help-27

[valid vector]

Almost there

Note that the leading term is negative

[hardy flower]

-3 is actually 5

And finally, 7 has me confused

[valid vector]

$y=a(x-h)^2+k$, where $(h, k)$ is the vertex, so $y=a(x-2)^2-5$ and thus $-13=a(4-2)^2-5=4a-5$, so $4a=-8$ and $a=-2$, so we have $y=-2(x-2)^2-5$

[hardy flower]

-2

MINUS TWO

Thats what was holding me

[woven radish]

mathisfun

[hardy flower]

It is x MINUS h

[valid vector]

Yes

[hardy flower]

🤦‍♂️

I was solving for a i just made a silly mistake

I can do it tho

[valid vector]

Good

[hardy flower]

I write these questions wrong

Its always the h and k values

I get confused whether h or k is negative or postive

Individually

So could u help with that

Here the vertex was 2,-5

And i wrote it as a(x-2)^2+5

I’ll correct myself since i am adapting and getting better

[valid vector]

Ah

[hardy flower]

Aight

Thats it

Tyy

[devout snow]

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[autumn briar]

i dont understand what they mean by as P inc dP/dt > 0 in the brackets for the top and bottom section

[valid vector]

That is the definition of increasing

[foggy vault]

When the derivative of function P with respect to time is positive, the function P is increasing (graph has a positive slope)

[valid vector]

If $f$ is increasing, then $f'>0$

[woven radish]

mathisfun

[autumn briar]

I got everything until P=10 but i dont understand what the stuff in the bracket is trying to say and idk if i need to write the workings that check the max to get the 2m

[valid vector]

^

[autumn briar]

oh okay but then now i dont get what the second check part is doing

[valid vector]

They did

They 100% did

[foggy vault]

wait what am i blind

oh yes I am

[valid vector]

They're checking to see if that value is a maxima, and thus testing whether (P')'' is <0 at that P value

[foggy vault]

yep I thought they were checking for P being max

didnt realize it was dp/dt they were checking

[autumn briar]

ooh okay

is writing the stuff in the brackets important when writing my working

or isit kind of a given

[valid vector]

It is implied, but you should probably write it out

[autumn briar]

okay thanks guys for the help

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[autumn briar]

wait sorry i realised i didnt get how to go from the 1st check step to the 2nd

[autumn briar]

like how does the d/dt the whole thing become the second step bc i got 2k d2p/dt2 instead of that

[valid vector]

You did not use product rule

[devout snow]

@autumn briar Has your question been resolved?

[autumn briar]

uhm i dont think what i did was right

[devout snow]

@autumn briar Has your question been resolved?

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[primal aurora]

Can anyone help me out ?

[primal aurora]

Find the equation of parabola whose focus is (0,-1) and directrix is x+y-1=0

[winter patrol]

what have you tried

[devout snow]

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[primal aurora]

.reopen

[devout snow]

✅

[primal aurora]

i have assumed a point on parabola i.e (x,y) and then i have joined it with directrix and focus

✅

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[thin geode]

i take first derivative and get( 4x^3 - 4^x *ln 4 )/ (pi sin(pi x)

[hollow ice]

shouldnt there be a cos in the denominator?

you chainruled wrong here

[fallen wolf]

Is it 16?

[full ferry]

Just use L hospital rule right?

[thin geode]

oh yh i got cos

i wrote it wrong

but i dont get right awnser

[thin geode]

no

this is awnser

[hollow ice]

that looks like what comes out when you simplify this using cos instead of sine

can you show your work? Maybe you missed something like ln4 = 2ln2

[thin geode]

alright a sec

here

[hollow ice]

ok? did you put in x = 2 to actually calculate the limit tho?

[thin geode]

ya but i instantly notice thati cannot factor out a 32 like the awnser

because 4^2 is 16

not 32, otherwise the function would work

[hollow ice]

Like I said before, you missed ln4 = 2ln2

[thin geode]

huh

how is ln4 equal to that?

[hollow ice]

4 = 2^2

use basic rules of logarithms

[thin geode]

oh and the ln moveds the 2 down

darn, so i was right all along

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[thin geode]

for some reason i get -tanx/cos x, which is not 1 when x goes to 0

so basically is raise the lower function to e^ln

then i move the limit inside so i dont focus on the e part just the natural log

,rotate

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[thorny cape]

Hello

[thorny cape]

I honestly dont know what im doing

[winter patrol]

start with
f(x) + g(x)
use what's given
then combine like terms

[devout snow]

@thorny cape Has your question been resolved?

[thorny cape]

@winter patrol so

step by step

i start with

(x^2-9x+x+4)(x)

then i get x^2-8x+4

what do i do with that extra x at the end

[winter patrol]

you shouldn't have an extra x at the end

[thorny cape]

in the problem

its (f+g)(x)

what do i do with that x

where does that come into play

[winter patrol]

(f+g)(x) is notation for
f(x) + g(x)

[thorny cape]

oo

so the answer for that would just be

[winter patrol]

replace those f(x) and g(x) with what you're given

[thorny cape]

^

?

[winter patrol]

and simplify

yes

[thorny cape]

okay okay

awesome thank you!

