help-10

[static fulcrum]

yeah, just a min

Is it fine?

@mental fiber

[mental fiber]

yes

[static fulcrum]

that -1/3 will become +c, right @trim portal ?

[mental fiber]

yeah

[static fulcrum]

okay

Thank you so much @mental fiber @trim portal

.close

[obtuse pebble]

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[deep gale]

hey! trying to prove that two sets are equal to eachother.

currently I have (X {intersection} x, Y {intersection} x) = (X {intersection} y, Y {intersection} y) where x,y belong to the power set P(X {union} Y)

trying to prove that f(x) = f(y) so that i can prove a function is injective

[dark stirrup]

I can't figure out what you're saying here: (X {intersection} x, Y {intersection} x) = (X {intersection} y, Y {intersection} y)

[deep gale]

(X n x, Y n x) = (X n y, Y n y) ?

[dark stirrup]

Oh, so $X \cap x = X \cap y$ and $Y \cap x$ = $Y\cap y$ for all $x, y \in P(X \cup Y)$?

[deep gale]

yeah

[warm shale]

SWR

[deep gale]

yeah thats it

not proficient with latex

wait no

its $(X \cup x, Y \cup x) = (X \cup y, Y \cup y)$

wait thats a union

ignore that

$(X \cap x, Y \cap x) = (X \cap y, Y \cap y)$

[warm shale]

kyIe

[dark stirrup]

Which sets are you trying to show equal?

[deep gale]

well not sets, expressions

trying to show that $(X \cap x, Y \cap x)$ is equal to $(X \cap y, Y \cap y)$ because the codomain of the function is a power set so is the format (x, y)

[warm shale]

kyIe

[deep gale]

if that makes any sense

[obtuse pebble]

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[deep gale]

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[thin scaffold]

Can someone help me with this

[obtuse pebble]

@thin scaffold Has your question been resolved?

[mighty forge]

b should be equal to 100° since this angle and 80° create an angle of 180°

[thin scaffold]

What would you put for the explanations

[mighty forge]

difficult for me to explain it in English, lemme think 😂

a straight line only has straight ancles, that means = 180°. Maybe write that 100° and 80° create a straight angle if this makes sense

[thin scaffold]

What about the explanation for a and c

[thin scaffold]

I explained that but it still says that it’s wrong

[mighty forge]

is the value wrong or just the explanation?

[thin scaffold]

It’s not telling me

[mighty forge]

a is correct and you'll have to calculate the angle at C

[thin scaffold]

A=50
B=100
C=70

That’s what I have

For the values

[mighty forge]

and they're all wrong?

[thin scaffold]

Yep

[mighty forge]

it's gotta be the explanation

do you have any rules on how to formulate them?

[thin scaffold]

Not at all

[thin scaffold]

do you have any idea what I should change with the explanations

[mighty forge]

maybe use just one to two words, e. g. for a: full circle

[thin scaffold]

It still says it’s wrong

Wait

For c the answer 30 worked

[mighty forge]

what did you write as explanation?

[thin scaffold]

If you add 50 and 100 you will get 150 and because the angles in a triangle adds up to 180 you would do 180-150 to get 30

[obtuse pebble]

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[obtuse pebble]

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[urban whale]

Help, I am really stuck on this 3d trig question

[urban whale]

usually i am good at trigonmetry especially 3d trig but i cant seem to figure this one out as when im doing TOA for the right triangle the value always seems wrong

[tacit gate]

@urban whale

draw 3 triangles

in a paper side by side

with the info you have

so you visualize it better and see where can you start calculating something and go on from there

[obtuse pebble]

@urban whale Has your question been resolved?

[urban whale]

hm okay well ty

ill try do that but itll be annoying cuz im in bed

[obtuse pebble]

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[karmic mural]

Why is C wrong

[warm canopy]

why do you think its true?

[karmic mural]

Because if it goes up, then down to reach 2, that’s another critical point to the ones we get from 11-12 and 13-15

13-14*

But if it goes straight down to 2, no critical points can be made

[ocean vector]

Can't the derivative take a value of 0 from the start?

Like for the open interval (10, 10 + episilon) ?

[karmic mural]

Right yeah

But wouldn’t that be a critical point?

Since derivative=0

[ocean vector]

Not necessarily.

[karmic mural]

Why not

[ocean vector]

For it to be a critical point, there must be a peak of some kind

[karmic mural]

Does sign have to change?

[ocean vector]

Excatly

[karmic mural]

Like negative to positive positive to negative?

