help-0

[pale kestrel]

well

its just

like uh

idk how u call it

[hasty elk]

(a geometric probability distribution)

[pale kestrel]

P(A) = P(A | B) + P(A | B')

Is it this?

oops not

P(A) = P(A | B)P(B) + P(A | B')P(B')

Is it this????

yes i think so

[pale kestrel]

It's from using this

repeatedly to infinity

[hasty elk]

ummm

[pale kestrel]

$$\mathbb{P}(A_W) = p + r(q + r\mathbb{P}(A_W))$$

@rich basin ^ A_W = A wins.

Can you see where this comes from

[ocean seal]

Shuri2060

[rich basin]

yeah

but then in the solutions they evalaute it down through the GP

[pale kestrel]

Expand this.

[rich basin]

but then what values of a and r did they use

[pale kestrel]

I believe.

Anyways, helping someone else atm 👀

sry lol

[rich basin]

that would be p + rq + rP(A_w))

[hasty elk]

it appears because of the ways A can win

A wins in the first turn with probability p

...actually let me just assume you proven part (i)

i'm lazy to type

[rich basin]

yeah but values for a and r in the GP

[pale kestrel]

btw without GP, try rearranging what I gave above. I hope its the same answer

[hasty elk]

well, each term increases by a ratio of r^2

and the first term is (1-r)(p+r)

so

[rich basin]

yeah but what about for r

[pale kestrel]

@hasty elkhelp

[hasty elk]

?????

[pale kestrel]

@rich basin let me 👀

[rich basin]

what o you think>?

[rich basin]

in the gp there is an r term but what is it though?

[pale kestrel]

uh

$$\mathbb{P}(A_W) = p + r(q + r\mathbb{P}(A_W))$$

[ocean seal]

Shuri2060

[pale kestrel]

$$\mathbb{P}(A_W) = p + r(q + rp + r(q + rp + r(q + rp + r(q + r\mathbb{P}(...)))))$$

[ocean seal]

Shuri2060

[rich basin]

I get that when you expand it out

you can refactor to get the answer again

but what about the GP solution?

[pale kestrel]

im checking

did i f that up

$$\mathbb{P}(A_W) = p + r(q + rp + r(q + rp + r(q + rp + r(q + rp + r(q + rp + r(q + rp + r(q + r(...))))))))$$

[ocean seal]

Shuri2060

[pale kestrel]

ok.........

[hasty elk]

r^2, looking at the solution

[pale kestrel]

$$p + rq + r^2p + r^q+ r^3 p + r^3p + r^4q + ...$$

[ocean seal]

Shuri2060

[rich basin]

but then it is 1 - 4

1-r

[pale kestrel]

$$(p + rq) + (r^2p + r^2q)+ (r^3 p + r^3q) + (r^4p + ...$$

[rich basin]

not r-1

[pale kestrel]

Ok, do you see what I've done?

wait wtf have i done

[ocean seal]

Shuri2060

[rich basin]

It doesn't seem to factor your solution

[pale kestrel]

Assuming this is right

$$\mathbb{P}(A_W) = p + r(q + rp + r(q + rp + r(q +$$

[ocean seal]

Shuri2060

[pale kestrel]

We get this right?

$$p + rq + r^2p + r^2q + r^3p + r^3q + r^4p + r^4q+...$$

[ocean seal]

Shuri2060

[pale kestrel]

$$p + (rq + r^2p) + (r^2q + r^3p) + (r^3q + r^4p) + (r^4q+...$$

[ocean seal]

Shuri2060

[pale kestrel]

So my ratio is r

eh wtf

[pale kestrel]

is this same as solutions

(p + rq) / (1 - r^2)

[hasty elk]

hoho

[pale kestrel]

need a 1-r indeed

p + rq <-- 1 - r?

[hasty elk]

1-r = p+q

[pale kestrel]

probably wrong

[hasty elk]

just fyi

[rich basin]

No

[pale kestrel]

p + q - pq - q^2

oh i seem to get something

p + q - pq - q^2
= (p + q) - q(p + q)

= (1 - q)(p + q)

= (1 - q)(1 - r)

= (p + r)(1 - r)

yeah, this is the same answer

but fuck this algebra

[hasty elk]

tadaaaa

[pale kestrel]

😂

like wtf

how is chopping into 1 = p + q + r

making this so dumb lol

[hasty elk]

welcome to probability

you haven't truly lived until you chop 1 = p+q into algebra spanning 20 pages

i had an assignment like that last semester

[pale kestrel]

@rich basin I think both answers are the same. Including the method

1 + r + r^2 + r^3 + r^4 + r^5 + ... = (1 + r) + r^2(1 + r) + r^4(1+r) + ...

If you rewrite a geometric series like this

you can powers of r as the ratio

Never realised this before tbh.

