help-36

[marsh temple]

You're just subtracting fractions, not subtracting the number of ways to get 12, 11, 10 and 9 heads

[shell musk]

Oh ok

3797

I forgot for a moment I was dealing with combinations

tks

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[young bobcat]

okay so this is impicit differentiation

[pine yarrow]

Ye ik

I just need help doing the e stuff

[young bobcat]

okay so what is the LHS derivtaive with respect to y

so whats d(e^2y)/d(y)

[pine yarrow]

e^2y dy/dx ?

[young bobcat]

okay so the rule is that the derivative of e^(cy) is c*e^(cy)

so its actually 2e^(2y)*dy/dx

[pine yarrow]

Oh

[young bobcat]

okay so whats the derivative of e^(y^2-y)

so let me clarify

[pine yarrow]

Didnt you already say it

[young bobcat]

this is chane rule

so we have two functions

f(y)=y^2-y

and g(y)=e^y

[young bobcat]

no that was just the derivative for e^(2y)

[pine yarrow]

Oh

[young bobcat]

we are now calculating the derivative for e^(y^2-y)

[pine yarrow]

Alright gotcha

[young bobcat]

so for this we use chain rule

we define f and g as i said above

so e^(y^2-y)=g(f(y))

moreover, the derivative of e^g(y) is g'(y)*e^g(y)

so what is the derivative of g(y)

[pine yarrow]

E^1?

[young bobcat]

okay so we defined g(y)=y^2-y

so what is g'(y)

[pine yarrow]

1^1? Idk

Wait

Can you show me the setup for the chain rule again? Its f’* g*g’ right?

[young bobcat]

um forget chain rule actually for a moment

so we have e^(y^2-y)

so we define f(y) as y^2-y

[pine yarrow]

Yes

[young bobcat]

so therefore, e^f(y) derivative is f'(y)*e^f(y)

so what is f'(y) (this is simply power rule)

[pine yarrow]

2y-1

[young bobcat]

yeah

so the derivative is (2y-1) times e^(y^2-y)

[pine yarrow]

So now continuing this problem, I plug-in the point at that slope?

[young bobcat]

so lets just recap

whats the derivative of the LHS?

[pine yarrow]

The dy/dx stuff

[young bobcat]

its (2y-1)e^(y^2-y)-2e^2y all times dy/dx right

so yeah now literally just plugin y=0

what does the LHS become

[pine yarrow]

Hold on I like witting stuff down

-1?

Idk if I did basic math weong

[young bobcat]

um yeah you did it right

except its (-1) times dy/dx right

[pine yarrow]

Yes

[young bobcat]

yeah so now just give me the derivative of the RHS

[pine yarrow]

4x^3-2x

[young bobcat]

yeah and plugin x=1 to that

[pine yarrow]

4-2

[young bobcat]

yeah

so that becomes 2

[pine yarrow]

So, dy/dx = 2/-1

[young bobcat]

yep so dy/dx=-2

[pine yarrow]

But

Earlier when I did this problem I put 2 as the answer and i checked it and it was weong

[young bobcat]

well the answer is negative

2

not positive 2

[pine yarrow]

There’s only 3 other choices and there’s no -2

[young bobcat]

oh let me check the work again

[pine yarrow]

Its 1/2, 0, and 2/3

Alright

[young bobcat]

wait

okay i was just being dumb

[pine yarrow]

?

[young bobcat]

so 2e^2y-(2y-1)e^(y^2-y) all times dy/dx is the actual derivative of the LHS

so now plug in y=0 to this

(the problem was that originally i didn't realize that in the original equation e^(y^2-y) was subtracted rather than added)

@pine yarrow yeah just now plug in y=0 to this new equation

[pine yarrow]

Alriuu hu r

Alright

Isnt it just 3?

[young bobcat]

yes

its 3

so our proper equation is 3*dy/dx=2

rather than (-1)*dy/dx=2

so therefore, dy/dx=2/3

[pine yarrow]

Thus 2/3

Yeah

Thank you

🙏🏻

[young bobcat]

okay np!

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[violet furnace]

Suppose you want to save in order to purchase a new boat. Take the APR to be 7.1%. If you deposit $255 each month, how much will you have toward the purchase of a boat after three years?

[marsh temple]

What's giving you issue?

[violet furnace]

how do I do it

[marsh temple]

If your APR is 7.1%, what is the monthly rate?

[violet furnace]

idk I didnt catch it on class

[marsh temple]

Do you know what APR stands for?

[violet furnace]

annual percentage rate

[marsh temple]

Indeed

That's the term for when you have a monthly rate (or other non-annual rate, be it weekly, bi-annual, whatever) that's been annualized

[violet furnace]

ok

[marsh temple]

So if your APR is 7.1%, how much interest is accrued each month?

[violet furnace]

7.1%?

[marsh temple]

No

7.1% is annualized

How many months in a year?

[violet furnace]

12

[marsh temple]

You earn 7.1% over the course of 12 months

[violet furnace]

yeah

[marsh temple]

So how much do you earn in a single month

[violet furnace]

0.59

[marsh temple]

0.59% yes

Now, if you make monthly deposits for 3 years, how many deposits are you making?