Ok so I thought that

But then I looked online and it just said f’=0 or nonexistent

[ocean vector]

but zero is signless, it is just zero

[karmic mural]

So I got really confused

cuz if sign change is required then yeah not C but if it doesn’t then it could be C

[ocean vector]

Yes

But here we are looking at open interval

[karmic mural]

Right

[ocean vector]

that is why looking from the left at 10 and it next couple of points

[karmic mural]

Right

[ocean vector]

and we know that derivatives does not exist for the boundries

hence we can't really say that the point next to the 10 can be critical

[karmic mural]

So

Critical means a change from positive to negative has to occurs

?

[ocean vector]

Generally, yes

[karmic mural]

Bc if not a line of say y=5 would have infinite critical points no?

[daring rock]

I don't think that's true

Critical points are where the derivative is either 0 or undefined

[ocean vector]

If we just require the the derivative to be 0 then the line would have infinite critical points

[daring rock]

They do not guarantee a change in sign

Yes

[daring rock]

what's wrong with that?

[karmic mural]

This is the question which I’m kind of confused on about

Like Why can’t C be correct

[daring rock]

Anyway for this question you only know that f decreases "in general" between x=10 and x=11

It could decrease sharply from x=10 to x=10.5

and then have a critical point

[karmic mural]

Right

[daring rock]

and increase from x=10.5 to x=11

and reach (11,2)

You said the first critical point is between 11 and 12

but actually it could occur between 10 and 11 instead

[karmic mural]

Yeah ur right

[daring rock]

and that's still only two total

[karmic mural]

That makes sense

But even with that

Why is C wrong

[daring rock]

C says that f is decreasing everywhere between 10 and 11

[karmic mural]

Ohhhh

Yeah I get that

Because the minima could be earlier and it could start increasing much earlier

[daring rock]

yeah

[karmic mural]

It just has to decrease and then start increase on the interval 10,12

[daring rock]

Right

[karmic mural]

Got it thanks

[daring rock]

np 👍

[karmic mural]

/close

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[astral oak]

these are margin of sampling and exponential distribution questions, would 22. be 56.1% and 23. be 12.6%?

[trail cloak]

Hmm

So like the density function is $f(x) = \lambda e^{-\lambda x}$?

[warm shale]

VulcanOne

[frosty spoke]

yeah I just used a calculator

the first one is right

but the second one

idk how you got 12.6%

furthermore, you probably need to indicate what how many standard deviations you're expected to use to compute the margin of error lol

or the % confidence interval thigny

[obtuse pebble]

@astral oak Has your question been resolved?

[astral oak]

well, there is an equation

2sqrt(p)-(1-p)/n

[frosty spoke]

I've never seen that one before

oh that one

[frosty spoke]

yeah that's definitely not what you wrote here lol

okay so it's 2 standard deviations

[astral oak]

I realize

I believe the error will be a percentage

[frosty spoke]

well

basically you say something like the centered 95% confidence interval for the proportion has a width of 0.126

[astral oak]

so, how I was taught for these problems, and I just want to hear a response is if we take the 40%, and the margin of error is 12.6% it would be 27.4% to 52.6% is the possible expectation for the express line (the words in the question)

further, if we do 2sqrt(0.40(0.60)/60 we would get 12.6%

@frosty spoke

I guess we are saying the same thing?

Is this answer D?

.close

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[timid silo]

i think its D too

[obtuse pebble]

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[narrow forum]

need help with both of these

[obtuse pebble]

@narrow forum Has your question been resolved?

[narrow forum]

<@&286206848099549185>

not for a test btw practice worksheet that doesn’t make sense to me

.close

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[next lantern]

could someone show me how to solve this without just subtracting 8 until i cant anymore

[next lantern]

have only been able to get to here

then stuck

[warm canopy]

Just look for the closest multiple of 8

I.e. 24

It's 3 less than 24 so 21 is congruent to -3 mod 8

Which is 5 mod 8

[next lantern]

but could i do that if i had this

[warm canopy]

I mean you could yes but it wouldn't be very fun

[next lantern]

yeah thats why i was asking if there was a more algebraic way

so for the first one youre saying i do this?

[warm canopy]

Long division if all else fails ig

Congruent to -3

[next lantern]

hm

[warm canopy]

Because its 3 less than 24

[next lantern]

why not 3?

oh

and 24 is congruent 3mod8

no

idk

[warm canopy]

24 = 0 mod 8

[next lantern]

right

[warm canopy]

Because its a multiple of 8

[next lantern]

right

so then i just subtract 3?

but then i have 21 congruent to -3mod8

but i need 21mod8 is congruent to something?

is there any transitivity that says -3 congruent to 21mod8 since 21 congruent to -3mod8

[warm canopy]

That is true

And its called symmetry

[next lantern]

ah ok

right

makes sense

[warm canopy]

a = b mod c iff b = a mod c

[next lantern]

right

logical

so then for that big one its just the same thing but a time killing process

[warm canopy]

Unless there's some trick which the numbers

Which I don't see

Your best bet would just be long division

[next lantern]

just to clarify

which 2 number am i long dividing with

im doing the large number/101 right

[warm canopy]

Yes

And you want the remainder

[next lantern]

right bc then its like

big number congruent to remainder(mod101)

and then symmetry

right?