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[primal shadow]

I’ve been thinking about this question for a while but can’t figure out how to mathematically work it out? The question requires me to show the full working out process but I don’t know how to really do that

[pseudo basin]

can you imagine like a timelapse of a clock going through 12 hours

[primal shadow]

i did come to the conclusion that it would be 22, i just don’t know how i can figure it out mathematically

🙀 🙀 🙀

[pseudo basin]

in 12 hours, the hour hand makes one full revolution around the clock face but the minute hand makes 12

so the minute hand will overtake 11 times

[primal shadow]

wow i didn’t even think of it that waay

thank you

sorry these questions are pretty easy

😼 😼 tysm

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[winged timber]

U0=7
Un+1=4Un-12
and Vn=4Un-4
prove that Vn is a geometrical sequence with a ration of q=4

[winged timber]

the teacher did Un+1=Un+1-4 why he needs to count Un+1?

[olive snow]

Tu veux dire Vn+1 ?

[winged timber]

yes

[olive snow]

Pour avoir le rang suivant

Et exprimer Vn+1 en fonction de Vn

Si tu as pour tout n cette formule

Alors tu l'as pour tout n+1

Tu vois ?

[winged timber]

yeah i understand what u said but hows that going to help him find q?

[olive snow]

Vn+1 = Un+1 - 4
Vn+1 = 4Un - 12 - 4

= 4Un - 16

Factor by 4

Oh its 4Un+1 - 4

Mb

But its the same thing

[winged timber]

he did the same steps as u did rn and than said 4Vn
alors (Vn)est une suite geometrique de raison q=4
but i didnt understand how 4Vn means that q=4

[olive snow]

Vn+1 = 4*Vn right ?

[winged timber]

yes

[olive snow]

Une suite geometrique c'est une suite dont la relation de reccurence s'écrit Vn+1 = a*Vn où a est réel

on appelle 'a' la raison de la suite

[winged timber]

oh i forgot the "terme generale d'une suite geometrique"

thx

[olive snow]

Non relation de recurrence ici

Le terme général c'est autre chose

Pour tout n, tu as Vn = v0 * q^n

v0 terme initial

q la raison

[winged timber]

so Vn+1=a*Vn is another formula of the geometrical sequence?

[olive snow]

C'est la relation de reccurence

C'est deux manière de la définir

[olive snow]

Celle là est appelé explicite

[winged timber]

THX

[olive snow]

Pas de souci

[olive snow]

Sache que ce sera toujours la même méthode

Pas de piege

[winged timber]

alr i have another problem in the next question

[olive snow]

Oui

[winged timber]

it says
exprimer Vn puis Un en fonction de n

[olive snow]

Et bien Vn tu fais la forme explicite

[winged timber]

Vn=V0*q^n?

how do i use it

not how

i meant why

[hollow pulsar]

cause Vn is also equal to 4Un - 4

tu obtiens l'égalité:
4Un - 4 = V0 × qⁿ

et tu résous pour Un

tu la trouve en fonction de n

[devout snow]

@winged timber Has your question been resolved?

[winged timber]

in the correction of the exercice the teacher wrote
V0=U0-4=7-4=4
Vn=V0q^n=34^n
Un-4=Vn
Un=Vn+4=3*4^n+4
i didnt understan this

[hollow pulsar]

mais est ce que Vn = 4Un - 4 ou Un - 4

[devout snow]

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[winged timber]

.reopen

[devout snow]

✅

[winged timber]

he determined that

he said in the first question that Vn=Un-4

[hollow pulsar]

oh, u wrote Vn = 4Un - 4

i got confused

so, the general term of a geometric sequence is given by:
Vn = V0 × qⁿ where q is the ratio of the geometric sequence

[winged timber]

yeah

[hollow pulsar]

cela est comment on peut exprimer Vn en fonction de n

donc, premièrement, il a calculé V0

V0 = U0 - 4 = 7 - 4 = 3

alors: le terme général de Vn est:
Vn = V0 × qⁿ = 3 × 4ⁿ

on a exprimé alors Vn en fonction de n

maintenant pour exprimer Un en fonction de n

on a Vn = 3 × 4ⁿ

et on a Vn = Un - 4

alors: Un - 4 = 3 × 4ⁿ

et par suite: Un = 3 × 4ⁿ + 4

c bon

[hollow pulsar]

ca c c'qu'il a fait votre prof

[winged timber]

so

Un=3*4^n+4 is the answer of this question

[hollow pulsar]

yes

[winged timber]

i didnt undestand the question

[hollow pulsar]

Exprimer Vn puis Un en fonction de n

[winged timber]

SO

[hollow pulsar]

it asks you to write Vn and Un in a form such that theres only n

in the expression

[winged timber]

aaaa

understood

[hollow pulsar]

no Un, no nothing else

just n

[winged timber]

huh

so u need to write n=?

[hollow pulsar]

no

u were given Vn = Un - 4

[winged timber]

yeah

[hollow pulsar]

thats in terms of Un

not n

so u want to write Vn such that Vn = f(n)

[winged timber]

so i need to write Vn= how much n's

[hollow pulsar]

not how much n

but like

an expression that only has the letter n in it

[winged timber]

the question is not clear but its ok i understood the basic thing

so i need to explain Vn en fonction de n and not Un

[hollow pulsar]

u should understand it tho, its a famous type of question asked in these exercices

[hollow pulsar]

oui

[winged timber]

mhm

[olive snow]

C'est la forme explicite ici qu'il faut utiliser

[winged timber]

he said than
S=v2+v3 jusqu'a Vn so in here i need to do the sum formula right?

