help-17

[ember latch]

i typed this out manually

[cyan talon]

it already did it for you

[ember latch]

well

it gives me the result

but i guess i dont want the result

it should give me <0,0,L,> also

maybe i inputted it weird

i just like want it to show me the undefined variables

well i guess they are defined

ah nvm

idek what i want

[cyan talon]

it will show you the variables when the result isn't as trivial as straight up 0s

[cyan talon]

rip

[ember latch]

also

[cyan talon]

so you want maple to not simplify the computation or what

[ember latch]

yee

sure

😭

what does this mean 🧐

[cyan talon]

you wanted to say something here ?

[ember latch]

nono

ig my problem is not a problem anyways

i'll leave now

wish me luck

[cyan talon]

aight

gl

[ember latch]

and a lack of crashes

.close

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[vocal sleet]

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[misty sundial]

can someone help me figure out how to apply velocity over time in desmos? i need to be able to do something like this:

P_theta=P_theta+P_velY

[vast shale]

what do you mean

you can use desmos actions

[vast shale]

do you want to plot or continually add by clicking a button?

you can use recursion if you want to plot, or actions if you just need the value

@misty sundial

[misty sundial]

continually

sorry, wifi keeps going out

[vast shale]

ok

one sec

[misty sundial]

i want to use a slider to add or remove to another var

[vast shale]

https://www.desmos.com/calculator/wlzqd0q6zd

[vast shale]

oh

ok

so like

when you change a slider

you can just do

[misty sundial]

this should work for now

[vast shale]

ok

[vast shale]

https://discord.gg/unofficial-desmos-655972529030037504 might help you

[misty sundial]

yea, this isnt working but i feel like its my fault for using desmos for something it was never meant to do

https://www.desmos.com/3d/twlvynliub

ill just wait till i get home where i can test this stuff in the engine im using, instead of desmos

@vast shale thanks

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[mild carbon]

can anybody help me with this?

i don't know where to start

I've been falling behind in math class so much 😭

[fervent wasp]

Even the first one?

[fervent wasp]

.

[harsh yoke]

basically you have to observe the pattern and build an general formula for it

[mild carbon]

im okay with sequences

the problem is making general terms and formulas

cuz i dont get how it works

i know it subtracts by 2

each number

[fervent wasp]

1,3,5,7,9 its general form is 2(n-1)+1

Do you get what to do now?

[peak matrix]

arent u supposed to do it recursively

like f(n+1) = f(n) + 2

and f(1) = 1

[fervent wasp]

Oh shit

True

[peak matrix]

idk how should the sequences be denoted

maybe a_n+1 = a_n + 2

why did I write * 2 instead of + 2

[mild carbon]

then how do i write the first one?

teach me

[vast shale]

what's the ratio

[mild carbon]

wdym ratio its an arithmetic sequence

[vast shale]

yes

what is

the ratio

[peak matrix]

there is no ratio in arithmetic sequence tho

[peak matrix]

alright, cool

what's the first term of the sequence?

[mild carbon]

💀

[mild carbon]

-2

[peak matrix]

correct

what would you do in your mind to generate the next element?

[mild carbon]

you subtract 2

[peak matrix]

correct

[peak matrix]

here we will write $a_1 = -2$

[twin meteor]

MethIsAlwaysRight

[peak matrix]

this denotes that the first element of the sequence a will be -2

[mild carbon]

Okie dokie

[peak matrix]

we will write this as $a_{n+1} = a_n - 2$

[twin meteor]

MethIsAlwaysRight

[peak matrix]

this means that next element is generated by subtracting 2 from the previous element

so $a_3 = a_2 - 2$

[twin meteor]

MethIsAlwaysRight

[peak matrix]

this would mean that third element is just second element - 2

[peak matrix]

and we write it generally like this

[mild carbon]

wait

[peak matrix]

is there some other notation you were taught?

[mild carbon]

yeah

[peak matrix]

ah, they used u instead of a

and also n instead of n+1 and n-1 instead of n

okay we will use their notation then

[peak matrix]

this means that nth element = (n-1)th element - 2

do you understand this?

this tells us the rule to generate next element basically

we have that first element = -2

and if we want the 2nd element, we do 2nd element = (2-1)th element - 2 = 1st element - 2 = -2 - 2 = -4

@mild carbon Do you understand how the notation works?

