help-27

[restive river]

oh he didn't say anything
Okay, thanks

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[orchid thistle]

How do you know whether the solution of a second order differential equation is going to be exponential vs. trigonometric?

[stone stump]

calculate it?

[orchid thistle]

Not sure I understand. Here is what I’m looking at:

y’’+16y=0

The answer should be y(x)=C1(cos(4x))+C2(sin(4x))

But I don’t know how to come to that conclusion, I see that the exponential equation works.

[devout snow]

@orchid thistle Has your question been resolved?

[supple knot]

trig functions are just complex exponentials.

It depends on the roots of the characteristic equation.
real roots (not your case): https://tutorial.math.lamar.edu/classes/de/RealRoots.aspx
complex roots (your case): https://tutorial.math.lamar.edu/classes/de/ComplexRoots.aspx

[orchid thistle]

Thank you! @supple knot

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[sharp sparrow]

I have a AP question

[woven radish]

everytimecrusader

[sharp sparrow]

There you go

Is this right?

[scarlet sequoia]

that bracket mean we have 5 terms, right?

[sharp sparrow]

yes

[scarlet sequoia]

you can check it using general formula

[sharp sparrow]

My question is: If a middle term can be discovered by the arithmetic divison of the side terms, then will the sum of those terms be the arithmetic division of their side terms?

[scarlet sequoia]

$$a_{2}+a_{4}=a_{1}+d+a_{1}+3d=2a_{1}+4d$$
$$\frac{a_{1}+a_{5}}{2}=\frac{a_{1}+a_{1}+4d}{2}=\frac{2a_{1}+4d}{2}=a_{1}+2d$$

[woven radish]

Modus

[sharp sparrow]

Oh, i got it

thx very much

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[frail lake]

if a matrix is idempotent, i know that means that A^2 = I, but does that also mean that A^x = I for some positive integer x?

[frail lake]

please @ me if you message me

[arctic field]

say for example we had A^3

then we can write A^3 = A * A^2

what do you think happens then

[frail lake]

its just A

but that's only a demonstration, not a mere proof

[arctic field]

well

how about A^4

A^4 = A^2 * A^2

what happens

[frail lake]

same thing, itll just be A

but how do i know its true and you didnt just get "lucky"

[arctic field]

wait idempotent means A^2 = A

not A^2 = I

[hollow pollen]

a matrix A is said to be idempotent if and only if A^2 = A

[frail lake]

thats what i mean

[arctic field]

my example still work though

im not providing you the proof

im motivating the proof

see if you can work it out

[frail lake]

okay let's see...

If x is some positive integer, and A^2 = A, then A^x / A^2 = A^x-2.

[hollow pollen]

cant divide matrices

[frail lake]

oh

then i have no idea how to go about this proof

actually nvm

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[arctic field]

use induction

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[wispy kayak]

Plzzzz help

[wispy kayak]

Really need help

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[peak cave]

how do I expand equations with negative powers? eg. (1+x)^-2? I get that its 1/(1+x)^2 but idk how to actually expand them?

[peak cave]

Can I use binomial expansion for it?

if so I'm not sure how to do that

[grim agate]

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

So you have 1/(1+x)^2 = 1/(1 +2x +x^2)

That’s it

[peak cave]

oh

i am very stupid please excuse me

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[silent plover]

Let A=111...1 (n times the number 1) and B=1000...05[(n-1) times the number 0]. calculate B-9A?

[midnight dirge]

um

[silent plover]

Pls help

[midnight dirge]

try writing it out as a summation

[silent plover]

How

[midnight dirge]

start with what is A and B when n=1

[silent plover]

A=1 and B=105
So ?

[midnight dirge]

eh have u learnt summation

ok then look at whats A and B when n=2

and try writing it in terms of a summation from n=1 to N

actually not summation but represent it as powers

was no we need both

wait no just powers is enough

[silent plover]

A=10^n +10^(n-1) +...+1

Like this?

[midnight dirge]

yea that works but u kinda want it in a form which that u can easily subtract B from that

u can actually just use 1 ^ sign

[silent plover]

Yea

But how for B?

[midnight dirge]

no for A

express it with only using one ^

[silent plover]

How

[midnight dirge]

consider 9A first

9, 99, 999,...

[silent plover]

-9A=-99999..99

[midnight dirge]

can u write that with just one ^

[silent plover]

I dont know

[midnight dirge]

notice that

9=10-1

99=100-1

999=1000-1

[silent plover]

Aaa

[midnight dirge]

u shld do something similar for B

[silent plover]

10^n -1

[midnight dirge]

yea

[silent plover]

B=10^n +5 ?

[midnight dirge]

um

try what happens when n=1

and what it is supposed to be

[silent plover]

B=105
1005
10005

...