[winged timber]

thx

[olive snow]

Pour les suites géométriques oui

[winged timber]

question says
ecrire S en fonction de n

[winged timber]

which is S=U0*(1-q^n/1-q)

[olive snow]

Sauf que tu commence depuis v2

[winged timber]

i dont have V2 so i need to determine it and than apply the formula and thats it riight?

[olive snow]

Utilise la formule et retire v0 et v1

Ça fait la somme pour v2 jusqu'à n

La formule te fait calculer ca : (V0 + v1 + v2 + ... + vn)

Donc

[winged timber]

yeah bc they said S starts from V2, i started to understand this thank u bro

[olive snow]

Si tu lui retire v0 et v1

Ça fait la somme de v2 à vn

[devout snow]

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[rustic barn]

suppose Xn and X are real valued rv. Then show that Xn converges in distribution to X if and only if E[F(Xn)] goes to E[F(X)] for all continuous CDF F.

im stuck in the part: expectation convergence implies convergence in distribution

[jaunty mantle]

Uh what do you have to work with ie. what’s the definition of convergence in distribution

And what does “E[F(Xn)] goes to E[F(X)]” mean

[devout snow]

@rustic barn Has your question been resolved?

[rustic barn]

portmanteau's theorem

[rustic barn]

lim n to infinity Expectation of F(X_n) = expectation of F(X)

[devout snow]

@rustic barn Has your question been resolved?

[devout snow]

@rustic barn Has your question been resolved?

[devout snow]

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[lofty verge]

How do I solve this?

[lofty verge]

I assume there is some formula that can be used

[valid vector]

Let $x=\frac{1}{5+\frac{1}{5...}}$. Then $1+x=\frac{1}{5+x}$

Ah wait

one second

[woven radish]

mathisfun

[valid vector]

There

[lofty verge]

I see

[drifting mauve]

quadratic

then make the quadratic solution in its lowest term

[valid vector]

$x^2+6x+5=1$ then just use regular quadratic stuff

[woven radish]

mathisfun

[drifting mauve]

and obtian the values

[valid vector]

Make sure you do not choose the one with negative value

[lofty verge]

so then $(x+1)(x+5)=1\x^2+6x+4=0\x=-3+-\sqrt{5}$

[woven radish]

UCYT5040

[valid vector]

Good

You can use $\pm$

[lofty verge]

why would it be the negative one tho?

[woven radish]

mathisfun

[valid vector]

It would be the positive one

[lofty verge]

oh i misread above

[valid vector]

Since everything in the fraction is positive

You are good

[lofty verge]

oh yeah so then final answer is 3+5+1=9?

but wait thats not right

the answer key says its 34

[valid vector]

Hmm

[valid vector]

This equality is true, I know so

Or did I mess up

[spring salmon]

Why is it 1+x on the left instead of x

[valid vector]

I did lmfao

[valid vector]

Yeah I was being stupid

[cerulean compass]

if we take the whole thing as x we'll get x = 1 + 1/4+x

[valid vector]

Looked at the value wrong

$x=\frac{1}{5+x}$

[woven radish]

mathisfun

[valid vector]

$x^2+5x-1=0$

[woven radish]

mathisfun

[valid vector]

$x=\frac{-5\pm\sqrt{25+4}}{2}$

[woven radish]

mathisfun

[valid vector]

$x=\frac{-5+\sqrt{29}}{2}$

[woven radish]

mathisfun

[cerulean compass]

😭 no

take the whole thing as x

[valid vector]

$1+x=1+\frac{-5+\sqrt{29}}{2}$

[woven radish]

mathisfun

[valid vector]

$1+x=\frac{-3+\sqrt{29}}{2}$

[woven radish]

mathisfun

[valid vector]

@lofty verge

[lofty verge]

how?

wait nvm

forgot how fractions worked for a second

that makes sense

thank you!

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[untold echo]

Q2: You are given functions f and g such that $f(n) = O(g(n))$. Is $f(n) * log_2(f(n)^c) = O(g(n) * log_2(g(n)))$? (Here C is some positive constant.) You should assume that f and g are nondecreasing and always bigger than 1.

[woven radish]

Wolverine

[untold echo]

Can someone explain this?

(This is from Asymptotic Analysis - Design and Analysis of Algorithms)

[winter torrent]

might help to know that log(a^b) = b log(a)

[devout snow]

@untold echo Has your question been resolved?

[untold echo]

$f(n) * clog_2(f(n)) = O(g(n) * log_2(g(n)))$

[woven radish]

Wolverine

[untold echo]

I understand that but I still do not fully get it?

[winter torrent]

definitely looks closer

[untold echo]

Is this the solution?

