'd have highest velocity when hitting the floor too

[novel magnet]

ok

ig the question really meant speed

[dull sequoia]

then it'd be as it hit the floor

(but then if you took resistance into account it could be before that)

but then you're looking at some wack ass fluids

[novel magnet]

if we account resistance then the greatest speed/velocity would be right after you fire the ball ig

[faint raptor]

wouldnt the physics server be a better place to ask

[novel magnet]

im so sorry I didn't know there was a physics server

[faint raptor]

lol nws

#old-network

[safe radish]

@novel magnet Has your question been resolved?

[safe radish]

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[obtuse copper]

there is not enough info here right?

[obtuse copper]

because you can't do pythagorean thrm

or am I wrong

[lean thorn]

yeah I don't think there's enough info (but take what I say with a grain of salt).

They are similar triangles but we know the value for DC so we could find ZY but not WZ since since we don't know AD.

I'm terrible at geometry though so I could be very wrong

[obtuse copper]

ima just trust it

atp

.close

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[lean otter]

Why did they divide by sin 90 here

[lean thorn]

law of sins with the right sided right triangle

[lean otter]

I did the same thing

but my answer was 7212

[flat frigate]

Result:

-2804.9872526717

[lean thorn]

ugh

well you're looking for the height

in yoru example you're looking for the left side

[lean otter]

what would i do then?

sorry this is kind of ne wto me

[lean thorn]

no worries

notice the straight line in their example?

that represents the height

[lean otter]

yes i see

but how would the height be 90 degrees?

[lean thorn]

you can turn the main triangle into 2 right triangles

[lean otter]

ahhhh i see

thats why

[lean thorn]

yep 🙂

[lean otter]

how would i incorporate 90 degrees into the equation then

[lean thorn]

A straight line always has a perpendicular angle to the ground (aka it's always 90 degrees)

forgive the crude drawing lol

[lean otter]

ahhh i see

.close

[safe radish]

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[safe radish]

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[manic path]

I have a general question about intergration

[manic path]

if I had something like 32x^2 + 8x^2pi

could i factorise it out like 8x^2(4+pi)

and differentiate it like this so it becomes, 16x ??

[pulsar pecan]

You can factor out constants

But you have to remember to put them back in afterwards

[pulsar pecan]

So that would actually become x16(4+π)

[royal kiln]

That factorization is incorrect

[royal kiln]

$8(4x^2 + x^{2\pi})$

[flat frigate]

Disorganized

[fluid token]

i think it’s (8x^2) * pi

[pulsar pecan]

$$ 32x^2 + 8x^2\pi $$

[flat frigate]

(a + b)^2 = a^2 + b^2

[royal kiln]

Why would they put a second coefficient at the end tho

Nonstandard

[fluid token]

that is very weird

[pulsar pecan]

you can do that in wolframalpha

cos^2x

[royal kiln]

I know you can

[pulsar pecan]

it gets interpreted as (cos x)^2

[fluid token]

[royal kiln]

But it goes against what is commonly understood about those expressions in a non-latex format

[manic path]

woops I forgot i opened this

I actually solved it

sorry :V

but thanks for your help guys

.close

[safe radish]

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[manic path]

.reopen

wait no

[safe radish]

✅

[manic path]

ok so I cannot just make some part of it disappear alright

thanks for the help guys

.close

[safe radish]

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[safe radish]

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[gritty umbra]

what is the DI method in integrating? Can I use it in finding the antiderivative of trigonometric functions?

[stray socket]

Is it like tabular?

I mean sure

Like if you have x^3 cos(3x)

Just google "how to do tabular integration"

[gritty umbra]

in what cases can I use that method

since I can use it with xsin(x)

can I use it with tan²(x)?

[stray socket]

No

[gritty umbra]

okay

what about

cos(x) - sin(x)

[stray socket]

You don't even use IBP for that

Thats good ol' regular integration

[gritty umbra]

okay so I can only use the DI method if I have two terms that is multiplying

[stray socket]

Well for any integrand that makes IBP repetitive or annoying

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[pulsar pecan]

you could write it as 2 sigmas, the second one would be ||10/9||

put spoiler for second one

[safe radish]

@sour ore Has your question been resolved?