[violet furnace]

36 deposits

cuz 12 months in a year

and 12*3 is 36

so 36 0.59% deposits

[marsh temple]

So 36 deposits, roughly 0.59% interest, $255 per deposit

You should hopefully have been given a formula (or a calculator/software) that computes the accumulated value after the final payment

[violet furnace]

I had a formula but that was 2 weeks ago and I forgor

[marsh temple]

Where did it go?

[violet furnace]

I forgot the formula

[marsh temple]

I advise finding it

[violet furnace]

bruhhhhhh

[final saddle]

@violet furnace Has your question been resolved?

[violet furnace]

<@&286206848099549185>

[violet furnace]

do you know it

[marsh temple]

I do

But it was your teacher's job to introduce it, and your job to write it down and remember it

[violet furnace]

bruvvvvvvvvvvvvvvvvvvvvvvvvvvv

[violet furnace]

can you gib it to me ill remember it

I cant find it anywhere in my notes

or atleast the name of it

@marsh temple can you please give me the name of the formula atleast

so it enlightens me and makes it eassier

[marsh temple]

Accumulated value of a stream of payments

[violet furnace]

P=PMTx1-(1/(1+r)^N)/r?

[marsh temple]

That's present value

[violet furnace]

P = PMT [((1 + r)n - 1) / r]
?

[marsh temple]

^n but yes

[violet furnace]

idk what to plug in though, is PMT 255

what is the 36 and the 0.59%

[marsh temple]

Yes pmt is 255

[violet furnace]

ok

[violet furnace]

is R 0.59 and 36 N

[marsh temple]

Yes for n, no for r

[violet furnace]

oh

what is R then

[marsh temple]

Your interest rate is 0.59%

[violet furnace]

ok

[violet furnace]

so P =255 [((1 + 0.59%)^36 - 1) / 0.59%]

which would be

10194.4186592

or 10194.42

its wrong

BRUV

Im gonna cry

[marsh temple]

Perhaps use more decimals for r

[violet furnace]

wait I think I know why

were you meant to put theR as 0.59%

or just as 0.59%

[marsh temple]

You put the same thing twice

[violet furnace]

OH I KNOW WHY

I THINK I KNOW WHY

is the answer 119.49

I mystyped it

this is my last try

[marsh temple]

You're depositing 255 every month

And at the end of 3 years you think you have 119.49?

[violet furnace]

wait thats impossible

[violet furnace]

4537709150.01336674

4537709150.01

I am putting this as my last try

if I fail this problem I do

[marsh temple]

That seems way too large

[violet furnace]

ok good thing I didnt submit it

[marsh temple]

The first answer you sent is the closest to what I got

[violet furnace]

10194.42?

but it was wrong

[marsh temple]

I said closest, not correct

[violet furnace]

I think R is wrong

whats messing me up is R

[marsh temple]

I mentioned one thing you could do regarding r already

[violet furnace]

huh this is weird

[violet furnace]

I did the [((1+0.59%)^36-1/0.59^] separately

then multiplied it times 255

it gave me 10194.4186467

then I simplified

its exactly the answer I put in wrongly

[marsh temple]

i'm not sure what you're getting at

[violet furnace]

nothing its just weird

[violet furnace]

which is

[marsh temple]

this

[violet furnace]

would 0.0059% work

[marsh temple]

that's a different number altogether

[violet furnace]

oop

then wym by mor edecimals

I am dumb if you havent noticed

[marsh temple]

how did you get 0.59% in the first place?

[violet furnace]

by getting how much interest I get per month

if its 7.1 per year

[violet furnace]

0.59 is per month

[marsh temple]

right but what is the calculation you did to get 0.59%

[violet furnace]

7.1/12

0.59166666666

shoter to 0.59

[marsh temple]

so when I say use more decimals, I mean don't round it so early

[violet furnace]

oh

so maybe 0.5916%?

[marsh temple]

sure

[violet furnace]

10197.35974816

which is 10197.36

@marsh temple I am gonna put this in as my final answer is this okay

it requires me to round the answer to the hundredths btw

[marsh temple]

10197 is correct, the exact decimal you get depends on how you round your interest rate

so I'd see if there's an expected rounding convention

[violet furnace]

it just says Round your answer to the nearest cent.

[violet furnace]

so its correct right?

[marsh temple]

10197 is the correct dollar amount

the cents depends on how you round

if you add more decimals, you'll get a slightly higher answer

[violet furnace]

I am gonna go with 10197.36

if its incorrect ill move on to the last problem

excuse me what the fuck

HUH

@marsh temple FUCK I WANT MY POINT

https://gyazo.com/2d6f9e0cb7ec63d3170807b505e156cb

IT SAYS ITS INCORRECT BUT ITS LITERALLY CORRECT???

[marsh temple]

your decimal is 36, the answer is 48

[violet furnace]

I put my answer as 10197.48

it says the answer is 10197.48

[marsh temple]

i thought this was your answer

[violet furnace]

even if I did it incorrectly I still got the answer right

no

10197.48

look I put 10197.48

NAHHH FUCK THIS SHIT

BS SITE

[marsh temple]

that's something your teacher will have to handle

[final saddle]

@violet furnace Has your question been resolved?

