help-23

[hasty blaze]

--be a biologist--

we dont have to do math

[chrome pond]

too much plants and insects

no thank you

[hasty blaze]

those 2 are the best part

im actually trying to be a botanist

[chrome pond]

damn thats sick tho

but ait good luck with ur math its clearly too late for me to do math so imma go sleep

[hasty blaze]

its actually 4 20 am for me too

but ty

.close

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[thin swan]

I need help with the quotient rule for following equation:

[empty gyro]

Derivative quotient rule?

[thin swan]

yes

[empty gyro]

!status

[safe radish]

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

[thin swan]

3

i can show work 1 sec

[chrome pond]

how did you get -5 ?

[thin swan]

derivative of (x-5)

[empty gyro]

Try again

[thin swan]

-4?

no

bruh mb

yeah i changed it to 1

[empty gyro]

-1?

[thin swan]

thank you guys

idk how i forgot basic derivatives

[chrome pond]

np happens to the best

[thin swan]

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[river field]

How would you approach this?

Also is that comic sans, what kind of kindergarten logarithm problem is this?

[grave adder]

idk can u solve it

[river field]

Looks kinda tricky

But I can only help you along, not solve it for you

[merry pelican]

Looks more like Century Gothic to me

[river field]

Upon closer inspection you may be right, but it's still too goofy for me to take it seriously

[river field]

Here's a hint, try taking log base 3 on the other 2 equations, and try rewriting log base 27 to be in base 3

[devout shale]

🙈

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[ionic nest]

hello chat can i get some guidance

i calculuated the unit vector for Force F

but idk where to move from htere

[empty gyro]

normalize the direction vector, then dot product with the force vector

aka: project the force vector along the direction vectors

[hardy lion]

you dont normalize

nvm you do

[ionic nest]

I'm having problems with it @empty gyro

[empty gyro]

why are you dividing by 3 here?

[ionic nest]

so i took the magnitude of the vector values?

in the step above to get sqrt (9)=3

[mellow cypress]

That would change the force. Only the direction needs to be normalised

[ionic nest]

ohh

so to normalize direction

what do u do?

[mellow cypress]

The direction is (i+j+k)/sqrt(3) right? Is that a unit vector or not?

[ionic nest]

i guess it looks like one

[mellow cypress]

Then it is already normalised

[ionic nest]

oh ok

but it isnt derived from force F right

its just a normalized vector

[mellow cypress]

So you just need to compute the dot product

[ionic nest]

oh so just do dot product

[mellow cypress]

It’s just a unit direction

It has no relation to anything other than a direction

[ionic nest]

oh ok ty

for this part

do we need to just normalize it

and then use dot product

right

[mellow cypress]

Yes

[ionic nest]

ok ty

!rep @mellow cypress

f

how do i say u were helpful n stuff

[mellow cypress]

No clue

Just close, i don’t want a helpful tag or some shit

[ionic nest]

alr

.close

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[unborn venture]

do i just draw a derivative of the graph and figure out each y point of the the x

[sleek plank]

you can just find the slope at the specific point for most of those by just using slope formula

since they’re on straight lines

[safe radish]

@unborn venture Has your question been resolved?

[unborn venture]

okok

let me try this lmk if i’m doing it right

[unborn venture]

the point slope forums?

formula?

.close

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[burnt umbra]

yo

[burnt umbra]

when we FOILed how did the 22a come from

shouldn't it be 11(-2) = -22

[granite idol]

Typo, probably

[burnt umbra]

but the whole equation is built around it and it's in khan academy

so the question is wrong?

[granite idol]

Well, it's wrong. Plug in what they get for a and b, see if it matches what it's supposed to

[lime dust]

You have to trust your basic knowledge a bit more

[burnt umbra]

ok thanks

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[frank dome]

can someone help me with this? my answer key says 12 but I don't get how it's 12

[granite idol]

It can't be 12...

[frank dome]

that's what I am saying it should be 33

but my answer key says 33 which is why I am confuced

I meant to say 12

my answer key says 12

I guess I will just to the teacher about it

yeah which is why it confuced me

confused

yeah thx anyways man

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[warm patio]

What's the reflection point in the function
X/(1-x²)

[warm patio]

I know it's (0,0) with graph

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[tribal inlet]