[grizzled shoal]

$\frac{k+1}{10^k}=\frac{k}{10^k}+\frac{1}{10^k}$

[flat frigate]

~Martin

[grizzled shoal]

that is how we can split it in two sums

the right one is a geometric series

now we find the two sums

and what they converge to

[plucky elk]

<@&268886789983436800>

[grizzled shoal]

you dont need epsilon here

for the right sum, we use the geometric series

for the left one i would advise first proving the convergence

then we can use some nice stuff

the convergence is not so difficult

you can do it

what

the convergence?

what kind of criteria do you know

https://en.wikipedia.org/wiki/Convergent_series#:~:text=If r <%201%2C%20then%20the%20series%20converges.,they%20work%20in%20similar%20situations.

under convergent test, they for example use the quotient test

function can converge

sums can converge

a lot of stuff can converge

$S=\sum_{k=0}^\infty a_n, a_n\neq 0$

[flat frigate]

~Martin

[grizzled shoal]

if we now find a q, such that $|\frac{a_{k+1}}{a_k}|\leq k<1$

[flat frigate]

~Martin

[grizzled shoal]

then the sum S converges absolutely

this comparison does not have to be true for all k though

so usually, what we do is, we get this fraction a(k+1)/a(k) and then take the limit with k->oo

if that is less than 1, then we have convergence

note that this does not give us the limit of the sum, it only tells us that the sum converges

but once you did that and find that it convergence we can rearrange the terms in the sum

for example:

S=1/10 + 2/10^2 + 3/10^3 + ...
consider S/10 = 1/10^2 + 2/10^3 + 3/10^4 + ...
look what you can do with that

just try your best

we need convergence

otherwise there is no solution at all

now that we have convergence we can rearrange the terms

this is not allowed if we dont have convergence

[grizzled shoal]

look at what you can do with this

[safe radish]

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[green storm]

Is there any way to solve this without having to expand the whole thing?

[ocean quiver]

binomial expansion

[green storm]

Isn’t that expanding the whole thing until u find it though?

I’m trying to see if there’s a way that you don’t have to do that

[velvet kettle]

Do you know binomial theorem

[green storm]

Yeah

[velvet kettle]

I don’t mean do you know how to expand binomials, do you know the theorem for it

[plucky elk]

Yes

Write the general term and solve for when the x exponent is 0

[plucky elk]

Using this

[green storm]

Got it

.close

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[worn yarrow]

For this one, the asnwer is

But i dont get the logic

like why the answer is this

can u tell me how u work this out

[safe radish]

@worn yarrow Has your question been resolved?

[echo kestrel]

AP formula for Sn

[worn yarrow]

Hmm?

What formula

Are we applying here

😮

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[thin bridge]

if your graphing a straight line, finding two points is sufficient

substitute in one nice value of x to get the respective y value (giving you a point)
repeat for another point

enough

then draw the straight line through those two points you just found

well the value of x=12 doesn't fit there, choose a better value

well the value of x=10 doesn't fit there, choose a better value

what ist he value of y when x=2

yes

however that's not what's represented on the graph

when x=2, your y value there is a bit above 1

yeh, but x isn't 2 where your y=0

also didn't you succeed in doing this like 10 minutes ago

exact same prinicple

forget about lines for now

yes

you did it

no

this is the easiest

forget about lines for now

do you know how to plot just points?

yes, you can

that's essentially what i tried to get you to do

pretty much just a dot on a graph

it'd be what you have to go through if trying to graph by a table

that's essentially what i tried to get you to do
but you only needed to pairs of values for two points, (and not that full table)

yes, i also said that earlier

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[thin bridge]

y = 2-2
using x=2, results in y=0
y = 5-2
using x=5, results in y=3

which if you insist on having an explicit table would be represented as
x | 2 | 5
y | 0 | 3

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[fringe linden]

Hi, guys I need some help as I have no clue how to continue at this point

[fringe linden]

Determine the rank of the matrix as a function of lambda (in my case a).

lambda = a, I use letters as I can distinguish them better when writing

How do I achieve a zero component in the last row

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@fringe linden Has your question been resolved?

[fringe linden]

<@&286206848099549185>

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@fringe linden Has your question been resolved?

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[austere spade]

Heya, mechanics question- trying part i) i'm trying to look at moments around axis of rotation B, how would I account for the weight? where would it act?

[austere spade]

Only ever really looked at moments on 1d models so I'm not sure what to do

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[uncut ocean]

If I have x marbles evenly divided into n colors, what is the chance that if I pick n marbles without replacement, there is one marble of each color? (i think i have a formula but i'm not sure)
What is the chance that if I pick n marbles without replacement from infinity marbles equally divided into n colors that there is one marble of each color? How come if I extend that formula to infinity, it gives a different answer than my expectation of (n-1!)/(n^(n-1))?

