help-42

[remote mural]

do you understand this definition?

[dapper moon]

yes

[remote mural]

perfect

do you think this series converges or diverges? (and why?)

[dapper moon]

diverges, because ~ (n^2*n^(1/2))/(n*n^(3/2)) = 1

[remote mural]

good

what is a very VERY popular divergent series that is also EASY to work with?

it's probably one of the first ones you learned about in calculus 2

[dapper moon]

1/n

harmonic series

[remote mural]

yes

indeed

how can you use this definition then? @dapper moon

[dapper moon]

so I did lim n->∞ an/bn with bn being 1/n. it's ∞?

[calm coral]

@dapper moon Has your question been resolved?

[dapper moon]

I'm still clueless I don't like series

[vernal valley]

imma help u

Lets assume the oppsite

let a(n) be a siries that approaches infinity when n approaches infitiy

let b(n) be a siries that approaches constant c , such that c is positive, finite and belongs to to the set of real numbers

t.f limit (an/bn) as n approcahes infinty approaches 0 meaning not possitve so we ruled out the first option

now the second option

let b(n) be a siries that approaches infinity when n approaches infitiy
let an) be a siries that approaches constant c , such that c is positive, finite and belongs to to the set of real numbers

t.f limit (an/bn) as n approcahes infinty approaches inifitiy meaning not possitve so we ruled out the second option

now lets assume minus

let a(n) be a siries that approaches infinity when n approaches -(infitiy)
let b(n) be a siries that approaches constant c , such that c is negative , finite and belongs to to the set of real numbers

notices the the negative cancels out because c must be possitve

let b(n) be a siries that approaches infinity when n approaches -(infitiy)
let a(n) be a siries that approaches constant c , such that c is negative , finite and belongs to to the set of real numbers

notices the the negative cancels out because c must be possitve

t.f both a(n) and b(n) must divrige or converge to cancel each other out (intuitivly)

@dapper moon any questions?

[calm coral]

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[remote mural]

From a deck of 52 playing cards, how many different 5-card hands
(a) are possible? (b) include only cards of the same suit? (c) include 3 black and 2 red cards? (d) include at least 1 heart?

[remote mural]

(A) C(52,5)

Now the rest I don’t know what to do

There are 4 suits for (b)

Clubs, diamonds, hearts and spades

So how can I choose a 5 card hand with the same suit

[rustic osprey]

Consider the number of ways to pick 5 cards for each suit

Then ||multiply by 4||

[remote mural]

So job 1: choose a suit

That’s 4

Then job 2: choose 5 cards within the suit

How many cards r in a suit tho?

13?

So I get 4 x c(13,5)?

[rustic osprey]

Yeah

[remote mural]

Ok

So for (c) now

Let me try to solve it myself and you tell me if it is good

[rustic osprey]

I gotta dip but I’ll come back later if nobody else answers

[remote mural]

C(26,3) times C(26,2)

For (c)

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[rustic osprey]

Claim

[rustic osprey]

Yup that’s right

👍

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[gusty summit]

LA question:

P_2(R) has iner product: <p.q>= int_0^1(p(x)q(x))dx

v_1=1 and v_2=sqrt(12)(x-½) are orthagonal unitvektors.

Find a base for this innerproduct room.

[gusty summit]

So I assume the base is gonna need 3 vectors, two of them could be v_1 and v_2, so I need to find a third one.

This third vector let's call it v_3 should follow this

<1, v_3>=0
<sqrt(12)(x-½, v_3>=0
|v_3||=1

[teal ridge]

hi

[gusty summit]

So I thought I could do some equation system , so find v_3 but I got stuck

$0=\int_{1}^{0}1\cdot v_3 dx=\int_{1}^{0}\sqrt{12}(x-\frac{1}{2})\cdot v_3 dx$

[potent lotus]

binnet

[gusty summit]

I tried simplifying this extression as:
$0=\int_{1}^{0} v_3 dx = \sqrt{12} \int_{1}^{0} (x-\frac{1}{2})\cdot v_3 dx$

[potent lotus]

binnet

[gusty summit]

But it looks like that would be:

$ 0=\int_{1}^{0} v3 dx = \sqrt{12} [ \frac{1}{2}x^2- \frac{1}{2}x]{1}^{0} \int{1}^{0} v3 dx $

[spare beacon]

I don't want to puzzle out what you are trying to do here, but you are supposed to take any linearly independent vector and apply the gram schmidt process to it then normalize it.

[gusty summit]

oh, derp

so:

v_3 = v_1 - v2 - something like inner product...

then normalize it

Okay will be a pointer in the right direction, closeing for now

!close

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[gusty summit]

.reopen

[calm coral]

✅

[gusty summit]

lol, where do i find the 3rd ortho vector to use though?

v_3 = (some vector) - <(some vector),v_1>/<v_1,v_1> - <(some vector),v_2>/<v_2,v_2>

is this correct?

anyone?