[mild carbon]

not really

this is something we weren't taught in school

[peak matrix]

so u_n in general is just nth element

meaning that e.g. u_1 is the first element

u_4 is the 4th element

so in our sequence, -2, -4, -6, -8, -10, -12...
u_1 = -2
u_2 = -4
u_3 = -6
u_4 = -8
u_5 = -10 ....

can you understand this?

[mild carbon]

yeah

[peak matrix]

alright, cool

so when we were finding the recursive definitiion of this sequence, we first built 2 ideas

1. the first element is -2

2. to generate next element, we take the previous one and subtract 2

[peak matrix]

How would you write point 1 using equation?

express the sentence "the first element of the sequence is -2" using an equation

[mild carbon]

U1 = -2

[peak matrix]

perfect

now the 2nd part is a bit harder

if $u_n$ is some element, then the previous element is $u_{n-1}$

[twin meteor]

MethIsAlwaysRight

[peak matrix]

for any n

can you understand this fact or should i further explain it?

[mild carbon]

nah i get that part

so basically un-1 means that

if u want u2

u take u1

cuz in this case

n is 2

[peak matrix]

yep

perfect

so how would you express the sentence
"any element of the sequence is just the previous element - 2"

[mild carbon]

un = u_n-1 -2

[peak matrix]

yes

and thats it

[mild carbon]

okie dokie

now to the next one

a geometric sequence isn't it?

[peak matrix]

it seems to be

[mild carbon]

how do we do it here?

is it

un = 4u_n-1?

[peak matrix]

why -1?

oh

it!s u_(n-1)

[mild carbon]

like u take the previous term

[peak matrix]

i see

correct

but you also need to add u_1 = 1

[mild carbon]

yeah

[peak matrix]

for recursive definitions you need the first element and the equation that helps you generate next elements

alright, we can do C) then

[mild carbon]

so it divides by 10

so is it

[peak matrix]

correct

[mild carbon]

u1 = 52

u_n = 0.1 U_n-1

[peak matrix]

yes

[mild carbon]

hold on

the answer shows something different

[peak matrix]

what does it say?

[peak matrix]

it might be equivalent

[peak matrix]

yeah, u_(n-1) / 10 is same as u_(n-1) * 0.1

its the same thing

[mild carbon]

okay nice

now the next one is a bit tricky

[peak matrix]

not yet, the next one is again a known type of sequence

[mild carbon]

its neither arithmetic or geometric

[peak matrix]

really?

[mild carbon]

hold on

+1

+3

+8

what pattern is there?

[peak matrix]

oh wait

you skipped d

[mild carbon]

oooh

right

yeah that ones easy

u_1 = 14

U_n = U_n-1 + 5

isn't it?

[peak matrix]

yep

[mild carbon]

e on the other hand

[peak matrix]

alright so now this

notice how quickly the numbers increase

this won't be just addition

this must be either some multiplication or exponentiation

or similar

[mild carbon]

wait

what can it be then?

what pattern is there?

[peak matrix]

ill give you a hint

it has something to do with multiplication

[mild carbon]

multiplied by 1.5

then 2.0

then 3.0

[peak matrix]

mhm

then?

[mild carbon]

then 6

[peak matrix]

then?

[mild carbon]

then 18

[peak matrix]

So we have sequence 1.5, 2, 3, 6, 18

does this look familiar?

[mild carbon]

OOOh

yeah

the later 4 terms are the same

[peak matrix]

indeed

[peak matrix]

how would you generate the next term of the sequence

[mild carbon]

not sure

like a formula? or

[peak matrix]

not formula

just explain it with words for now

we will then convert those words to formula

[mild carbon]

we multiply 1944 by 18

[peak matrix]

You sure?

[mild carbon]

wait hold on

[peak matrix]

We did that to get from 108 to 1944

[mild carbon]

cuz we multiply 2 by 1.5

3 by 2

6 by 3

18 by 6

[peak matrix]

108 by 18

1944 by ?

[mild carbon]

1944 divided by x =108

[peak matrix]

that would get x = 18

[mild carbon]

yes

oh fuck

then i have no clue

[peak matrix]

See the pattern?