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[royal arch]

How can I create a function that has the point (0,1) and its inverse having a point (3,5)

[faint seal]

let the function be f(x)

then you know that f(0)=1 and f^-1(3)=5 i.e f(5) = 3

you can create an infinite number of functions with those 2 conditions

[dull sequoia]

f(x) = {1, x = 0; 0, x = 1; 3, x = 5; 5, x = 3}

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[prisma swift]

can someone help me understand why in space a line has 3 equations and why we can mess around with the variables so much

[tepid walrus]

What exactly don't you understand?

[thick sparrow]

Can you give an example to illustrate your point? 🙂

[prisma swift]

yeah sure

here are my notes

it doesnt really make sense to me how we can use any pt A on the line for the eq

like

doesnt that mess with the results

[tepid walrus]

That, again, isn't very clear. Can you formulate a question?

ideally include an example

[prisma swift]

also sorry for the handwriting

[prisma swift]

it says that the parametric eq for a line D is
{ x= ak+xA
y= bk +yA
z= ck+zA

[viscid ore]

https://tutorial.math.lamar.edu/classes/calciii/eqnsoflines.aspx

[prisma swift]

where A belongs to D

[prisma swift]

nah nah ik how to use it and all

i just cant visualize it

i think id undertand it better if i could

[prisma swift]

for example we have the line
D {
x=2k+1
y=-3k+5
z=4k-7

and pt A(1,5,-7) on the line

we can plug in any value of k to find the corresponding coordinates for a pt on the line

for example k=1

[deep creek]

https://www.math3d.org/ maybe this 3d calculator can help you visualize better

[prisma swift]

aight one moment

[deep creek]

you can choose to add an object, either a line using two points or a parametric curve

[prisma swift]

i can see it better now

thanks for the help

[deep creek]

np, i wish i had this tool back when i took multivariable calc

it can even do vector fields and parametric surfaces

very useful

[prisma swift]

i didnt even know this was multivariable calc 😭😭😭

[deep creek]

i mean someone posted paul's online notes for calc 3 earlier...what class is this for? lol

[prisma swift]

sounds cool

[prisma swift]

the education system here is diff but im in grade 11

its general math class

its so random

[thick sparrow]

There are commonly two types of equations.

1. Variables are inter-related in one single equation like the usual one.

2. We use some "parameter variables" to tell how each "main variable" should behave.
   Like your example is using parameter variable to model for the behavior on the main variable x y z.

[prisma swift]

like for my final coming up in a few days i have these to study

[prisma swift]

ye i figured

you cant have x y and z in one eq in space

[deep creek]

oh i see, looks like a precalc class with some pretty random topics

[prisma swift]

because thatll be a plane

not a line

[prisma swift]

mhm

we also took circles, solid geometry and other stuff this year

we will take trigonometric functions in summer 💀

anyways thanks for the help everyone

.close

[safe radish]

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[white tendon]

Hey, I need help with a couple of these problems

[white tendon]

<@&286206848099549185>

<@&286206848099549185>

[weak garnet]

just eliminate that term for the last one

[white tendon]

wym? like putting it was 25+4+4=100

[weak garnet]

no

like 25x^2 + 4y^2 = 100 for z = 0

[white tendon]

does that follow with the other two pictures as well?

[weak garnet]

ye

[white tendon]

for the 9x^2+8y^2+z=0 and the picture below it?

[weak garnet]

that one only the zeros cancel

otherwise you just plug in z

[white tendon]

oh okay

thank you

.close

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[fickle trail]

a) det(AB) = det(A) * det(B)
-3 * -9 = 27

27 would be correct for a?

[hot thistle]

yes

[fickle trail]

I think these are correct

now just for B^4

[hot thistle]

check your answers again

[fickle trail]

for which one?

[hot thistle]

im not gonna say, just that you should double check

[fickle trail]

oh ty

-2A = 6

I wanna say the last one is 81?

because -3 ^ 4 = 81

[hot thistle]

you did A^3

[fickle trail]

oops

6561

thats a big determinant

[hot thistle]

sure is

[fickle trail]

hmmmm...

[hot thistle]

oh right

[fickle trail]

it was -6?

[hot thistle]

what is det(2 * I)

no

[fickle trail]

-3

[hot thistle]

no

[fickle trail]

I or 1?