$v_3 = ?? - \frac{<??,v_1>}{<v_1,v_1>} - \frac{<??,v_2>}{<v_2,v_2>} $

$$ v_3 = ?? - \frac{<??,v_1>}{<v_1,v_1>} - \frac{<??,v_2>}{<v_2,v_2>} $$

[potent lotus]

binnet

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[tight elbow]

How i Can find it

[lethal sail]

is that supervision?

what is the question lol

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[noble island]

all i know is that alex finish 1 lap in 88 sec and becky finishes 1 lap in 76 sec

[calm coral]

@noble island Has your question been resolved?

[noble island]

<@&286206848099549185>

<@&286206848099549185>

[honest quiver]

What are their speeds in cycles (laps) per second?

Think of it in terms of relative speed

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[shut niche]

simplified, would this be 3x/x?

the textbook apparently says the simplified version of this is 1/2

[halcyon rock]

can I see your work

[shut niche]

@halcyon rock

[minor gust]

Hm try factoring the denom on left term

First

[halcyon rock]

you forgot the 6

6x^2+6x = 6(x^2+x) = 6x(x+1)

[noble island]

.reopen

[shut niche]

wait wdym @halcyon rock

ohhh

i forgot to

i gotchu

[halcyon rock]

ofc

[minor gust]

Well I would just take out a 3x and not a 6x

For cancellation purposes

Same thing tho

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[minor gust]

Can someone explain to why it must be a

And why c isn’t necessarily true

[crystal forge]

what do you know about odd functions?

[unreal viper]

yeah can you write the definition of an odd function

[minor gust]

Diffirent end behaviors

-f(x)= f(-x)

[unreal viper]

that isnt right

that is right

[minor gust]

?

I thought odds have diffirent end behaviors

[unreal viper]

yeah but they are symmetric in some sense

its not just the end

[crystal forge]

yeah, so what is a geometric interpretation of that, if you look at the graph of an odd function? (hint: what kind of symmetry doesx that imply?)

[minor gust]

Symmetric over the x axis

[unreal viper]

yes

[crystal forge]

no

[minor gust]

Even is y axis and odd is x axis

[unreal viper]

yeah so if you have a maximum at f(3) then what is going on at f(-3)

if the function is odd

[crystal forge]

odd isn't symmetric over the x axis, it's symmetric over the line y = x, or you might hear it referred to as symmetric over the origin

^ example

[unreal viper]

thats just pedantic lmao

[minor gust]

Oh origin

[unreal viper]

of course he doesnt mean literally a mirror

[minor gust]

Oops it’s Oregon

Origin

[unreal viper]

because then it wouldnt be afunction

i get what you meant propus

[minor gust]

Ye mb

[crystal forge]

what do you mean pedantic, its clearly not symmetric over the x axis, that has a very exact definition

[minor gust]

Oh I get it now

[unreal viper]

yes but i understood what he meant

i guess you didnt Soosh

he drew picture

[minor gust]

Bc of the symmetry

[unreal viper]

its clear he knew what he meant

when he said symmetric on the x axis he meant its vertically symmetric when odd and horizontally symmetric when even

which is a good way to remember the difference

[crystal forge]

so what it is good teaching to tell someone theyre correct when they say the wrong thing? im confused why are arguing over this

i didnt see the picture they wrote on the original question paper

[unreal viper]

i think propus understands now

[minor gust]

Ye I got it

Thanks

I wasn’t thinking about symmetry

[crystal forge]

@minor gust anyway so if there is a local max at x = 3, what would be happening at x = -3?

[minor gust]

Min

Minimum

[crystal forge]

yeah and which one of the answer options?

[minor gust]

A

[crystal forge]

yeah you got it

[minor gust]

Ty

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[dense lion]

\

[dense lion]

essentially how do i turn the x^2/3 into a u so i can do trig sub

[unreal viper]

well isnt the derivative of y actually x^{-1/3}

but regardless of that

[dense lion]

yes it is

but i have to square the derivative right

for arc length

[unreal viper]

yeah but that should give you x^{-2/3}

[dense lion]

my friend told me it becomes positive

[unreal viper]

the exponent doesnt

[dense lion]

BREUH

[unreal viper]

think about exponent laws

you multiply -1/3 to 2

thats -2/3

[dense lion]

yeah

that makes sense

[unreal viper]

anways

[dense lion]

i got 63

[unreal viper]

you could maybe try x^{-1/3} = tan(theta)?

for your sub

im not sure if itll work

[dense lion]

cant i do u sub?