[mild carbon]

oooh

so 1944 multiplied by 108

[peak matrix]

nice

now look again at just this sequence

how do you generate next term? (Describe it in terms of previous term/terms)

you can also use the term before previous term

[mild carbon]

u1 = 2

[peak matrix]

good start

[mild carbon]

U_n = U_n-1 X U_n-2

[peak matrix]

niiice

one more thing needs to be done here

Imagine you had just

u1 = 2
U_n = U_n-1 X U_n-2

How would you generate U2?

[mild carbon]

hmmm

[peak matrix]

in case you think its not possible, then think about why its not possible

[mild carbon]

because it doesn't work with the formula

[peak matrix]

yes,

because we have no U_(2-2)

there is no U_0

so we will have to also include u2 = 3

So we will have

u1 = 2
u2 = 3
U_n = U_n-1 X U_n-2

using this, we can generate whole the infinite sequence

(in theory)

[mild carbon]

i see

alright so i include both U1 and U2 in this case

gotcha

[peak matrix]

mhm

[mild carbon]

now last one

[peak matrix]

you need to include enough terms, to be sure that you can always generate the next element

yep

[peak matrix]

1, 2, 6, 24...

[mild carbon]

+1

+3

wait

[peak matrix]

+4 you mean?

[mild carbon]

yeah

+1

+4

+18

[peak matrix]

when you dont see pattern in this, its usually good idea to try also multiplication

[mild carbon]

so

1.5

3

[peak matrix]

1.5?

[mild carbon]

1 times 1.5

[peak matrix]

= 1.5, not 2

[mild carbon]

ooh

2

3

4

yeah i see a pattern

[peak matrix]

cool

[mild carbon]

U1 = 1

[peak matrix]

you can not only reffer to n-1th term btw, you can also refer to the number N itself

[mild carbon]

this is a little trickier to write

oh i know

U_n = n* something

[peak matrix]

good progress

what's the something?

[mild carbon]

wait

U_n = n*U_n-1

[peak matrix]

mhm

correct

this operation is also known as factorial btw

its basically the product of all natural numbers lower than n

[mild carbon]

naaaaaaahhhh

did i do something wrong? 😭

[peak matrix]

huh

this is kinda weird

that would mean u2 = (2+1)*u1 = 3*1 = 3

but u2 = 2

[mild carbon]

am i still right?

[peak matrix]

im fairly sure their solution is incorrect

[peak matrix]

i think so

[mild carbon]

okay

a question

do you know about the sigma notation?

[peak matrix]

yep

[mild carbon]

i need to do these too

:/

[peak matrix]

1 or 2?

[mild carbon]

both

[peak matrix]

hmm

maybe just open a new channel for that bc i will have to go soon

[mild carbon]

alright

well thanks for your help 🙏

[peak matrix]

np

[mild carbon]

really appreciate it

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[peak matrix]

yw

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[glossy pagoda]

here is the question

[glossy pagoda]

is my approach correct

any one here working on sequential continuity?

[vagrant plume]

i can try to help

;-;

[vagrant plume]

wait is that n^(pi/2) or n*(pi/2)

[glossy pagoda]

n times pi/2

simply npi/2

[vagrant plume]

ah ok

i think ur right but

im not very good at analy

[glossy pagoda]

any one else working on sequential continuity pls?

[vagrant plume]

or well atleast i agree with the first page you wrote and the second

i got lost i couldnt figure out which question was what paper

[glossy pagoda]

here are the questions again

my answers

[vagrant plume]

okay i agree

i figured out which one goes where

[glossy pagoda]

any one else willing to help?

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[vast shale]

I need to find if it is bounded or not

<@&286206848099549185>

[vocal sleet]

@vast shale Has your question been resolved?

[vast shale]

.Close

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[vast shale]

⊕

[vast shale]

what does this symbol mean in math?

context

[leaden mulch]

XOR

[vast shale]

that is also xor?

[leaden mulch]

yeah

[vast shale]

ok, thank you

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[vast shale]

How would you do this?

[minor light]

Take ln?