!help

[safe radish]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[tribal inlet]

when you rotate shapes by 80 190 270 degrees

why is there a pattern

i mean 90 80 270

like every time you rotate it by 90 the x and y coordinates change in a specific way

everytime you do it by -90 it changes specific way

eveyrtime you do it by 270 -270 it changes specificlly different

[lean otter]

wdym

by that>

[tribal inlet]

well

i dont need help

but its just like

im curious i guess

[lean otter]

ok

but like

what are you

curious about

[tribal inlet]

you have the triangle ABC

point a is (3, 5)
point b is (6, 8)
point c is (2, 4)

the triangle abc rotates 90 degrees

if that were to happen the new points would be

[lean otter]

that's a line

segment

[tribal inlet]

where did you get line segment

if i said triangle

which is not a line segment

[lean otter]

y=x+2

[tribal inlet]

no

[lean otter]

3, 5

[tribal inlet]

i said triangle

[lean otter]

but

[tribal inlet]

ok imagine it is a triangle

[lean otter]

ok

[tribal inlet]

ok i didnt mean to make it line segment

whatever 3 random points

that makes it a triangle

[lean otter]

k

[tribal inlet]

if you rotate it by 90 the x and y coordinates change

differently

llike for example

[lean otter]

yea

[tribal inlet]

(-7, -3)
(-5, 4)
(-2, 1)

you rotate that 90 degrees its

(3, -7)
(-4, -5)
(-1, -2)

but if were to be 180 degrees it would look different

the x and y coordinates would be

(7, 3)
(5, 4)
(2, 1)

so do u see how the x and y coordinates change differently depenidng on how you rotate it

180 90 270 -180 -90 -270

[lean otter]

yEA

but

they change differently when you rotate at different angles

[tribal inlet]

yea

well i know the differences

but i was just wondering why lol

[lean otter]

why what?

[tribal inlet]

why its in that fashion

[lean otter]

because

if you rotate the points around the origin

it becomes it

[tribal inlet]

well

apprarently

the answer is because of linear algebra

matrices

but i dont understand the order

[lean otter]

oh

can't help you w/ that

[safe radish]

@tribal inlet Has your question been resolved?

[sly crown]

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

you may also want to examine how complex numbers behave

[safe radish]

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[tiny tusk]

can someone explain to me the steps you use to change an equation into general form

[tiny tusk]

i just need to know for in general but i will send this question so we have an example to work with

[bleak saffron]

the general form im assuming is ax + by = c?

you would just add 1/2x to both sides of the equations and there is your answer

simple algebra

[tiny tusk]

𝑥 + 𝑏 𝑦 + 𝑐 = 0 i belive

[bleak saffron]

then you would then minus 6 to both sides

and then multiply every term by 2

with that you should have something that looks like x-2y-12=0

[tiny tusk]

so what is my end goal? to make everything =0?

[bleak saffron]

yeah]

[tiny tusk]

so why cant i just take away y

[bleak saffron]

if that general form is what you gave me

you could do that too

[tiny tusk]

so 0=y-1/2x+6-y?

[bleak saffron]

yeah

either way will give the same result

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[sly elm]

So uhm I am 13 years old and in 6th grade, long ago we had this test that i missed a long time ago about this topic that i have forgotten and i want someone to help me.

[novel stag]

,rcw

[dry egret]

what is this book..

[sly elm]

Its in lithuanian "matematika tau+ 2 dalis"

[dry egret]

oh yeah which one u need help on

[sly elm]

the first three

[dry egret]

where do i start..

[sly elm]

119 C variant please

[dry egret]

so 23.23.23

its (2 1/3)^3

or (7/3)^3

[sly elm]

Can you help me solve the c variant of 119 please? i want to understand how to solve it as i will have to rewrite this test

[dry egret]

um ocay

[sly elm]

because i got 7/3 .7/3 . 7/3

idk what to do next

[dry egret]

its (7/3)^3

u learnt the ^ right?

[sly elm]

idk what that is sorry

do you mean like

i have to divide the 7 and 3

[dry egret]

i can write it out

[sly elm]

Yes please

[lean otter]

he meant 7/3 to the power 3

[dry egret]

bad handwriting sorry

i just played badminton

[sly elm]

Ohhh i undersetand

so its (7/3) and 3 because there is three 7/3 ?

[dry egret]

yes!!

[sly elm]

Tysm why cant my teacher teach like this

[dry egret]

..

practice more

and goodluck in your test

.close

😡

[sly elm]

Wait

do i have to do it

[dry egret]

yes

[sly elm]

.close

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[fast bobcat]

I’m stuck on this question

[kind forge]

post the question

[fast bobcat]

23c

[kind forge]

there. that's a little easier to read. lemme take a look

[mortal sandal]

Law of cosines?

[fast bobcat]

Yes I tried that and I got 89 metres but it says the answer is 97.7 meters

[kind forge]

what do you have for path 2's length?