[final saddle]

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[lapis forge]

if f(x) = √x
does f(f(x)) = √√x? and if so, does √√x = x^1/4?

[tranquil pine]

Yes

[lapis forge]

cool, all dat correct?

[tranquil pine]

Yes

[lapis forge]

swag ty

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[jaunty frigate]

HELP!!!

[versed crater]

What do you know about asymptotes

Or is that just solve

[tranquil pine]

ignore all the terms other than those with x^3 because they are infinitely smaller

[glacial ruin]

I would factorise to see if anything cancels out.

[final saddle]

@jaunty frigate Has your question been resolved?

[tranquil pine]

or if you want to make that more clear then divide the numerator and denominator by x^3, you'll see all the other terms approach 0

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[lapis forge]

I have the answer key, but I cannot solve the equation necessary to figure this out. I tried placing y in place of x and moving the parts around like that but I don't seem to find the right answer when plugging values back into it.

[lapis forge]

<@&286206848099549185> ping cuz 15 min. still not sure how im supposed to solve this.

[outer current]

@lapis forge seems like you just solve by substituting into that formula

hopefully you can use a calculator?

[final saddle]

@lapis forge Has your question been resolved?

[lapis forge]

how do i plug it into my calc?? im not even sure on that part

i can plug 130.25x^-0.1 into my Stat Plot Y =

and then i can pull up a graph

is there a way to use Calc or Trace in order to find when y = 97.5?

i can get close using trace but not close enough

[outer current]

i tried doing some algebra on it, trying to confirm if it works

I started with this

[lapis forge]

ok, i started here too.

then could i bring 97.5 to the root of 0.1?

as well as 130.25h?

[outer current]

hmm

I think I got it, but I'm not sure, and not even sure if this is the best method

I simplified it for myself and changed that exponent from negative to positive

then the trick is to just substitute the H thing for an x and forget about the exponent

i tried to find x, and once you get it, you need to solve that equation you create for x

[lapis forge]

hmm

x^-0.1 = 1/x^0.1

correct?

[outer current]

yes

[lapis forge]

yee, ok. so then
97.5 = 130.25 * 1/x^0.1

[outer current]

mhm

you are still thinking of h tho, not x

[lapis forge]

then my next step would be....?
97.5/130.25 = 1/x^0.1

[outer current]

ok I don't know if I should have you figure this out, it's just a trick you can often use

you can solve for x then

it would have probably worked for the negative exponent too, that step might have been redundant from my side

[lapis forge]

i don't understand how x = h^0.1 relates to solving the amount of time that's passed when given y

[outer current]

first you get the numbers and stuff out of the way, once you figure out the x

you can perform a root to kind of "reverse" or whatever

and you can get the actual h value, which is the time, in hours

[lapis forge]

so w(h) = h^0.1?

[outer current]

em, I don't think so? I mean, I got the first value for that table, it seems reasonable

it doesn't have to be x, often they use u. you just introduce a variable

to make things easier

but you don't have to I guess. as long as you get the h^0.1 to be the only thing on the left/right, you can do the root of the other side to get rid of the exponent, and get just h

[lapis forge]

so to get h^-0.1 by itself I need to divide 130.25h^-0.1 by 130.25, and cause im doing that to the right side of the equation im also doing it to left correct?

so 97.5/130.25 = h^-0.1

[outer current]

yeah looks correct I think

[lapis forge]

97.5/130.25 = 0.75

0.75 = h^-0.1

0.75 = 1/h^0.1

[outer current]

yes yes

[lapis forge]

now what do i do with 0.75 = 1/h^0.1

[outer current]

you want h^0.1 to be alone

shuffle it around

[lapis forge]

uhhh what i get is to multiply the fraction by it's denom, same for 0.75

[outer current]

oh, oh no, this is very simple

[lapis forge]

yeah sorry don't know what to do to isolate it

[outer current]

just multiply by something on both sides

then divide by something on both sides

[lapis forge]

so multiplying both sides by h^0.1?

pls bruh it's almost 2 am T_T

[outer current]

10 am for me

and I haven't slept tonight! anyway, to ease the suspension, yes, do what you said

[lapis forge]

this is what i end up with

[outer current]

oh my. I'm not sure why

[lapis forge]

??????????

[outer current]

I mean if you show the work I can tell you why. but h01 is supposed to be on only one side

how did you end up with two of them! : )

[outer current]

unfortunately no, that's not correct either

you need to up your algebra game!

[lapis forge]

this wasnt gone over in class at all, there's no references to it in the bookwork either

it's why im having so much trouble with it

[outer current]

what would happen if you multiplied both sides by h01?

[outer current]

so here's the problem. that's now what happens

[lapis forge]

x^-0.1 * x^0.1 = x ?

[outer current]

try it, change h01 for x, and do it again

what to do now?

[lapis forge]

nope sorry still don't get what yer tryin to explain

[outer current]

ok how about this

what happens when you multiply both sides by 5

[lapis forge]

right?