[vast shale]

wym

[hallow plover]

Yeah just take ln

ln the whole expression

like

ln (3^x) = ln (3root(3)*9^(y+1))

[vast shale]

isn't ln the indirect process of 'e'

[glass zenith]

you can convert the right hand side into terms of 3

using exponent rules

for example sqrt(3) is 3^(1/2)

@vast shale

[hallow plover]

oh right

so you can do log3

instead

or without logging at all

compare the exponents

after you simplify

[glass zenith]

fr

[vocal sleet]

@vast shale Has your question been resolved?

[vast shale]

$3^{x} = 3^{\frac{3}{2}} \cdot (3^{2y+2})$

is this fine?

@glass zenith @hallow plover

[glass zenith]

yes

[vast shale]

now what do i do from jere
?

[glass zenith]

though note that on the right hand side its y not x

[vast shale]

mb

[twin meteor]

$a

[glass zenith]

if instead of having 2y +2 in the exponent it were a single number, say u, how would you do the right hand side

[vast shale]

6y + 6?

[glass zenith]

how would you simplify using exponent rules

[vast shale]

3^3x/2

[glass zenith]

remember that when you multiply the same base you add the exponents

[vast shale]

u mean multiply?

nvm

ye u right

[glass zenith]

ye

[vast shale]

3^3/2 + 2y + 2

?

$(3^{\frac{7}{2} +2y})$

[glass zenith]

yeppers

fr

[vast shale]

yeah now

what do we do

[glass zenith]

well for starters you could simplify it to 2y + 3.5 to make it look nicer

then you have the same base on both sides of the equation

[twin meteor]

$a

[vast shale]

log base?

log_3

[glass zenith]

yeah

[vast shale]

log_3(x) = log_3(7/2 + 2y)

?

latex is fun to write, lmao

[glass zenith]

the log_3 shouldve gotten rid of the 3 on both sides only

[glass zenith]

fr

[vast shale]

$\frac{numerator}{denominator}$

[twin meteor]

$a

[vast shale]

wym

$log_3 3 = 1$

[glass zenith]

we originally had 3^x = 3^thing right

[twin meteor]

$a

[vast shale]

yes

[glass zenith]

so taking the log_3 on both sides gets rid of the 3 and leaves us with x = thing

[vast shale]

$\integrate{4}{0}$

[twin meteor]

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

[vast shale]

lmao

wait

we log both sides>

?

$log_3$ both sides

[twin meteor]

$a

[glass zenith]

ye

[vast shale]

which means

[glass zenith]

hold on

[vast shale]

$x = \frac{7}{2} + 2y$

[twin meteor]

$a

[glass zenith]

yes

[vast shale]

u could've divided both by 3

shoot

i gotta revise logs and natural logs before my exam

but yeah so now

[glass zenith]

its not dividing by three its taking log base 3 but yeah

so now

transform it into the form y = mx + b

so basically get y on one side

[vast shale]

$2y = x - \frac{7}{2}$

[twin meteor]

$a

[glass zenith]

yes

then divide by

2

[vast shale]

$y = \frac{x}{2} - \frac{7}{4}$

[twin meteor]

$a

[glass zenith]

so true

fr

[vast shale]

LMAO

[glass zenith]

🔥

[vast shale]

this bot is really fun wth

wait so could u explain the $log_3$ stuff again

[twin meteor]

$a

[vast shale]

so when it was

[glass zenith]

$log_a (b) = c$

[twin meteor]

MerryTacoGamerCat

[vast shale]

$3^x = 3^(\frac{7}{2} + 2y)$

[glass zenith]

this can be rewritten as $a^{c} = b$

[twin meteor]

MerryTacoGamerCat

$a

[glass zenith]

hold on

[vast shale]

yes

ah wait

[glass zenith]

we do $log_a (a^{c}) = log_a (b)$

[twin meteor]

MerryTacoGamerCat

[glass zenith]

then from this

we see that $log_a a^{c} = c$

[twin meteor]

MerryTacoGamerCat

[vast shale]

it's cause $log_3 3 $cancel out to 1

that's why we're left with thingy

[glass zenith]

basically log cancels out the base

[vast shale]

yeah i just clocked

lmaoo

[glass zenith]

and that leavs you with the exponent

fr

[vast shale]

thank you bro

can i add u

[glass zenith]

ofc np

sure

[vast shale]

ur a goat

🔥

thank you, gonna close this channel now

.close

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[small jacinth]

if you have 680$ and thats 34% less than the original price whats is the original price then? and how do you solve it

[light aurora]

Make an equation first

So it's 34% of x is $680

Just a starting point

[small jacinth]

wouldnt it be easier to just do 680 divided by 0.66?