[fast bobcat]

128.6m

[kind forge]

is that right?

[fast bobcat]

yes

[kind forge]

also, are u sure ur calculator is in degrees? it's easy to forget these things

[fast bobcat]

Yep it is

[kind forge]

cool

ok lemme refresh my memory of the cosine ruel

oh i think i know

[dry egret]

did u use sin cos tan on these

[kind forge]

@fast bobcat when u did the cosine rule did you put in use the 114m and 128.6m?

[fast bobcat]

yea

[kind forge]

well that's weird

i put $\sqrt{114^2 + 128.6^2 - 2 \times 114 \times 128.6 \times cos(47\degree)}$ into my calc and it said 97.6587...

[fast bobcat]

Oh so it might be my calculator as I’ve checked it all and it says 89.04657921

[flat frigate]

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

[kind forge]

did u remember both squares?

[fast bobcat]

Yep

114 and 128.6

I’ve just changed calculators and put it in and it’s now coming up with the right answer. Tysm all of you for the help 😁

[kind forge]

well that's baffling

[safe radish]

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[solemn anchor]

If 2^mt = 64 what does m have to be?

m = t-4
m = 6-t
m = 6t
m = 6/t

[somber parcel]

First make the bases same

In the lhs the base is 2, so write rhs such that it is 2 raised to some power

[solemn anchor]

first one

[solemn anchor]

wdym

its 6

yeah

[somber parcel]

When there are same bases you can directly compare the powers, so the rhs, write it has 2 raised something

[solemn anchor]

the power needed is 6

[somber parcel]

Yeah

[solemn anchor]

wouldnt mt be equal to 6

?

i picked answer c

im now starting to think its a

[lime dust]

So if mt=6, what is m

[solemn anchor]

6/t

ohhhhh

[lime dust]

Good

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[crisp gyro]

for this question i differenciated to get f'(x)= 12x^2 +2ax +4 then i equated it to 0 since its a point of inflection and i subbed in x=1/6 to get a=13. what did i do wrong?

[safe radish]

Please don't occupy multiple help channels.

[rough storm]

points of inflection are where f'' changes sign from - to + :)

[crisp gyro]

like this? so g''(x)= 24x +2a, do i make it = to 0 now?

[rough storm]

yes, also remember the point of inflection is at x=1/6

[crisp gyro]

so a=-2 and i sub it into g(x)=0 to find b

and sub in x=-1/2

thanks guys i got b=3

[safe radish]

@crisp gyro Has your question been resolved?

[safe radish]

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[slate elbow]

So defining continously is doing limit

But how?

[tardy pivot]

imma try to solve it

like the exact value

assuming it convergesthat is

[slate elbow]

I mean

Just help me how to solve it

Give me hints

Ill follow and show what i calculated

Its math analysis 2

[flat frigate]

Obotron

[slate elbow]

So does anyone know ?<@&286206848099549185>

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[granite yoke]

2 The Trapezium and Midpoints
In trapezoid ABCD, sides AB and CD are parallel. Let M be the midpoint of the diagonal AC, N be the midpoint of the diagonal BD and P be the midpoint of the side AB. We know that AB = 15 cm, CD = 24 cm and the height of the trapezoid is h = 14 cm.
a) Calculate the length of the segment MN. b) Calculate the area of ​​the triangle MNP.
I'm from Brazil, my English isn't very good, I'm sorry if there is any error because I translated it using Google Translate

[safe radish]

@granite yoke Has your question been resolved?

[crude bear]

O que você tentou

@granite yoke

Ajudaria saber o que vem antes kkk, essa questão aí não é mamão com açúcar não

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[honest wolf]

help

[knotty pier]

Write log1000basex as log1000/logx

Put logx is t and solve

[honest wolf]

is it 0.1?

[knotty pier]

Idk i didnt solve

[knotty pier]

The x?

[compact quartz]

it is but how

[knotty pier]

Then yes

[honest wolf]

ye

[knotty pier]

But there is another solution also

logx = 1.5?

@honest wolf

[honest wolf]

i guess

thanks

[knotty pier]

Np

[compact quartz]

how did u do it>

?

[knotty pier]

Whaat

Put logx is t

And solve for quadratic equation

Then find x from that

[honest wolf]

yeah

[safe radish]

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[granite yoke]

eu literalmente so fiquei encarando a questão depois de atribuir as igualdades dos lados, não sei o que fazer lol

[granite yoke]

the area of ​​the yellow polygon with vertices at grid points is 30cm². What is the area in cm² of each square in the grid? idk how to do this lol

[south sparrow]

you can find interesting questions by playing around with the shape. for example I found this question: are MN always parallel with CD and BA?