$f(n) * clog_2(f(n)) = O(g(n) * log_2(g(n)))$
because c is constant,
then the equation is true

[woven radish]

Wolverine

[winter torrent]

i'm actually not sure if it's true or false

[untold echo]

I already know that the answer is true but I am not sure if this is all thats needed to understand the solution

[winter torrent]

yeah so then you'll want to refer to the defn of O(....)

[untold echo]

Upper bound (worst case)

• Assuming f(n) and g(n) are non-negative functions:
  • $f(n) = O(g(n)) \iff f(n) \leq c*g(n)$ for all values of n where $n \geq n_o$ and $c$ and $n_o$ are constants.

[woven radish]

Wolverine

[winter torrent]

would recommend using a letter that isn't c for that

or replacing the original c with k

[untold echo]

you are right but why is that?

[winter torrent]

why use a different letter?

because they mean different things

[untold echo]

yeah like how does it help

[devout snow]

@untold echo Has your question been resolved?

[devout snow]

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[granite anchor]

can someone help me with factoring 3x^3 + 9x^2 + 21x?

[granite anchor]

im confused on how to do trinomials that have multiple exponents

[iron kindle]

what common factor do they all have

[granite anchor]

3

[iron kindle]

yes, so how can you factor that out?

[granite anchor]

i have no idea

[iron kindle]

9=3*3 right?

and 21=3*7?

[granite anchor]

yeah

so 3 and 7?

[iron kindle]

so if i write 3(x^3+3x^2+7x), would that make sense that its equal?

[valid vector]

Notice that there is an x common to all terms

[granite anchor]

yeah that looks right

[iron kindle]

okay nice

but there is also a second common term

what could that be?

[granite anchor]

OH so i can turn it into 3x^2 +9x +21?

[valid vector]

x(3x^2+9x+21), yes

[granite anchor]

here lemme see if i can take it from there

cause i know how to do the M A N method

[valid vector]

The hell is that

[granite anchor]

find what multiplies to 21 and adds to 9

[valid vector]

Ok that

Wait

Not right here

You need to consider 3x(x^2+3x+7). Do you see why?

[granite anchor]

because 3 is common to all of them?

[valid vector]

Yes

[granite anchor]

ok i think im starting to understand

[valid vector]

Bro is understanding it now

[granite anchor]

would it be something like 3x(x+3)(x+7)? or do i need to figure out what multiplies to 7 and adds to 3 first

[valid vector]

||Actually this is not factorable anymore||

[granite anchor]

oh so the furthest you can go is 3x(x^2+3x+7)

[valid vector]

Yes

[granite anchor]

ok got it

what about something like 27x^2-3x^3?

[iron kindle]

||technically you can but its just not a clean answer||

[valid vector]

||Yeah I think this is with respect to integers as factors so||

[valid vector]

What is the common term

[granite anchor]

3

so 3x(x^2 - 9x)?

or 3x(9x-x^2)

[valid vector]

One more common term

[granite anchor]

isnt 1 the lowest we can go?

3x^2(9-1)?

3x^2(9-x)?

[valid vector]

W

[granite anchor]

awesome

what about something like 9x^2 - 16?

[valid vector]

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

[woven radish]

mathisfun

[granite anchor]

?

im not too sure what that means

how would i find the ab that cancels out

it would start with (9 - right?

[valid vector]

$(3x-4)(3x+4)$

[woven radish]

mathisfun

[granite anchor]

OH

same thing if the x^2 is on the other side like 32-50x^2?

[valid vector]

Yes

[granite anchor]

got it

wait but what if they dont have simple square roots? like 9 and 16 is 3 and 4 but 32 and 50 dont have that

or am i just not seeing it

2(8-5x)(8+5x)?

or 2(4-5x)(4+5x)?

what about (2 - a)^2 - 81?

[devout snow]

@granite anchor Has your question been resolved?

[frigid iron]

$a^2-b^2=(a-b)(a+b)$
so what would be a and what would be b in this equation

if it isn't a simple square root then you'll just have it not neat
so like x^2-32 = (x-sqrt(32))(x+sqrt(32))

[granite anchor]

would a be 2 and b be 81?

[frigid iron]

no

b is ^2

[granite anchor]

the exponent?

[frigid iron]

so it`d be 9

[frigid iron]

just trying to say you can`t use 81 as is and you have to put it's sqrt as b, so 9

does that make sense?

[granite anchor]

yes but then what do i do with the (2-a)^2?

[frigid iron]

well the equation is
a^2+b^2 right
and we have b so all we are missing is a^2

so what would a^2 be

[granite anchor]

4? like 2^2=4?

[frigid iron]

okay so like, we want a^2+b^2
so a^2+b^2=(2-a)^2-81
and we know b^2=-81
so a^2=(2-a)^2
right?

so then what's a

[granite anchor]

-2?

the a is throwing me off

[frigid iron]

let's say we say it's -2

then we have.... 0=(2-a)^2-4

[frigid iron]

try isolating a in a^2=(2-a)^2

just ignore the, context just try to find what a would be there

but , we'll say it`s (2-q)^2 instead instead of being a
so what is a^2=(2-q)^2
@granite anchor

[granite anchor]

still here just thinking

[frigid iron]

let`s say you have, 2y=2(x+2) how do you isolate y

you would have to reduce it right?