[vast shale]

1-0.34

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[undone aurora]

not sure how to do this

[tame garnet]

Idk if im correct but would it not be r between $\sqrt{2},2$ and $\theta$ between $\pi,\frac{3\pi}{2}$ ?

[twin meteor]

Hemesfere

[undone aurora]

how did u find this doe

[tame garnet]

Do u know what the 3rd quadrant is?

[undone aurora]

yes

oh ok i understand the pi and 3pi/2 bound

but not the bound for r

oh r^2 = x^2 + y^2

ok nvm im dumb i get it

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[unique pivot]

If you know Fn, can you calculate F?

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[tepid hound]

Calculate the following double integral (directly and with Gauss Green formulas)
$$\iint_D xy,\mathrm{d}x,\mathrm{dy}$$ $$D = (x,y)|x^2-2\le y\le x,0\le x\le 2$$ $\int_{0}^{2} \int_{x^2 - 2}^{x} xy \ \ \mathrm{dx},\mathrm{dy} = \frac{2}{3} $

[twin meteor]

alee

[tepid hound]

I calculated it directly, now its asked to use the Gauss Green formulas, but I don't know what to do

I should always get 2/3 right?

[vocal sleet]

@tepid hound Has your question been resolved?

[tepid hound]

<@&286206848099549185>

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[ripe relic]

I’m stuck on getting this derivative

[ripe relic]

Idk what to do next

U is (x+2)

Original is 1/sqrt(x+2)

[silk osprey]

whats the original question

[silk osprey]

oh sorry ok

do you know power rule?

d/dx(x^n)=nx^(n-1)

[ripe relic]

Ye

I need to use the definition of a derivative to solve it

Are u allowed to do this?

[unique elm]

no unfortunatley not

[ripe relic]

Rip

[silk osprey]

yea nope

[silk osprey]

unfortunate

[ripe relic]

Welp it’s test time, ima ask my teacher before class

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[orchid pier]

how do i check this easily

[cyan talon]

@orchid pier hey

[orchid pier]

yo whatsupp

[cyan talon]

well one way is to get the eigenvalues of the matrix you're asked to find

[orchid pier]

yh i know but then ill get a polynomial of a third degree

is there another way to see the definites?

by looking at the matric A^TA e.g?

|3 4 0|
|4 4 0|
|0 0 5|

[cyan talon]

eh it's not hard to find the roots here really

[orchid pier]

its (3-x)(4-x)(5-x) -80 =0 right

[orchid pier]

plugging it into wolfram alpha gives me a negative eigenvalue which isnt indefinite

[cyan talon]

wdym not indefinite

if you have positive and negative eigenvalues, bam the matrix is indefinite

[orchid pier]

but theres only a negative eigenvalue

[cyan talon]

yeah

so what

as long as there's at least one pos and at least one neg eigenvalue

the matrix is indefinite

[orchid pier]

but it doesnt have a pos

[cyan talon]

yeah I think your char poly is wrong then, no way there's only one eigenvalue

[orchid pier]

omg...

can you check?

[orchid pier]

this is the matrix no?

[cyan talon]

and 5 is an eigenvalue anyway

so if you don't find it there's a problem pal

[orchid pier]

but the matrix is correct no?

[cyan talon]

yes

[orchid pier]

|+3 -4 +0|
|-4 +4 -0|
|+0 -0 +5|

@cyan talon

like this?

[cyan talon]

uh maybe

what do you plan do to with that

[orchid pier]

i think i made an error in the signs

[cyan talon]

I mean send a pic of your computation and we'll see where you screwed up

[orchid pier]

aight 1 sec

i used cofactor expansion

[cyan talon]

the 5 on the second term should be 5-lambda tho

[orchid pier]

fuck

bro this poly is hard

isnt there another way to look at the matrix?

to tell oh thats ...definite

[cyan talon]

you sure abt that ?