[hot thistle]

I

[fickle trail]

ummm

2

[hot thistle]

no

take I to be 4x4

and do 2I

what is the determinant

$\begin{bmatrix} 2 & 0 & 0 & 0 \ 0 & 2 & 0 & 0 \ 0 & 0 & 2 & 0 \ 0 & 0 & 0 & 2\end{bmatrix}$

[flat frigate]

maximo

[fickle trail]

aren't we just multiplying I by the scalar 2?

[hot thistle]

what is the determinant of this

do you remember how to compute a determinant?

[fickle trail]

2 * 2 * 2 * 2?

diagonal

[hot thistle]

this one is particularly easy since it's a diagonal/triangular matrix

yes

[fickle trail]

so 16

[hot thistle]

yes

in general

for an nxn matrix A

[fickle trail]

but the identity is 1

[hot thistle]

det(cA) = c^n * det(A)

[fickle trail]

so 2 * I = 2

[hot thistle]

.

it's not just 2 * det(A)

it's 2^n * det(A)

[devout shale]

because think about the rule for scaling rows

when you scale a row, you scale the determinant

when you scale an entire matrix, you scale all of its rows

[fickle trail]

A is
-3 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1

det(A) = -3

-3 * -2 = 6, no?

[devout shale]

-3 * -2 = 6, but that is not how you find the determinant.......

maximo just demonstated above why it doesn't work like that

[hot thistle]

you multiply every row

avid multiply A by 2

[fickle trail]

ahh right right

sorry

[hot thistle]

np

[fickle trail]

6 * -2 * -2 * -2

-48

[devout shale]

sure, but weird way of writing it

-3 * (-2)^4

is really what you did anyways

so it might help you remember it if you don't simplify one of the -2's out

[fickle trail]

I am doing scalar first

but it's actually -2

so that's how I got this: 6 * -2 * -2 * -2

now I multiply the diagonal

woot

tyty

[devout shale]

I think you are again getting too attached to specific matrices btw

[hot thistle]

the idea is you should think

det(cA) = c^n * det(A)

[fickle trail]

hmmm

I will write that down

ty

[hot thistle]

but if you want to do the diagonal way, we won't stop you

[fickle trail]

OK haha

.close

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[wide trellis]

heres the question:
3/4 m - 6p = 3/4 q [q]

basically, i have to change the subject of formula (i forgot T.T)

(the next step)
3/4 q = 3/4 m - 6p

and now i have absolutely no idea what to do

[quasi bison]

if the equation was

3/4 q = 11

would you be able to solve this

[wide trellis]

uhhh

ok wait

11 divide by 3

then x 4?

[quasi bison]

almost

[wide trellis]

ok then

[quasi bison]

don't use the letter x as a multiplication symbol

[wide trellis]

divide by 4

[wide trellis]

oh

why?

[dull sequoia]

Cos x is a variable

[quasi bison]

you will confuse it with the letter x

anyway ok so like

[wide trellis]

oh alright what should i use then?

oh ok

[wide trellis]

ahh alright thanks!

[quasi bison]

yeah so from (3/4)q = 11 you can multiply by 4 and divide by 3 on both sides

or to consolidate these into one, multiply by 4/3 on both sides

[wide trellis]

ohh

wait let me try now

q = m - 4.5

[quasi bison]

❌

[wide trellis]

oh

[quasi bison]

where did p vanish to and how did 4.5 happen

[wide trellis]

😭

[quasi bison]

6*4/3 isn't 4.5

[wide trellis]

wait lemme retry

[quasi bison]

show your work this time

[wide trellis]

OH OK I GOT IT

q = m - 8p

thank you so much i really apprieciate the help :))

.close

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[wide trellis]

just 6 * 3/4

it was a careless mistake earlier

👍

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[lean otter]

In triangle pqr , PQ = QR = 9CM and the height of the triangle measured from Q is 7cm , find the length of PR

topic = pythagoras theorem

How do you do the working ? I’m learning it for tmr test

Thanks !

[dull sequoia]

Could you draw a diagram?

[lean otter]

And send it here? Yes sure

[wintry sigil]

@lean otter have a look

[lean otter]

When you write PR = 2 square root 32 = 8 square root 2

Isn’t it suppose to be only square root 32?

[lean otter]

The last step

[wintry sigil]

32=16*2

And the square root of 16 is 4

So I bring 4 out of the root and multiply it with 2 and I get 8

[lean otter]

Ohh

OH

Now it makes sense to me!