[warm canopy]

Sure

[next lantern]

ok 🙃

.close

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[astral oak]

2 is a reference for 4 and 5

so for 4 and 5, is it A and A?

[still wind]

diko alam yan solving lang alam ko wahhahaha

AwitNamanSayoPar

[astral oak]

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[atomic lichen]

why does (-100)^1/2 equal root(-100) and not - root(100)??

[latent walrus]

$\sqrt{-100}=\sqrt{-1}{ \cdot \sqrt{100}$ so what youre trying to say is that $\sqrt{-1}=-1$ which isnt the case

the exponent 1/2 is over everything inside the bracket, you cant just factor out the -1

[warm shale]

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

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[reef trail]

Help

[reef trail]

Did I do something wrong with the set up of my integral? Because I get the wrong answer when I evaluate it

<@&286206848099549185>

It's been 30 minutes and still no luck with this problem

[obtuse pebble]

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.

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[plush girder]

1+1=?

[nocturne minnow]

Don't troll

.close

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[hushed bear]

how do i write an equation of a line from an ordered pair?

[drifting cypress]

Ordered pair such as?

[hushed bear]

(2,4) (5,8)

[drifting cypress]

Ok

So first we find the slope of the line

[hushed bear]

rise over run right

[drifting cypress]

Yea

Can you do that here

Hello?

[fierce lagoon]

Ah yes

[obtuse pebble]

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[fringe schooner]

anyone can share some reference how to prove this DFT pair? I tried by myself and still ended up with lots of sine and cosine function that cannot be eularized

[fringe schooner]

I attempted to solve problems similar like this one. I just tried to integrate the x part only, but I dunno what i should do next. Should i change the boundary or any other suggestions??

[obtuse pebble]

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[unkempt sable]

What is the slope of the function y = x^3 at the point (2,8). How do you do this question, isn't it like using delta and then shrinking it to 0? I'm not sure how to start.

[unkempt sable]

actually nevermind i got it

.close

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[lone bolt]

for a) how come they dont use this formula?

[green epoch]

You'll get a similar formula when you integrate that dN equation

[lone bolt]

i meant picture two

how come they dont use picture 2's formula

rather they use N(t)=N_0 e^-kt

[kind hawk]

not like there is a huge difference?

[lone bolt]

?!

[kind hawk]

subscript 0 is better for starting values imo

second picture has P_0(t) = P e^-kt

[lone bolt]

i agree

[kind hawk]

yours is N(t)=N_0 e^-kt

where is the big difference

[lone bolt]

which has the P's switched

[kind hawk]

ehh

notation

[lone bolt]

u see that ?

thats sus

[kind hawk]

the P's mean different things. its the same formula

just the _0 is at different places and means different things

[lone bolt]

forget about N and P

they mean the same sht

im talking about where the _0 goes

thats the important part

[kind hawk]

they use _0 to denote different things

the one means present value, the other means starting value

[lone bolt]

right so

when they presented

their problem

here

i used the present value function formula

[kind hawk]

you cant just blindly use a formula without thinking what each value stands for

[lone bolt]

or is that only for compounded continuously at a decay

[kind hawk]

they use _0 differently

think about what it means

P=N_0

[lone bolt]

_0 means initial value

[kind hawk]

P_0 = N

not in the other formula

[lone bolt]

like primary investment

[kind hawk]

in the other formula it means present value

[lone bolt]

yes

that confuses

the fk outta me

which formula

to use

[kind hawk]

they use bad notation. get over it

[lone bolt]

thats their formula

im ok with their variables

just need to understand what to use

and when

[kind hawk]

its the same formula

[lone bolt]

also when to plug what in where

[kind hawk]

just different notation

[lone bolt]

P_0 is swapped

= dif formula

not same

[kind hawk]

_0 is swapped

and means other things

[sonic anchor]

you know what to use because they tell you

[kind hawk]

I give up. I cant help you. maybe someone else can

[lone bolt]

said my dad

[sonic anchor]

picture 1 they tell you

N_0 represents initial value (t=0)

and picture 2 they tell you

P_0 represents present value

so you just go off what they actually tell you the variables mean

you dont have to guess

[lone bolt]

gotcha

i just saw "present"

and my mind told me to use

that formula

from 2nd photo

which is bad

incorrect*

[sonic anchor]

you are still using that formula

what is present value in picture 1?