[rich basin]

‘
The one here is quite different

[pale kestrel]

Algebra gets u there

let me show . . .

$$\frac{p + rq}{1 - r^2}$$

[ocean seal]

Shuri2060

[pale kestrel]

$$=\frac{p + (1 - p - q)q}{1 - r^2}$$

[ocean seal]

Shuri2060

[pale kestrel]

$$=\frac{p + q - pq - q^2}{1 - r^2}$$

[ocean seal]

Shuri2060

[pale kestrel]

$$=\frac{(p + q) - q(p + q)}{1 - r^2}$$

[ocean seal]

Shuri2060

[pale kestrel]

$$=\frac{(1 - q)(p + q)}{(1-r)(1+r)}$$

[ocean seal]

Shuri2060

[pale kestrel]

$$=\frac{(p + r)(1 - r)}{(1-r)(1+r)}$$

[ocean seal]

Shuri2060

[pale kestrel]

$$=\frac{p + r}{1+r}$$

[ocean seal]

Shuri2060

[pale kestrel]

like magic.

[hasty elk]

[rich basin]

How did you go down there

[pale kestrel]

each bracket corresponds to the same one

1=p+q+r

[pale kestrel]

god now i realised how bad that inclusion exclusion was lol

[hasty elk]

LOL

[pale kestrel]

not even sure u can apply it on that kindof problem

[hasty elk]

you can't, i think

or well

[pale kestrel]

much more complicated than counting positively

[hasty elk]

PIE is so prone to errors it's good to save it for truly desperate times anyway

[pale kestrel]

what is the acronym

Principle of Inclusion Exclusion?

[hasty elk]

Principle of Inclusion and Exclusion

[pale kestrel]

yh ok

maybe if i do PIE and then permute after

permute the order after

for each individual case . . .

uhhh

[hasty elk]

[rich basin]

Now can you please explain the GP solution?

[pale kestrel]

uh

$$1 + r + r^2 + r^3 + r^4 + r^5 + ... = (1 + r) + r^2(1 + r) + r^4(1+r) + ...$$

[ocean seal]

Shuri2060

[pale kestrel]

@rich basin All geometric series can be written with ratios that are powers of r

ok?

the above is a general r

$$a + ax + ax^2 + ax^3 + ax^4 + ax^5 + ... = (1 + x)a + x^2(1 + x)a + x^4(1+x)a + ...$$

[ocean seal]

Shuri2060

[pale kestrel]

So if you expand this

[ocean seal]

Shuri2060

Shuri2060

Shuri2060

[pale kestrel]

this has ratio r. If I bracketed it another way, I could have ratio r^2

[rich basin]

Yeah

[lone heart]

@rich basin Has your question been resolved?

[lone heart]

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[rancid trail]

Did I do it right?

[rancid trail]

I think I messed up

The question was to find the first, second, third derivatives

[bright hedge]

well 60*7 is not 42

its 420

[rancid trail]

Thanks

[bright hedge]

i think that's it tho

[rancid trail]

Oh

Thanks

.close

[lone heart]

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[empty ivy]

I’m stuck on how to label this triangle cause I tried different ways on another piece of paper but it’s not working, can someone plz help, would be much appreciated

[frigid geyser]

huh i think you just have to write what the angles are

[empty ivy]

Am I supposed to write 21 at the beginning and 35 at the end or…

Thx for the fast reply

[remote heron]

theyre headings

so you were going 90 degrees

saw the cloud

then changed direction to 21 degrees north of east

makes that angle 21 degrees

idk if thats what youre asking

then you know the other angle since its given explicitly

,calc 180-35-21

[ocean seal]

Result:

124

[remote heron]

3 angles and a side length is enough to solve

well more than enough, but enough

[empty ivy]

So first angle is 21 right?

[remote heron]

yea

[empty ivy]

And the total length of the triangle is 70 for the base or is that for when I split the triangle

And the top angle is 35?

[remote heron]

no

[empty ivy]

I meant end angle

So first angle is 21 last angle is 35

[remote heron]

yup

[empty ivy]

And I’m confused about the 70 still

Is that the full triangle base because I didn’t know if u said no to that aswell

[remote heron]

well 70 is the distance from where you leave your original bearing to where you rejoin it

so between the 21 degree angle and the 35 degree angle

you can imagine a side of length 70

[empty ivy]

Oh ok

Then I just split the triangle?