[outer current]

yes

[outer current]

yeah

that's correct

[outer current]

yes!

[lapis forge]

ok, how do i use this in correlation with the weight values?

to find t?

[outer current]

do you have h01 alone?

[outer current]

yep, ok

now that thing on the right, you can calculate this

then notice this

in our case we can even do this

because we don't have to worry about negative solutions

[outer current]

yes

[outer current]

yeah

[outer current]

well true, but this is the point I recommend just taking a calculator

[lapis forge]

i can't plug the root of 0.1 into my calc, but i can take 1.33 to the power of (1/0.1)

[outer current]

yep, that's the same thing basically

so it works

[lapis forge]

uhhhh

no

or atleast im not gettin the answers

i plugged 1.33^(1/.1) into my Y Plot, then used 97.5 as the X value

[outer current]

0.1 = 1/10

1/(1/10) = 10

so this is 1.33 to 10th power

[lapis forge]

yeah, 1/.1 = 10

doesn't matter if i plug in (1/0.1) or 10 as the exponent, same results

[outer current]

don't plot anything there's no need for that

just use the normal buttons

it should be x^n or smth

[lapis forge]

where would i use x?

[lapis forge]

i have a ti-83, we don't have the use of multiple variables

[outer current]

hold on then

https://www.youtube.com/watch?time_continue=58&v=S-H3taxKC-Q&feature=emb_logo&ab_channel=mathsgotserved

[lapis forge]

yes, just like i said

x to the 0.1 root is x to the power of 1/0.1

which is what i plugged into my calc

1.33^(1/0.1)

or 1.33^10

[outer current]

yep

[lapis forge]

as 1/0.1 = 10

and when i plug in the weight of the bat (97.5) I get 17.31

which isn't the answer

[outer current]

it should be like 18, isn't it?

[lapis forge]

yeah. i need a variable x somewhere in 1.33^10

or i solve 1.33^10

[lapis forge]

yes

[outer current]

let me check the answer for real then

don't scare me

[lapis forge]

17.32 = 1???

[outer current]

h = 17.32

17 hours

I don't know, seems reasonable for a bat

[lapis forge]

unfortunately i dont think i'll be gettin it tonight, i do appreciate the help anyways

[outer current]

I computed the whole original thing, a good approximation is 18.1 hours

we got it right

[lapis forge]

we got 17.32?

[outer current]

well you got some bad approximations

along the way

you cut quite a bit of decimals

I thought you knew what you were doing!

97.5/130.25 = 0.75

that's what you said, that's not actually true

[lapis forge]

true

[outer current]

when you deal with things like taking to 10th power

those decimals matter

with ti83 you could have put it as a fraction, and gotten as close as the calculator would let you

[lapis forge]

is there legit no easier way to solve this problem? the path seems extremely complicated

[outer current]

I don't think so honestly

h^(0.1) is too nasty to deal with

looks like a task to test knowledge of using the calculator

would be insane to do it on paper. but after a good night's sleep you can come here again

and try to get second opinion

especially since they gave you exact values for grams, like 97.5 instead of something pretty

[lapis forge]

if ya dont mind im just writing out the steps we took real quick so ya can see if im right about the method

[outer current]

with ti83 you could probably input the whole thing and compute, never having to do any of what we did today

[lapis forge]

and i could replace 97.5 in step 7 with variable x in order to plug in the other weight values

omg yes

thank you so much, this does give me the formula to solve the question

there MIGHT be an easier method, but i have this for now and that's great i really do appreciate the effort mate

thank ya for being patient with me

[lapis forge]

.close

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[thorny viper]

Hello! Can I have somebody to assist me solving this Graphing Parabola equation? I just wanted to learn more and correct my mistakes

[thorny viper]

!close

.close

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[jaunty yew]

I need help with this question (iii), this is what I have so far for the proof, but I don't know where to go from there (idek if you can do a proof by contradiction either)

[jaunty yew]

this is the rest of the question parts you need to know for context

[final saddle]

@jaunty yew Has your question been resolved?

[jaunty yew]

<@&286206848099549185>

[jaunty yew]

boop

😭

[jaunty yew]

.close

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[soft zealot]

Icarus

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@faint hornet Has your question been resolved?

[final saddle]

@faint hornet Has your question been resolved?

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[ruby depot]

I don't know how to do part b, can somebody show me how to tackle it

pq is 6

i cannot work out the shorter sides to find the overall area

also part a's answer is 9

This question is relevant to Polar coordinates and finding areas

[final saddle]

@ruby depot Has your question been resolved?

[final saddle]

@ruby depot Has your question been resolved?

[ruby depot]

not yet

still cannot work through b

damn it

[final saddle]

@ruby depot Has your question been resolved?