[midnight dirge]

mhm so when n=1 B is

[silent plover]

105

[midnight dirge]

so would this work

[silent plover]

B-9A=10^n -1 -9[10^n + 10^(n-1) +...+1]?

[midnight dirge]

what is this when n=1

[silent plover]

B=105 when n=1

[midnight dirge]

and what does this evaluate to

[silent plover]

B=1005 when n=2

[midnight dirge]

and what does this evaluate to

[silent plover]

10^n +5

I think

[midnight dirge]

what does this evaluate to when n=1

[silent plover]

Nembres of zeros

n = times of zeros

[midnight dirge]

what does this evaluate to when n=1

u would get a number right? what is that number

[silent plover]

Not number

n is variable

Is random

[midnight dirge]

if n=1

[silent plover]

Yea

[midnight dirge]

what does this eval to

[silent plover]

Make B=105

If n=2 than B =1005

[midnight dirge]

well, good luck

[silent plover]

Hehe

[midnight dirge]

my words are not getting thru

[silent plover]

What ever ty

Lets A=111...1 (n times the number 1) and B=1000...05[(n-1) times the number 0]. calculate B-9A

[midnight dirge]

ye i

think i looked at the Q wrong

well

anw it shlda been 15

when n=1

oh and, sorry abot reading the Q wrong

[silent plover]

I think i can add -1 to A like B-9A=B-1-9A+1

1000...05-99...999=100...004-1000...00

100...04 have n+1time of number and -1000...0 have n+1 Time of numbers too

So 100...04-100...0=4

.Close

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[fresh sentinel]

im confused how to find them

well i got 3.4

3/4

and apparently it was wrong

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[vivid wren]

The highest-velocity stars an astronomer might observe in the
Milky Way Galaxy have velocities of about 400 km/s (4.00 3 102
km/s). What change in wavelength would this cause in the
Balmer-beta line? <@&286206848099549185>

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[vivid wren]

The highest-velocity stars an astronomer might observe in the
Milky Way Galaxy have velocities of about 400 km/s (4.00 3 102
km/s). What change in wavelength would this cause in the
Balmer-beta line? <@&286206848099549185>

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[true jasper]

i need help w a question

[true jasper]

im not sure how to solve part c

<@&286206848099549185>

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[flint eagle]

What does the cpdfficient of x mean in a square root function

[flint eagle]

For example in a

The square root function is 4x to the square root

But what does the 4 mean

How do U come up with that

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[midnight dirge]

whatve u tried

[restive river]

is it 0.99 * 0.0001?

[midnight dirge]

theres also the chance someone who doesnt have covid tests positive

[restive river]

yes, but isn't it only the people who have covid?

[restive river]

or is it 0.99 * 0.0001 - 0.002 * 0.0001?

[midnight dirge]

its like

given probability

whats the probability of someone having covid

given

they tested positive

[restive river]

oh i see

[restive river]

0.0001/(0.99+0.002)

[midnight dirge]

i didnt rly c what u did but they wasnt a division

wait no this is

not

[midnight dirge]

use this

[restive river]

so probability they have covid/probability they tested positive?

oh wait probability they have covid and tested positive/probability they have tested positive?

0.0001*0.99/(0.99+0.002)

@midnight dirge is this how you do it?

[midnight dirge]

um

bottom u shouldnt get 0.99

it for both terms

should be something * something

anyway imma get gg now

atb

❤️

[restive river]

what?

so you can't help me anymore

<@&286206848099549185>

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[topaz blade]

so the descriptoon for the span would be adding v1 and v2 multiplied by any real numbers could create a point on the plane that is written as span{v1,v2}

because in the answer key it says all points on the line through v1 and 0

wait

its the same vector just different scalar

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[midnight dirge]

i think its like length of vectors

❤️

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[midnight dirge]

what a way to close

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[warped falcon]

when the focal distance of a parabola is zero the graph will only show the directrix. Is this true or not?

[devout snow]

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[warped falcon]

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[loud root]

It is true

I mean, the parabola would coincide with the directrix

It would be just a line, not even a parabola

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[obsidian yacht]

Can anyone check my work and pls help me at 8 i dunno how to do dat @_@

[low fossil]

wheres the work?

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[wanton rapids]

$A=\begin{bmatrix}0&1&2\ 1&1&1\ -1&2&5\end{bmatrix}$

[woven radish]

AuHasard

[wanton rapids]

How do I get it in this form?