[remote heron]

you can use whatever method you want

if it were me yea id probably split it

since i dont remember anything cool from geometry

i guess law of sines maybe?

actually yea, law of sines id probably use

[empty ivy]

Ok

Thank you

Wait how do I use sines in the formula cause I only have one measurement being 70

[remote heron]

thats fine

youll need to solve for the remaining angle

law of sines says the proportion between the sine of an angle and its opposite side is preserved for every sidelength/angle pair in the triangle

so make one pair from the 70 and the now-known angle

and another pair from some unknown side and a known angle

[empty ivy]

Ohhhh

Ok

[remote heron]

this is enough information to get the remaining side in that equation

[empty ivy]

I’ll try it

And come back if I have trouble

Thanks again

[remote heron]

[dawn timber]

hi

can anyone pls help

[empty ivy]

So this is half the triangle

[dawn timber]

i suck at math and just 4 mins to submit my assignment

[empty ivy]

And I don’t know how to solve the side lengths

[remote heron]

#❓how-to-get-help

yea thats gonna be hard toasty

i think law of sines is going to be easier here

were you able to try using it?

[empty ivy]

Wait was 70 supposed to be at the bottom

[remote heron]

yea lol

[remote heron]

no

[empty ivy]

Wait 70 was half the triangle

[remote heron]

no

[empty ivy]

Wait it’s full

[remote heron]

you dont know what proportion it is

you could figure it out

this all seems like more work than its worth

[empty ivy]

I’m lost lmao

I’m bad at math too

[remote heron]

we can just use law of sines here

lemme draw

[empty ivy]

Ok

Thx

[remote heron]

shit sorry

someone just responded to my 2 day old question on another server asking for help

[empty ivy]

It’s fine lol

[remote heron]

heres the triangle

[empty ivy]

Ohhhhh

But how did that work tho

[remote heron]

huh?

[empty ivy]

Cause I was taught to split the triangle

Oh wait nvm

So I add them together

And get the top angle

But how do I split that triangle to get the answer

[remote heron]

you dont

use law of sines

[empty ivy]

Wait so if I do sin 21 degrees

That’s the answer for B length?

Wait nvm I think I get it

Thx

[remote heron]

no

[remote heron]

you sure? 😄

you just wanna pick out like

[empty ivy]

Ye after that response I think I’m wrong lol

[remote heron]

everything circled in green is just a number

so say you want to know A

[empty ivy]

Yup

[remote heron]

pull out some equation that has A as the only unknown

$\frac{\sin 35 }{ A } = \frac{\sin 124 }{ 70 }$

[ocean seal]

jan Niku

[remote heron]

by tricky tricky algebra rules, its okay to just flip these both

$\frac{A}{\sin 35} =\frac{70}{\sin 124}$

[ocean seal]

jan Niku

[remote heron]

then isolate for A, so multiply across the sin 35

$A = \sin 35 \frac{70}{\sin 124}$

A = (some number)

[ocean seal]

jan Niku

[empty ivy]

Oh

[remote heron]

,calc sin(35) * 70 / (sin(124))

[ocean seal]

Result:

30.102619858852

[remote heron]

about 30

[empty ivy]

Wait so the equation is that to get side A

[remote heron]

yup

as you can imagine maybe the process to get B is almost identical

only sin35 changes

[empty ivy]

Oh

Ok

Thx a lot, this was really helpful

[remote heron]

no problem 😄 you sure you got it?

lol the why cat

[empty ivy]

Wrong cat lol

[remote heron]

[empty ivy]

I’m can you go over it one more time just so I don’t screw up for side A

Then I should do the rest easily

[remote heron]

you wanna vc?

[empty ivy]

Sure

[remote heron]

you dont have to talk

[empty ivy]

Ok

[remote heron]

come to 384

on the left

<----

[empty ivy]

Ok

[lone heart]

@empty ivy Has your question been resolved?

[remote heron]

@empty ivy

[empty ivy]

Thx again so much

🙏

[lone heart]

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[tardy robin]

Can someone help me out with this question

[lone heart]

@tardy robin Has your question been resolved?

[tardy robin]

<@&286206848099549185>

[empty ivy]

Can someone help me on this question

[lone heart]

@tardy robin Has your question been resolved?

[strong hornet]

#❓how-to-get-help

[covert agate]

.close

[lone heart]

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[buoyant kayak]

you just opened a channel

no need for 2

[severe sluice]

pYTHAGOREAN tHEOREM

[scarlet surge]

k

[dense gust]

Bruh.. Why'd you open two..

[sly mantle]

@scarlet surge for future reference pls dont multipost

.close

[lone heart]

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[scarlet surge]

idk

im new here

[sly mantle]

see help rules in #❓how-to-get-help

[lone heart]

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[valid rivet]

help plz

[lone heart]

@valid rivet Has your question been resolved?

[fickle canopy]

Can i ask for help please with calculus?

[hybrid blade]

you may

since you just asked

[buoyant kayak]

bro said help, didn't ask a question, then came back to tell the bot their question wasn't resolved lmao

[hybrid blade]

lol

[lone heart]

@valid rivet Has your question been resolved?