[granite anchor]

yeah

[frigid iron]

so you can reduce it by dividing by 2 right?

so then y=x+2

[granite anchor]

yeah then you would have y=(x+2)?

[frigid iron]

yeah

[granite anchor]

yeah

[frigid iron]

and we have...a^2=(2-q)^2

how can we reduce a

[granite anchor]

a=2-a

[frigid iron]

yes

[granite anchor]

1?

[frigid iron]

you have to understand that, a in the first part and a in the second part is not equal

it's just the variables being named similiarly

[granite anchor]

you know we're factoirng right

[frigid iron]

yes

[granite anchor]

gotcha

[frigid iron]

so then we had (2-a)^2-81
a^2-b^2=(a-b)(a+b)

and
a = 2-a
b= 9

so then's how can we factor (2-a)^2-81

[granite anchor]

(a+9)(a-9)?

[frigid iron]

what`s a

[granite anchor]

2-a

[frigid iron]

yes

so then it's (2-a+9)(2-a-9)

does that make sense?

[granite anchor]

ohhh

[frigid iron]

just make sure to get rid of the 2- so it's really (-a+11)(-a+7)

[granite anchor]

where did the 11 and 7 come from?

wait

[frigid iron]

simplified the equation

2-a+9=-a+2+9

[granite anchor]

2+9 2-9 nvm

[frigid iron]

yeah

[granite anchor]

ok i understand now

thanks

.close

[devout snow]

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[valid barn]

Quick question
a(b/c)=de, could be written as
a=de/(b/c), right?

[valid vector]

Put parenthesses please

[low coyote]

a/b/c can be ambiguous

[valid barn]

And say if we have
500/3•x=760y•500x

[valid vector]

If you mean $\frac{a}{(\frac{b}{c})}=de$

[woven radish]

mathisfun

[valid barn]

oh mb

[valid barn]

Yes

[valid vector]

Yeah the logic doesn't check out

Should be $a=\frac{b}{c}\cdot de$

[woven radish]

mathisfun

[valid barn]

OH

wait

I mistype

[valid vector]

Ok

[valid barn]

meant to a(b/c) not a/(b/c)

[valid barn]

Anyway this could be wrote as
x=760y/(1/3),?

[valid vector]

So is this $\frac{500}{3}\cdot x=760y\cdot 500x$

[woven radish]

mathisfun

[valid barn]

Yes

[valid vector]

Yes

[valid barn]

Ight ty

[valid vector]

Which is just 760*3y=2280y

[valid barn]

.close

[devout snow]

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[devout snow]

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[gleaming socket]

!status

[devout snow]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[wind mason]

Multiply by conjugate

[solar goblet]

[jolly pulsar]

it didn t work

[solar goblet]

why not divide both sides by x

[exotic hollow]

I think the limit is dne

Nvm

Hey @jolly pulsar I think you should do first is divide by the highest denominator power

$\frac{1}{x^2}$

[woven radish]

nerfLeander

[exotic hollow]

Both sides of the function

[jolly pulsar]

i ll try it

[exotic hollow]

Alr then tell me watchu get

[jolly pulsar]

ok

[exotic hollow]

Goodboy 😏

[devout snow]

@jolly pulsar Has your question been resolved?

[wind mason]

Hmm.

Have you tried dividing by |x|?

In both the numerator and denominator.

[devout snow]

@jolly pulsar Has your question been resolved?

[devout snow]

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[formal venture]

whered i go wrong?

[plush bronze]

why are you sure its wrong?

im pretty sure its correct

[formal venture]

the homewokr is lol

[plush bronze]

think its cause they wanted a decimal answer

[formal venture]

yup

thank you

just submitted and got an 100 after i fixed some otehrs

.close

[devout snow]

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[obsidian glen]

am i visualizing this correctly

[spring salmon]

yes

[fossil locust]

yes and now this is the next step

[obsidian glen]

ooo powerpoint

can r(x) just be x in this case

[fossil locust]

yep

[obsidian glen]

because its unknown

yay

do i get a cookie

[spring salmon]

no cookie for u

I eated them all.

[fossil locust]

okay now the height is the most important part

when you draw a horizontal line to the curve from some point on the y-axis

you want the height to be inside the region

[obsidian glen]

um does h(x) be x^(3/2) with something to do with 8

since it can only go up to 8

[fossil locust]

yes, something to do with 8

[obsidian glen]

but no x^3/2

[fossil locust]

and you need this too

[obsidian glen]

(8-( x^3/2) would be wrong?

[fossil locust]

that's correct!

if you put this all together

[obsidian glen]

So the distance is still the same as disk/washer method

[fossil locust]

uh that's different

so how I remember it is, disk/washer method has the same d(something) as the axis

so the disk/washer method would have dy instead

the shell method has the opposite one, hence we have dx

so you should pay attention to the limits

x ranges from 0 to 4

[fossil locust]

but yeah I mean the r(x) = x in the shell method

is indeed the same as the disk method

except in the disk method you can't have x, so you need y^(2/3) = x instead

[obsidian glen]

i been doing washer method using dx ;w;

[fossil locust]

it depends on the axis of revolution!!