[south sparrow]

what proportions the lines divide the quadrinhos?

[granite yoke]

no is this, sorry

but

So I have to measure how many squares each line traces? and after that define how many centimeters each line is?

[south sparrow]

from cm^2 we know it is an area measure

oh, the question asks for area

[granite yoke]

yeah, the area of quadrinhos

quadrinhos is this mini square

[south sparrow]

the area of one square of the graph

is the unknown

[granite yoke]

30 square in the graph

[south sparrow]

30 is the area of the shape no?

area do poligono amarelo

[granite yoke]

the only information we have is that the yellow figure has an area of ​​30cm² and that there are 30 squares in the graph, what is requested are the areas of the squares

[granite yoke]

yeah, but also have 30 squares

sorry if I'm expressing myself poorly, I'm not good at English

[south sparrow]

from this, we know that this line halves the 6 squares

do you see?

this is half of 6 squares, minus half of 2

[safe radish]

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[thick fox]

prove

[thick fox]

i need help

$(b-a)/(c-a) = (b-a)/bar(b-a)$

[flat frigate]

ATAE

[thick fox]

this is where I get stuck

[zealous olive]

multiply divide by (b-a), do the manual calculations and you will get there

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[jaunty storm]

Hi

[jaunty storm]

When you have figured out m1, how do u figure out m2 for perpedicular linear relationships

[empty gyro]

$m_1 m_2=-1$

[flat frigate]

SWR

[jaunty storm]

I know that

I'm trying to figure out what m2 is when I have the m1 value

[tall hedge]

Just -1/m1

[jaunty storm]

$m_2 = 1/4/3$

[flat frigate]

umk

[tall hedge]

Please correct me if i may be wrong.

[jaunty storm]

4/3 is m1

[jaunty storm]

I don't think there's a -1

just 1

[tall hedge]

there is a -1 in this equation

[jaunty storm]

I meant the other equation to find m2

[tall hedge]

oh alright

[jaunty storm]

that formula is check if they are perpendicular

[tall hedge]

Oh i see thank you so much.

[jaunty storm]

You in the same boat as me?

[tall hedge]

I don't know, does that make you proud?

[jaunty storm]

No, I didn't mean it like that. Usually a lot of people here are in higher grades and know this stuff better than me. I was just asking if you were also learning linear relationships.

[thin bridge]

dividing both sides by m_1 will give
m_2 = -1/m_1

[jaunty storm]

I was told it was 1/m_1

[thin bridge]

you were incorrectly informed

[jaunty storm]

wait nvm I'm wrong. The negative value was already taken out of m_1 in my formula

the negatives in yours cancel out while mine never had any negatives

So @tall hedge you were right as well

[tall hedge]

Oh no worries mate, but no i'm not learning that for the moment, i'm focused into integrals and feynman technique

[dusk sparrow]

think about what you were thinking before

m = 5

bottom 5 left 1 or sometjing

you want to go perpendeculae firection

down 1 right 5 for example

you get m = -1/5

[jaunty storm]

if its a positive gradient , the y value goes up
If it's a negativ gradiente, the y-value goes down

[dusk sparrow]

i think you figured it out before

[jaunty storm]

I figured out the sketching line thing

and I kinda figured out how to do perpendicular calculations

[dusk sparrow]

yes

[jaunty storm]

I think everyone knows what si means.

[dusk sparrow]

m_1 times m_2 = -1

[jaunty storm]

My Exams today so i hope I do well. Have a nice day everyone

[dusk sparrow]

gl with your exam

[jaunty storm]

thx

My hand hurts from all the studying and writing

Well good bye then

[empty gyro]

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[lean otter]

x(kx-56)=-16 in the given equation, k is a integer constant. if the equation has no real solution what is the leas tpossible value of k>?

[empty gyro]

discriminant time

[lean otter]

bro what is that

can anyone give me advice

i have 0 clue where to even start

[empty gyro]

look up quadratic discriminant

[lean otter]

oh is it

b^2 - 4ac

[thin narwhal]

yea

[lean otter]

if its less than 0

no solutions

[thin narwhal]

yea

[lean otter]

i can get the means equal to each other

but im not sure what "the smalles tpossible different" means

like do I take the smallest means of both?

then take the difference

[dusk sparrow]

if the means equal to each other

what would the difference be then?