Thank you so much !
Much appreciated 😁

Is it okay if. I save the photo?

[wintry sigil]

Hehe np

[wintry sigil]

Ofc u can do it.

[lean otter]

Thank you
Great day !

[wintry sigil]

To you as well!!!

[safe radish]

@lean otter Has your question been resolved?

[safe radish]

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[zenith dagger]

can someone help me with this question thx

[sudden forum]

so we need to prove that

opposite triangles are complementary

[zenith dagger]

oh just that?

[sudden forum]

supplementary*

[sudden forum]

I think so 🤔

[zenith dagger]

damn

[sudden forum]

That's majorly the only property cyclic quadrilaterals have I guess?

[zenith dagger]

wait let me process

wait but how does that prove

its just a property no?

[sudden forum]

Its a property

[zenith dagger]

but how do we prove that QRST is a cylic quadrilateral

[sudden forum]

cyclic quadrilater <=> opp angles supplementary
so i think proving opp angles supplementary should be sufficient to prove its cyclic

but how to prove supplementary

We are also given a QT
But why is it there why not a little above or below

[zenith dagger]

i mean we dont know any angles so

[sudden forum]

yeah

maybe thats not the correct approach

What do you have in mind?

https://media.discordapp.net/attachments/903481106819612714/1115996216057143296/Screenshot_2023-06-07_at_9.30.13_PM.png

ignore, just sharing for easy access

[zenith dagger]

i was thinking of subsituting one angle with like a letter or smth

and like 180-n

and name all the things we know

[sudden forum]

Have done any work yet?

[zenith dagger]

yeah but i still cant find

like i subsituted PQT as n

so then RQT is 180-n

and TSR is 180-180-n which is just n, which can also be get straight from one of the thereoms

but it dosent give me the things i need to prove

[sudden forum]

it is i guess

both of them add up to 180

[zenith dagger]

hm but i cant prove it

[sudden forum]

you just did?

[zenith dagger]

but like

PROVE prove it

[sudden forum]

yes

prove prove it

[zenith dagger]

i wonder how

i wonder why

[sudden forum]

TSR is n how

[pulsar pecan]

remember the property that the tangent angle must equal the internal angle in the alternate segment?

[zenith dagger]

uh wait let me find my notes for that

[pulsar pecan]

hint(spoiler, do not click unless you’re really stuck):

|| you can use corresponding angles with parallel ||

[zenith dagger]

ok

ill clikc that later

wait so

angle outside of point S is equal to QRT

QRS*

the same other way

HEUH

[pulsar pecan]

which angle outside point s?

[zenith dagger]

the one near T right

[pulsar pecan]

I don’t understand, can you use letters

[zenith dagger]

uhhh

like

OH WAIT

NO

other way

[pulsar pecan]

that angle is between a circle and a line

[zenith dagger]

this

[pulsar pecan]

this is correct, can you justify why?

[halcyon halo]

ncert??

[pulsar pecan]

what do you mean?

[zenith dagger]

oh wait uh

uh i dont know all i know is the tangent angle must equal the internal angle in the alternate segment thing you told me

[pulsar pecan]

you should be able to find the reference in your notes

[zenith dagger]

i only wrote the equal sides

i didnt write the justification

[halcyon halo]

its a book for maths based on indian board education

[pulsar pecan]

next you can find angle RQT

[zenith dagger]

wait so if RST is a, then RQT is 180-a right

but how that prove

[pulsar pecan]

no, that is exactly what you’re trying to prove

[zenith dagger]

wait but

how do we prove that using other sides

OOHHHHHHHH

wait

what

[pulsar pecan]

what have you realized

[zenith dagger]

no i wrong

[pulsar pecan]

hint: you don’t need to use the circle to prove this bit

[zenith dagger]

wait how

[pulsar pecan]

think and describe your thought process

[zenith dagger]

i dont understand

[pulsar pecan]

hint 2: use parallel lines

[zenith dagger]

OH NO

WAIT

RST is x too right?

wait

no

nvm

[safe radish]

@zenith dagger Has your question been resolved?

[safe radish]

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[safe radish]

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[blazing roost]

the mod question

[hazy elbow]

form three inequalities

[blazing roost]

umm there is one method that is really long

[safe radish]

Show your work, and if possible, explain where you are stuck.

[blazing roost]

is there any graph method?

[hazy elbow]

Do you know the method of dividing the number line and forming separate inequalities

[blazing roost]

i mean if you show me ill figure out what you mean