[ruby depot]

no

[mellow cedar]

I guess I know how

we have :
$r =3\sqrt{cos(2\theta)}$

[soft zealot]

Mehdi_Moulati

[mellow cedar]

and we know that in the polar coordination
$r = y sin(\theta)$

[soft zealot]

Mehdi_Moulati

[mellow cedar]

so $y = \frac{r}{sin(\theta)}$

[soft zealot]

Mehdi_Moulati

[mellow cedar]

if we replace r in term of y and theta we will have

[waxen briar]

if we replace \verb+sin(\theta)+ by \verb+\sin(\theta)+, we'll have $$y = \frac{r}{\sin(\theta)}.$$

[soft zealot]

vin100

Mehdi_Moulati

[mellow cedar]

y is maximum when $\frac{d(y)}{d\theta} = 0$

[soft zealot]

Mehdi_Moulati

[mellow cedar]

so you will have just do the derivation of y

and solve the equation

of course the value that you will found is QR/2

,w d(3sin(theta)*sqrt(cos(2theta)) )/dtheta = 0

[soft zealot]

Results provided by WolframAlpha

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

Requested by Mehdi_Moulati#1210

[mellow cedar]

so y is maximum when $\theta = \frac{\pi}{6}$

[soft zealot]

Mehdi_Moulati

[mellow cedar]

,calcul 3sin(pi/6)sqrt(cos(2pi/6))

[soft zealot]

Result:

1.0606601717798 ul

[mellow cedar]

so y = 1.06066 = RQ/2

[final saddle]

@ruby depot Has your question been resolved?

[vital crag]

what da hecking is ul

[hybrid heath]

unsigned long?

No that can't be right...

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[stark apex]

it says to find the principle angle but where'd he get the 4 from ?

[trail mango]

4pi/2 is 2pi

it's just for the fraction arithmetic

but it's the same as subtracting 2pi repeatedly

[stark apex]

ohh

okay

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[lean field]

need to find the maximum volume of a box inside a sphere

[lean field]

I used the spherical coordinates system and had to find the max value of
8r^2 cos(phi)sin^2(phi)cos(theta)sin(theta)

maximum of cos(theta)sin(theta) is 1/2, but the maximum of cos(phi)sin^2(phi) took forever

I wrote sin^2(x) in terms of cos(2x) and cos(2x) in terms of cos^2(x) before differentiating which takes a very very long time

is there an easy way to do this

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[sturdy panther]

A factory makes auto parts. each part has a code that consist of a digit, an alphabet and a digit, where each digit is distinct from each other.
a) how many possible codes are there
b) the factory made 7000 parts, what's the minimum number of parts that must have the same serial number

[sturdy panther]

for a) i did 10 x 26 x 9
cuz 10 numbers are possible for the first, then 26 letters, then 9 digits, given the numbers are distinct

for b, I'm thinking that all the parts must share...

[quaint sail]

what is the difference between a digit and number

[sturdy panther]

a digit is like, 0-9

0,1,2,3,4,5,6,7,8,9

sorry i meant alphabet >.<

if it's by pigeonhole principle... each serial number will have 3 parts.

since 10 * 26 * 9 is 2340

and for 2340 * 3 is 7020

so 7000 is still within 7020, so each code will have at least 2 parts

[quaint sail]

seems right

[sturdy panther]

hmm ok

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[wispy sequoia]

Hello :)

[wispy sequoia]

so I need help with math but its not exactly like

an equation

here:

basically

i chose a reciprocal function

and i have a real life example

which is this

now

idk how to like explain this

or anything else

[paper zodiac]

It means that if you have a pipe that is long, a lower pitch would be produced

So as pipe length increases, pitch decreases

length decreases, pitch increases

[wispy sequoia]

Oh okay

One sec

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@wispy sequoia Has your question been resolved?

[wispy sequoia]

sorry working on the slide

wait how do i find the answer to this uestion @paper zodiac

[paper zodiac]

Just substitute y with 277

It's already stated there that y = pitch

[wispy sequoia]

oh

ok

mb

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@wispy sequoia Has your question been resolved?

[wispy sequoia]

yeah i guess

not really

bevaise iy asks for the inverse variation

what does that mean?

[wispy sequoia]

@paper zodiac

[spring echo]

ok im not him but

I think that the inverse variation is switch X and Y in the equation, and then solve for Y again

like the inverse of 3x+1 = y is 3y+1 = x -> (x-1)/3 = y

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[wispy sequoia]

thank you

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[fickle coral]

normal people: why are u screaming?

[fickle coral]

Me: I HAVE SURFACE AREA

normal people: whats wrong with surface area?

[thorny tendon]

?

[fickle coral]

me: 3x4/2x2+5x3+4x3+3x3x5

[worldly vale]

Unless you have a serious maths question, close the channel for other people

[thorny tendon]

.close

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[rain barn]

How can factoring this
(e^x)-(1)-(x²e^x)-(x)
To : (x+1)((e^x)-(xe^x)-1)

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[next pagoda]

For this question, would I use the x or y values to show that it is a arth sequence?

[next pagoda]

OR can I use either?

for #56

<@&286206848099549185>

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@next pagoda Has your question been resolved?