$A=\begin{bmatrix}0&1&2\ 1&1&1\ 0&0&0\end{bmatrix}$

[woven radish]

AuHasard

[midnight dirge]

do u mean using elementary operations?

else i would day they are not equal

[wanton rapids]

Gaussian elimination

@midnight dirge

[midnight dirge]

ye thats

elementary operations

anyway

u can try equating the terms

[midnight dirge]

so from here u can guess that r3 is some linear combination of r1 and r2

so let it be

[wanton rapids]

$\begin{gathered}A=\begin{bmatrix}0&1&2\ 1&1&1\ -1&2&5\end{bmatrix} \ A=\begin{bmatrix}0&1&2\ 1&1&1\ -1&2&5\end{bmatrix}_{+1} \rightarrow \begin{bmatrix}0&1&2\ 1&1&1\ 0&3&6\end{bmatrix} \ \ \end{gathered}$

[midnight dirge]

r3=ar1+br2

[woven radish]

AuHasard

[midnight dirge]

then solve from there

[wanton rapids]

Then I divide the third row by 3?

[midnight dirge]

i

u can just take the 3rd row from here

n minus 3r1

[wanton rapids]

Hmm

$A=\begin{bmatrix}0&1&2\ 1&1&1\ 0&0&0\end{bmatrix}$

[woven radish]

AuHasard

[wanton rapids]

@midnight dirge Is what we did called elementary row operations?

[midnight dirge]

yea

its like multiplying by elementary matrices

[wanton rapids]

@midnight dirge So do we have 2 leading elements?

I don't know if that's the right word

The first one is the second column, first row

The other in the second row, first column

[midnight dirge]

er

[wanton rapids]

The 1's

[midnight dirge]

idk the term T T

2 linearly independent rows?

[wanton rapids]

Hmm

[midnight dirge]

ahh

its rank

the rank of A is 2

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[nimble eagle]

I see here they multiply all terms by t^2 to get a cleaner result, but the term inside ()^2 gets multiplied by t. It makes total sense, but what is the general rule / law for this behavior? I.e. what would happen if that denominator were ()^(4/3) or so? I don't know how to google this

[winter patrol]

general fraction simplification

usually you want to rid yourself of skyscraper and nested fractions

[nimble eagle]

so if the bottom part was (t + 1/t)^3 I would need to multiply that by t^3 to get (t**2 + 1)^3, is that correct? And yeah this is something that hadn't occured to me and seems essential so I'm trying to build an intuition for it

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[restive river]

can someone explain this to me please with the awnser becasue my teacher isnt a good explaintion-er

[restive river]

please someone help me

<@&286206848099549185>

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

[near trout]

what have you tried

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[cold anchor]

how do you solve this?

[sand dove]

angle JIF + angle HIF = angle JIH geometrically

this gives an equation on x

[cold anchor]

x=9

[somber harbor]

correct

[cold anchor]

then plug 9 in for x?

if so Hif=77

[somber harbor]

Yes

[cold anchor]

thank you

is this similar to the other one or

[somber harbor]

Yes it is

do you know what bisector means

[cold anchor]

no

[somber harbor]

it basically means that it splits the angle perfectly at the halfway point

so since one half is 33

then the other one has to be 33

[cold anchor]

so x=8

[somber harbor]

yessir

[cold anchor]

so cad is 66

[somber harbor]

yes

[cold anchor]

so is cba 65?

or is CBA 115

<@&286206848099549185>

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[full pilot]

How would I go about doing this?

Draw a labeled picture of the unit ball in R2 and its image under A, together with the singular vectors, with the coordinates of their vertices marked.

[full pilot]

Singular values: $10\sqrt{2}, 5\sqrt{2}\newline \text{Left values:}\begin{bmatrix}\frac{1}{\sqrt{2}} \frac{1}{\sqrt{2}}\end{bmatrix},\begin{bmatrix}\frac{1}{\sqrt{2}} \frac{-1}{\sqrt{2}}\end{bmatrix}\newline \text{Right values:} \begin{bmatrix}\frac{-3}{5} \frac{4}{5}\end{bmatrix},\begin{bmatrix}\frac{4}{5} \frac{3}{5}\end{bmatrix}$

[woven radish]

Maxerature

[devout snow]

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@full pilot Has your question been resolved?

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[devout snow]

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[solemn pendant]

Celsius = 5/9 x (F-32)

158 F = ___ Celsius

[solemn pendant]

<@&286206848099549185>

Im kind of stuck on the question and very much confused

Hi thank you for helping me

[placid narwhal]

Solve that in terms of celsius

[solemn pendant]

How do I do that?

I have never learned this concept

[placid narwhal]

C = 5/9 * (F - 32)

Find what F is equal to

[solemn pendant]

158?

this is the question

[hybrid snow]

!15m

[devout snow]

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

[hybrid snow]

You just plug 158 into the equation

[solemn pendant]

Oh ok thanm you

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[opal wing]

Hey, i was wondering if somebody could help explain something that I am not getting in this book that I am reading?