[lean otter]

0

[dusk sparrow]

🙂

[lean otter]

but thats incorrect

lol

i think the wording here is bad

[dusk sparrow]

me thinks so too

[thin narwhal]

what mean did you get

[lean otter]

there r multipole

p[ossible

means here

bcuz it doesnt say an actual value per frequency

its a range of values

[thin narwhal]

ok then what mean did you get

[lean otter]

which variation

[thin narwhal]

you said you "got the means equal to each other"

[lean otter]

yea

37.25

or smth like that

using a random variation

i think tis wrong tho

[thin narwhal]

are you sure you can get that exact mean using both datasets

[lean otter]

You can’t

That’s the issue lol

So you have to choose a condition

[thin narwhal]

you have to choose a mean of set a

and a mean of set b

such that both of the means are as close as possible

[safe radish]

@lean otter Has your question been resolved?

[lean otter]

I alr did that

And I was able to get them equal

Meaning the difference was 0

And it was wrong

I probably did smth wrong

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[carmine sluice]

just wanna know if i have the correct answer

[exotic bolt]

ye

u do

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[arctic kelp]

how do i do this?

[arctic kelp]

i understand the function but how do i show it

[safe radish]

@arctic kelp Has your question been resolved?

[arctic kelp]

<@&286206848099549185>

[empty gyro]

What would you define as that "total mass" of the rocket?

[arctic kelp]

at the start mr +mf

then at t=T, just mr

[arctic kelp]

.

[empty gyro]

That's a good view. Yes. In short, I meant to have you arrive at this conclusion: "the total mass is just the sum of the mass of the rocket itself and the mass of the fuel"

So you could write $m(t)=m_r(t)+m_f(t)$ and the solve for the functions $m_r(t)$ and $m_f(t)$

[flat frigate]

SWR

[arctic kelp]

so $m_r(t)=m_r$ and $m_f(t)=m_f(1-t/T)$ yeah?

[flat frigate]

Oli

[arctic kelp]

thanks

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[arctic stone]

how does the top row equal logb(2)

[junior smelt]

Remember the log rule for log(x) + log(y)

[arctic stone]

ah I see

1/10*20 = 2

thx

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[quaint aspen]

I am confused about this explanation it says u = squaroot(17x) where did they get this from as there is no squaroot(17x) in the origignal question

[granite idol]

so they can have u^2 = 17x^2

[quaint aspen]

am confused what do u mean?

[granite idol]

if u = sqrt(17) x, then u^2 = 17x^2

[quaint aspen]

but i thought for substitution we have to make u = a term in the equation

why did they do u^2 = 17x^2?

[mellow cypress]

the premise of substitutions is to simplify integrals into ones you already know

[granite idol]

you can substitute whatever you want, basically

[granite idol]

did you read the rest of the solution? it explains what they do

[quaint aspen]

i did

i just lerned substitution today so am still kina confused

[granite idol]

they explain it. they do it because 1 / (u^2 + 1) is the derivative of tan^(-1)

so it makes it easier to take the integral of the original function

[quaint aspen]

ok thx

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[valid mauve]

is $a^p - a$ always divisible by 2 where $p$ is prime and $a$ any integer?

[flat frigate]

Halex

[safe radish]

@valid mauve Has your question been resolved?

[quiet plume]

Yes it is

I'm not sure you need p to be prime even?

[valid mauve]

I just noticed that it is not necessary

[quiet plume]

It's easy to see by writing $a^p - a = a(a^{p-1} - 1)$.

[flat frigate]

Azyrashacorki

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[ashen dagger]

help with that

[quiet juniper]

induction

yw

[ashen dagger]

yes it's induction

a version of ZIM

[ashen dagger]

how to prove it

[quiet juniper]

Prove it for A - a (or A - (a - 1) if your version of induction starts at 1)

A-a being the set of elements of A, each subtracted by a

[ashen dagger]

isnt it the definition of induction itself?

[quiet juniper]

Well I was assuming you already knew induction for n = 0 or 1 was true

Idk if u start at 0 or 1

[ashen dagger]

there was question to prove formulas using induction

and other question telling

"prove the other variations of induction"

[quiet juniper]

ok then you can assume those are true I guess

In proving this

[ashen dagger]

how to use TeXit

[quiet juniper]

$like this$

[flat frigate]

992HallucigeniaEnthusiast

[ashen dagger]

$\allfor$

[flat frigate]

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

[ashen dagger]

$\forall$

[flat frigate]

Princ. Noctis

[ashen dagger]

$\forall n \in \mathbb{N}, n \in A \implies (n+1) \in A$

[flat frigate]

Princ. Noctis

[ashen dagger]

yes

this is the definition of induction right?

[ashen dagger]

.

