help-10

[stable rain]

errr

im mind reading that ur Q is on the alt exp?

[tardy epoch]

find 1^2 + 3^2 + 5^2 + ... + (2n+1)^2 first using summation properties

[distant moth]

One series can be sum of squares of odd numbers, the other can be sum of squares of even numbers, write general terms for both and you can evaluate using sigma

[shell hull]

I don't know sigma

[shell hull]

Any other solution?

[tardy epoch]

sigma is just notation for a lot of addition

you know addition

[shell hull]

Yes but I don't know how should I change a formula to another one...

[obtuse pebble]

@shell hull Has your question been resolved?

[shell hull]

.close

[obtuse pebble]

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[timid silo]

Hi

[timid silo]

Are you available to help at the moment?

[marble junco]

https://dontasktoask.com/

[timid silo]

Am I on the right track with regards to 5.1.1

.close

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[timid silo]

why is this not a lattice?

do you know the definition for a lattice?

every pair of elements has a join and a meet

does 7 and 2 have a join?

no, it would be 14

but then why is this a lattice?

check that everything has a join

(or draw the lattice out)

ah, because the join of 24 and 6 is 24 etc

okay got it

yup

and 1 is always a meet

yes

okay cool

ty very much

.close

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[grave zodiac]

Someone help me?

[solar trellis]

Which question

[grave zodiac]

P1) calculate in each triangle the amplitude of the angle ↑

P2) draw a right triangle with basd= 3 (cm), height 5 (cm) and determine: (a) triangle are , (b) barycenter, (c) perimeter

[obtuse pebble]

@grave zodiac Has your question been resolved?

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[agile robin]

is this like taking the highest order power so 2n^1/n^1

2/1 =2 ?

i might be completly wrong

[tepid minnow]

Yes ! Kind of but we should be more precise :

2n / (n*(1+4/n))

And as n--->+infty , 4/n --->0

So we just have 2n/n = 2

[agile robin]

why the 1+4/n

ur losing me there

[tepid minnow]

I'm factorising

[agile robin]

OH

[tepid minnow]

n + 4 = n * (1 + 4/n)

And here we see very clearly that 4/n --> 0

[agile robin]

i see now

[tepid minnow]

That's the real proof

[agile robin]

do u mind if i send a pic of the solution theres one thing i have toruble understanding

same question

[tepid minnow]

go ahead

[agile robin]

they write +2-2...

the fact its alt series i get the + and -

but the fact sequence =2 we just plug that in series it seems

and all good to go?

[tepid minnow]

This is the sum of 2n/n+4 ?

[agile robin]

ye

[tepid minnow]

but i don't get it

[agile robin]

fr

[tepid minnow]

for n=1 we have 2/5

[agile robin]

hes not reqiring as much work

[tepid minnow]

not 2 or -2

[agile robin]

well divergence test was done and we saw that the lim n to inf an was not equal to 0

so we know it diverges

then

[tepid minnow]

but what i'm telling you is that the series of 2n/n+4 can't be +2-2+2-2+2-2

i don't understand

@agile robin ?

[agile robin]

i agree

[tepid minnow]

what's the exercise ?

[warm shale]

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Page 4/4

[tepid minnow]

so 3) is sum of (-1)^n * 2n/n+4

[agile robin]

yes

[tepid minnow]

well it diverges because as you said we're going to have a -2+2-2+2-2+2 as n---> infity

so oscillations means divergence

the first values of the series don't affect the divergence or convergence of it

[agile robin]

does that apply to all series

?

[tepid minnow]

yes

[agile robin]

or this specific scenario

[tepid minnow]

ALL

[agile robin]

got it

TY

[tepid minnow]

it's quite logic

[agile robin]

.close

[obtuse pebble]

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[obtuse pebble]

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[strange salmon]

can someone explain

[solemn osprey]

Move the k into the numerator by multiply both sides of the equation by k

U get 4 = 6k/11

Isolate the k by multiplying both sides by 11/6

4 * 11/6 = k

K=4 * 11/6

[strange salmon]

7.33?

[solemn osprey]

,w 44/6

[warm shale]

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[solemn osprey]

Yeah

[strange salmon]

ok thx

[solemn osprey]

U understand everything?