[lone bolt]

yeah but with the _0 swapped tho

also 2nd photo is compounded yearly

this ex is dif

[sonic anchor]

what is present value in picutre 1?

[lone bolt]

have to solve for that i think

thats the formula

present value is just N_0

infront of the e

[sonic anchor]

yes, here we are starting with N_0 and decays to N after some time t

and in 2nd we are starting with P which decays to P_0. the reason its like this in the 2nd is becuase of the real world application

so its just P=N_0 and N=P_0

really its because P was 'in the past'

[lone bolt]

[sonic anchor]

i think almost everyone prefers first picture notation though

P=P_0e^(-kt) where P_0 now represents how much money you intiially put

[frosty spoke]

P_0, P, N, N_0 are literally just different letters

you can replace then with whatever you want

I could replace P_0 with K_1, P with R_2

and as long as I write what they mean, I can do that

[sonic anchor]

ye but it can be confusing maybe to understand why they do it in the questions

like if you have to figure out what letters to replace with what

you need to understand the meaning behind them

not just that they are notation

so you can be notationally flexible

[lone bolt]

sometimes they use r vs k

its anoyying

but

i understand

which is improtant

for notation flexiblity

anyway what about c here

cant i just plug 2 into dn/dt formula?

[sonic anchor]

,w 259*(-0.074)

[warm shale]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Køter#5504

[sonic anchor]

rounding error?

[lone bolt]

its mymathlab

igot it right dw

just revisiting it

like i told u i was going to

im just trying to understand why c) wasnt found by using the dN/dt formula

[sonic anchor]

it is

[lone bolt]

ik but like

N notation

wth is that

[sonic anchor]

$\frac{dN(2)}{dt}=-0.074 * N(2)$

[warm shale]

Køter

[sonic anchor]

$N(2)=259$ from part b

[warm shale]

Køter

[sonic anchor]

or in prime notation $N'(2)=-0.074 * N(2)$

[warm shale]

Køter

[lone bolt]

fk me it says N

not N(t)

how am i suppose to know that

[sonic anchor]

you know from what they said that N is a function of t

and you are also differentiating w.r.t t so if its not nothing really makes sense

sometimes you just dont bother typing out the t or x because its obvious

or you want it to be more general

like the product rule: f'g+fg'

it can be w.r.t t,x or anything

[lone bolt]

koter

have i ever told u

that your the man

?

u give off big d energy my boy

bigger than all 45k ppl in this discord

[sonic anchor]

💀

ok man

[lone bolt]

🔸

ty koter

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[flat condor]

Is it possible to make the notation shorter in the following: $\lim_{x_1,x_2,\dots,x_n \to \infty} F_\textbf{X}(\textbf{x}) = 1$? The numbers $x_1,x_2,\dots,x_n$ are entries in the vector $\textbf{x}$.

[warm shale]

Anders

[obtuse pebble]

@flat condor Has your question been resolved?

[obtuse pebble]

@flat condor Has your question been resolved?

[warm canopy]

I mean you could just define x -> infty to be the thing you want

[fringe schooner]

.reopen

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[old hedge]

My teacher has tried to explain me this, but I really don't understand. I hope someone can help me with this.

a cylinder
a cone
a box with a square base
There should be no lids on the containers, represented as white in the figure.

All containers must have a volume of 10 liters.

Determine the values of r and h for the cylinder and cone, and the values of b and h for the box that result in the smallest surface area.

Which type of container has the smallest surface area?

[old hedge]

I got no numbers to work with, only 10 liters.

[jolly ginkgo]

Enough

[old hedge]

10 liters is enough? Hmm... well I don't really understand this. I will keep looking, I must find an answer on how to solve this xd

[obtuse pebble]

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[uneven palm]

am I doing #3 right? wtf is arcsin(1/3)?

[unreal musk]

Dividing by cos(theta)

[uneven palm]

is that legal

[unreal musk]

I mean, you’d be under investigation at the very least

(cos(theta) can be zero so make sure you check that separately as well)

[uneven palm]

oh

so what should I do instead

if I don’t want to divide by cos theta

[unreal musk]

Well you can divide by cos(theta) provided you check the values where it can be zero, after all, that would be equivalent to…

…factoring out the cos(theta) if you gathered everything on one side

[obtuse pebble]

@uneven palm Has your question been resolved?