[polar wharf]

To me it's easier to imagine separating the root like this

Sqrt(xyz) = sqrt(x) * sqrt(y) * sqrt(z)

Then simplify each type of object individually

The way it is explained in your book is not the clearest way to visualize what's going on

[opal wing]

What i am not understanding in the example that they are providing is how they get y^4 from (y^1)^3* y^1. Wouldnt that give them y^5?

[polar wharf]

(y^1)^3

Is y^3

You multiply the exponents in that situation

"Power to a power" you multiply the exponents

Then y^3 * y^1.

There you add

[opal wing]

So from my understanding

[polar wharf]

Add exponents when multiplying

Multiply exponents when doing "power to a power"

[opal wing]

In the part of the equation where the parentheses are included i multiply

And in the part of the equation where they are not included i add

[polar wharf]

You multiply when an exponent is raised to another exponent

E.g.

(x^2)^3 = x^6

This is true because

(X^2)^3 =

x^2 * x^2 * x^2

Three x^2

So when they write

(x^5)^3 they mean

Raise x^5 to the power of 3

[opal wing]

So...x^125 in that case

[polar wharf]

It would be x^15

The exponent itself is not raised to power 3

The entire object (x^5) is

It would be

x^5 * x^5 * x^5 = x^(5+5+5) = x^15

Try

(x^4)^5

[opal wing]

X^20

[polar wharf]

Yea perfect

The parentheses are used only to make it clear that the second exponent applies to the entire object

Otherwise you might read it as x^125 like you did earlier

They're not actually necessary but they do make it much neater to interpret

[opal wing]

Thank you so much.

[polar wharf]

Yw good luck with your work

[opal wing]

.close

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[winged root]

How to determine the Interval of Existence (-x/2 + y)y' = y/2 +x. I've solved for the genearl solution by 1) determining that it is indeed exact. Next, I used the function Phi_x (x,y) = -y/2 - x , (This represeting the My component of an exact differential equation) and integrated with respect to x. Once integrated, (-1/2)x*y -(1/2)x^2 +h(y), is the equation I came to. Upon the differentiating with respect to y, I came to (-1/2)x +h'(y). Which following the method of solving for exact differential equations, set equal to "N", to get:

[winged root]

I've already solved everything, but not sure how to get the interval of existence for the solution I got.

The red questionmark is an attempt to isolate y and see where the function is discontinuous. Thank you

<@&286206848099549185> anyone know Diff eq?

[long kettle]

Assuming that the general solution you got is correct (which I haven't checked yet), notice that you have a quadratic in y

[winged root]

Would I treat x as a constant?

[long kettle]

I guess, but it's not like you have to. The quadratic formula works for non constant a, b, and c

[winged root]

Then what about c? As you can see, (if its correct) i have -x^2 and the "=-1/4" components. Would c for the quadratic be both of them? as in (-x^2 +1/4) represents c in the quadratic equation?

[long kettle]

Well, to use the quadratic formula, you need to get it in the form ay² + by + c = 0

c would be the portion that doesn't contain a y

And I looked over your work, the solution seems correct

[long kettle]

Why -1/4 in the last line?

[winged root]

This is what I came to. But would x=0 be discontinuous?

thats what C came out to be in solving for the general solution

I moved it the left side to set up the equation

y^2 -xy -x^2 +1/4 = 0

[long kettle]

Which means it should be +1/4 after moving it over

[winged root]

yeah, i just didnt show it in the work

[long kettle]

And yes, -x² + 1/4 is your c

[winged root]

or no

yes

I'm not so sure on this, but are complex numbers considered discontinuous?

[long kettle]

Generally we restrict the range to just the reals, so we wouldn't allow complex outputs

[winged root]

So, would we restrict the interval to not include x=0?

[long kettle]

Not just 0

[winged root]

what other value?

sqrt(1/5) just produces a 0

[long kettle]

What about 0.0001?

[winged root]

so numbers approaching 0

hadnt thought of that

[long kettle]

Well no. There's a specific range of x values

First though (and I should've done this first), you need to find out if the equation is + or -

Which you can do with the initial value

[winged root]

positive

y(1) is the intitial value

[long kettle]

You sure it's positive?

[winged root]

before we continue. Can you clarify what equation you mean?

the sqrt?

[long kettle]

The entire equation for y after using the quadratic formula

For it to be a function, we need to figure out if we're using + or -

This doesn't really matter for the domain of existence, but it's something you should do in general with something like this. It's good practice to do so

[winged root]

oh

do i plug in the x-value into the equation?