[unreal viper]

im not sure

but try the trig sub maybe

although it may be icky

[dense lion]

im going to cry

ok thx

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[barren sail]

hello! i'm having trouble figuring out how to create an adjacency matrix for this problem. i know how an adjacency matrix works but i don't understand how to apply it in the scope of this problem ^^'

[barren sail]

<@&286206848099549185>

.close

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[still dove]

Yooo!

[pallid halo]

duplicate of #help-41

.close

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[orchid palm]

am I missing something here?

what is wrong about this, it seems like I just take the provided identity and subtract cos^2(theta) from 1

[swift laurel]

with trig identities you have to match the angle on the inside/the input

so $\sin^2 (\theta) + \cos^2(4\theta) \ne 1$ because the inputs don't match

[potent lotus]

cloud

[orchid palm]

ah

7theta

slipped my mind

I was hyperfixated on if the formatting was correct instead of the actual math...

.close

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[thorny sorrel]

how do we find the rightmost column? (the pink numbers)

[pallid halo]

!original

[calm coral]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[pallid halo]

oh, you're asking how did someone find the vector in pink?

[thorny sorrel]

Yeah

i thought we just row reduce

but its weird answer after calculating

[pallid halo]

you have a lot of freedom, there are infinitely many valid answers
one way is to say ok, this is two equations with five variables, so i can set three of them freely, like this:

[x y 0 0 0] for example

then take the dot product of [1 0 1 -1 0] with [x y 0 0 0], set it equal to 2

take the dot product of [1 1 0 0 -1] with [x y 0 0 0], set it equal to 1

two equations, two unknowns

solve for x and y

[thorny sorrel]

OH shiii

so i can row reduce

and then just put randoms for the frees

[pallid halo]

yep

correct!

[calm coral]

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[remote mural]

Someone please help me

[remote mural]

It’s the night before an exam

I know all of the material

But I keep messing up my algebra

Anybody have any videos to refresh memory on algebra 😭

My exam is on composite functions, arithmetic combinations of functions, and inverse functions

Like I said, I know all this material

But for some reason I keep screwing up the algebra

If anyone has any tips/videos to save me please..

I keep ending up with total messes/disasters like these

[remote mural]

Bro pls someone help, I keep searching up algebra refresh on YouTube but idk even know what this kind of algebra is called

[leaden thunder]

"inverse rational functions"

or just "inverse functions"

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[trail ingot]

!status

[calm coral]

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

[lunar token]

not sure what its asking

[trail ingot]

it wants you to, for each k between 0 and n, count how many subsets there are of S with size k that don't contain {1,2}

[lunar token]

isnt it 1 to n

[trail ingot]

i dunno, it's not clear

[lunar token]

and without containing that set wouldnt it just be 2^n - 1

[trail ingot]

no

{1,2,3,4} has {1,2} as a subset for example

[lunar token]

oh

[trail ingot]

and you're supposed to count them for each k

not just total subsets of S

[lunar token]

what does each k mean

[trail ingot]

count subsets with size 0, with size 1, with size 2, with size 3 and so on separately

[lunar token]

is it 2^n-2

[trail ingot]

what is?

[lunar token]

the subsets that dont contain the elements 1,2

[trail ingot]

no

wait do you mean 2^(n-2)? still no though

[lunar token]

ye

[trail ingot]

i'm guessing you were thinking of subsets of {3,4,5,...,n} but that wouldn't count example {1,3}

which doesn't have {1,2} as a subset

[lunar token]

yeah

[trail ingot]

and still you seem to be just trying to count total subsets

but you need to count them for each size

[lunar token]

is it not what its asking

[trail ingot]

no, it's asking for this

[lunar token]

what dsoe taht mean

like how do you k its asking this

[trail ingot]

it says
How many subsets of S have size k and do not have {1,2} as a subset?
but you are treating it like
How many subsets of S do not have {1,2} as a subset?

it wants you to count the subsets of an arbitrary size k

[lunar token]

oh

n - 2 choose k-2

how many ways to choose n as a subset of size k excluding 1 and 2

[trail ingot]

you might be doing this again

[lunar token]

so n choose k - (n -2 choose k-2)

[trail ingot]

yea i think so

well just gotta be careful with k < 2 or n < 2 ig

but otherwise yea

[lunar token]

wdym?

[trail ingot]

what is (n -2 choose k-2) when k < 2 or n < 2?

it's probably not even a detail you're expected to deal with

and i think it's ok anyway for any n and k if you define choose the right way with negative numbers and 0s and stuff

i would just ignore me

[lunar token]

idek what that means

[trail ingot]

lol just ignore me

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[verbal lava]

First Query: I'm calculating expected value... Am I right in these expected values?