[quiet juniper]

and you have to start at a base case also

[ashen dagger]

and 1 in A

and A subset of N

[quiet juniper]

yup

[ashen dagger]

and then A = N

yeah

and u can prove this

by lets say theres set B

$B := \mathbb{N} \setminus A$

[flat frigate]

Princ. Noctis

[ashen dagger]

yeah and B cant be empty

is A =/= N

so it must have smallest element

lets call it a

so a isnt in A

and a > 1 cuz 1 is in A

so a - 1 > 0

so a - 1 is a natural number

but its not in B because a - 1 < a

and a is smallest in B thus a - 1 must be in A

and if a - 1 is in a

[ashen dagger]

by definition

a - 1 + 1 is in A

so a is in A

and its in B

contradition

so A must be = to N

[ashen dagger]

yeah and now i must prove this instead of A = N

that was for more context

[quiet juniper]

Wait shouldn't the 2nd line say $\forall n \in \mathbb{Z}$ ? Otherwise, say the set ${-848484848} \cup \mathbb{N}$ satisfies this

[ashen dagger]

ill send again

[quiet juniper]

[ashen dagger]

2nd lise is what

[flat frigate]

992HallucigeniaEnthusiast

[ashen dagger]

try different messages

[quiet juniper]

Cus the inductive step only starts at 1

[ashen dagger]

for text and latex

oh i see which line

let me check book again

its correct as in book

[quiet juniper]

hmm maybe I'm tripping but

Again say you have like -2 in A

[ashen dagger]

yes

$\cap$

[flat frigate]

Princ. Noctis

[quiet juniper]

there's nothing to say that -1 should also be in A because n implies n + 1 only applies to n greater than or equal to 1

[ashen dagger]

is common part of sets

hmmm

2nd line tells i think

that all natural numbers have their consequents

or more precisely

[quiet juniper]

yeah but -2 isn't a natural number

[ashen dagger]

so there can but doesnt have to be -1

and lets say a = -5

[quiet juniper]

but according to the third line -1 (it's consequent) should be there

[ashen dagger]

-5 to infinity \cap Z

[quiet juniper]

Since it's an integer greater than or equal to -2

[ashen dagger]

hmmm

[quiet juniper]

[ashen dagger]

u could be right

[quiet juniper]

What's the book

Maybe u can Google the errata

[ashen dagger]

check maybe i retyped it wrong

(3)

[quiet juniper]

books have errors sometimes, I've caught them before

[ashen dagger]

ohhhhh

but its all Z numbers

so will include -1

[quiet juniper]

hell I've caught error snot in the errata and that's been a pain in the ass

[ashen dagger]

author said that there have been made many corrections caught by readers

its page 3 i doubt no one would notice

[quiet juniper]

[ashen dagger]

its all integers >= a so it will include -1

say -2 is in A

[quiet juniper]

yeah but

[ashen dagger]

all Ns have consequent

[quiet juniper]

That doesn't follow from the inductive step

[ashen dagger]

not all Zs have consequent

[quiet juniper]

Yeah exactly

[ashen dagger]

vut

but

left side

oh but A doesnt have to contain it

[quiet juniper]

yeah

what's the book title

I'll Google it

[ashen dagger]

matematyka olipmijska algebra i teoria liczb

[ashen dagger]

but could be that u should prove that its wrong

[quiet juniper]

oh

well there's ur counterexample

[ashen dagger]

its not said that the formulas are correct

or incorrect

[quiet juniper]

ah

[ashen dagger]

okay but lets continue with second line having Z instead of N

i still dont know how to prove it

[quiet juniper]

sooo

[quiet juniper]

A - (a - 1) is a subset of N

[ashen dagger]

by contradiction?

[quiet juniper]

That has 1

Use induction on that

Then add a to all the elements of A - (a - 1)

[ashen dagger]

A - (a-1) is what

A\{a-1}

[quiet juniper]

all the elements of A subtracted by (a-1)

So {b - (a - 1)| b \in A}

[ashen dagger]

subtracting a-1 from all elements?

[quiet juniper]

wait slight error in my proof

yeah

A - (a - 1) wouldn't be a subset of N, so take the intersection of N with that set

Show that intersection equals N

And show that the intersection + (a - 1) is a subset of A

The trick is that $ 1 \in A - (a - 1) \cap \mathbb{N}$

Since a is in A

So a - (a - 1) = 1

Then the induction hypothesis also still applies to the set

[ashen dagger]

and what do u think about this method

[quiet juniper]

well I can already tell by reading the word chat gpt that it's wrong

chat gpt can't do math

[ashen dagger]

but its 4o

[quiet juniper]

it's really good at speaking like a human but it cant do math at all

[ashen dagger]

could be

but he read my image correctly

that impressed me

he did induction with offset

suppose a = -7

he did k is in N

so induction works for k

and he did a + k

[quiet juniper]

ok yeah

I figured out why now

it can also google

ngl tho that was better than I expected

[ashen dagger]

same for me

[quiet juniper]

well any more qs?