[strange salmon]

yeah im in 7th grade

[solemn osprey]

Ok

[strange salmon]

alr thx

.close

[obtuse pebble]

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[flat kestrel]

Why am I incorrect here? The power would go down to 0, making the value of (x+4) go to 1

[knotty crow]

it's product of two functions

[flat kestrel]

Oh wait nvm

[knotty crow]

use product rule or expand and then use power rule

[flat kestrel]

I distribute first gotcha

That's my b, sorry

.close

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[fast cliff]

(c) have no intersects

id like to discuss with someone on this question

[fierce lagoon]

These 3 lines are gonna be parallel to the plane

[fast cliff]

what

they arent lines they are planes

[fierce lagoon]

Planes I meant planes

Lol whoops

[fast cliff]

ok so like what would an answer be

[fierce lagoon]

ax+by+cz = d-1

Etc etc

[fast cliff]

for the last one?

that makes sense

[fierce lagoon]

It could be

[fast cliff]

i just did

x3=1

x3=2

x3=3

i hope that works

[fierce lagoon]

I mean there's an infinite number of solutions

[fast cliff]

for the first one

if theres a free variable, is that the answer

[fierce lagoon]

As long as you keep a, b, c the same because these planes gotta have the same normal vector

[fast cliff]

whats a normal vector

[fierce lagoon]

The vector normal to the plane

[fast cliff]

oh ok

wwhat about for (a) and (b)

for a i made it so there was a free variable

[fierce lagoon]

a) is easy

The easiest way is to make any arbitrary plane

Like

bx + ay + cz = d

Just swap the coefficients around

As long as their normal vectors aren't the same, they will intersect at a line

[fast cliff]

what about a point

how do you know they intersect at a line instead of a point

with three vectors

idk about that

[fierce lagoon]

Although at a singular point, I don't think that's possible for planes

[fast cliff]

yes it is

the intersect between two lines

two planes

is aline

the intersection between a line and a plane

is a point

[fierce lagoon]

Well 3 planes can intersect at a point

[fast cliff]

yea the question is about 3 planes

[fierce lagoon]

But 2 planes will either not intersect, or intersect at a line

[fast cliff]

ye

[fierce lagoon]

Oh I read it as 3 pairs of equations

Not sets of 3

💀

Create two arbitrary planes that intersect at a line

And then cross their normal vectors

I think that should work

[fast cliff]

yea but my textbook hasnt covered normal vectors

[fierce lagoon]

That's lame

For the plane $ax + by + cz = d$, the normal vector to that plane is $\langle a, b, c \rangle$

[warm shale]

Umbraleviathan

[fierce lagoon]

So you create two arbitrary planes and then cross them

Or

Alternatively

The easiest way is to have one plane, find an orthogonal plane, and then take the cross product of the two planes

If you have the normal vector <a, b, c>, what is one vector orthogonal to <a, b, c>?

@fast cliff

I think this way is gonna be a lot eaiser

[obtuse pebble]

@fast cliff Has your question been resolved?

[fast cliff]

yea i dont know that word either

[fierce lagoon]

You're telling me you're dealing with planes without learning the basics of vectors

Orthogonal vectors are "perpendicular" vectors. Their dot product is 0

[fierce lagoon]

Are you familiar with dot products

[fast cliff]

yea the textbook is kidna stupid

it talks a lot about matricies and

equations

it barely relates them to the plane counterpart

or visualization in general

[fast cliff]

nioe

[fast cliff]

and yea

[fierce lagoon]

so basically orthogonal vectors dot to 0

so <a, b, c> ⋅ V = 0

Find V (theres an infinite number of V's, but there's a couple that are optimal)

but like

its gonna be hard to create these planes without knwoing what vectors are

[obtuse pebble]

@fast cliff Has your question been resolved?

[fast cliff]

yea

anyways i think i got it right

[fast cliff]

.close

[obtuse pebble]

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[frozen swift]

Give me formula

[marble junco]

,rotate

[marble junco]

what do you know?

[frozen swift]

Nothing about this

[marble junco]

ok, google quadratic formula

[frozen swift]

Ok thx

[abstract flame]

me when quartic formula

[obtuse pebble]

@frozen swift Has your question been resolved?

[obtuse pebble]

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[rustic copper]

<@&286206848099549185> how would I go about solving For “T” in the distance formula d=rt

[haughty onyx]

t= d/r

[sour ether]

You want to isolate the the T to one side of the equation. Algebra tell us that we can divide both sides of an equation by the same number/variable/whatever. so d/r = rt/r Simplify the right hand side by crossing out r/r (since that just equals 1) and you get d/r = t

[rustic copper]

Omg thank you. Now the second question is solving a2 + b2 = c2. To solve for B, how would I go about that

[sour ether]

do you mean a^2 + b^2 = c^2?

[rustic copper]

Yes

[sour ether]

You undergo the same basic steps. First isolate the variable "b" to one side of the equation

b^2 = c^2 - a^2

then, to get rid of the power you use its inverse, the square root function

[abstract flame]

dont forget ±

[sour ether]

I was just gonna leave the right hand side all under the square root

lemme find the fancy version, because I can't type it easily in discord

[abstract flame]

b=±sqrt(c^2-a^2)

[rustic copper]

?

Like this

[abstract flame]

but remember that b can also be negative

otherwise ur good

[sour ether]

i mean, does the negative come up that often in the pythagorean theorem

[abstract flame]

yes it does

a lot

in optimization it's very important

[sour ether]

fair enough

[rustic copper]

Ok thanks for the help guys

.close

[obtuse pebble]

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[primal idol]

How do i solve this

help

that answer is incorrect

[obtuse pebble]

@primal idol Has your question been resolved?