[obsidian glen]

woosh

thank goodness

[fossil locust]

you need to really carefully read and see if the axis is horizontal or vertical

[obsidian glen]

for wsher/ or in general

[fossil locust]

in general

for all volume of revolution problems

remember this was a shell one

[obsidian glen]

i been doing washer/disk on x axist, havent dont it on y. first time im doing this on y and its with the shell method

so can washer/disk be on y and shell on x?

[fossil locust]

yes

[fossil locust]

these two cases are for a vertical axis of revolution

the other case you forgot, shell on y, is for a horizontal axis

[obsidian glen]

if i want pratice and learn this, do u have a quick ex of this or golook at youtube

[fossil locust]

go look on YouTube

but also check out Paul's Math Notes

[obsidian glen]

what would this be called shell/disk/washer method on vertical?

[fossil locust]

yeah, look for vertical axis of revolution / y-axis

vertical can also be like x = 5 or something

it's not too different but you have to watch out; don't just blindly apply something

[obsidian glen]

ill keep that in mind thank you

any idea what does invalid implied multiply mean on a nspire cx II

my calator is giving an error message when i imput it so i decided to do the math by hand and i got something simiar but its off

the correct answer is 384pi/7

[devout snow]

@obsidian glen Has your question been resolved?

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[rocky marlin]

Is my formula correct for d?

[fossil locust]

,rotate

[fossil locust]

yes, that is indeed correct

you are missing brackets around the (n - 2) though

$\frac{180(n-2)}{n}$, use a fraction and it looks a bit better also

[woven radish]

south

[rocky marlin]

oh so its that not what i put? also how would you solve for the sides given 1 interior angle?

[fossil locust]

essentially for an n-sided polygon, you can draw (n - 2) triangles, each with sum of angles = 180 deg

[fossil locust]

you can't have a 1 sided polygon

or a 2 sided polygon

[fossil locust]

I get what you mean but you have a mathematical communication issue with your notation

[rocky marlin]

no like how do you solve for the sides given one angle interior

[fossil locust]

ohhh

[fossil locust]

say $\frac{180(n - 2)}{n} = 170 \implies 180(n - 2) = 170n$

[woven radish]

south

[rocky marlin]

how does that happen?

[fossil locust]

multiply both sides by n

[rocky marlin]

ok i just dont why you would do that

[fossil locust]

you want to solve for n right?

n being the number of sides

[rocky marlin]

ye its just i find it hard to understand why you do what you do in math

[fossil locust]

now 180(n - 2) = 170n is a linear equation!!

it becomes 180n - 360 = 170n, distributive law

[fossil locust]

hmmm

yeah we do tend to choose steps that bring us closer and closer to the answer, in not-obvious ways

but you should recognise common types of equations, so a linear equation is the most basic type

quadratic equations are a pain to solve actually
and don't get me started on cubic equations or any higher degree polynomials

a linear equation only has n and other numbers

a quadratic equation can have n^2, n, and other numbers

a cubic equation now can have n^3, n^2, n, and other numbers

[rocky marlin]

k ye its just i struggle understanding why in math

[fossil locust]

that's a very good thing to do actually

be curious, try to understand things by yourself after looking through materials (your textbook, online as well)

[fossil locust]

this topic is actually related to rational functions

in say maybe 2 years or so you might see $\frac{7x + 9}{4x + 3}$, and those functions have a special kind of graph

[woven radish]

south

[fossil locust]

the keyword for this is asymptote

but then if you just want to solve $\frac{7x + 9}{4x + 3} = 2$, you can just do $7x + 9 = 2(4x + 3)$ after multiplying both sides by $4x + 3$

[woven radish]

south

[fossil locust]

and now it's not so hard again

[fossil locust]

so if you think logically, the interior angle of a regular polygon is always increasing with the number of sides

but it can never reach 180 degrees exactly, can it?

that would be a straight line, and no two adjacent sides can make a straight line

but the interior angle does get super super close to 180 degrees

say with 100 sides

,calc 180 * (100 - 2) / 100

[woven radish]

Result:

176.4

[fossil locust]

or with 1000

,calc 180 * (1000 - 2) / 1000

[woven radish]

Result:

179.64

[fossil locust]

or with 1,000,000

,calc 180 * (1000000 - 2) / 1000000

[woven radish]

Result:

179.99964

[fossil locust]

so something that gets infinitely close, but never exactly equals

that's called an asymptote

[devout snow]

@rocky marlin Has your question been resolved?

[devout snow]

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[restive river]

is this correct

[smoky nimbus]

Do you know what a line of reflection is?

[restive river]

yea

[smoky nimbus]

And what is it?

[restive river]

its lkke

a mirror image

[rocky marlin]

k tysm

[restive river]

or a line that create one atleast

[smoky nimbus]

Yeah it's the line that creates the mirror image

So it flips over that line

Why is your line vertical?

[restive river]

because the shape is vertical

[smoky nimbus]

It has nothing to do with the shape

[restive river]

ok

[smoky nimbus]

It has to do with what the mirror image looks like

[restive river]

ok

so what do i do

[smoky nimbus]

Like for example, notice how the line of reflection is in between the two shapes?

[restive river]

oh

so where would i put the end points

at the end?