99.99% (99% * 101)
99.96% (98% * 102)
99% (90% * 110)
96% (80% * 120)
98% (70% * 140)
105% (50% * 210)
105% (35% * 300)

I may misunderstand the formula as I'm not a stats student

Second Query: How much of your capital would you invest at any give time?

For example, the venture enterprise bond you're getting 2.1x return. So you could start with 10% of your portfolio and invest that 10 times, which I believe is better than 100% 1 time. Is that true?

[potent smelt]

https://en.wikipedia.org/wiki/Kelly_criterion

And yes, your EVs seem to be correct

[verbal lava]

Ok so following the formula:

0.5 - 0.5 /1.1 = 4.5%
0.35 - 0.65/2 = 2.5%

Is that correct?

[calm coral]

@verbal lava Has your question been resolved?

[calm coral]

@verbal lava Has your question been resolved?

[calm coral]

@verbal lava Has your question been resolved?

[calm coral]

@verbal lava Has your question been resolved?

[potent smelt]

,w 0.5 - 0.5/1.1

[potent lotus]

Results provided by WolframAlpha

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Requested by omnipotententity

[potent smelt]

,w 0.35 - 0.65/2

[potent lotus]

Results provided by WolframAlpha

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Requested by omnipotententity

[potent smelt]

Looks good to me @verbal lava

You'll want to read the section labeled proof to find the expectation value to choose between the two scenarios, also if you can make multiple investments simultaneously, this can change which one is better

[verbal lava]

Yes you can do it simultaneously

[potent smelt]

So if you can make simultaneous bets (betting 40 times on the risky investment, for instance) this might be both safer, and faster than betting just once

You'll need to work out the expectation value

[verbal lava]

Sorry I meant you can invest in both of the last two options

[potent smelt]

Oh, then yeah, you'll want to calculate the expectation of doing both.

Simultaneously

And find the correct proportion, this would be an optimization in two variables.

[calm coral]

@verbal lava Has your question been resolved?

[calm coral]

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[calm coral]

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

[fringe reef]

let the speed be x km/h

the fast speed in the first half

so carlos cycles for 2 hours at x

then for 3 hours at x-10

[mortal spindle]

yes

[fringe reef]

awesome

[mortal spindle]

would we make a equatoin then subsitiute

[fringe reef]

yes

what's the formula for distance

[mortal spindle]

d=s*t

[fringe reef]

yep

[fringe reef]

you have two speeds and two times

so you can just add them together

makes sense?

[mortal spindle]

so 2x*3(x-10)=90??

[fringe reef]

replace the * with +

then yes

[mortal spindle]

then just solve for x?

[fringe reef]

yes

that will be your answer

[mortal spindle]

i thought we are finding speed not distance

why would we add

[fringe reef]

indeed

2x+3(x-10)=90

2x is the distance travelled in the first part

3(x-10) is the distance travelled after speed changed

the total distance is 90

so we can just add them

[mortal spindle]

oh ty

bcs the overall distance of the trip is 90 and we have already stated that x is the speed

[fringe reef]

yes

so solve $2x+3(x-10)=90$

[potent lotus]

artemetra

[mortal spindle]

120/5=x

[fringe reef]

simplify

[fringe reef]

what's 120 divided by 5?

[mortal spindle]

24

[fringe reef]

yep

that's your answer

[mortal spindle]

do you have time for one more?

[fringe reef]

yes

[fringe reef]

oof

i don't know shares/dividend problems

language barrier tbh

[mortal spindle]

wt abt this

[fringe reef]

let a be the number of students in class A

then the number of student in class B is 40-a

[mortal spindle]

yep

[fringe reef]

cordial per student in class A is thus 6/a

and cordial per student in class B is thus 5/(40-a)

now we know that each person in class A got twice the amount each person got in B

[fringe reef]

can you combine these two now into an equation?

[mortal spindle]

so am i going to solve it in terms of how much cordial or amount of people

[fringe reef]

you need the number of students in class A

which is the variable a

[fringe reef]

so amount of people

[mortal spindle]

6/1+5/(40-a)=40?

[fringe reef]

no

$\frac{6}{a} = 2\cdot \frac{5}{40-a}$

[potent lotus]

artemetra

[fringe reef]

this is the equation

cordiol per person in class A is twice as much as cordiol per person in class B

@mortal spindle does that make sense?

[mortal spindle]

yes

[fringe reef]

great

[mortal spindle]

do u have any tips on worded problems

its my weakest area in maths

[fringe reef]

practice tbh

[fringe reef]

it's everyones weakest area in math

no one likes thinking lol

[fringe reef]

other than this, i can't really offer much

oh and thinking what would make more sense within the context of the problem

so if you get that Billy had -42,000 apples then something's gotta be wrong

[mortal spindle]

hmm

yep ty

.close

[calm coral]

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[calm coral]

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[compact drum]

!status

[calm coral]

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

[compact drum]

we have three informations given

from each, we can set up an equation

[mortal spindle]

i have done that but it doenst work

when i substitute

[compact drum]

can you show your work?