[dry light]

Depends

Wel no

Use n and a_n

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[steady ravine]

Um can someone explain the difference between barycenter and centroide

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[light wren]

pretty sure a centroid is geometric and barycentre is dependent on mass and the energy in the system

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[vague vale]

ok so i've never tried to do anything like this before and i've had no formal education to try to teach me how to do something like this so im not even sure this is possible but here it goes: lets say i have two independent variables for a function (x and y), and a dependent variable z. x is the market value of a good, and y is the percentage of that item that is actually sold of the amount made available each day. z represents the maximum percentage of the market value i want to purchase a particular good at. lets say I want z to be anywhere between 35 and 80. I have various points such as [100,000, .01, 80], [1000, .04, 50] etc etc. I can get more points i just wanted to give a couple examples. is there a way to find the function by using two points like in a standard linear function?

[icy glacier]

x and y are clearly not independent tho. And find the function? There are an infinite amount of functions with those requirements

[vague vale]

sorry independent and dependent aren't right my bad

like i said im new to this lol sry if im wasting ur time

what im trying to do is basically guess z based on x and y

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[radiant burrow]

how do you prove that cube root 5 + sqrt 2 is irrational? Can you just say irrational numbers closed under additon, because these two obviously don't cancel out?

[dim cargo]

irrationals aren't closed under addition

sqrt(2) + (-sqrt(2)) = 0

[amber holly]

That's not enough of a proof probably, because sqrt2 + (1 - sqrt2) = 1 is a counterexample

[tired walrus]

the reason OP's proof is insufficient is because the assertion "irrational numbers are closed under addition" is plain wrong lmao

[radiant burrow]

uhhh so what do i do?

[tired walrus]

this looks kind of annoying to write explicitly

but it sounds like you could consider the 6th power of this number

perhaps you can find its minimal polynomial this way

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[mystic spear]

What is <B> in html?

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@whole nest Has your question been resolved?

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[tranquil pine]

hi

[tough kelp]

so its root 11 /root 11 -3 * root 11+3/root 11 + 3 right?

[tranquil pine]

Multiply the denominator by the numerator

[tough kelp]

yeah

but dont u multiply the inverse?

so instead of - its +

[green parrot]

I believe you are correct corrupted, simply multiplying by the numerator would leave a radical in the denominator, multiplying by the conjugate will only leave a radical in the numerator

[tough kelp]

after multiplying my fraction is root 11(root11+3)/11-9

[tough kelp]

thats looks wrong ngl

[tough kelp]

u multiply by the inverse not the same

u multiplied a - with a -

[tranquil pine]

where

[tough kelp]

ur meant to do - and a +

[green parrot]

Wait so it's (11-3)^1/2 or is it 11^1/2 -3?

[tranquil pine]

oh

[tough kelp]

Ignore the top line it was for a diff question

[green parrot]

U distributed in the numerator wrong

[tough kelp]

Wdym ?

[green parrot]

You get 11+3(11)^1/2

Or 11+3root11

[tough kelp]

I'm confused xD

How was I meant to do the numerator then?

[green parrot]

One sec

[tough kelp]

Kk

[green parrot]

Yes what mojt has

[tranquil pine]

now it's true

[tough kelp]

ohhh wait yh i forgot to multiply the 3 by the root 11 too

makes more sense now ty

[tranquil pine]

@green parrot hi

[green parrot]

Allo

[tranquil pine]

@green parrot how are you?

[green parrot]

Procrastinating and you?

[tranquil pine]

i can't understand

[green parrot]

My bad, it's nothing I am well

[tranquil pine]

ohh i think you are bussy sorry

[tough kelp]

.clowse

.close

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[south warren]

What am I doing wrong here?

[unique eagle]

What did you even try?

[south warren]

I'm trying to find the function y

[unique eagle]

So what are you doing to accomplish that? This is just separable

[south warren]

If I recall correctly, you multiply each part with the integral of p(t) first which would be t/100000, then you can write it as (y*e^(t/100000))'=50e^(t/100000)

then integrate on each side?

[unique eagle]

Oh, those small squiggles are e?

[tranquil pine]

How can I read this

[unique eagle]

@tranquil pine find an empty channel

[south warren]

oh yeah sorry

[tranquil pine]

Okay

[south warren]

should probably write it in a more proper way haha

[tranquil pine]

How can I remove my post

[unique eagle]

No no I understand the idea now. So you are trying to use an integrating factor

[south warren]

yes

I know you can do it the other way aswell, but I'm trying to practise it using the integrating factor

[unique eagle]

Ok, you can do that, but this is separable so maybe that’s easier? (Since g(t) is constant)

Ah I see. Ok that’s fine. Let me take a quick look see where you went wrong

[south warren]

thanks a lot

[unique eagle]

Ok, line 3 onwards doesn’t really make sense to me

So we find our integrating factor $e^{\frac{t}{100000}}$

[soft zealot]

Learath2

[unique eagle]

Then we need to multiply both sides of the equation by this

Oh, you just skipped that step

[south warren]

yes, and then we get (y*e^(t/100000))'=50e^t/100000 and integrate on each side?

yeah

[unique eagle]

Ok, so what is the problem? 😄

Your solution looks fine

[south warren]

I have the answer when using the other other method, and when putting in y(0)=0 they get that C=50

[unique eagle]

Well idk the question but, I get the exact same answer as you do, both with an integrating factor and with separating it

Wolfram also agrees with us. So either your answer sheet is wrong or the very first line is wrong