[tardy epoch]

Write g(x) as the derivative of a power series

[primal idol]

how

I don't get it

we already have g(x)

should i rewrite g(x)

[obtuse pebble]

@primal idol Has your question been resolved?

[tardy epoch]

Write it as a power series if you know how. the derivative part was if you didn't

[obtuse pebble]

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[small rock]

I am trying to parametrize the upper branch of a hyperbola but I am not sure how.

[small rock]

The equation is y^2/9 -x^2 = 1

So far I have gotten to gamma(t) = (tan(t), 3sec(t))

But I don't know what to do to only parametrize the upper branch

[royal basin]

p sure you can accomplish that by only having t go from -pi/2 to +pi/2

[small rock]

What the heck it worked

But why tho

I tried doing stuff like 0 to pi

Wasn't even close

[royal basin]

0 to pi would've let the 3sec(t) cross its asymptote and go negative for the later half

[small rock]

ahh

[obtuse pebble]

@small rock Has your question been resolved?

[obtuse pebble]

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[junior zephyr]

i have a dataset of 1300 sport podcasts, out of which 450 are of football , and 500 are of basketball and the remaining 350 are of 'other sports' . can i test for two proportion difference with this dataset?

[junior zephyr]

i mean should i random sample again?

[obtuse pebble]

@junior zephyr Has your question been resolved?

[junior zephyr]

.close()

.close

[obtuse pebble]

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[junior zephyr]

lol

[obtuse pebble]

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[finite glen]

idk if this is legal but i would like some help with logs and fractions in the $ notation

[finite glen]

i found this message in another channel and wanna try to use it to help me

Split $\log_a \frac{a^3x}{y^2}$ into 3 parts using log property

[warm shale]

WhyWouldYouKap

[finite glen]

$frac{\logx}{\2log3}$

[limber quartz]

product and quotient rules of logs.

they're in every logarithm cheat sheet

[finite glen]

im not struggling with the question

im struggling with the notation with the $ in this discord

thats all mate

[finite glen]

this is what I am trying to show

[limber quartz]

LaTeX?

[finite glen]

but am failing miserably

whats that

[limber quartz]

$\frac{\log{(x)}}{2\log{(3)}}$

[warm shale]

Disorganized

[finite glen]

thanks mate

appreciate it

why is there so much notation for one fraction tho

[limber quartz]

$y = \log_b{(x)}$

[warm shale]

Disorganized

[finite glen]

do u need both sets of brackets?

{} and ()

[limber quartz]

the curlies, you need

[finite glen]

$log{x}$

[warm shale]

WhyWouldYouKap

[limber quartz]

the round braces, I put there because it makes the argument of the log function more clear

[finite glen]

ok thanks

that makes sense

[limber quartz]

you forgot the backslash

[finite glen]

$\log{(x)}$

now i get the log part

how do u do the fraction part

[limber quartz]

you forgot the backslash

[finite glen]

whats the backslash for?

[limber quartz]

\

\log{x}

[warm shale]

WhyWouldYouKap

[finite glen]

oh

that makes sense

[limber quartz]

variables are supposed to render italiced but functions are not

the backslash's only purpose is to make the symbols render the way they are supposed to

for example:

[finite glen]

$\log{(x)}$ $\2log{(3)}$

[limber quartz]

$\log{x} \
\sin{(x)} \
\sqrt{x}$

[finite glen]

ok thanks

[limber quartz]

ugh, hang on

[warm shale]

Disorganized

[limber quartz]

there we go

[finite glen]

ok thanks

the last part im confused with is fraction notation

like how would u do 2/3x

[limber quartz]

you can also make bigger or smaller round brackets of every kind, or brackets that fit their contents automatically

[limber quartz]

\frac{numerator}{denominator}

[finite glen]

ok

$\frac{2}{3x}$

[warm shale]

WhyWouldYouKap

[finite glen]

oh wow

this is revolutionary

[limber quartz]

$\frac{\text{numerator}}{\text{denominator}}$

somtimes it fails for no reason at all EDIT or because I forget ta closing dollar-sign

[finite glen]

ok thanks

let me try to do this myself before i close

u bloody legend

[warm shale]

Disorganized

[limber quartz]

let me link you to my favorite reference

[finite glen]

$\frac{\log{(x)}}{2\log{(3)}}$

[limber quartz]

https://math.meta.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference

[finite glen]

whats the issue?

[remote fiber]

oh and btw for that question x= positive or negative 3

[warm shale]

WhyWouldYouKap

[finite glen]

omg i got it

thanks so much

[limber quartz]

.