[mortal spindle]

i did sa=50-f

Su=80-sa

i rearranged it

but didnt work

[compact drum]

50 more people attended on saturday than on friday

so let's say we know that 100 people went there on friday, how many went on saturday?

[mortal spindle]

150

[compact drum]

yes

you did: Fr + 50

so Sa=Fr+50

not with the minus

same goes for the other equation

Su=Sa+80

and the third equation is just that the sum of all three is 540

[mortal spindle]

wont there be two unknowns/

[compact drum]

well

we have three unknowns

Fr, Sa, Su

but also three equations

[mortal spindle]

Sa=Fr+50, Su=Sa+80 and Fr+Sa+Su=540

[compact drum]

yep

what you could do here is rewrite the first one to Fr=Sa-50

that way we can input the two equations into the third

which will then only depend on Sa

[mortal spindle]

so we finding Sa?

[compact drum]

we are finding all of them

oh wait

yeah we only need Fr, but might as well get them all

you know? gotta catch'em all

to get Fr, we need Sa, and Sa is pretty straight forward to get

you could also rewrite them to:
Fr=540-Sa-Su
Fr=540-(Fr+50)-(Sa+80)
Fr=540-Fr-50-(Fr+50+80)
...

[calm coral]

@mortal spindle Has your question been resolved?

[mortal spindle]

idk why im getting different asnwers

sorry nvmd

[calm coral]

@mortal spindle Has your question been resolved?

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[calm coral]

Please don't occupy multiple help channels.

[potent igloo]

.close

[calm coral]

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[potent igloo]

stay in #help-35 please

[calm coral]

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[sudden nebula]

Why is this wrong? I was helping someone and I thought this was fine..

[carmine sorrel]

the numerator is indeterminant the way you factored it, you get 0*(infinity) inside the root

[calm coral]

@sudden nebula Has your question been resolved?

[sudden nebula]

Remind me why that's a problem ?

Does that mean 0/0 or infin / infin

[carmine sorrel]

those are common indeterminant forms, yeah.

[sudden nebula]

So what's the problem rn

[carmine sorrel]

0 * (infinity) is also indeterminant. It isn't 0

[sudden nebula]

No way

I thought infin * 0 was 0

[carmine sorrel]

nope.

[sudden nebula]

Dang

Well that fixes that ty

What would have been a more appropriate way to factor

[carmine sorrel]

you don't need to factor, but if you want to, factor the x out.

so you get x(9 + 1/x^2) inside the root

[sudden nebula]

Hmmm

Oh that just gives you infinity

So the limit is infinitiy

Ty

[calm coral]

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[ebon harbor]

hey guys, i'm trying to figure out how to integrate this but i'm just lost

[blazing coyote]

Hint:- The derivative of sin(x) is cos(x)

It's also a variable separable DE

[ebon harbor]

i mean

i'm still confused(not your fault) after my teacher explained it

she kinda just gave us the answer key and said "yeah"

[blazing coyote]

Are you familiar with variable seperable DEs

[ebon harbor]

yeah

[blazing coyote]

Can you re-write this after seperating variables then?

[ebon harbor]

cos/cosy * e^sinx/cosy

no

cause then cosy would be squared

cosy dy = cosxe^(sinx)

damn im stupid

[blazing coyote]

$\cos\left(x\right)e^{\sin\left(x\right)}dx=\cos\left(y\right)dy$

[potent lotus]

Why am. I here

[blazing coyote]

yeah

can you do it from here?

[ebon harbor]

yup 😂

thank you so much!

[blazing coyote]

np

[ebon harbor]

ok so i solved it

it's either A or B

how do we know which one it is?

[blazing coyote]

What do you think?

hint:- The range of C should be R

@ebon harbor

[calm coral]

@ebon harbor Has your question been resolved?

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[ebon harbor]

didn't see this till now, sorry

it's def B

[calm coral]

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[plain moss]

for this derivative

[drifting seal]

yes

[plain moss]

Would I do it like this? I’m thinking

Hard

[drifting seal]

what am i looking at?

[plain moss]

Just guide me pls

[drifting seal]

what’s f(x)

[plain moss]

Oh nothing

[drifting seal]

what’s the derivative of 3h(x)

[plain moss]

sorry wrong questions posted above

finsihed that one

[drifting seal]

oh

[plain moss]

sorry

[drifting seal]

ok

no worries

so product rule with 3 functions

do u know how to do that

[drifting seal]

essentially take the derivative of one and multiply the regular functions for the other two

and add up all the ways

with each function being differentiated

yea or that

if we have

f g and h

then it’s ghf’+fgh’+fhg’

[plain moss]

ohh yea i rmbred now yes

if i do this way

then multiply the first one as is

Much worse way then u explained tbh

going to do it ur way

correct?