[south warren]

ahhhhh i might be really really dumb

they have K=50 where K=+-e^(c/100000)

when putting in y(0)=0 they get y(𝑡) = 5 000 000(1 − 𝑒^(−𝑡/100 000)).

and that is diffrent from my equation

[unique eagle]

No it’s not

Plug in 0 for y in yours and figure out your C

[unique eagle]

After that plug your C in and get your final solution for y, which matches exactly

[south warren]

ohhhhh man yeah I just misunderstood the answer sheet....

thank you so much for helping me realise it was right, thought I just did something wrong

[unique eagle]

Np, sometimes you just need a second pair of eyes 😄

[south warren]

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[mint orbit]

hello

[mint orbit]

I wanted to ask about typing up this proof, I think I'm on the right track?

but it seems like I end up needing to relate the sequences alpha and beta?

would it be valid to just define that $\alpha_i = (\lambda_i-\lambda_{k+1})\beta_i$

[soft zealot]

jan Niku

[mint orbit]

or does that place a restriction im not allowed to make

[unique eagle]

Your (2) looks wrong. Shouldn’t it be $\beta_1 \lambda_{k+ 1} v_1…$ ?

[soft zealot]

Learath2

[mint orbit]

ah, small typo, _ instead of +

excuse the all caps 😅

does the rest make sense?

i mean that method

[unique eagle]

The method is I THINK sane, but I haven’t touched linear algebra in 5 years now

[mint orbit]

lol

alright, thanks

guess ill leave it open and see if someone else is around

[unique eagle]

So with the subtraction, you lose the last term. Now you get that a linear combination of v_1…v_k must be 0. However we assumed v_1…v_k linearly independent. Which is a contradiction, right? That is what you are going for?

[mint orbit]

yea

i guess im just not sure if that relationship between the two sequences is violating something

like, i need one or the other to be more general than the restriction allows

does that concern make sense

but it should be fine, that definition that i gave above means that each alpha_i wont be 0

i think?

as its assumed that each beta_i isnt 0

and no two eigenvalues are equal

idk maybe i just should think on it

the concern might be emotional

i appreciate your help

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[quick bronze]

Ok so like I got that special formula but based on the values I determined (which I hope are right), now what

<@&286206848099549185>

[tranquil flume]

Find x

[quick bronze]

really?

Cus like she wants us to more so simplify it and not actually solve

yeah, simplify the expression and I'm almost there, just that final what do I do with the double cos and all that

Would I end up just squaring it

[final saddle]

@quick bronze Has your question been resolved?

[quick bronze]

hah anyways

so like the formula is basically double cos minus double sin

so like when trying to like plug that and all that jazz, would I have to square the values I'm putting in

[quick bronze]

<@&286206848099549185>

yk I could turn this into a competition

how long I can hold this channel

genuinely

BUT HEY guys would I have to like square the thingies

[charred fulcrum]

What's the question ?

Do you need to find theta ?

[quick bronze]

ok so like here, have to finish simplifying the expression

the question is worded a lil odd imo cus like for the whole formula thingy, it's the cos squared theta thing

when I put in the values there, would I have to square them

so for cos^2(theta) for example, would I put sqrt(1-x^2) squared

[charred fulcrum]

no

its the cos that is squared not the value inside cos

[quick bronze]

ok

so like how would that work then, to get rid of the cos^2

[quick bronze]

yk it's fine

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[low sorrel]

how to find part f? i know residual is y-yhat

in part e i found my yhat with x being 20 cigars a day and i plugged it into my equation in part b, but in part f idk what to do with the 4.2 kg

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@low sorrel Has your question been resolved?

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@low sorrel Has your question been resolved?

[vital crag]

,calc 3.8944-4.2

[soft zealot]

Result:

-0.3056

[finite moth]

hi

How do you do Box and Whisker Plots?

[vital crag]

read #❓how-to-get-help

[finite moth]

ok sorry

[low sorrel]

where does the 3.8944 come from?

[vital crag]

.

Your yhat from b)

[low sorrel]

oh yes and why do you use that value?

[vital crag]

You're asked for residual. You gave its definition here

[low sorrel]

the answer is incorrect

[vital crag]

What did you input

[low sorrel]

-0.31

[vital crag]

Ohhhh you have to use the measurement from part e)

Not b)

[low sorrel]

so 4.2-3.16 ?

[vital crag]

Which one should be yhat?

[low sorrel]

3.16

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@terse aspen Has your question been resolved?

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[wind geode]

if the points (h^2,0), (0,k^2) and (4,4) lie on the straight line show that h^2 + k^-2 = 2^-2

[wind geode]

help

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@wind geode Has your question been resolved?

[radiant laurel]

lol no help

[cloud zephyr]

By any chance do you mean h^-2 + k^ -2 = 2^-2

Instead?

@wind geode

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[wide nova]

can anybody help?f

this is what i have

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[thorn minnow]

Hello I got a question I got the sum $$ \sum_{k=1}^n \frac{p(x)}{(x - a_k)}$$ and I multiply that by $$(x - a_k)$$ can I just cancel that out then? and my result is just n*p(x)

[soft zealot]

Eichhorst

[thorn minnow]

.close

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[mossy totem]

Are you looking for a human calculator? xD

[dark grotto]

yeah lol

idk how to type it anyway

how would i do this?