[empty ivy]

@remote heron thanks so much, I took a quiz after you helped and got 18/20

[lone heart]

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[lone heart]

@undone agate Has your question been resolved?

[lone heart]

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[hot smelt]

Can you help me?

<@&286206848099549185>

[smoky cloud]

with ?

[median dirge]

Hello.

Eh,

[hot smelt]

9. first

[median dirge]

Find fog(x) and then find fog(0) and equate it to -8

You'll get a quadratic eqn. Solve it for a

[hot smelt]

wait i find fog(x) already

[smoky cloud]

i'll take a leave ig u guyss can help

[median dirge]

Eh?

[hot smelt]

wait imma try to understand your explanation

give me a min

[smoky cloud]

if that looked complicated feel free to ping

[hot smelt]

So after f(x) found what should i do?

OOO OK LET ME TRY

this is the step where i dont write lmao

cuz i dont think that way

[smoky cloud]

do uk what fog(x) means ?

[hot smelt]

yea

[smoky cloud]

f(g(x)) right ?

[hot smelt]

yea

i know about that

[smoky cloud]

what is given ?
fog(0) = -8 right ?

[hot smelt]

cuz my previous answer fog x was an equation that has a in it

[hot smelt]

yes

[median dirge]

Put x=0

[smoky cloud]

fog(0) = f(g(0)) = f(a) [ bcos g(0)=a]

now u can solve easily ig

[hot smelt]

ok imma try to understand it

[smoky cloud]

see fog(0 ) = f(g(0)) right ?

[hot smelt]

I actually dont understand a single thing about this because this is a question that my teacher randomly gave to us

[smoky cloud]

this u understood ?

[hot smelt]

Yeah

[smoky cloud]

what is g(0) ?

[hot smelt]

but why this fog(0) = f(g(0)) = f(a) [ bcos g(0)=a]

[smoky cloud]

I'm explaining that only

[smoky cloud]

?

[hot smelt]

hold on let me try it

[smoky cloud]

see the qn and tell

btw do uk what f(0) or g(0) means ? @hot smelt

[hot smelt]

i dont really understand it cuz why the 0 replaces x?

and i dont know how to find g(0)

[smoky cloud]

read the question

oh

ok

[hot smelt]

what is qn sorry i dont know

[smoky cloud]

^

[median dirge]

Short form for question.

[smoky cloud]

oh lol kk

[smoky cloud]

(0) means replace x with 0

[hot smelt]

so if i just replace f(x) 3x^2+7x-6

and replace x as 0?

[smoky cloud]

yup

[hot smelt]

OOOOOOOOO THNAK YOU

[smoky cloud]

so now tell what is g(0)

[hot smelt]

g(0) =a ??

[smoky cloud]

yup

so now u got
how f(g(0)) = f(a)

[hot smelt]

yeaaaaa i see

[smoky cloud]

now replace x with a then equate it to -8 and find a

[hot smelt]

ok let met try

imma tell you what my answer after this

[smoky cloud]

k

[hot smelt]

a=-1/3 and a=-2?

[lone heart]

@hot smelt Has your question been resolved?

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[alpine sable]

Yes

[tranquil kestrel]

but why is it not 10p3?

[alpine sable]

Wut

[craggy salmon]

how the points are arranged doesn't matter

only that you choose the 3 points

[alpine sable]

Why

Ohhhh

So there’s 10 ways of choosing 1st point

9 of next

And then 8

So 10p3

Got it

[craggy salmon]

but you double counted

choosing 1,2,3 is same as choosing 2,3,1

[tranquil kestrel]

oh i see, got it guys, thank you very much

[craggy salmon]

so you count 6 times how much you actually should've counted

10*9 *8/6

[alpine sable]

Dayum

[craggy salmon]

or 10c3

[alpine sable]

Bruh

That was my answer in the first place

Literally 10 C 3

[alpine sable]

This

[tranquil kestrel]

yep thanks man

.close

[lone heart]

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[craggy salmon]

yee i was explaining ciao

[lone heart]

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[sage surge]

so can you help me with this?

[alpine sable]

With what

[sage surge]

wait

[alpine sable]

Determinants

I run

[sage surge]

no

oh wait yea

[alpine sable]

I mean this is basic matrix multiplication

Which I hate

Do u know matrix multiplication

[sage surge]

yea

but i dont know what to do

should i go to a different help

?

or someone will come

[craggy salmon]

do you know the property that each matrix satisfies it's own eigen equation?

if not, just get A^2

by A*A

then just put in all the values the hard way

it's a bit long, but doable

[sage surge]

can explain a little more

[sly mantle]

just explicitly compute the left side A^2+…, it should simplify to 0 matrix

[sly mantle]

this is cayley hamilton for 2x2 so using it here is circular

[craggy salmon]

fair enough, by bad

[sage surge]

why tho

i dont know the values of abcd

.close

[lone heart]

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[teal fox]

how to do this one

[gray isle]

you could first consider whether 50 is:
-a multiple of 3
-1 less than a multiple of 3
-2 less than a multiple of 3
to first determine which column the plane will be in

[teal fox]

isnt 50 1 less than a multiple of 3

(51)

@gray isle

[gray isle]

yes

and from that determine whether the plane will be in column B,C,D

[teal fox]

c?