[finite glen]

so the full line of working would be

oh wow

$\frac{\log{(x)}}{2\log{(3)}} + 1/2 = \frac{\log{(x)}}{\log{(3)}}$

[warm shale]

WhyWouldYouKap

[finite glen]

beautiful

[limber quartz]

there is a channel here that is just for texting LaTeX commands

#latex-testing

[finite glen]

ok thanks

[limber quartz]

and help

[finite glen]

didnt see that until now

[limber quartz]

#latex-help

[finite glen]

i didnt know it was called latex until now

thanks so much mate

u legend

.close

[obtuse pebble]

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[icy cape]

Bacteria cells split in 2 every 5 minutes. New cells also continue splitting in the same way.

How long will lit take for 1 cell to divide into 16 cells

[finite glen]

hey mate

[icy cape]

hello

[finite glen]

we start at 1 correct

[icy cape]

yes

[finite glen]

which is 2 to the what?

[icy cape]

0 right?

[finite glen]

yep

2^x = 16?

[icy cape]

we can use factorisation right

[finite glen]

you can

[icy cape]

...............16
8 (2)
4 (2)
(2) (2)

2^4

[finite glen]

or u can use prior knowledge to know that it is 2^4

which means u start at 2^0

and finish at 2^4

[icy cape]

yes

[finite glen]

adding 1 to the power every 5 mins

[icy cape]

20 minutes?

[finite glen]

yep

if u do it manually

[icy cape]

alright thanks

[finite glen]

u get the same answer

hope this helped u mate

[icy cape]

👍

it did 🙂

alright goodbye

.close

[obtuse pebble]

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[reef orbit]

Let's say we have a data 1,2,3,4,5,6
And we want to figure out the Q1 which is 1.75. the Values above this Q1 value are 2,3,4,5,6 which are about 83.4% of the data and below Q1 is 1 which is 16.6% of the data . But doesn't a Q1 separates a data at a point where 75% of observations are above that point and 25% of observations are below that point. can anyone explain it to me what's the reason behind it?

[reef orbit]

Hello can anyone help me explain the logic behind this ?

[finite glen]

ill be honest

i put it into my physical calculator and got 2 and 5 as the q1 and q3 values respectively

which doesnt make sense either

for the iqr

[reef orbit]

Q1 is (N+1/4) so using that value we get = 7/4 which 1.75

[reef orbit]

So what's wrong here ?

[finite glen]

u got 1.75

and i got 2

we cant both be right

isnt q1 and q3 found by the median of each side of the median

so if u have 1 2 3 4 5 6

the median is 3.5

which means the median of the lower side is 2

and the median of the higher side is 5

which means the iqr is 3

[reef orbit]

Even if your q1 is 2 the values above q1 are 3,4,5,6 which means 80% of values are above it which isn't right

[finite glen]

how is that 80%

its 4/6 mate

which is 66%

[reef orbit]

Then again not 75% above that point

[finite glen]

how can u find 75% of 6 without a fraction

thats 4.5 numbers

[reef orbit]

The Q1 for sure is 1.75
Its calculated by (N+1/4)
So when you get 1.75 you have 5 values above it and 5/6 is 83.33% and Q1 separates a data at a point where 75% values in the data lie above it and 25% values in the data lie below it.

[finite glen]

i think i get whats wrong

actually i have no idea sorry

if ur doing this to win an argument

im not here for that

all of my sources including my own knowledge, online and physical calculators

all say that q1 is 2

https://www.calculatorsoup.com/calculators/statistics/quartile-calculator.php

[reef orbit]

I'm not here to win any argument. I'm quite confused with concept for like 4-5 days and want someone to clear this up

[finite glen]

put it in here

also u can read the bottom section of how to find it

[reef orbit]

Calculator soup doesn't provide accurate values

[finite glen]

why not

[reef orbit]

Wait

http://www.alcula.com/calculators/statistics/quartiles/#gsc.tab=0 use this

[finite glen]

ive never seen this method anywhere else tbh

[reef orbit]

https://www.cuemath.com/quartile-formula/

[unreal skiff]

Actually, wikipedia says there are multiple way to calculate quartile and it ususally yields different results hope that settles the argument

[finite glen]

ok

all ill say

ive been taught it to be the median of the median

other stuff isn't how its taught in australia

[reef orbit]

But still if you take it as 2 the values lying above it are 4 and below it are 1 still doesn't make the ratio of 25% and 75%

[unreal skiff]

If you think about it, the method you are using doesn’t give the value at 25%

It should be 2.25

[reef orbit]

N is 6 and N+1= 7 and dividing 7 by 4 gives the value 1.75 isn't it ?
And values above 1.75 are 5 and below it is 1
Again doesn't satisfy the definition where quartile is said to be a point that separates data in a way where 25% of the observations are below Q1 and 75% of them are above it.

If you use the different method where 2 is the answer it still doesn't satisfy the condition

[unreal skiff]

It is kinda difficult to answer your question because the definition for quartile for me is the middle number between smallest and median

What does professor told you about thedefinition

Of quartile

In your formular especially

[reef orbit]

You can refer to this image where 25% of observations are below q1 and 75% of them are above it

[unreal skiff]

I feel like if you want exact 25% the formular should be (n+3)/4 isn’t it

[reef orbit]

If we take that formula that answer would be 2.25 and still Values above it are 4 and below it are 2
Still doesn't meet the criteria

[unreal skiff]

There is no way to count the data and make it 25 that is why we are using middle value between two data. So in my case there are 2.25 below it

To simply put, if the number of data is 7 then you can’t make 25 from 7 as denominator.