[long kettle]

Yes, and see whether + or - gives you -1/2

[winged root]

minus

big brained

[long kettle]

Yep

[winged root]

yo, thats dope

[long kettle]

So we can stop writing the +

Now for the domain of existence

When is the square root undefined?

[winged root]

we set the inside = 0

or when its negative?

[long kettle]

When it's negative, yes (finding when it's 0 is relevant though)

So in order to find where the function exists, we need the values of x where 5x² - 1 ≥ 0

Can you find the intervals where that's the case?

[winged root]

yes?

one moment pls

x comes out to be sqrt(1/5) or -sqrt(5)/5 and its plus equivalent

[long kettle]

We're looking for interval(s) though

It's an inequality after all

[winged root]

quick clarification

the [] represents included right?

[long kettle]

Yes

[winged root]

(-infinity, -sqrt(5)/5] U [ sqrt(5)/5, infinity)?

[long kettle]

Yes

And which interval contains our IVP

[winged root]

ohh, anything passed that -sqrt(5)/5 is what you were talking about with the small x-values

where we get a negative

so the positive side

[ sqrt(5)/5, infinity)

[long kettle]

Specifically, it's that interval because it contains x = 1

[winged root]

we look at the x value correct?

in our ivp

[long kettle]

That's our interval of existence

[long kettle]

Yes

[winged root]

broooooooooooo

Gamer Dio

youre a genius

Ill remember you forever

[long kettle]

Please don't

[winged root]

Check the custom status

Keeping that forever

[long kettle]

[winged root]

Thanks again. Take care 👍

[devout snow]

@winged root Has your question been resolved?

[winged root]

Yes

[devout snow]

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[wet coral]

what formula will I use if I want to know if an estimated value is same with the confidence interval? only 4 values along with the sample size and confidence level was given

[devout snow]

@wet coral Has your question been resolved?

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[jagged ore]

help

[jagged ore]

how do u do bii

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@jagged ore Has your question been resolved?

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[vale plover]

Does anyone knows the equation of the tangent line written in terms of f(c)?

[vale plover]

I tried looking it up but just didn’t find it

[zinc veldt]

hint: do you know the slope of the line and a point that it crosses?
that's all the info you need to find the equation of a line

[devout snow]

@vale plover Has your question been resolved?

[devout snow]

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[thin gust]

is there smth wrong with the question HAHAHA

wait why u delete HAHA idk if it’s wrong

adds up to 34

[quick marsh]

I'm not a helper, I shouldn't be talking too much haha

[thin gust]

me neither

[quick marsh]

Oh? You got a color on your name tho, what does that mean?

[thin gust]

idk

it means active

idk I suddenly got a colour HAHAHA

I think there’s smth wrong w the qn tho

[midnight zealot]

dont mind it

so

i need

now

is

[quick marsh]

This is assuming the people that love math and english are also included in the people that love math and people that love english.

[midnight zealot]

oh so its needed like that?

alr ima redo it

[quick marsh]

Bro idk

[thin gust]

nono

[midnight zealot]

what

[thin gust]

the group of ppl who math

[thin gust]

ONLY love math

[midnight zealot]

mine the 3rd circle is away from them

[thin gust]

the grp of ppl who love math and English are different

[midnight zealot]

yea it must be in the like the middle of the circle

[thin gust]

is it not?

[quick marsh]

If they were, then it would be more than 30 students?

[thin gust]

ya

[midnight zealot]

yea..

[thin gust]

that’s why HAHA

[quick marsh]

Yea, so I assumed that the people who love more than one subject are also listed as one of the those people that love a singular subject.

[midnight zealot]

so what

i got 10 mins lefrt

[quick marsh]

Since it was not specified that "x" amount of people ONLY love "n" subject.

[thin gust]

u can use the helper thing

call for helpers HAHA

[quick marsh]

Lmao call helpers for a venn diagram

[thin gust]

this qn is so vague

but eng isn’t my first lang so idk

[midnight zealot]

Find the cost of 4 ½ kg of sugar at 20 pesos per 500 g.

here

[thin gust]

are u Filipino

[midnight zealot]

yes

[thin gust]

pesos P$

[midnight zealot]

yes

omg

5 mins left

oh no

[thin gust]

:OO

[midnight zealot]

WHAHAHA

[thin gust]

HAHAHAHAA

OMG

[thin gust]

okay so 20 pesos for 500g

they want 4.5 kg

[midnight zealot]

yes

[thin gust]

how many g is 4.5kg

[midnight zealot]

4500

[thin gust]

it’s 4500g yes

yesh

4500 divide 500 is

or maybe

to make u see clearer

500g —> 20P

1g —> 20/500 P

4500g—> (20/500) x 4500

[quick marsh]

3 mins

[thin gust]

shd be 180P

shd*

[midnight zealot]

thats cheao

cheap

frfr

[thin gust]

I want

cheap

esp in this inflation

istg

HAHAHAHA

@quick marsh

[quick marsh]

Oh?