[gray isle]

yes

[teal fox]

yay!

what about rows now

[gray isle]

the relation between the row number and the plane number is much simpler

and you should be able to see that without much effort

[teal fox]

oh yeah

just +1

so C51

.close

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[rancid trail]

8a.

[rancid trail]

I'm stuck

I know $\int{e^x} {dx} = e^x + c$

[craggy salmon]

assume 7x=t

[rancid trail]

Ok

[craggy salmon]

dt= 7dx

dx=dt/7

[vale wigeon]

missing dx

[rancid trail]

:(

[craggy salmon]

so $$ 8/7 \int e^t dt $$

[ocean seal]

Dev Shah

[vale wigeon]

what

[ocean seal]

ThickduckPlayz

[vale wigeon]

if you don't write the dx you will not be perplexed as to where the 1/7 factor came from

also, $\frac{8}{7}$

[ocean seal]

Ann

[craggy salmon]

ye, thanks :)

[rancid trail]

Wait I don't get it

Can I know why you differentiated 7x?

[craggy salmon]

I didn't

it just used substitution

[craggy salmon]

that's just for substitution

to substitute dx

[rancid trail]

OK is there like a rule or something?

[craggy salmon]

kinda yeah

it's more a method

[rancid trail]

Like $\int{e}^{f(x)} dx$

[craggy salmon]

no

one sec

[ocean seal]

ThickduckPlayz

[craggy salmon]

$$ \int{e}^{f(x)} f`(x) dx $$

[ocean seal]

Dev Shah

[craggy salmon]

i dunno the latex for f prime

but that

$$ = e^{f(x)} $$

[ocean seal]

Dev Shah

[rancid trail]

Oh

Ok

So for each question, I need to work them out

[glass lichen]

+c

[craggy salmon]

yeah +c, thanks

[craggy salmon]

yup

[rancid trail]

ok

Thanks

.close

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[lone heart]

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[thorn dagger]

wait what

wrong question

[lone heart]

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[copper pawn]

Hello, how I can find the diameter of a sphere if I have the a

[elfin ermine]

the a?

[solar merlin]

^ the surface area?

[copper pawn]

yes

[solar merlin]

do you know the formula for the surface area

[copper pawn]

4 pi r^2 ?

[elfin ermine]

take the formula for surface area of the sphere and solve for the diameter (or radius and multiply by two)

[solar merlin]

mhm

so you know 4 pi r^2 = your surface area

[copper pawn]

yes

[solar merlin]

and you just want to get 2r (2r is the diameter)

how would you do that?

[copper pawn]

a / pi ?

[elfin ermine]

yup, that would be the first step

oh actually, I think I helped you with somethign simlair, xyz

[copper pawn]

and / 4 ?

[copper pawn]

yes ^^

[elfin ermine]

yes! this is right

so you now have

[copper pawn]

diameter

[solar merlin]

r^2 = a/4pi

[elfin ermine]

$\frac{a}{4\pi}=r^2$

[ocean seal]

Luca

[elfin ermine]

awesome, two more steps

[solar merlin]

so now you just want r

how can you get rid of r^2 and just have r?

[copper pawn]

√r^2 ?

[solar merlin]

that's right

[copper pawn]

i have the r

[solar merlin]

$\sqrt{\frac{a}{4\pi}}=r$

[ocean seal]

alias

[solar merlin]

so now you want the diameter, which is r times 2

so what's the diameter?

[copper pawn]

r * r

[elfin ermine]

nono, times to

not times r

[solar merlin]

r * r would be r^2

[elfin ermine]

if you multiply by r you go one step back

[solar merlin]

we want 2r

[copper pawn]

r * 2

[solar merlin]

that's right

[copper pawn]

okaaay

[elfin ermine]

on both sides

yields

[solar merlin]

so multiply on the other side

$2\sqrt{\frac{a}{4\pi}}$

[elfin ermine]

$d=2r=2\sqrt{\frac{a}{4\pi}}$

[ocean seal]

Luca

alias

[solar merlin]

perfect!

[copper pawn]

okay thx you

.close

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[formal spoke]

Question 14

.close

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[manic pike]

could anyone help me with part b, I have no idea where to start from

[solar merlin]

$-x^2+4x+k<0$, so
$x^2-4x-k>0$

[ocean seal]

alias

[solar merlin]

find the roots of the last quadratic, and figure out if it'd be smaller between the roots or outside

[manic pike]

find the value of k?