[desert mantle]

that's not how binomial coefficients work

[mossy totem]

true. nvm my answers

[desert mantle]

not sure if there is a smart way to do this. there probably is. but I would just set up pascals triangle and then add up

[dark grotto]

how would i use it?

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[tranquil pine]

I have question

[tranquil pine]

Can a dirichlet function have darboux propriety

[fallow wren]

?

[tranquil pine]

What?

[fallow wren]

what's the definitions of this strange object

[worldly vale]

,w dirichlet function

[soft zealot]

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[worldly vale]

,w darboux property

[soft zealot]

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[worldly vale]

Thanks wolfie

[vital crag]

,w you're useless

[soft zealot]

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[tranquil pine]

=))

[worldly vale]

Explain darboux property

[fallow wren]

solo i don t think because the only value of the d. function are 1 and 0....so 1/2 cannot be reached

[tranquil pine]

I know that a function has darboux propriety when we can take either one a and b with a<b and either lambda between f(a) and f(b) so that exist a c between a and b where f(c) is lambda

I was curious to see if there exist such that function wich is dirichlet and darboux

Cuz we know there exist darboux function with is discontinuous in every point

And dirichlet function can be also discontinious in every point

[vital crag]

[fallow wren]

derivative of fap ?

[vital crag]

dirichlet functions only take on 2 values so it can't take on any intermediate values soooo no?

[tranquil pine]

Yes you are right

[fallow wren]

this is an evil property so see other math object

[tranquil pine]

It is very important in continuity

[fallow wren]

i never use it

and it s essentially "the immage of a connected set is connected"

[tranquil pine]

Yes

[fallow wren]

but the other direction is false

[tranquil pine]

But is very interesting to see that darboux function is not continuous everytime

.close

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[desert mantle]

the cursed property of darboux functions is that any real valued function can be written as the sum of two of them

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[surreal gate]

Hey
I was going through these questions with someone since I was having a hard time grasping the concept of linear transformations.

It timed out before we were done,
The last things I asked were:

[surreal gate]

What would be the defined as the matrix of since it isn't the matrix yet without the function on the right

Let me know if I went ahead and did that one right

Is there a rule that let's you know if modulus of a1 +b1 +a2 + b2 is equal to modulus (a1+b1) +modulus of (a2 + b2)

Do we still use 2 rows for the arbitrary vectors for d since x is only one constant? Or would we just use
For example
Let u=a and v =b
For the formula
T(u) + T(v) = T(u+v)

<@&286206848099549185>

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@surreal gate Has your question been resolved?

[surreal gate]

<@&286206848099549185>

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@surreal gate Has your question been resolved?

[surreal gate]

<@&286206848099549185>

[surreal gate]

<@&286206848099549185>

[surreal gate]

<@&286206848099549185>

[surreal gate]

<@&286206848099549185>

[surreal gate]

<@&286206848099549185>

[plain cairn]

Hello

Can you restate your question

@surreal gate

[surreal gate]

Hi
Sorry it was a continuation from previous assistance I was getting

[surreal gate]

Which one would you like me to restate?

If u meant so it'd be I'm front

If you're still on now I guess we can go through 1 by 1
So you wouldnt get confused in a chain of messages

For c
Is there a rule that let's you know if modulus of a1 +b1 +a2 + b2 is equal to modulus (a1+b1) +modulus of (a2 + b2)

Do we still use 2 rows for the arbitrary vectors for d since x is only one constant? Or would we just use
For example
Let u=a and v =b
For the formula
T(u) + T(v) = T(u+v)

[tender jewel]

They are not always equal

[surreal gate]

Is there a condition on which they usually would be or there's just nothing special

[tender jewel]

I mean if they are all strictly positive

But say if b1 and b2 are negative and a1 a2 pos

Clearly the mod of the sum is less than the sum of the mods

[surreal gate]

Ahh makes sense thanks

[surreal gate]

Are you able to help with any of the other questions ?

[tender jewel]

Smwhcih one

[surreal gate]

This one @tender jewel

[tender jewel]

The x’s u use should be arbitrar

[surreal gate]

But should I use 2 or 1?

Cause for b I used 3

[final saddle]

@surreal gate Has your question been resolved?

[rancid wren]

if you're doing a counterexample, you can choose specific numbers (i.e. showing it is NOT a linear transformation). if you're trying to prove that it is, you want to keep it arbitrary.

for c you can just do something like T(-1,0)=|-1|=1 not equal to -T(1,0). thus, it doesn't satisfy the scalar multiplication property.

@surreal gate

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[unkempt swift]

can someone help me with part b

@grim nebula

.close

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[plucky umbra]

ive got 10 mins to do 1hr of my math hmw

[plucky umbra]

someone pls tell me the answer ive tried 4 times

[terse siren]

what?

solve for a

[plucky umbra]

this is the answer format

then the second box is a number

pls help

AHHHH PLSLSSSS

[terse siren]

solve for d