[ashen dagger]

no

thanks for help and good luck

👊

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[wispy coyote]

if the determinant of the hessian matrix is 0 can it still be diagonalisable

[honest perch]

um yes, consider the 0 matrix

[crystal halo]

the determinant of a diagonalisable matrix is the product of its eigenvalues (counted with multiplicity)

so a matrix (a hessian, or any other matrix really) can totally be diagonalisable and have determinant 0, it just means that it has 0 as one of its eigenvalues

the null matrix works, but any matrix which diagonalises into

0  *```

works too

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[wispy coyote]

ah ic

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[tame zephyr]

how do you differentiate between a hypergeometric or binomial distribution

[tame zephyr]

for hypergeometric distribution, the total population is given, but some questions make it confusing to differentiate

for example, this one

oh I guess by 25, they mean the trial sample size

[rigid inlet]

Your "population" here would be all cars (or at least all in the region) which is ideally much larger than 25

[tame zephyr]

makes sense

[rigid inlet]

The 25 is just the bunch you're observing

[tame zephyr]

alright

thanks

[safe radish]

@tame zephyr Has your question been resolved?

[tame zephyr]

@junior smelt Hi!

[safe radish]

@tame zephyr Has your question been resolved?

[tame zephyr]

for this question, if you are using negative binomial distribution, the probability you are using is the probability of success but the random variable represents failures..

I think

ahh okok

yes it is

oh i gotta mention, the random variable Im referring to is not the X in the question

Y= total num of failures

[safe radish]

@tame zephyr Has your question been resolved?

[tame zephyr]

RAHHHH

ok all content covered!!

woooo!

[tame zephyr]

now,

im back

totally did not just scrolled on my phone for 2 hours...

[glacial sonnet]

not the doomscrolling

[tame zephyr]

mental health break, mental health break😅 😆 uuhnn

[tame zephyr]

shhh its okk, everything is okk

a-okayyyy🤩

[glacial sonnet]

[tame zephyr]

see I could be living my hot girl summer right now on a beach drinking a cocktail but see

this is what I got myself into

counting probability of rolling a dice

okok

time to lock the fck in

[tame zephyr]

bye bye😃

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[elfin crane]

how to do 2.15 a)

[elfin crane]

Do I use inference of mean response or prediction intercal for a new observation

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[elfin crane]

.reopen

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✅

[elfin crane]

<@&286206848099549185>

.close

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[lean otter]

Can someone help me with this?

[hollow knot]

what exactly are you stuck with

for (a) consider the number of permutations where kristen sits at the leftmost seat, then number of permutations where she sits at the rightmost

[lean otter]

How to solve number of permutations Kristen sits at the leftmost seat and rightmost seat?

[hollow knot]

you know how to get the number of permutations without restrictions right

just think about it this way: if kristen is anchored onto one seat (i.e. for all permutations she sits there), what would be of the remaining 7 people?

[lean otter]

Is it 7 factorial? 5040?

[hollow knot]

yup thats because giving kristen one seat leaves everyone with 7 seats left

but then you also have to account for kristen sitting at the other end

[safe radish]

@lean otter Has your question been resolved?

[lean otter]

So there are two 7 factorials?

[hollow knot]

yes

[lean otter]

What about question b.)?

[hollow knot]

i'll try to explain the concept of repetition and you can try it out yourself on this problem

what the problem is asking is how many possible distinct lists of surname first letters can be formed from these 8 people

we are given that 2 of them share the same first letter (K) and another 3 of them share the same last letter (S), and the rest are different

so let's try a simpler problem: suppose you have 5 books and all of them are different except for 3 books which are identical to each other

and you want to find the number of ways you can arrange them

but here's the thing: among the 3 identical books, IF they were different, they would have had 3! permutations among themselves

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[lusty trench]

i got value h as -12

but the answer was "all h"

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@lusty trench Has your question been resolved?

[median vigil]

if you get something like
0x + 0y + 0z = 1
for example, that's inconsistent. but the opposite is not true:
0x + 16y + 0z = 0
is consistent, the solution is simply y = 0

[lusty trench]

0x + (12+h)y = 0

ahh i think i got it

than you

.close

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[verbal forge]

Is c right. The qu asks to differentiate btw

[fair fossil]

,rotate

[restive niche]

No

Use the chain rule correctly

[wintry locust]

$log_e \pi^x = x log_e \pi$

[flat frigate]

fukwerint

[wintry locust]

And derivative (wrt $x$) of $a^x$ is not $xa^{x-1}$, for $a$ constant.