[uneven palm]

okay yeah it would be the same, so theta = pi/2, 3pi/2, and arcsin(1/3)

but that still begs the question

how am I meant to find arcsin(1/3) without a calc

@unreal musk 😩

[unreal musk]

Do they expect you to find its value? That sounds pain, do they not e.g. want you to leave it in exact form?

[uneven palm]

idk there arent directions

but i guess it’s okay to leave it like this

thanks

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[desert helm]

Does anyone know how to re-explain the question?

[desert helm]

Or maybe

like

Give another example?

Because

Im confused on the h metres and after t years

Does anyone get this question ?

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[copper spoke]

Can someone give me a introduction to trigonometry ..?

[fierce lagoon]

https://www.khanacademy.org/math/trigonometry

[copper spoke]

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[fierce lagoon]

You won't believe how resourceful google is.

[obtuse pebble]

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[woven creek]

helo

[woven creek]

how did they factor out the 1/2

[fierce lagoon]

$5x + 2 = 2\parens{\frac52 x + 1}$

[warm shale]

Umbraleviathan

[woven creek]

ok what happens after taht

[fierce lagoon]

Well they simply rewrote $\frac 52x + 1 \rightarrow 1 - \parens{- \frac 52x}$

[warm shale]

Umbraleviathan

[woven creek]

thank you

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[woven creek]

.reopen

[obtuse pebble]

✅

[woven creek]

how did theu turn it tinto 1+ (3/x-3)

[warm canopy]

Takeaway and add 3 on the numerator

[woven creek]

i dont undersatnd

[warm canopy]

Write x as x-3+3

Then split the fraction

[woven creek]

can u show pls\

[warm canopy]

Try it yourself

x = (x-3)+3

Split the fraction into two

[woven creek]

i dont get it

?

[obtuse pebble]

@woven creek Has your question been resolved?

[woven creek]

<@&286206848099549185>

[obtuse pebble]

@woven creek Has your question been resolved?

[woven creek]

<@&286206848099549185>

[jade veldt]

1 + (3)/(x-3)

= (x-3)/(x-3) + (3)/(x-3)

= (x)/(x-3)

[jade veldt]

does that make sense

[woven creek]

(x)/(x-3)

[jade veldt]

then for the last step they multiplied the fraction by -(1/3)/-(1/3), or divided both the numerator and denominator by -3

[woven creek]

(x-3)/(x-3) + (3)/(x-3)

[jade veldt]

yes

which is equivalent to x/x-3

does that make sense

[woven creek]

if you only subtracted -3 from the numerator then why all the extra steps for teh denominator

(x-3)/(x-3) + (3)/(x-3)

[jade veldt]

huh

(x-3)/(x-3) = 1

you need same denominator to add

[woven creek]

i dont get it

you subtracted -3 from numerator why the denominator get the 3/(x-3)

[jade veldt]

im so confused what ur asking

did u learn simplifying rational expressions in alg 2

[woven creek]

we didnt take alg 2

[jade veldt]

bro

are u in precalc then?

[woven creek]

im in calc 1 lmaaaooo

[jade veldt]

you should review simplfying rational expressions

i can try to write it out for you in like 10-15 mins

[woven creek]

that would be very helpful tahnk u

[jade veldt]

👍

[jade veldt]

heres the full explanation

[obtuse pebble]

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[strange yoke]

I don't understand how i would do this. i know that i need to set it up as a limit

As k go to infinity

But i don't know how to evaluate that limit

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[dark stirrup]

.reopen

[obtuse pebble]

✅

[dark stirrup]

@strange yoke, if you can prove that the sequence of individual terms diverges, then it follows that the sum will diverge

That is, prove that k/lnk itself diverges as k goes to infinity

[timid silo]

@dark stirrup From what they said you can imply they don't know how to do that

[dark stirrup]

Not sure if they meant as sum goes to infinity or terms

[timid silo]

From the possible answers given in the screenshot I'd assume they mean the terms

[dark stirrup]

Well I pinged, so maaax can ask for more help

[timid silo]

fair enough

[obtuse pebble]

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[timid silo]

I Need Help

[obtuse pebble]

@timid silo Has your question been resolved?

[frigid prism]

doing what..

[timid silo]

yes Got It Done

[oblique glacier]

.close

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[bleak eagle]

im having a bit of trouble interpreting the definition of an eigenspace from my textbook

[bleak eagle]

so each eigenvalue gives rise to a different eigenspace, but the way eigenspace is defined, does an eigenspace for each eigenvalue contain exactly the number of vectors equal to the multiplicity of the eigenvalue?