[reef orbit]

Looks like I've to look for more info on books about but thanks anyway

[obtuse pebble]

@reef orbit Has your question been resolved?

[obtuse pebble]

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[spice isle]

I'm stuck with a question .can someone plz help me how do I find the power x

[spice isle]

Q11

[royal basin]

sqrt(81) = ?

[spice isle]

The would be 9

[royal basin]

and 3 to what power gives 9?

[spice isle]

I understand tht one but not

E

There's a power 4

[royal basin]

well you should have told us it's E you are struggling with

[spice isle]

Srry

[royal basin]

that is a fourth root though not a fourth power

anyway

32 is 2 to what power?

[spice isle]

5

[royal basin]

right

and recall that taking the nth root of a number is the same as raising it to the power of 1/n

so (2^5)^(1/4) = 2^?

[brave ravine]

ann do u know arithmatic progressions?

[royal basin]

@brave ravine if you have a problem you need help with then open your own channel. see #❓how-to-get-help for instructions.

do not pester individual users.

[brave ravine]

oh sorry

im new i didnt know

[spice isle]

The answer is 5/4 tho

[royal basin]

...yes? i expected you to say 2^(5/4) to my prompt

[spice isle]

Ohhh

[royal basin]

recall the exponent law (a^m)^n = a^(mn)...

[spice isle]

Ohh now I understand thank you for the help

[unkempt shard]

hi

i need help

with math

algebra

how to get help

[nova bane]

#❓how-to-get-help @unkempt shard

[unkempt shard]

ok

ty

[obtuse pebble]

@spice isle Has your question been resolved?

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[obtuse pebble]

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[buoyant marsh]

How can i show/prove this

[royal basin]

what do the T's mean? and what are n, m and a?

[obtuse pebble]

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[obtuse pebble]

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[timid silo]

Just wanted to make sure, but did I graph the vectors correctly?

[timid silo]

it is a bit iffy but since the y component is equal to the x component, there would only be change in the x direction, or am i mistaken?

[valid crown]

why r is cos + cos?

[timid silo]

my same question

it is a physics question, which is why i did not include it in my original question

but here is the full question (even if it is off-topic)

[valid crown]

oh

quaternion notation

[timid silo]

yes

[valid crown]

crap, i recall accelerations radial was r×omega^2 and tangential r×epsilon

guess Vr would be r×omega

[timid silo]

this is the velocity we are talking about

and like those two fromulas

are derived from this

[valid crown]

if phi(t) = t^2 then omega(t) = 2×t

[timid silo]

im just really confused on the understanding of this question lmao

it has no change in the y velocity, right?

[valid crown]

why not?

[timid silo]

how can the y component be Rcostheta tho

i tried drawing it

because it is just the adjacent over the hypotenuse by costheta = r(x)/R

[valid crown]

welp if it's cos + cos instead of cos + sin then the movement wouldn't be circle, but an elypse

[timid silo]

that makes sense for the horizontal component, but idk how costheta = r(y)/R makes sense

[valid crown]

not sure whether not actually linear

[timid silo]

oh what?

im so confused haha 😅

understanding vectors are hard

[valid crown]

Ever looked into light phase?

[timid silo]

what is that

[timid silo]

also it is, cos^2 + cos^2

because we are assuming theta = t^2

[valid crown]

depending how much in phase E and M are they have a different overall movement

[valid crown]

crap

how do you think trajectory looks like?

[timid silo]

I am still thinking of a line

but if you were to ask me to back up that claim, I wouldn't know how to answer you

[valid crown]

in certain 2d it might be a line

I think

[timid silo]

😅

okay wait, so let's do it step by step

[valid crown]

I'm not in home so can't ilustrate it to you

but

there is analogue in light phase

[timid silo]

I am not really familiar with that concept

sadly

im just a lowly physics 101 student haha

[valid crown]

if phase of E and M are at 90deg (so cos is 90deg from sine) then they make up perfect spiral and their movement from one plane looks circular

if it's 0deg then it's linear (cos + cos or sin + sin)

and between an elypse

you can look it up

it may clarify a bit

cos squared would still be from -1 to 1

and periodic

so it shpuld be linear

[timid silo]

huh

so wait

was my idea correct

at the end of the day?

and since the velocity is -2Rsin(t^2)i^ -2Rsin(t^2)j^

[valid crown]

equations seem legit

[timid silo]

it is the same idea, just that there is only tangential component

and not the x compnent

[valid crown]

but I doubt the graphics are

[timid silo]

oh that was just at one point

tbh idk, i am not sure of the technicalities just yet

but i will just assume that v_R = 0 and v_T = -4Rsin(4)

we can talk about this afterwards @valid crown

i have to submit it today and it seems like I still failed to completely understand this

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

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[indigo sphinx]

.close

[slender lagoon]

Hi

[slender lagoon]

What does it mean a set is countable

[rigid lintel]

there exists a bijection between that set and the natural numbers

suppose the set of integers

you can map each element of N to Z and vice versa

so it is countable

[obtuse pebble]

@slender lagoon Has your question been resolved?