[smoky nimbus]

It's just a line, any two points makes a line. You can pick whatever points you want

[restive river]

so is it js this then

[smoky nimbus]

Try it and see

[restive river]

thanks brodie

🙏

i didn’t know that

also i have a eoc tmr what are some stuff i can do for practice

.close

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[unique wyvern]

how do i make r the subject

[supple knot]

Multiply both sides by the denominator first

[pseudo basin]

current progress?

if none, seconding riemann.

[unique wyvern]

none im completely lost lol

[pseudo basin]

ok then i am seconding what riemann said.

[unique wyvern]

how does that help though

[pseudo basin]

do it and show us what happens

[unique wyvern]

V(R-r)=2R

?

[pseudo basin]

2rR?

how did an r appear out of thin air on the right hand side?

[supple knot]

Do you think the semicolon means multiplication

[unique wyvern]

oops that was a typo

[pseudo basin]

V(R-r) = 2R then

yeah ok good

[unique wyvern]

i accidentally wrote the lowercase, and then forgot to delete it before adding the capital

[unique wyvern]

okay uhhhh

divide by V?

[pseudo basin]

yes that's a good step

[unique wyvern]

and then

uh

-R

[pseudo basin]

wait

one thing at a time

show what you get after dividing by V

[unique wyvern]

R-r=2R/V

[pseudo basin]

ok

and then after subtracting R?

[unique wyvern]

so to get rid of the R on the left i minus R

-r=2R/V-R

[pseudo basin]

those brackets are redundant but yes

now you are one step away

[unique wyvern]

oh wait yeah i didnt think of that

i was just thinking bc the fraction has to be seperate

[pseudo basin]

\verb|2R/V - R| \textbf{never} means $\frac{2R}{V-R}$; \ that would have to be typed as \verb|2R/(V-R)|

[woven radish]

Ann

[unique wyvern]

yes right

[pseudo basin]

but putting spaces around the minus sign doesn't hurt

[unique wyvern]

i knew that

i think

[pseudo basin]

anyway -r = 2R/V - R

[unique wyvern]

that wouldve been a good idea

[pseudo basin]

you are one step away

[unique wyvern]

multiply by -1?

surely theres a way to simplify that

OH WAIT

wait no

idk

how does one simplify this

[pseudo basin]

bad notation

this looks like subtracting 1 instead of multiplying by -1

[unique wyvern]

yeah i forgot it at and just added it at the end

[pseudo basin]

better $r = -\paren{\frac{2R}{V}-R}$

[woven radish]

Ann

[unique wyvern]

yes okay got it

hollon lemme rewrite

okay

done

now

how on earth can i simplify that

oh waity

distrib

so -2R/V + R

?

is that right

or

am i lost again

[pseudo basin]

yes that's correct

[unique wyvern]

okay right

[unique wyvern]

am i able to add the +R to the numerator?

[pseudo basin]

what do you mean

[unique wyvern]

like could that become

(-2R+R)/V

[pseudo basin]

no

[unique wyvern]

shucks

oh right yeah bc different denoms

[pseudo basin]

if you wanted to put it as one fraction the correct result would be (-2R+VR)/V

[unique wyvern]

uhhh

right yes

yes that tracks

okay

[unique wyvern]

how can i simplify this further

[supple knot]

Why do you want to

[unique wyvern]

... so its simpler?

[supple knot]

Why do you think it can get simpler

[unique wyvern]

because it dosent look very simple ig

[supple knot]

You want like a magical answer like just R?

[mental mica]

well you could combine the terms ig

but like

why

[unique wyvern]

wouldnt one fraction be simpler than a mixed number

[mental mica]

sure ig

You can combine them to one fraction

they just need to have a common denominator, then you can combine

and that’s probably the simplest it’ll get

[unique wyvern]

could this be simplified further

it looks like it could i think

maybe

[pseudo basin]

it could but not worth the effort

[unique wyvern]

but wouldnt it be simpler

oh god thats not even the right answer

.close

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[hushed plover]

Equation of tagent line y=50x-125

Then i integrate from 0 to 5 of int{(5x^2)-(50x-125)dx

[hushed plover]

i get 625/3 but its not right, is my tangent line wrong?

[pure kelp]

how did you get that as the tangent?

[hushed plover]

y-y1=m(x-x1)?

oh dear

[pure kelp]

you differentiate both sides to get the tangent to the parabola

the slope of the tangent*

so you did all that?

[hushed plover]

yeah slope at 5 is 10 no?

[pure kelp]

no

[hushed plover]

f'(5) = 10(5) = 50

[pure kelp]

its 50 at x=5

f'(5) = value of slope at x=5

[hushed plover]

yoops i corrected myself afterwards but yeah

yeah its 50

then i use y-y1=m(x-x1)

[pure kelp]

yup

[hushed plover]

i get y-125= 50(x-5)?

y = 50x - 125

[pure kelp]

then find the x intercept

[hushed plover]

125/50?

what does that do for us

oh i see

[pure kelp]

yes

[hushed plover]

its asking for above the x-axis

i calcuated udner too

[pure kelp]

this will be the upper bound

[hushed plover]

ye let me try now

[pure kelp]

integrate ydx from 0 to 125/50

[hushed plover]

yes it worked thank you

i see why i needed the x intercept

.close

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[sweet cedar]

Hello everyone I got stuck on #24 and I’m not sure how to go about this LMK

[sweet cedar]

Also I apologize for the bad handwriting

What would cot^2t integrate to?