[solar merlin]

nah, find the value of x in terms of k

[manic pike]

ohh

[solar merlin]

just do it like a normal quadratic inequality

you'll find out what k CAN be to make x < 0

would you need me to help with that or should you just try?

[manic pike]

sure I guess, I dont really know what to do after finding x

[solar merlin]

when you solve the quadratic $x^2-4x-k$ you'll find solutions for when it's equal to 0. at what points would x be smaller than 0? would it be between those values or outside?

[ocean seal]

alias

[solar merlin]

here's a graph of an unrelated quadratic, it has 2 points when it's equal to 0

[manic pike]

hmm

[solar merlin]

in this case, between those 2 solutions it's smaller than 0, but outside it's greater than 0

without a graph, you can figure that out if you just take your quadratic and put a value outside the roots and inside, and see when it's smaller or greater than 0

makes sense?

[manic pike]

what do outside and inside mean?

[solar merlin]

i'm talking a little visually here. if you look at the picture, you can see the 2 roots , right?

[manic pike]

yes

[solar merlin]

when x is greater than the 1st root but smaller than the 2nd root, it's "between them" on the graph

[manic pike]

ohh

[solar merlin]

and in the case it's "between them" it's always negative

so do you know what to do now?

[manic pike]

hm

not quite

but I get the “between them” part

[solar merlin]

i'll walk you through them. i've rearranged the inequality $-x^2+4x+k<0$ to be $x^2-4x-k>0$ (dividing by -1 and 'flipping the signs') because having a negative x^2 is nasty

[ocean seal]

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

[manic pike]

okay..

[solar merlin]

my goal is to find the points where $x^2-4x-k = 0$ in terms of k, and then find out if a value between the roots in terms of k would be greater than 0 or smaller than 0

[ocean seal]

alias

[solar merlin]

for example, if the "roots" were 2k and k/2, would k be positive or negative? if k was positive the points between 2k and k/2 would be positive

1 sec

[manic pike]

k would be negative

[solar merlin]

right, i'm gonna show you how to solve it now

i'm gonna use the quadratic formula on $x^2-4x-k = 0$

[ocean seal]

alias

[solar merlin]

$x = \frac{4 \pm \sqrt{16+4k}}{2}$

[ocean seal]

alias

[manic pike]

understood

[solar merlin]

$x = \frac{4 + \sqrt{16+4k}}{2} and \frac{4 - \sqrt{16+4k}}{2}$

[ocean seal]

alias

[solar merlin]

these are the points that $x^2-4x-k = 0$

[ocean seal]

alias

[solar merlin]

now that we've got that, we need to find where x^2-4x-k > 0

1 sec

here's a visual

we know that anything starting with x^2 would be "positive", like a smiley face

so we have this

[manic pike]

yeah

[solar merlin]

when would we have a y value greater than 0?

between our 2 points, or outside?

[manic pike]

between?

[solar merlin]

nah, remember

our straight line is where y=0

the red area (between the roots) is below that, so it's negative

we need it to be positive

[manic pike]

ohh

so it will go outside of the roots?

[solar merlin]

yeah

so it's basically the stuff in green

remember, our roots were
$\frac{4 + \sqrt{16+4k}}{2} and \frac{4 - \sqrt{16+4k}}{2}$

[ocean seal]

alias

[solar merlin]

let's say the root i drew on the left was $\frac{4+\sqrt{16+4k}}{2}$, and the one on the right $\frac{4-\sqrt{16+4k}}{2}$

[manic pike]

yea

[solar merlin]

lol

[manic pike]

oop

[solar merlin]

thanks, doc

anyways, we know x would be positive when it's smaller than $\frac{4-\sqrt{16+4k}}{2}$ or bigger than $\frac{4+\sqrt{16+4k}}{2}$

[pale kestrel]

uh wheres this from

your roots suddenly changed

[solar merlin]

oh fuck

[pale kestrel]

just call them alpha and beta

xddd

painful writing this every time

[ocean seal]

alias

alias

[solar merlin]

that's been fixed

anyways, we can say this final statement

$x<\frac{4-\sqrt{16+4k}}{2}$ OR $x>\frac{4+\sqrt{16+4k}}{2}$ for x > 0.

[ocean seal]

alias

[solar merlin]

can't be both, only one

@manic pike did you get that? sorry if my writing got confusing haha

[manic pike]

yep kinda

its fine xD

[solar merlin]

alright, just read over that a couple times so you know the plan for next time when you have a question like that

[pale kestrel]

There is a slight shortcut

for this particular question

@manic pike do u notice the function only changes sign at the roots

[manic pike]

when u rearrange it?