[slender lagoon]

Nope

[obtuse pebble]

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[timid silo]

Hello!

I'm taking an advanced algo class and I'm studying for the exam. Say we are working with the Minimum Vertex Cover problem. How would one go about designing a certain time algo that returns a vertex cover of a certain size with a certain minimum probability.

Take last years exam question for instance: To design a O(|V|^2) time algo, with size <= 1.5m (m being optimal that is) with probability of at least 0.999.

The probability part is tripping me up a bit. I know it's pretty basic but we went through this in the beginning of the course and all the others courses in between have made me forget most of it, context switching really isn't my strong suit lol.

[obtuse pebble]

@timid silo Has your question been resolved?

[timid silo]

No :/ Really stressed about this doesn't seem like I can find anyone who can help me understand it..

[timid silo]

<@&286206848099549185> Maybe :)?

[obtuse pebble]

@timid silo Has your question been resolved?

[timid silo]

Someone mentioned chernoff bounds and deleted, but yes I think that might be right since it has to do with probability, but chernoff bounds as i understand is in regards of a sample size, this has nothing to do with a sample size really so not sure how it fits.

[timid silo]

.close

[obtuse pebble]

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[silver plover]

Help plz

[royal basin]

your H1 is ambiguous

do you mean "the proportion of numbers with leading digit 1 isn't 30%" or do you mean "the proportion of numbers with leading digit not 1 is 30%"

[silver plover]

The first one

[royal basin]

right...

[silver plover]

I get what u mean by ambiuous now

"the proportion of numbers with leading digit not 1 is 30%"

[royal basin]

congratulations you just shit yourself

seemingly on purpose too

[obtuse pebble]

@silver plover Has your question been resolved?

[silver plover]

Right k then

[snow sequoia]

sa

[royal basin]

and by this i mean that "the proportion of numbers with leading digit 1 isn't 30%" was actually the correct H1 for your H0

remember that the null and alt hypotheses should be COMPLEMENTARY

[silver plover]

Yh ok

Sorry mb

[obtuse pebble]

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[ocean kestrel]

I’m stuck at this equation, could someone help me with this one?

[spice citrus]

if you have x^2 = 4 + 9 for example x = sqrt(4) + sqrt(9) = 5 doesn't work

you can't take the square root like that at the 5th line

[ocean kestrel]

Can’t I sqrt everything on the left side of the equal sign and sqrt everything on the right?

[spice citrus]

you can, but you can't distribute the square root like you did in the picture

[tepid minnow]

u can but sqrt(a+b+c) isn't equal to sqrt(a) + sqrt(b) +sqrt(c)

its just sqrt(a+b+c)

[ocean kestrel]

Then what’s sqrt (a+b+c)?

x = sqrt (k^2/2 - k + 1)

Is that correct?

[spice citrus]

if you look at the first equation you have, you can just move the (2 - k)^2 to the other side by adding it to both sides of the equation

[obtuse pebble]

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[opaque cairn]

.re

.reopen

.close

[obtuse pebble]

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[heady socket]

<@&286206848099549185> literally last problem cant figure this shit out at all finna kms

[obtuse pebble]

@heady socket Has your question been resolved?

[novel ridge]

I think i have an idea

You there?

ok so if you have 200 bars with $1 and every 0,16 increase gets you 3 buyers out

the general for of any case would be

1+(0,16 n) ---- 200 - 3n

n as the variation

and you know the revenue would be the product

so you have (1 + 16n/100) (200 -3n), which will be maximized

now, the max product of two (at least whole positive) numbers happens when those numbers are the same

now

you will give the expression another form

1 + 16n/100 can be written as

(48n + 300)/300

and 200 - 3n can be written as (3200 - 48n)/16

final form

1/4800 x (48n+300)(3200 - 48n)

and that would be your revenue

as 1/4800 is constant

for max result 48n+300 needs to be equal to 3200 - 48n

if you sum those you get 3500

and since they need to be equal the each one is 1750

so 48n+300 = 1750

48n = 1450

30.2083333333

30.208

and if that's n

so if the price is 1 + 0,16 n

then that's 1 + 0,16 x 30.208

4.83328 + 1

[obtuse pebble]

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[novel ridge]

5.83 as price????

[obtuse pebble]

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[primal idol]

How do i find the interval of convergence hefe

Here

[obtuse pebble]

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[obtuse pebble]

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[teal slate]

Hi would this be right?