[orchid pier]

idk im asking you

is there a way?

[cyan talon]

yeah you could just not use the matrix at all if you want

I just went with the eigenvalues cause they told you to find the matrix and stuff

[cyan talon]

idk if the technique I want to show you has a name in english

[orchid pier]

and does the 4 on row 2 column 1 need to be + or _?

if i do + i get three eigenvalues

with - just 1

[cyan talon]

negative yes

nvm, how are you computing your cofactor expansion ?

[orchid pier]

but my solution will just be x = 5 ........

(3-x)(4-x)(5-x) -(4(-4)(5-x)) =0 like this

[cyan talon]

ok but along which row/which col ?

[cyan talon]

if you just tell me that, I straight up can't answer

[orchid pier]

oh along the first row

oh i thnk its siposeed to be + when you do 2x2 matrix

[cyan talon]

alright

[orchid pier]

so you can just ignore

right?

[cyan talon]

well there's no sign to add, you're already in the 2x2 determinant yes

[cyan talon]

so -(4 * 4 * (5-x)) you should have

[orchid pier]

ah thx

i got one more

tho

when doing pap^-1

do you compute from right to left?

with diagonalisation ? @cyan talon

[cyan talon]

doesn't matter

[orchid pier]

no?

the order which you do matrix multiplaction does matter right?

[cyan talon]

AB != BA in general sure

but as long as you're not switching matrices around, you perform the computation in whatever order

you're confusing associative vs commutative

[orchid pier]

what about p^-1 =p^t

[cyan talon]

?

[orchid pier]

pap^t

does the order matter then?

for PA(P^T)

[cyan talon]

associativity is just a thing for whatever matrix product you're looking at

there's no "does it work here or there?"

it works all the time

[orchid pier]

how is this different from pap^-1?

[cyan talon]

it has nothing to do with your question

associativity (i.e. computing left to right or right to left, or any other way, gives you the same result) is true for matrices

commutativity (AB = BA for all matrices A, B) is false

@orchid pier

[orchid pier]

Wgat is commutativity

[cyan talon]

I literally wrote what it means

[orchid pier]

57 = 75 no?

[cyan talon]

just next to it

yes

[orchid pier]

Then does it only apply for inverses and transposes

[cyan talon]

and powers

"does it only apply" is going too far, it really depends on the matrices you have

the identity commutes with everything after all

[orchid pier]

What does the transpose even do?

I cant visualize a geometric representation

And why does it even equal to the jnverse for symmetric matrices @cyan talon

[cyan talon]

it's wacky really

[cyan talon]

no that's for orthogonal matrices

A*A^T = identity

[orchid pier]

Oh my bad

[orchid pier]

Can you draw it ? Lol

[cyan talon]

no

but this video prolly does a fine job https://www.youtube.com/watch?v=g4ecBFmvAYU

[cyan talon]

it's still not an easy thing really

[orchid pier]

Do you use yt or wikipedia as a source for learning the theory?

I use wikipedia more often recently

Or othrr sources *

[cyan talon]

for learning I always use books really

[orchid pier]

I find only stewards a good book😭

Stewarts calculus

[cyan talon]

the problem with wiki is it's hard to get a coherent view of a subject most of the time, & hard to know what's very important or no

it's very fine when I have to look up something I forgot, or to extend your knowledge on a subject you already know pretty well

[cyan talon]

in a book the author does that selection work for you really

if I knew literally zilch about a subject, I definitely wouldn't use wiki to learn about it

my 2cents here

@orchid pier

[orchid pier]

Ah okay

Bro respond to my dm 😭

You left me on read for 1 month

[cyan talon]

I almost never see when I have a new dm that's the problem

damn discord ui

[orchid pier]

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[vast shale]

How would u do this?

would litres be x and distance be y

[minor light]

No

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[vast shale]

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[vast shale]

How do I do this

my eyes hurt

mine too

yes

write tanx as sinx/cosx

then multiply both sides by cosx

alright

and then its obv

4(sin/cos)x

?