[cerulean compass]

write cot^2x as cosec^2x - 1

[sweet cedar]

Ohhh and then integrate that?

[cerulean compass]

yep

integral cosec^2x is -cotx

[sweet cedar]

Ohh okay I understand

Thank you so much

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[mossy falcon]

Hey, I have a question regarding geometry and proving that a specific angle is 90 degrees. I am not going to post the question because it is part of a competition, I just have a General question:

[mossy falcon]

The Figure is give in this style without any Angeles or lengths: The circle kA touches k at point C, the line MA at point D it goes on for quite a while

Am I allowed to measure the length of MA for example to use the intercept Theorem or do I have to prove it in a different way chasing a lot of angles?

thanks in advance!

<@&286206848099549185>

[devout snow]

@mossy falcon Has your question been resolved?

[winter patrol]

not allowed to measure anything

stick to established theorems

[mossy falcon]

ok, so i cant use things like AB/AD=BC/DE, that's a pity, because I already tried like everything to chase this angle, but maybe i try to proove that it cant be not equal to 90 degrees instead.

Are there some theorems that are maybe not that common on which i should have an additional look?

[noble acorn]

Do you get explicit values in your question?

[mossy falcon]

no, just descriptions where things intercect and a picture of the Figure.

essentially i have to prove that two links are parralel

[noble acorn]

Are there any circles/semicircles involved in the question

Or intersecting secants or chords

[mossy falcon]

circles and lines and Triangels are in a semicircle, i was able to create a 90 degree angle with the Theorem of thales, but i cant prove that this created line is parallel to the line of the question

aand Yeah also intercecting secants but i wasnt able to use them.

[noble acorn]

Check if there is another right angle along a transversal from the already proven 90* angle?

[mossy falcon]

The problem with the transveral is that i cant prove that the angle when intersecting the line from the question is the same as the angle when it is intersecting my line i created with the Thales Theorem

[noble acorn]

Consider cyclic quadrilaterals, use alternate interior angles(via inscribed angles), look for similar triangles.

Maybe thales’ converse?

[mossy falcon]

thanks i will try these. I will close this for now, can i maybe later DM you when i finished trying out these approaches?

[noble acorn]

Sure

[mossy falcon]

thanks

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[pastel sphinx]

Why is this working wrong? the answer is supposed to be tan(a/2)

[devout snow]

@pastel sphinx Has your question been resolved?

[pastel sphinx]

<@&286206848099549185>

[kind parrot]

sorry cant read ur handwriting

[pastel sphinx]

its that bad? 🥲

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@pastel sphinx Has your question been resolved?

[valid vector]

I think someone already answered your post in other math server

Their method is good so i don't wanna spoil it

[pastel sphinx]

.close

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[sinful fable]

Why cant i apply lhopital after factoring out n?

[sinful fable]

Cause doing that nets 1/2

[fossil locust]

L'Hopital is just for a limit, not a limit of an integral

e.g 1/n goes to 0 as n goes to infinity

but the integral of 1/n from 0 to infinity is +infinity, i.e diverging

[sinful fable]

Wait but the integral here converges right? Also the course/series im watching does apply it on integrals

And makes sense why wouldnt you

Integral converges to 0 right*

Oh aait

Aaah

Got it

No i dont think the integral converges to 0

Thats the uhh issue

Like it behaves like 1/x right near 0 so

You cant say anything

Ok

Thanks

One more doubt

This makes sense

I get what this is doing

But what if i factor out x^n and then take the limit

One sec ill write it

Nope nvm cleared

Sorry

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[quasi ravine]

Is this correct?

[devout snow]

@quasi ravine Has your question been resolved?

[foggy ermine]

It is correct.

[quasi ravine]

ok thanks

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@quasi ravine Has your question been resolved?

[umbral torrent]

!done

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[dawn lava]

,,cos(\theta)tan(\theta)

[woven radish]

☠ cj Σ

[dawn lava]

i just need to simplify it

[pseudo basin]

do you know the definition of tan?

[tropic skiff]

can you try rewriting tan in terms of sin and cos

[dawn lava]

oh my god

i might actually

like

crash out

[tropic skiff]

lol did you get it

[dawn lava]

i was writing tangent as cot

ty

it just cancels out right?

[tropic skiff]

!done

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[dawn lava]

ty

.close

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[west turtle]

I need help finding the integrating factor. I identified M(x,y)=2x^2y and N=-5x^3 and took their partial derivatives. I'm having trouble with the next steps afterwards

[west turtle]

actually wait i might've figured it out

yep i found the integrating factor

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[somber mulch]

hey could someone help me find out how to make this into the form of the power series of e^x, i know it is from the answer key but im getting weird values and idk where im going wrong

[somber mulch]

bottom equation should have x^4 /24 not x^4 /12 mb

<@&286206848099549185>

<@&286206848099549185> please

[muted mural]

I think you were supposed to subtract 1 when calculating y_2

[somber mulch]

ohh

[muted mural]

Cause f didn't change

[somber mulch]

yeah i had that just come up in another problem thank you