[drifting seal]

yea it takes longer but

it works still

[drifting seal]

yes

[plain moss]

gotcha appreciate it

thanks mate

[drifting seal]

ur welcome

[plain moss]

.close

[calm coral]

Channel closed

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[calm coral]

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[plain moss]

is the top function like 2x^3*k(x)

because i was taking it like that

but book takes it as one function

is the outcome the same? or is book method better (probably it is)?

[drifting seal]

what was their method?

[pallid halo]

that's true as far as it goes

[drifting seal]

they’d still do product rule

[pallid halo]

but they'll need to use the product formula again on that first factor

[drifting seal]

doesn’t matter

[plain moss]

Tbf I’m confused on this here’s my work

i started foiling

but then realized thats hella wrong

since they are being added

i cant foil it

[drifting seal]

hmmm y did u get /(3x+2)^2

y did u rewrite it like that

[plain moss]

quotient rule

[drifting seal]

before differentiating

[plain moss]

no?

oh idk i just write it

shouldnt do it?

leave it till the last step?

[drifting seal]

u did 2x^3k(x)(3x+2)/(3x+2)^2

u didn’t differentiate yet

u essentially added an extra 3x+2

that only makes it more complicated

[plain moss]

oh really?

how should i begin then?

[drifting seal]

yea u square the denominator when doing the quotient rule

not before differentiating

u just manipulated the expression

[drifting seal]

how they did

then use product rule

[plain moss]

i see thing is in some questions they use k(x) as multiplies to another function is some they dont

i just cant see the difference each time

i just get stuck to being used one

[drifting seal]

well they r being multiplied

wdym

[plain moss]

like for this they used it as different

each to their own right

[drifting seal]

for quotient rule

it’s (low d high - high d low)/low^2

low is the denominator

high is the numerator

[plain moss]

cuz u see, 2x^3 is being multiplied to k(x)

[drifting seal]

which is 2x^3 k(x)

low is 3x+2

the denominator

[plain moss]

ok so i got a question here ok

[drifting seal]

ok

[plain moss]

so is thing wrong?

yes it is right

i think i see what i am doing it wrong

[drifting seal]

ur all over the place

[plain moss]

i got the funcdamentals all worng for quotient rule

[drifting seal]

u always treat the numerator and denominator as one function

respectively

[plain moss]

THIS

OKAY

[drifting seal]

if we have f(x)=x/y

[plain moss]

respectively?

[drifting seal]

then f’(x)=(yx’-xy’)/y^2

[drifting seal]

like

they each have their own

[plain moss]

gotcha

[drifting seal]

function

[plain moss]

okok

okok i see

so it can never be that it is like

h(x) = f(x) * j(x) / g(x) right... since the quotient rules is only this

three different functions

[drifting seal]

think of it like f’(x)=(denominator)(derivative of numerator)-(numerator)(derivative of denominator)/(denominator squared)

[plain moss]

so it can never be that it is like

h(x) = f(x) * j(x) / g(x) right...

[drifting seal]

wdym

whats h

[plain moss]

this

just gave it a different name

[drifting seal]

y r there four functions

[plain moss]

sorry mate im just getting rid of all my mathematical brain damage, that gets in the way of my thinking while doing these questions

[drifting seal]

lol no worries

[plain moss]

doesnt this also have three functions

my question is, it cant be like that right

[drifting seal]

it has j f g f’ and g’

[plain moss]

a quotient rule can never have 4 functions right

[drifting seal]

wdym

sure it can

it can be fgh*k…/j

u just take the derivative of the numerator

and denominator

and use quotient rule

[plain moss]

no matter how big it is, its one function

the numerator?

it can be like

[drifting seal]

anything

it can be arctan(x^3)(ln(3x)(x^5/2)

doesn’t matter

[plain moss]

the top is always one function? yes?

DAMN. i overthink.

[drifting seal]

yea but the derivative may need product rule

[plain moss]

gotcha

damn. man.

but then inside for example f(x) then?

whats f(x) and whats g(x)

given that

since we also have the denominator to bring it upwards

[drifting seal]

wdym

there’s no denominator here

this is product rule

[plain moss]

but when we implement it on the f(x) what...

oh....

this is wrong ehhhhhhhh

clearly stated that bottom is g(x)

[drifting seal]

where’s the lnx

from

[plain moss]

now on the above function how do we do the product rule

[plain moss]

dont mind that sorry

i jsut made it by example

cuz it could be as big as possible right

[drifting seal]

oh ok so product rule

the same rule holds

with 2,3,4 doesn’t matter

how many functions

derivative of one

multiply by all other functions

and add up all iterations

with each function getting differentiated

[plain moss]

so in this case for example

[6x^2 * ..... ] + [k'(x) * .... ] + [j'(x) * ......] +

bro i aint gonna lie all this u did for me is gonna acc help me soo much

thank you for reall holy

helped me open one side of my brain hopefully i can acc get this shit through my head

i think this prlly jsut the last thing knief

[drifting seal]

ur welcome

[plain moss]

so this yea?