NOOO

4sinx/cosx

$(\frac{4sinx}{cosx})$

[twin meteor]

محمد احمد

[vast shale]

5cosx^2

yes

$5cos(x)^2$

[twin meteor]

محمد احمد

[vast shale]

cos^2x + sin^2x =1

$4sin(x) = 5cos(x)^2$

[twin meteor]

محمد احمد

[vast shale]

this is normal sin, not sin^2

[glass zenith]

the cos tho

[vast shale]

yeah true for x as arguement too

so what do we do

$5cos(x)^2 - 4sin(x)$

we got this currently

[twin meteor]

محمد احمد

[vast shale]

BRO

THEY WANT IT IN SIN FORMAT

BRUU

bruh waht

what

i am high rn

lemme look

cook up

yeah i am correct even when i am high

$4(\frac{sinx}{cosx}) = 5cosx$

so

[twin meteor]

محمد احمد

[vast shale]

use cos^2x = 1-sin^2x

$4sin(x) = 5(1-sin^2(x)) => 4sin(x) = 5 - 5sin^2(x)$

[twin meteor]

محمد احمد

[vast shale]

yeah

thats it

$=> 5sin^2(x) - 5 + 4sin(x)$

[twin meteor]

محمد احمد

[vast shale]

gg

thank you

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[vast shale]

@vast shale

not done yet

.reopen

[vocal sleet]

✅

[vast shale]

how would i do part b

wha

t

okay

just solve the quadratic

[kind wadi]

express tan in terms of cos

or cos in terms of tan

[vast shale]

solve this

ima shoot

cuuh

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[vocal sleet]

Please don't occupy multiple help channels.

[vast shale]

,rotate

[hallow plover]

What have you tried so far?

[robust python]

hve u trued the arclength formula maybe

[vast shale]

what is it ?

[near tartan]

try completing the square then you can apply one of the forms

this one specifically

[robust python]

huh

[robust python]

,,L=\int_a^b\sqrt{1+\left(\frac{dy}{dx}\right)^2}dx

[twin meteor]

ᚸᚸᚸ᛫ᛈᚢᛋᛠᛞᛖᛋᛏᚱᚩᛁᚱ᛫ᚸᚸᚸ

[robust python]

length of a curve from a to b

[vast shale]

how i can completing square

?

i trued completing square and it was like -(x^2+1)-8

all under the root

[robust python]

what

[vast shale]

how i do completing sqaure

??

[vast shale]

here

@robust python

[robust python]

bro i have no idea

[vast shale]

np np thx

[strange crater]

it'd actually be 10 - (x - 1)^2

[vocal sleet]

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[next burrow]

i need someone to fact check "D" my tutor and i both agree the answer should be 0.0192 but the website is saying its not

[silk osprey]

i get 0.0197

[next burrow]

lemme try that

ya the website says thats true

it is 0.0197

you think you could help me with this

[silk osprey]

yea sure do you know what this means

[next burrow]

i just know it has to do with Normal Distribution

[silk osprey]

but connect it to a z score

what does the z score tell you

[next burrow]

this is the previous answers i got for B

[silk osprey]

what would the interval be

[silk osprey]

this is the empirical rule

but they wanted to two decimal places

but yes

generally it’s 68,95,99.7

[next burrow]

hm

[silk osprey]

i can get my calculator

do you know what the interval would be

<z<

[next burrow]

i got

One standard deviation: 68.00%
Two standard deviations: 95.00%
Three standard deviations: 99.70%

[silk osprey]

those are approximations

the real value is from the normal distribution which i showed right above

[next burrow]

oh

[silk osprey]

do you have a ti-84

[next burrow]

yes

[silk osprey]

ok so you’re going to want to go to the distributions menu

[next burrow]

k

[silk osprey]

hit 2nd then stats

you should see like normpdf normcdf etc

norm cdf is what you want to use

you just put in the lower and upper bounds

and then the mean and standard deviation

but for a standard normal distribution the mean is zero and standard deviation is 1

[next burrow]

ya i see them

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[twin spear]

how do i prove that a quadrilateral is a rhombus without using a graph

[twin spear]

how do i determine if the slopes are perpendicular

and how do I know which coordinate points to use as the slope

[dapper jay]

graph it

then determine the equations of each line

[twin spear]

im supposed to solve it without graphing it

[dapper jay]

ok

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[haughty sierra]

wondering where the population variance and sample variance came from

[strange crater]

they give you the population stdev and sample stdev

,calc 8.3 * 8.3

[twin meteor]

Result:

68.89

[strange crater]

,calc 6.7 * 6.7

[twin meteor]

Result:

44.89

[regal bane]

Variance is just the SD squared

[haughty sierra]

ahh ok

thx

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[vocal sleet]

Please don't occupy multiple help channels.