[sudden lagoon]

no it doesnt

each eigenspace contains infinitely many vectors (over a field with characteristic 0)

what you meant to ask is whether dimension of that space is equal to algebraic multiplicity of eigenvalue

and the answer is no as well

its less than or equal to it

[bleak eagle]

how can that contain infinitely many vectors based on this definition though?

i feel like im just being dumb

[sudden lagoon]

its a vector space afterall

if v has eigenvalue a, then so does bv for every b \in field

[bleak eagle]

wait wait

ohhhh okay i got it!

thank you!!

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[umbral hornet]

Hello there, can someone help clarify this? (part c)

I got x^2 - 16x - 16 = 0, which yielded two answers (-0.944 and 16.944). -0.944 is what x is when y=-4 and not y=4, so 16.944 is the right answer. Instead of plugging it back in and checking, is there another way of just looking at it and knowing -0.944 is incorrect?

[plain stag]

you can look at the original function and see that any x<0 gives a negative output, in this case

but in quite a few cases there isn't a simple way to verify, so you do have to plug it back in and check manually

[umbral hornet]

ah gotcha, thank you

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[flat apex]

What happened after the third step?

[flat apex]

how did he get rid of the integral?

[teal turret]

Do u know fundamental thm of calculus

[flat apex]

yes

[teal turret]

First one

That’s how they did it

[flat apex]

can you send me a proof of this?

Just curious

[nocturne minnow]

fundamental thm of calculus

Literally that

[flat apex]

i mean the first one

the second one is fundamental theorem

[nocturne minnow]

They're both fundamental thm of calculus concepts

[flat apex]

Ok, then can you send me a source that exactly proofs first equality?

[nocturne minnow]

You are capable of using google

[flat apex]

Ok, thank you for your input

[flat apex]

could you please explain why the first equality holds?

[teal turret]

Honestly I don’t know the proof for it, or why it works lol, internet would probably be better as dldh suggested

[flat apex]

Oh okay

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[flat apex]

thanks

[teal turret]

np

[obtuse pebble]

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[dreamy sierra]

Hey

[dreamy sierra]

does sm1 know how to do thois

[trim locust]

Keep adding more terms to the Taylor series and subtracting cos x until the error is 4 and 7 dp?

[dreamy sierra]

we have to do this

[trim locust]

I read about this somewhere for a software project I made but I’m not confident enough to be able to help you here sorry

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[dreamy sierra]

.reopen

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✅

[obtuse pebble]

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[pure walrus]

Does there exist a periodic function f(x) such that f(x) times f'(x) equals 1?

[dark stirrup]

start with the second part

$y\cdot y'=1$

[warm shale]

SWR

[dark stirrup]

solve for y

[pure walrus]

This is just for my curiosity, I don't know how to solve that differential equation

[dark stirrup]

$y'=\frac{dy}{dx}$

[warm shale]

SWR

[dark stirrup]

So $ydy=dx$

[warm shale]

SWR

[dark stirrup]

Integrate both sides

$\frac{1}{2}y^2=x+C$

[warm shale]

SWR

[pure walrus]

.close

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[teal turret]

Bruh

[dark stirrup]

(a thanks is always appreciated)

[obtuse pebble]

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[obtuse pebble]

@dreamy sierra Has your question been resolved?

[dreamy sierra]

<@&286206848099549185>

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[supple stream]

I’m in trigonometry

[supple stream]

so I don’t understand how they got x=3/4 to (4x-3)?

for the first problem

I just thought it’d be (x-3/4)

[nocturne minnow]

Yes

That's also valid

[supple stream]

oh

that works too?

[nocturne minnow]

But notice how (4x-3) doesn't have any fractions

[supple stream]

ya

[nocturne minnow]

So it means that they multiplied by 4, correct?

[supple stream]

Oh yes

[nocturne minnow]

Do you understand now?

[supple stream]

a little

[nocturne minnow]

If you took this, (x-3/4), and multiplied by 4, what do you get?

[supple stream]

4x-3

thank you

[nocturne minnow]

Another way to look at it, you know the zero product property, correct?

[supple stream]

yes

[nocturne minnow]

So it meant that x = 3/4, right?

[supple stream]

Yes

[nocturne minnow]

What if you multiplied by 4 as the first step, to remove that fraction?

[supple stream]

(x-3/4)4?