[drifting seal]

mhm

[calm coral]

@plain moss Has your question been resolved?

[calm coral]

@plain moss Has your question been resolved?

[calm coral]

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[remote mural]

can anyone explain why there is a k

[tepid anvil]

That's the density constant. The density at any point is kr

[remote mural]

what

how do u know that

[tepid anvil]

We know that the density at any point is proportional to its distance from the axis of the cylinder $r$.

[potent lotus]

thedude365

[remote mural]

ye

[tepid anvil]

Since it's proportional, we can introduce a proportionality constant to make an equation for the density at a given point $\rho = kr$

[potent lotus]

thedude365

[remote mural]

how were u able to a decipher that we need that constant

cuz when we do center of mass and stuff like there where they give us the density function

we don't need k

[tepid anvil]

Whenever you're given that some variable is proportional to another, this means there's a proportionality constant. For example, if you're told that $ Q \propto T^2$, that's the same as saying $Q = cT^2$, where $c$ is some constant

[potent lotus]

thedude365

[remote mural]

bruh

so for example when we have a problem involving mass

and they say constant density

then we can just use k/p

[tepid anvil]

Yes, where $k$ or $\rho$ is constant

[potent lotus]

thedude365

[remote mural]

yoooooo

that's so lit bro

.close

[calm coral]

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[calm coral]

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[subtle turtle]

Hey

[calm coral]

Please don't occupy multiple help channels.

[subtle turtle]

<@&286206848099549185>

<@&286206848099549185>

?????

<@&286206848099549185>

[serene bloom]

its been 5 minutes dude

[subtle turtle]

shi

mb bro can help tho

lol

[serene bloom]

!status

[calm coral]

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

[subtle turtle]

1

[serene bloom]

ok, so let's start with theoretical probability

[subtle turtle]

okayyy

[serene bloom]

theoretically, since all 6 sides have an equal chance of getting rolled, what's the probability of each one getting rolled?

[subtle turtle]

1 out 6?

[serene bloom]

yeah

good

[subtle turtle]

so i write 1 over 6?

[serene bloom]

mhm

[subtle turtle]

okay

[serene bloom]

and then experimental probability is the actual probability you got in the experiment

lets use the first one as an example

[subtle turtle]

wait so for

2

[serene bloom]

mhm

[subtle turtle]

is 2 over 6

[serene bloom]

no it's also 1/6

[subtle turtle]

and 3 over 6 and so on?

[serene bloom]

think of it like this

the chances of getting a 1, 2, 3, 4, 5, or 6 are equal

right?

cause it's a fair die

[subtle turtle]

for probabilitry?

[subtle turtle]

yeahhhhhh

[subtle turtle]

yeah

[serene bloom]

if you said that the probability of rolling 2 was 2/6, but 1 was 1/6, that would imply that it's more probable to get a 2, right? but we know that's not true

[subtle turtle]

ohhh okay

so what would 2 be?

1 over 6

[serene bloom]

right

[subtle turtle]

for all of them?

[serene bloom]

they should all be 1/6 mhm

[subtle turtle]

since its fair for all

[serene bloom]

yep

[subtle turtle]

ohhh okayyyy

got it

now for experimental?

how would that work?

[serene bloom]

yeah ok so

experimental probability uses the data you actually collected in the experiment

so it should roughly line up with your theoretical, but since there is random chance and error, it might not be exactly the same

[subtle turtle]

so 6,4,3,6,7,4

[serene bloom]

thats how much times you rolled each one, yes

[subtle turtle]

yeahhhh

[serene bloom]

to calculate probability what do you do?

[subtle turtle]

since we rolled the dice 30 times

[serene bloom]

mhm

so what would be the experimental probability?

[subtle turtle]

thats what im stuck on

[serene bloom]

you can think of probability as asking the question "if i do something this many times, how much times will i get this result?" and then write it as a fraction

so

using the first one as an example

you rolled the die 30 times

[subtle turtle]

yes

[serene bloom]

and got the number 1 6 times

[subtle turtle]

yeah

so 16 over 30?