[teal slate]

I Jsut had to find the radi and idk if it’s right or wrong

No I was looking for the radi

Not the area

The question wants the radi

So I want to know if I leave the radi as is

[potent monolith]

1/4 pi r² = 4²
Then find r

[teal slate]

With the area?

[potent monolith]

Tell me,is the area 4²?

[teal slate]

16

[potent monolith]

Duh
So they want you to find the radious?

[teal slate]

Yeah

They want the radi

[potent monolith]

Exactly
The formula of the area is 1/4 pi r²
Means
1/4pi r²= 16

[teal slate]

So that would be the radi?

If so why was I given the area of the Quarter circle

Let me send you a picture

[potent monolith]

U dont get it...wait

[teal slate]

Yeah I don’t I’m quite confused 😭

[potent monolith]

U get it now?

[potent monolith]

K

[teal slate]

Oh so the radi would be 4.5?

[teal slate]

I think I get it now

If it was a semi circle it would be 2 sqaured?

[potent monolith]

Appoximately ..yes

[potent monolith]

What ..area?

[teal slate]

No just if it wasn’t a quarter circle

Also what is this part saying 2r= 20.372

?

It’s not that clear

Just need some clarification

[potent monolith]

Ok lemme make it clearer ...wait

[teal slate]

Okay thanks 🙏

[teal slate]

Oh it was saying r^2 okay I think I’m fine now 🙏😁

[potent monolith]

Cool

[teal slate]

Wait r would be what for the first part?

[potent monolith]

What do you mean?

[teal slate]

Where you said 1/4 py r^2

=16

What would r be?

[potent monolith]

Its the radious

[teal slate]

Or is it unknown

[potent monolith]

Yes its unknown
Thats what i just found the value of

[teal slate]

Oh okay so 1/4 times py = 16?

[potent monolith]

1/4 time pi times r² =16

Why are you cutting off r²?

Do you know what the area of a circle is?

[teal slate]

Yes I do

I was getting confused

[potent monolith]

Np

[teal slate]

Nvm thanks your help 😭🙏

I Jsut had to look at your example properly

[potent monolith]

You can tell me if still confused

[teal slate]

Last question how does 16 turn into. 64?

That’s all I’m confused at

[potent monolith]

Ok wait

[teal slate]

👍

[potent monolith]

Anything else your confused at?

[teal slate]

Oh okay now I’m good thanks 🙏

Bye I appreciate it

.close

[obtuse pebble]

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[potent monolith]

Happy to help

[obtuse pebble]

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[hexed carbon]

It takes 52 seconds to get 25,000.
This can be repeated as many times as wanted.
It then takes 10 minutes to set up a duplication.
The duplication will increase the total money by the amount of money owned at the start and it takes 18 seconds.
E.g. if enter duplication with 100,000, total money will increase by 100,000 every 18 seconds.
Can leave the duplication and take all money but will take 10 minutes to set up again.
E.g. if enter duplication (10 minutes) with 100,000, do duplication 5 times to get 500,000 (1.5 minutes) then leave duplication and re enter (10 minutes)
and do duplication 5 more times (1.5 minutes) will end up with 2.5 million. I.e. increasing by 500k second time

[hexed carbon]

is there a quick method to find answer such as excel or a formula or is it just trial and error as have been doing?

[obtuse pebble]

@hexed carbon Has your question been resolved?

[obtuse pebble]

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[warped fulcrum]

How can I go about proving the solutions of an ODE are analytic without solving the ODE?

[warped fulcrum]

To add. Analytic for all points in R

[obtuse pebble]

@warped fulcrum Has your question been resolved?

[kind hawk]

well that probably depends a lot on the particular ODE

[warped fulcrum]

Right. It's a linear 2nd order Ode given by y"+ty'+y=0

[obtuse pebble]

@warped fulcrum Has your question been resolved?

[warped fulcrum]

I read something about analytic coefficients being related to the solution being analytic

Or maybe something with singular points? No singular points at all perhaps?

<@&286206848099549185>

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[timid silo]

Hey i have this i am not very sure result here

[timid silo]

can someone confirm the result of the limits here ?

in the limit -∞ it should be +∞

and in the limit +∞ ????

i think its an error

it somehow said the limit is 2

i think the limit is 1 idk what is the correct awnser

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[turbid zealot]

Hello! I just want help confirming that I am negating the statement properly. We are doing proof by contradiction. So if I am given this prompt and want to negate If Fn is not a perfect cube, then n is not in the set of {1 , 2 ,6} I would state If Fn is not a perfect cube, then n *is* in the set {1,2,6} ?

[turbid zealot]

Or I suppose I could also do If Fn *is* a perfect cube, then n is not in the set {1,2,6} ?

[obtuse pebble]

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[next lantern]

what is b asking?

[fossil crag]

Find g''(x)

You will be able to write it as ...... + ...f''(x)

[next lantern]

ohhhh

so A and B

are "coefficients

i just took the second deriv

makes sense now

[fossil crag]

Maybe they are coefficients

[next lantern]

they are function

correct?