[midnight zealot]

last one

[thin gust]

oh?

what’s 2/5 of 60

[quick marsh]

1 minuteeeeee

[thin gust]

2/5 x 60

which is 24

so 24 sold

remaining is 36

half of 36 is 18

36 -18 remaining

[quick marsh]

Was the cookies sold first and then the half of what remained given to the lola?

[thin gust]

yes

sold first

[midnight zealot]

1

[midnight zealot]

pano dito?

like

20 divided by 500? x 4500?

[thin gust]

what about there

[thin gust]

yes

[midnight zealot]

alr

[quick marsh]

Hm? What does that mean?

[thin gust]

idk HAHA

totally not Filipino

okay I’m actually not Filipino HAHHA

[quick marsh]

[midnight zealot]

ist how here

idk

WAHHAHAHAA

[thin gust]

[quick marsh]

Some people out here asking about differential calculus, then we have the occasional "My lola gave me 2/5 of her cookies".

[thin gust]

HAHAHAH

different levels

I’m in the middle somewhere

[quick marsh]

Very surreal experience haha.

[thin gust]

ikr

[quick marsh]

And where is that?

[thin gust]

idk

I’m in limbo

[quick marsh]

Isn't it against the rules to be chatting casually on help channels?

[thin gust]

calculus ❤️

technically it’s abt math

wait actually

ya nvm

I don’t want to get banned

[quick marsh]

@midnight zealot close? question mark?

[thin gust]

@midnight zealot

she’s in class

[quick marsh]

She? You know her?

[thin gust]

nope

OH NO

[grim agate]

[thin gust]

he/she

or wait

nvm

they

it’s 2022

[midnight zealot]

.close

[devout snow]

Channel closed

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[midnight zealot]

Thanks!!

[thin gust]

welccc!

[quick marsh]

Were you using discord while in class?

[midnight zealot]

yea

:>>>

[thin gust]

woah

[devout snow]

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[vale plover]

Question, on the right side of the equation, what happens to that -1/2 power, it goes down right?

[vale plover]

And turns positive in the bottom right

[thin gust]

what is 2 multiplied with -1/2

[vale plover]

You mean the power right? It should reduce in the bottom?

Giving me a plain x

[thin gust]

yesh the power

[thin gust]

do u know how it got there

[thin gust]

^^ what’s the ans to this

[vale plover]

So is that the right step?

[thin gust]

yeshh that’s right

[vale plover]

Wait

Is supposed to be a x^2 to the 1/2 power

Wouldn’t that give you a plain x

[thin gust]

oh yaya sry my bad

[vale plover]

And then give you x/x which is one

[thin gust]

2 multiplied 1/2 is 1

[vale plover]

Just wondering

It would be the same answer right

Cos square root of x^2 right

Just kinda a different format

Well anyways thank you. Have a good night

.close

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[feral scarab]

I know the amplitude is the height but i’m not sure how I find that

[copper flower]

you can represent the depth as a sin function of time

the lowest value it has is 5

the highest 25

[feral scarab]

Hmm

I’m still lost

[topaz axle]

subtract them

[feral scarab]

20

[topaz axle]

that's the one

[feral scarab]

Why does answer say 10?

Thats what i did, subtract before too

But then i saw the answer and got confused

So i guess its wrong

[topaz axle]

um

like, it sneakily meant semi amplitude

[feral scarab]

Wdym by that?

Oh like half ok nvm

Hmm very weird but ok

Ok thanks

.close

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[fringe lichen]

Ims tuck on this i factored out to get (x-2)/(x+2)(x^2+1)

[devout snow]

Please don't occupy multiple help channels.

[fringe lichen]

Idk if i plug in the 2 once i factor ¡

[remote meteor]

1. apply lhopital (woohoo)
2. evaluate the limit
3. plug in 2 for all instances of x

[supple knot]

you can also factor

some things should cancel

[remote meteor]

Tru

[fringe lichen]

Okay so its just 2x-4/4x^3-6x

Then i just plug in 2?

[fringe lichen]

When i factored the top came out as 0

[supple knot]

shouldn't

top factors nicely. then write u = x^2 and factor the denominator

[fringe lichen]

Am i factoring wrong or sum cause i got (x-2)^2

For the top

[supple knot]

this is right

factor the den using my suggestion

[fringe lichen]

I got (x-2)(x+2)(x^2+1) for den

[supple knot]

do you see anything cancelling?

[fringe lichen]

Yes the x-2 cancels out

Do i just plug in 2 then once finished?