[serene bloom]

you mean 6 right

[subtle turtle]

6. sorry

[serene bloom]

yeah yeah exactly

and that would just simplify to 1/5

in general experimental probability is [how many times you got the desired result]/[how many times you conducted the experiment]

[subtle turtle]

so the experiimental would be 6 over 30

and 4 over 30

[serene bloom]

mhm

[subtle turtle]

and so on?

[serene bloom]

now try for the second collumn

[subtle turtle]

wait so

[serene bloom]

mhm?

[subtle turtle]

kinda not getting it

so for the frist experimental question it would be

6 over 30 right?

[serene bloom]

yes

[subtle turtle]

and then it would be 4 over 30

[serene bloom]

yes

[subtle turtle]

then 3 over 30?

[serene bloom]

yes

[subtle turtle]

and then 6 over 30?

[serene bloom]

mhm

[subtle turtle]

and then 7 over 30

[serene bloom]

yep

[subtle turtle]

and 4 over 30

[serene bloom]

just remember to simplify your fractions

[subtle turtle]

ohhhhh okay

and how much would i need to simplify?

[serene bloom]

down to its simplest form

so that you cant simplify it any more

[subtle turtle]

so for 6 over 30 i can do 1 over 5?

[serene bloom]

yes

[subtle turtle]

and for 4 over 30 it would be 2 over 15?

[serene bloom]

mhm

[subtle turtle]

okay

i got it

[serene bloom]

great

[subtle turtle]

but for 7 over 30

you cant?

right

[serene bloom]

exactly

cause there are no common factors between 7 and 30

[subtle turtle]

okayyy bro

im done i can go to sleep stress freeee

thankkk youu so muchhhh

brooooo

[serene bloom]

no problem man

[subtle turtle]

wait what grade are yoou in?

[serene bloom]

im in 8th, but ive been learning some calculus and trying to do linalg

[subtle turtle]

thankksss bro

i gotta go to bed tho

but thanks alottt bro

[serene bloom]

welcome to

[calm coral]

@subtle turtle Has your question been resolved?

[calm coral]

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[remote mural]

Does this imply that the matrix is linearally independent?

[spark stratus]

wdym linearly independent

[remote mural]

There exists a pivot position in every column and the only solution to Ax = b is the solution where x is the zero vector

[spark stratus]

you mean the only solution to Ax = 0

[remote mural]

yeah

[spark stratus]

you can say it that way

but the usual way is "the matrix is invertible" instead of "the matrix is linearly independent"

[calm coral]

@remote mural Has your question been resolved?

[calm coral]

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[remote mural]

do you have a question to ask

[torpid brook]

.close

[calm coral]

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• Show your work, and if possible, explain where you are stuck.
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[lyric ice]

hello

[lyric ice]

so for (a)

i have

x = (2,0)
y = (0,0)

what exactly do i test for symmetry

[remote mural]

Graph your equations first

[lyric ice]

or how

uh

how would i do that

[remote mural]

Do you have a graphing calculator?

[lyric ice]

yes

[remote mural]

Pull it out, is it ti-84 plus?

[lyric ice]

yeah

84 plus ce

do i just put the intercepts into the equation

[remote mural]

Don't graph any of your equations yet

solve for x on the second equation(b)

[lyric ice]

-5

x = -5 for second equation

[remote mural]

if u can send pictures, that would be helpful, since i cant rn bc im on my laptop

[lyric ice]

0^2 = 0

-5 = x

im on pc i cant either

lol

[remote mural]

Also,

[lyric ice]

my brain is fried

man

[remote mural]

You solved the seconf equation wrong

its okay

im here to help

[lyric ice]

wdym second equation

[remote mural]

equation b?

[lyric ice]

i have a exam tmr and i didnt know i had it lol

so its 4am now

and im tryna learn all this shit

[lyric ice]

so

for equation b

if i am solving for x int

set y = 0

x = (0)^2 - 5
x = -5

am i dumb

[remote mural]

No you're not solving for the intercepts yet

You're just solving for the equation first

[lyric ice]

wat

[remote mural]

You identify intercepts once you've graphed both equations.

[lyric ice]

okay so can we just scrap everything and start from scratch

[remote mural]

Yes

[lyric ice]

so lets look at (a)

[remote mural]

Don't freak out

Yes,

[lyric ice]

im freaking out

[remote mural]

That is an upside down parabola

[lyric ice]

i have like 3 hrs before i need to leave

[remote mural]

Equation a is an upside down parabola

Relax

[lyric ice]

yes

[remote mural]

You're not gonna learn anything if u panic

[lyric ice]

okay

[remote mural]

Okay, solve for y on equation b, it's because if you try to graph equation b on a calculator, there won't be an option for that. Solve for y on equation b

mb

its 1 am rn💀

[lyric ice]

wait i thought we were looking at a

ur good bro its 4am here

lol

[remote mural]

we don't need to look at a rn

[lyric ice]

okay

so