4x-3

or you mean

(x=3/4)4
4x=3

[nocturne minnow]

This

[supple stream]

ohh ok

for b

should I remove the cube root? Probably?

oh I know

[nocturne minnow]

I don't see any cube roots

[supple stream]

for problem B

[supple stream]

this doesn’t look right

Omg

I did so much math today

I meant square root

ok I think

that B problem only has one solution

y=x^2-5

thankxz

I know u don’t care but I’ve been behind on math a little but today is the day I change and get back on my feet

[nocturne minnow]

Just an fyi, $-\sqrt{5} = -1 * \sqrt{5}$

[warm shale]

dldh06

[nocturne minnow]

So $(-\sqrt{5})^2 = (-1 * \sqrt{5})^2 = (-1)^2 * (\sqrt{5})^2$

[warm shale]

dldh06

[supple stream]

Ohh yea

so that’s when we use those

‘imaginary numbers’

[nocturne minnow]

Imaginary numbers are when the negative is under the root, like $\sqrt{-5}$

[warm shale]

dldh06

[supple stream]

will the 5 have the i?

(-1)(5i)

it should? right?

[nocturne minnow]

Not quite, if you were using $\sqrt{-5}$

[warm shale]

dldh06

[nocturne minnow]

$\sqrt{-5} = \sqrt{5} \cdot \sqrt{-1} = i\sqrt{5}$

[warm shale]

dldh06

[supple stream]

is that also a right answer?

OMG

I thought the - was inside

[nocturne minnow]

Well does it make sense now?

[supple stream]

yes

ok so problem B

it wants me to put it into vertex form?

[nocturne minnow]

Not quite

Equation of a circle

[supple stream]

that 10y is looking strange

Oh I know

Nevermind

I don’t know

we have to remove the little 2 in x and y

or no?

[nocturne minnow]

No

Recall that the equation of a circle is in the form of (x + h)^2 + (y + k)^2 = r^2

[supple stream]

yes sir

[nocturne minnow]

So you need to complete the square to get it into that form

[supple stream]

I’m not really sure how to do that

because my teacher be using Punnett squares to do that

OHH

I KNOW

[nocturne minnow]

Punnett squares?

[supple stream]

yes ..

ok

I think I know

so

u want me

to do this

u want me to factor out y^2+10y+25?

[nocturne minnow]

Yes

[supple stream]

I’ll show u how we do it here

I’m helping u now

nvm I’m just gonna use quadratic formula

[nocturne minnow]

I've never heard of a "Punnett square" factoring method so I'm intrigued

[supple stream]

I CAN still show u

ok so

have u

ever heard of the box and Diamond

[nocturne minnow]

I've heard of the diamond method for factoring but not box and diamond

[supple stream]

Diamond method same as this maybe?

I don’t use her method to complete the square when going from standard to vertex form

[nocturne minnow]

Interesting

[supple stream]

u get it?

ok

I got. 0

[nocturne minnow]

I guess this method is more of getting it into vertex form and not factoring it into two binomials like below

[supple stream]

wait

I forgot

ok I got -5

[nocturne minnow]

Fyi a hint is, it's a perfect square

[supple stream]

oh yes

I’m so confuse

btw do u know where the 25 come from in problem B?

[nocturne minnow]

By completing the square

For y^2 + 10y

[supple stream]

Ohhhh

ok

omg

problem C

I split the equation into two equations

x^2+18x+47

&

y^2-8y+47

I think that’s right and then u complete the square?

[nocturne minnow]

Not quite

[supple stream]

Omg

how to do this what the heck

I’m going to take a 5-10 min break

[nocturne minnow]

https://www.youtube.com/watch?v=0iDCLcrCqwE&ab_channel=BrianMcLogan

[supple stream]

Tyyy

you’re the best and sweetest

[nocturne minnow]

I gotta go now

[supple stream]

it’s okay u can go

bye bye thank you

[obtuse pebble]

@supple stream Has your question been resolved?

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[wooden jay]

Guys, how do I start this question?
Find all the multiplicative inverse pairs in modulo 20.

I only know how modulo works in addition and kinda subtraction, but I’m completely lost in modulus and inverse

[obtuse pebble]

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[plush mist]

Need help/clarification on 3 or 2 Algebra II questions

[plush mist]

1. How to factor (x-1)(3x^3 + 5x^2 - 4x - 4) when finding rational roots

2. How to set up the problem "Write a polynomial with the root 6 - i"

[frigid prism]

youre asking how to factor a cubic?