[pale kestrel]

f(x) = quadratic

imagine the function as you move to the right along the x axis

The function wont change sign (go from positive to negative or negative to positive)

Unless you cross a root

So there are 3 regions for a quadratic. If you just consider the sign.

[manic pike]

oh

[pale kestrel]

Sometimes to check the sign. You find the roots. Then you can just try a point between the roots. And see the sign. Maybe this is confusing

[pale kestrel]

Here, you might notice x = 4/2 must be between the roots

but yeah, just in case that helps

[manic pike]

yep tysm

@solar merlin thanks as well!!

[solar merlin]

np!!!

close the channel if you need to with .close

btw that's a super challenging question, so i'm glad you understood. even i struggled a bit trying to wrap my head around it haha

[manic pike]

xd

.close

[lone heart]

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[serene flame]

i have a succession

[serene flame]

a_(n+1) = a_0*a_1*a_2*a_3 ... *a_(n-2)*a_(n-1)*a_n

how am i supposed to take it to analytical form

i have literally no idea where to begin from

[alpine sable]

What u mean by analytical form ?

Ohh

This is a bunch of factorials

A_n+1 = (a_n)!

What is a_0 first

[serene flame]

it's the first term

[glass lichen]

not how factorial works

[serene flame]

it's not though

[alpine sable]

Oh wait

[serene flame]

it's a succession

[alpine sable]

I thought it was consecutive terms

[serene flame]

not 1*2*3*4*5

[alpine sable]

My bad

I’m being dumb rn sorry

[serene flame]

issokay

[severe sluice]

well, let's take a_0 = n. then, a_1 is also n, and a_2 will be n^2. you can kinda continue this to see where the sequence goes

[serene flame]

why would a_0 be n

[alpine sable]

If it’s x

It will be the same

[severe sluice]

arbitrary variable name

well

should have used another one

[alpine sable]

Geometric progression ?

[severe sluice]

...no? why? why would it be a geometric progression?

[alpine sable]

Uhhh

[craggy salmon]

Nvm

[alpine sable]

Why not

[severe sluice]

now this definitely isn't true

[alpine sable]

U just said a0 is x

[craggy salmon]

1,1,2,4,8,16

[severe sluice]

it goes n, n, n^2, n^4, n^8, n^16, n^32, ...

[alpine sable]

Then a1 is x

[severe sluice]

so

shouldn't be geometric

[alpine sable]

Oomph

I see

[craggy salmon]

GP in powers except the a_0

[serene flame]

i did it fucking hell

thank you so much

[alpine sable]

How?

Can u show me pls

[severe sluice]

epsilon wants help?

[alpine sable]

Ye

Everyone in this world needs help at one point or another

And I’m just a high schooler

[lone heart]

@serene flame Has your question been resolved?

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[serene flame]

.reopen

[lone heart]

✅

[serene flame]

whoops didn't see that

[alpine sable]

Np

I got it

Meg explained to me

[serene flame]

anyway basically I expanded the series and found out I got x^2^n

alright

.close

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[weak jacinth]

Hello, in excel I have a set of 10 numbers in a column. I would like it display somehow the order of the number from lowest to highest. I am looking to have another column next to it to display this. Is there a way to automate this?
Something along the lines of the picture.

[median dirge]

Hi...

Is your Excel sheet Macro-enabled or not

[weak jacinth]

Im actually using Google Sheets, my mistake.

[median dirge]

Oh...

[weak jacinth]

Can it still be done?

I can record macros on sheets too

[median dirge]

Oh well.

I just meant you could use VB Script

A little loop through the cells.

Or ya need to wait till I create a complex mesh of excel formulae

And see if it works.

After my dinner tho

[weak jacinth]

Sure no problem, Ill wait

[lone heart]

@weak jacinth Has your question been resolved?

[median dirge]

Oh Sorry to keep ya waiting

@alpine sable why ya messing with the ❌ button hahaha

[weak jacinth]

No worries

[alpine sable]

Jaja is a joke

In gartic phone i do the same joke

[median dirge]

Eh. I suppose I got an answer.

Is very complicated tho

And difficult to reproduce.

@weak jacinth

[weak jacinth]

Is there no easy way to do it?

[median dirge]

Um not other than using VBS

It works fine with every value I put in these 10\

Well the formula

Just a min

The whopping-ly large formula

[weak jacinth]

For every cell?

[wary stream]

What exactly are you trying to do?

[median dirge]

Some excel stuff he wants to automate

[wary stream]

Because if you're trying to sort, there's a built in sort button

[weak jacinth]

I need it to display a number, because i also have to input some numbers so it would move it all around.

@median dirge Will it work if i just copy the formula you sent?