.close

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[devout snow]

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[covert scarab]

can yall help with this the first pic is related to the 2 answer question

[midnight dirge]

um

the

std is only 0 when all data is the same

[covert scarab]

so is the answer true or false

[devout snow]

@covert scarab Has your question been resolved?

[covert scarab]

no it has not

[cosmic juniper]

False

[covert scarab]

ok thanks

umm btw why is it false

[cyan obsidian]

.close

[devout snow]

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[hollow yacht]

I got a question

[devout snow]

Please don't occupy multiple help channels.

[hollow yacht]

How do i solve this

[wooden zodiac]

What does a negaitve exp do

[hollow yacht]

Wdym

[coral pecan]

What does a^-2 does?

@hollow yacht

[hollow yacht]

Yo bro i solved it

I got another q thi

Tho

[coral pecan]

Close it 👍

Oh alr

-1/2 means square root :)

[hollow yacht]

Lemme try this

And ill let yk if i solved it

[coral pecan]

and proceed with same logic

[hollow yacht]

Is this correct

[coral pecan]

Flip it over, you forgot about the minus thing.

@hollow yacht

[hollow yacht]

Alr

How do i close this now

[coral pecan]

use .close

[hollow yacht]

.close

[devout snow]

Channel closed

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[coral pecan]

🎉

[devout snow]

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[earnest narwhal]

Hey. Can anyone help me figure out the equation for velocity of x and velocity of y in relation to time to create movement along the curved lines of a graph like this: https://cdn.w600.comps.canstockphoto.com/sunburst-background-with-black-white-eps-vectors_csp79485030.jpg

[earnest narwhal]

I’m trying to do particle movement in a game

[arctic field]

if you want it moving outwards

it could be like

[earnest narwhal]

Inwards ideally… 😅

But the equation for outwards could be useful for later

What is the squiggly B?

[arctic field]

beta

it could be a constant or it could depend on x, y, or t or whatever

[earnest narwhal]

I’m really bad at math… I majored in dance at university. Can I have an example to follow?

Sorry

[woven radish]

\[
\dv t  \begin{bmatrix} \map x t \\ \map y t \end{bmatrix}
= \map \alpha t \begin{bmatrix} \map x t \\ \map y t \end{bmatrix}
+ \map \beta t \begin{bmatrix}
\cos \theta & -\sin \theta \\
\sin\theta & \cos \theta
\end{bmatrix} \begin{bmatrix} \map x t \\ \map y t \end{bmatrix}
\]

[arctic field]

hmm

the left side is saying

d/dt (position)

[earnest narwhal]

Delta time?

[arctic field]

which is the velocity

derivative

so the left side of the equation is just velocity

the right side of the equation is saying

[earnest narwhal]

How do I handle things inside brackets?

[arctic field]

this is your position written as a vector

you can also just break it down into components

the x component and the y component

if you want two equations separately

here is what it looks like

[earnest narwhal]

Maybe I need it explained like this:
x is my current position of x (at the current time) to produce the next x position, I will have to do x = x + ??

[arctic field]

yes

so the whole RHS

is what you would add to your current x/y

[earnest narwhal]

x = x + (cos(theta)*x - sin(theta) * y)
Is that correct?

[arctic field]

you would do

[arctic field]

and the deltas are given by

[earnest narwhal]

How do I calculate beta time?

Or alpha time

[arctic field]

for example

if you have a large positive alpha

then you would be going fast outwards

if you have a large negative alpha you would be going fast inwards

small positive alpha => slow outwards

[earnest narwhal]

Ok and beta controls the curvyness of the curve?

[arctic field]

small negative alpha => slow outwards

yes

so

i think you want to just keep theta = 90 actually

[earnest narwhal]

Ok. I think I might get it. I just choose any constant I like for those two. Playing around with the numbers until I get a result I like.

[earnest narwhal]

Theta?

[arctic field]

like this

and just play around with alpha and beta until you get something you want

alpha and beta doesnt have to be constant either

it can also depend on x, y, time

[earnest narwhal]

Wait so those Sin and cos you put before… ignore that?

[arctic field]

yeah

the θ was meant to be like

for arbitrary rotation

but i realised i think you dont need it

alpha and beta cover it all

[earnest narwhal]

Now this is for one curved path…

If I want 10 particles going out to different spots…. I’ll need theta?

[arctic field]

note this is assuming the centre is at the origin

nope you dont

if you want the centre to be not at the origin

you'll have to recentre everything

[earnest narwhal]

Center at the origin is fine. I just want to make an image like I showed.

[arctic field]

the equations will always produce a spiralling path

what changes the path is the starting position

not theta

[earnest narwhal]

Not just one curve. A sunburst.

[arctic field]

so you can use the same equation for all of it

[earnest narwhal]

All coming from the same center (0,0)?