[restive niche]

Put {}s around the x-1

[flat frigate]

fukwerint

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[magic tendon]

The circumference of a circle is increasing at a rate of 0.5 meters per minute, what's the rate of change of the area of the circle when the radius is 4 meters?

[restive niche]

!status

[safe radish]

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

[magic tendon]

1

[restive niche]

Begin by finding the rate of change of the area of the circle

(i.e differentiating the expression for the area of a circle)

[magic tendon]

But that is the required

[restive niche]

Exactly

This question is fairly direct

[magic tendon]

Idk where to begin

Where is the function

[restive niche]

.

It is your job to find the function

[magic tendon]

Shouldn't area and circumference be differentiable with respect to radius not time

[restive niche]

Write out the area first

πr² is the area

[wintry locust]

dr/dt is not 0

[restive niche]

Differentiate this to find the rate of change of the area

[wintry locust]

radius is also changing

with time

[magic tendon]

Pi 2r ?

OH

that is the circumference

[restive niche]

Not quite

2πr • dr/dt

This is the chain rule

[magic tendon]

Ohh

What is after

[restive niche]

We know that the rate of change of the circumference is 0.5

[magic tendon]

So
da/dt = circumference x dr/dt

[restive niche]

So d(2πr)/dt=0.5
=> 2π dr/dt =0.5

[magic tendon]

😔

[restive niche]

The rate of change of area is 2πr dr/dt

[magic tendon]

0.5r

[restive niche]

Right

[magic tendon]

So 4 × 0.5 = 2?

[restive niche]

Yes

[magic tendon]

Ah i see

That was a question from a stardew valley cutscene btw

Ty

[restive niche]

Type . close

[magic tendon]

.close

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[keen ginkgo]

Hey could anyone help with a statistics question?

[steel gulch]

Watchu having trouble with?

[keen ginkgo]

I sort of have no idea how to start this one and the mark scheme is making no sense

[steel gulch]

i or ii? Or both?

[keen ginkgo]

Both 😅

[steel gulch]

Okay, let’s start with i

So we really want P(rain, no rain, no rain, no rain, no rain) where this sorta indicates what day has rain respectively. Does that make sense?

Then we’ll assume that it raining on any given day is independent of whether is rained on any other day, which seems reasonable

So then we can write the probability as P(rain)*P(no rain) *P(no rain) *P(no rain) *P(no rain)

[keen ginkgo]

The question started with a normal distribution, do you think it would be used in this part of the question too?

And im sort of confused abt what your saying

[steel gulch]

Wait wtf did I write rain?

So sorry

[keen ginkgo]

It’s okay lol

[steel gulch]

So where I wrote rain = temp more than 33, and no rain = not more than 33

Haha

No idea where the rain came from

[keen ginkgo]

That makes more sense 😭

[steel gulch]

But yeah, this seems odd.

[keen ginkgo]

Wait let me send the full question

[steel gulch]

Because treating it as repeated Bernoulli trials seems better

[steel gulch]

Might help

[keen ginkgo]

Part a went well but part b I am stuck on

I think I get what you were saying abt the probabilities a bit tho

[steel gulch]

Tbh, not really sure why you would want to use a normal distribution on b

Unless you use it to approximate a binomial dist ig

[keen ginkgo]

Oops then I don’t think it is relevant

I think i get the first part

[steel gulch]

First part of b?

[keen ginkgo]

Yep

I’m still confused on b ii tho 😅

[steel gulch]

Sick, so the second part is a bit similar.

Yeah so we want P( hot > 1 day)

So we can pretty much write that as 1 - ( P( hot exactly 0 days) + P(hot exactly 1 day))

So those probabilities should be easy to work out, very similar to part b i

[keen ginkgo]

Wait I don’t really understand this part

[steel gulch]

So if you want the probability that it is greater than 1 day. You want everything except anything less than or equal to one day

So 1-P(hot <= 1 day) just by taking the complement

[keen ginkgo]

Ohhhh

How can i find the probability of P(hot<= 1day)?

[steel gulch]

It’s probably easiest to just brute force it and see that P(hot <= 1day) = P(hot exactly 0days) + P(hot exactly 1 day) which we can do because it is discrete

[keen ginkgo]

Okayy so if its discrete can I put it into a binomial distribution so work out the probabilities?

[steel gulch]

No, it means that we can compute the cdf by the sum of the events in the interval