[fossil crag]

Maybe they depend on x

[fossil crag]

Correct

[next lantern]

ah

got it

just had to actually derive

ty

[obtuse pebble]

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[quick arch]

I'm not understanding how to graph this

[obtuse pebble]

@quick arch Has your question been resolved?

[mystic hill]

T is on the x axis and y is on the y axis

Plus in the coordinates to your equation and that will be your slope for that point

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[timid silo]

What the hell am i doing wrong

[timid silo]

Oh

Teehee

Ty

.close

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[tight wigeon]

How do I prove this?

[tardy epoch]

write 49 = 7^2

[tight wigeon]

then...

[tardy epoch]

try calculating the ratio now

[foggy forge]

try to change like, 7^(n+1) = 7^n * 7

maybe you will get something:)

[tight wigeon]

let me see

like, I've just tried that minutes ago, but I get stuck

i will try again

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[mint topaz]

In Exercises 21-24, use a graphing device to approximate, to one decimal place, all solutions to the equation. 24. xe^x = x^2 +4x+2

[nocturne minnow]

Did you use a graphing device?

[mint topaz]

Would xe^x be the exact same as just Y= on my calculator?

[nocturne minnow]

No

It's two separate equations

Plot them both

Find where it intercepts

[mint topaz]

xe^x then x^2+4x+2?

[nocturne minnow]

Yes

[mint topaz]

I got -3.373, -0.116 and -0.715, -0.35

[nocturne minnow]

Then sure. I didn't try the problem myself

[mint topaz]

Ok np, thank you!

How do i mark as resolved?

.close

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[royal shard]

@mint topaz

there is another point

at x=1.94 roughly

[obtuse pebble]

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[woven marsh]

Course: Complex analysis

Question: What do they mean by finding the sum of this series? Am I supposed to write out a value of what it sums to?

[woven marsh]

I first wrote out the series.... 1 + 1/2 cos(x) + 1/4cos(2x) +1/8 cos(3x)+... , but I don't know what to do next or if this is nessesary

This problem has the variable x and that confuses me the most

<@&286206848099549185>

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[strong nebula]

Hey Im not really sure why my way did not work, the left side is the solution and the right is my work

For the teacher's solution he found the derivative but it isnt simplified and isnt necessary right?
I simplified mine but it seems like after plugging 0 our answers differ

[mental plaza]

uh

aye

wassup

ure not following

the quotient rule

also not following proper rules

when finding derivative

numerator has

2xe^x

when differentiating that

use product rule

but ultimate mistake is I don’t see the use

of quotient

rule

[strong nebula]

I didnt write the denominator but it comes back later,

[mental plaza]

where

okay later

but still

numerator isn’t right

use product rule for 2xe^x

[strong nebula]

(-3)^2 is the denom. replacing x with 0

[strong nebula]

why cant i distribute like this problem

[mental plaza]

distributing is fine

that’s not the prob

the prob is u didn’t use product rule

when finding deriv of 2xe^x

[strong nebula]

I dont follow.. i wrote it as the quotient rule f(x)g'(x) - g(x)f'(x) / g(x)^2

[mental plaza]

okay

f(x) is 2xe^x yes?

differentiate this

now

and tell me what u get

[strong nebula]

its the same

[mental plaza]

nope

it will be the same if it was 2e^x

but it is MULTIPLIED to an x

so u use product rule

f’(x)g(x) + g’(x)f(x)

in this case f(x) is x and g(x) is e^x

[strong nebula]

so it will be 2e^x+2xe^x

[strong nebula]

wait why is f only x, its 2x*e^x

[mental plaza]

yes

[mental plaza]

u can take it as 2x if u want

doesn’t make a difference

[strong nebula]

but the solution i just gave you has another 2xe^x

[mental plaza]

I would factor it out

[mental plaza]

that’s following quotient rule

rn ure performing product rule in the midst of quotient rule

[strong nebula]

ok ic

factor that out would be 2e^x(x)

not exactly sure what to do with that so im jusst going to try distributing

[real prawn]

.claim

[strong nebula]

my teacher has only thought us composite functions today and it wont be on the midterm review which im working on right now..

the answer is right i guess?

[obtuse pebble]

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[golden path]

Hey

[strong nebula]

what math is this btw?

[golden path]

<@&286206848099549185>

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[rare onyx]

how to integrate this?

[rare onyx]

can someone show me the steps plz? i tried several times

[timid silo]

$\int x^n dx = \frac{x^{n+1}}{n+1}+C$

[warm shale]

♡LexQa♡

[obtuse pebble]

@rare onyx Has your question been resolved?

[rare onyx]

how did we get the 3?

[timid silo]

it is the integral of x^2/8 right?

integrate that

going to be x^3/24

sub in the bounds

you get 64/24 - 0

64/24 is simplified to 8/3

[rare onyx]

thank you

[obtuse pebble]

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