[daring marsh]

on problem 4 the anser was 17

what I got was -1

(-1)^2 = (1)

[stone gazelle]

i =/= -1

[daring marsh]

-(1)=-1

i^2 does

[stone gazelle]

yeah, then why have you written 16 - (-1)^2

[daring marsh]

that's not a minus

but stay on problem 4

[strange crater]

they are looking at problem 4

[stone gazelle]

i^2 = 1 -> 16 - (-1)

[stone gazelle]

the very last line

[daring marsh]

I am not sure what you are asking

-i*i = -i^2

[strange crater]

i^2 = -1

[daring marsh]

unless I flip before

the exponenet

[strange crater]

so -i^2 = -(-1)

[daring marsh]

-(-1)^2= (1)^2

[stone gazelle]

after expanding, you get - (i)^2 not - (-i)^2

[daring marsh]

that's what I have

-(i)^2

[stone gazelle]

and you said i^2 = -1

[daring marsh]

but i^2 = -1

so it's --1

[stone gazelle]

yes

then 16 - - 1 = ?

[daring marsh]

well that depands if in which order I do the exponenet

[stone gazelle]

what do you mean

[daring marsh]

16-(i)^2

16-1

oh nvm I see

I am doing the exponenet when I shouldn't

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[wild meteor]

the answer is no right?

and are these right?

[dull bear]

[assuming "join points" is supposed to imply that the relations are linear, sure ]

[wild meteor]

yeah i got no clue

if you had to guess do you think that would be what they are asking

[dull bear]

I think that's what they mean, esp with the context of the first question, but I'm not liable if that isn't what they mean

[strange crater]

you could put yes for the second one IMO

[wild meteor]

im down to do that but idk what teacher will say

and i dont want to get into an argument

[strange crater]

neither of those relations are necessarily linear

[wild meteor]

also

the thing on my paper

has one spot in x and one spot in iy

how many should i do of each

acording to the question i should be able to do one of each

[dull bear]

Guessing for the first, they're assuming constant rate of flow though? In which case it would be?

[wild meteor]

but idk if the teacher wlil get mad

[strange crater]

as many as are required to plot it?

[wild meteor]

so 2?

idk how many

[strange crater]

depends on the shape of the jug, right? though I doubt the question is taking that into account

[strange crater]

yeah, you can do it w/ 2 points

[wild meteor]

it prob means volue as size

[dull bear]

By "size" I'm asssuming they're referring to capacity, e.g. like 1L to 2L or so

[strange crater]

ah, makes sense. i was thinking diameter or similar

volume is more sensible

[wild meteor]

is this right?

sawp the last 2

[strange crater]

yes, swap

[vast shale]

I think I had something like this in my finals last year. It’s probably correct

[wild meteor]

so do you think it will be okay if just use two points

like use f(x)=1

and f(x0)=2

[vast shale]

The teachers first marked me wrong but after seeing how nice, sexy and smooth my curve was, they gave me the mark

[strange crater]

I don't know. depends on your teacher

[vast shale]

Consult with your teacher

[dull bear]

"Hey, you didn't specify how many points there should be, and lines are uniquely defined by two points they pass through, soooo "

[wild meteor]

ill send them that if it gets marked wrong

[wild meteor]

part of me wants to say yes on both o ftehse and be a bit** about it

but i dont wanna risk it

[dull bear]

"you didn't explain what you meant by 'join points' either, I thought you wanted us to find an estimate or something"

[wild meteor]

💀

for this one

if i did f(1) and f(2) my answers would be 1,2 and 2,5 right

[dull bear]

Yep the points (1, 2) and (2, 5)

[wild meteor]

if i used

y(0)

and

y(1)

it woudl be