[plush mist]

think so

[frigid prism]

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

[plush mist]

okay thank u

and the 2nd one

im confused

[frigid prism]

that just means (x - (6-i)) is a factor

which iirc means that (x + (6-i)) is also a factor

either that or (x - (6+i)) is also a factor

i forget exactly

[plush mist]

the answer was x^2 - 12x + 37

i tried (x+ 6 +i)(x - 6 +i)

that was wrong

so im wondering how you would set it up

[frigid prism]

well you need to expand out the factors

using foil

,w expand (x+6+i)(x-6+i)

[warm shale]

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[frigid prism]

nope

[plush mist]

yeah

[frigid prism]

,w expand (x+6-i)(x-6+i)

[warm shale]

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[frigid prism]

,w expand (x-6-i)(x-6+i)

[warm shale]

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[frigid prism]

aye

[plush mist]

there

[frigid prism]

okay so

(x-(6-i)) is a factor

we know that

but also (x - (6+i)) is a factor

so you switch the imaginary component

yep

[plush mist]

so for like

2 - 3i

it would be (x - 2 + 3i)(x - 2 - 3i)

[frigid prism]

yes

[plush mist]

for this one i got 3 + i, 2 and -4

i did (x - 3 -i) (x - 3 + i)

then foiled that

then did (x - 2)(x + 4)

is it the same if its positive

,w expand (x - 3 -i)(x - 3 + i)

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[plush mist]

okay good

,w expand (x - 2)(x +4)

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[frigid prism]

same what

[plush mist]

theres the problem

i got it now

simple sign error

[frigid prism]

so now it has 4 factors

meaning its a quartic

[plush mist]

what if its like i + 4

write a polynomial function using root i + 4

[frigid prism]

you always do real + imaginary

in that order

[plush mist]

okay

so i would do 4 + i and do the same as before then

[frigid prism]

yes

[plush mist]

thanks

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[desert valve]

can someone help with c is that some bernoulli trial thing?
like
if you roll n times
prob(2 is not rolled)^(n-1) prob(2)

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[orchid badger]

this is for a review which wont let me see if the answer is correct without restarting. I feel like I have made a mistake in this one

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[left jetty]

what circumstances would f prime of c not exist?

[obtuse pebble]

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[onyx geode]

hi

[onyx geode]

lets say you have 3 buttons in front of you that you will have to press them consecutively:
Red, Green, and Blue

Each button has a chance of you winning a reward.
Their chances are 20%, 30% and 40% respectively.
Their rewards are a $10 bill, $20 bill and a $50 bill respectively.

If you have won a reward from one of the buttons, you can't continue on pressing the other buttons.
(this applies to red and green only bcs theres no other button after blue)

What is the formula for

1. Calculating the chances of you winning something
2. Calculating the average value/money you get.

an example of an answer that i would understand bcs i only know very basic math is:
3. Calculating the chance of you winning a $20 bill from the green button

chance to fail Red Button * chance to succeed Green Button =
80% * 30% = 24%

[obtuse pebble]

@onyx geode Has your question been resolved?

[onyx geode]

@ruby fulcrum

anyone ? ;-;

[timber island]

aight

lets see

Lets start with 1st part

it'd mean that anyone of them gives you a reward, its satisfied

so that means we're asking for P(A union B union C)

[onyx geode]

i dont understand xd

[timber island]

....

Well if red,blue OR green gives you a reward

the first parts condition is satisfied, yes?

[onyx geode]

on one try, if red gives you a reward, you wont be able to press blue or green anymore
on another try if red fails, you get to press blue, and it succeeds, you get a $20 bill, and can't press blue

you have to press red, green, blue consecutively

[timber island]

Ah

[obtuse pebble]

@onyx geode Has your question been resolved?

[drifting wraith]

so 0.2, 0.24 and 0.224 respectively

0.664 total

then for average money you multiply the chance by reward and add up

2 + 4.8 + 11.2 = 18 dolers

no wait

sure, yeah

[obtuse pebble]

@onyx geode Has your question been resolved?

[onyx geode]

how did you get that

[drifting wraith]

like you did

in the example

[onyx geode]

so lets say if have 10,000 tries of having the opportunity to press the row of buttons. I can keep failing and to press the row of buttons. And on average i will get around $18 for each try?

[drifting wraith]

uh huh

[onyx geode]

thanks!

.close

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[stable rain]

whats the superscript (r) mean

https://www.nature.com/articles/s41586-022-05172-4

[deft crescent]

think it might be Einstein notation

[stable rain]

um what does it mean?

[deft crescent]

there would be another implied summation where r is the summation script (not a power)

so u^0 tensorprod v^0 tensorprod w ^0 and so on

[stable rain]

hm

thanks but i think

this is a bit out of my league haha

i dont know too much about tensors

💕

.close

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[silver oracle]

how to solve for x when the interval is between (0, 2pi), and the equation is sinxcosx + 1/2 = 0

[obtuse pebble]

@silver oracle Has your question been resolved?

[queen panther]

you might have to check that all of these solutions satisfy the original equation