[arctic field]

you cant start at the centre i think

because it needs to know which direction to go off in

so you need to start somewhere nonzero to give it an initial direction

,w plot x' = x - y, y' = y + x

[earnest narwhal]

Hmm

Ok I’ll play around with it and see. I think I understand what you said, for the most part. 😅

[arctic field]

heres what wolfram tells me

kinda hard to see

but

its a spiral already if you set alpha = 1, beta = 1

[midnight dirge]

:O

[earnest narwhal]

What was the equation you typed above the graph?

[earnest narwhal]

Just for my reference. 😁 thank you.

[arctic field]

np

[midnight dirge]

how did u even figure that

[arctic field]

because i studied dynamical systems?

this is very usual

[midnight dirge]

good on u

[earnest narwhal]

I imagine this sort of movement comes up in programming games quite a lot

I’m just hopeless at maths. So I appreciate your help.

[arctic field]

its also a point of study in dynamical systems where you look at coupled ODEs in higher dimensions

so

this kind of shape is pretty common

[earnest narwhal]

Thank you so much again.

.close

[devout snow]

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[crisp cliff]

Having trouble understanding how to convert radians to degrees. I don't know how to multiply a fraction like this picture by 180/pi

[crisp cliff]

I can use a calculator to figure out the value of 5 pi over 3 is but how do I multiply the fractions without a calculator?

When I google it they just show simple solutions. They say multiply 180/pi by the number of radians, but they'll use integer examples not fractions.

[tawny needle]

(5pi/3) * (180/pi) = 5*180/3

[devout snow]

@crisp cliff Has your question been resolved?

[crisp cliff]

Oh, so I just ignore the pi?

Oh wait, that makes sense the 180 replaces pi. THanks

[devout snow]

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[devout snow]

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[toxic glacier]

i need help understanding side-angle-side criterion and Angle-Angle criterion.

[lunar harbor]

Is there a specific question?

[potent nebula]

@toxic glacier
Side angle side can be used to prove congruence between triangle or similarity depending on if the two triangles have sides that are equal (congruent) or proportional (similar) with an equal angle between them.

AA is just used for similarity between triangles

[toxic glacier]

yeah i have worksheet for sss,sas, and aa criterion. i would like help with one problem of each criterion. i can send a picture in a minute.

[potent nebula]

I'd really reccomend watching khan academy videos for high-school level math as they are pretty concise and straightforward

[toxic glacier]

ok i think i understand what you are saying.

should i go and try khan first or should i continuue here?

[potent nebula]

try khan I'd say

[toxic glacier]

ok i'll go do that

.close

[devout snow]

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[dire palm]

Did i do it correct?

[devout snow]

@dire palm Has your question been resolved?

[echo ore]

Yeah, it looks perfect.

I double checked on a calculator

[devout snow]

@dire palm Has your question been resolved?

[devout snow]

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[glacial lava]

I'm trying to find the fraction form of the following number by using geometric series: 0.857142857142...

[glacial lava]

I can find easier numbers like 0.5555.... or even 0.685555....

[stone stump]

well geometric series seems a bit overkill

[near trout]

eh

it's a good way to do it from the ground up if you don't know fractions

i mean what else is there? brute force?

serious question

[stone stump]

how do you not know fractions but know the geometric series

[near trout]

well what if it were a bit more complicated

like who knows how the hell 9/13 recurs

it's not fundamentally wrong

[stone stump]

just multiply by a high enough power of 10 so that the first period ends at the decimal

then subtract the decimal part away

then divide by 99...9

and then reduce

[near trout]

right so basically yeah

let x = 0.857142857142...

then 1000000x = 857142.857142...

so then what's 1000000x - x?

[glacial lava]

I'm in a class where they are using geometric series to find fractions

So I kinda have to use it

[near trout]

ok fine

then you have x = 0.857142 * (1 + 10^-6 + 10^-12 + ...), right?

[glacial lava]

the way I wrote was as: 857142(1/10)^6n

With n=1

until infinity

[stone stump]

also works

[glacial lava]

$\sum_{n=1}^{\infty} 857142(\frac{1}{10})^{6n}$

[woven radish]

Santiniko

[glacial lava]

oh perfect, the LaTeX worked

[wild hawk]

how do u not feel like crying

[glacial lava]

And then I used the formula:

$\frac{a}{1-r}$

[woven radish]

Santiniko

[glacial lava]

where $a=\frac{857142}{10^3}$ and $r=\frac{1}{10}$

[woven radish]

Santiniko

[near trout]

no

[glacial lava]

But yeah, I got it wrong haha

[near trout]

the formula is right, those a and r values are wrong

a is just the first term so it's 0.857142