[median dirge]

=IF(LARGE(A1:A10, 1)=A1, 1, IF(LARGE(A1:A10, 2)=A1, 2, IF(LARGE(A1:A10, 3)=A1, 3, IF(LARGE(A1:A10, 4)=A1, 4, IF(LARGE(A1:A10, 5)=A1, 5, IF(LARGE(A1:A10, 6)=A1, 6, IF(LARGE(A1:A10, 7)=A1, 7, IF(LARGE(A1:A10, 8)=A1, 8, IF(LARGE(A1:A10, 9)=A1, 9, 10)))))))))

[wary stream]

What exactly do you mean, display a number?

[median dirge]

Just change the bolded values for every next cell.

And this is only for 10 cells.

If you know how it works, you can expand it

[weak jacinth]

Im going to try it real quick, and that formula is for every cell correct?

[median dirge]

.

Youre using Google Sheets

?

[weak jacinth]

yes

[median dirge]

Wait lemme test it

I used it on Excel because Ive had a fair use of this IF function

[weak jacinth]

sure

[wary stream]

If you're honestly just sorting from biggest to smallest, just sort it that way

[weak jacinth]

Im sorting from biggest to smallest, but instead of it swapping things around I want it to display a number.

[median dirge]

I Dmed you with a Spreadsheet link

Test it

[weak jacinth]

That works awesome. Is it possible to switch it to smallest to biggest? If not thats fine

[median dirge]

Smallest to biggest in the sense? The smallest gets rank 1?

Yeah

[weak jacinth]

yes

[wary stream]

I honestly think biggest to smallest is better than assigning a number. Because then you don't have to search and find every value you need, it'll be in order

[median dirge]

In all of the formulae swap LARGE with SMALL

Do a replace.

But yeah it will work only for ten cells, and for the cells in range A1:A10

Since you want this automated and not to change positions post-sorting it only complicates stuff, otherwise, the sort function was really good.

[weak jacinth]

Youre correct, but i need it like this specifically. Thanks for your advice though.

@median dirge Thanks alot, its perfect!

[median dirge]

Welcome

Dont mess up the brackets anywhere

Or the cell ranges

If youre stuck, ping me or DM me

[weak jacinth]

Will do thanks again.

[median dirge]

Welcome! G'day

[brave garnet]

can someone explain to me why n! + 1 isnt always prime?

[pale kestrel]

#❓how-to-get-help

[pale kestrel]

but consider n = 4

[weak jacinth]

.close

[lone heart]

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[brave garnet]

oh sorry thought I was in available, apologies.

[lone heart]

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[alpine sable]

Ok

[alpine sable]

@gloomy portal here

[gloomy portal]

Tysm epilson nought you are very helpfull

[alpine sable]

Ok

[gloomy portal]

Has the room opened

[alpine sable]

Post your question

[gloomy portal]

Where sorry

[alpine sable]

Here

In chat

[gloomy portal]

Okay

Okay so the thing is I kinda understand i need to square the first then multiply the product by 2 then square the second

But how I square these

When there already squared

[alpine sable]

They want u to expand them

[gloomy portal]

No find the square

[alpine sable]

Ik

That means expand these

[gloomy portal]

Okay I’ll let you do the teaching

[gray isle]

think the question is just poorly worded

and you should just expand the expressions given

[gloomy portal]

Epilson nought after this down for a round of chess you to ramonov

[alpine sable]

Chess ?

I don't play chess

[gloomy portal]

Hello

Okay so back to the square question

[alpine sable]

Ok

[gloomy portal]

You there if your concentrating sorry to bother

[alpine sable]

No

I'm here

So to square something

U multiply it by itself

For example in 1 u multiply y^5 -9x^4 by itself

Can u do it

[gloomy portal]

Ummm

Sorry this seem a bit to advanced for me

I am used to Australian curriculum

They don’t teach us this stuff

At this year level

[alpine sable]

Ok

[gloomy portal]

Can you write down answer and explain please I want to learn so badly how to do this

[alpine sable]

I'm very tried atm

I am also going to sleep in a few mins

[gloomy portal]

Oh okay

[pale kestrel]

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

[ocean seal]

Shuri2060

[pale kestrel]

expand.

[gloomy portal]

Hello Shuri

Shuri can you help me please

[lone heart]

@alpine sable Has your question been resolved?

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[fading eagle]

hello I need help reading this

[fathom mantle]

For all epsilon greater than 0 there exist k_0 element natural numbers. you can go from there

: means such that

[fading eagle]

I got that first part right but with the part starting from the colon, I am getting confused

[pale kestrel]

not necessarily

here it is just dividing the quantifiers and the statement

I dont think i would translate it as such

[pale kestrel]

The part after it?

[fading eagle]

well, I'd appreciate to have the whole transliteration

[pale kestrel]

Do you get the inequality?

[fading eagle]

as I am practicing rewriting these

[pale kestrel]

We dont need to give that right?

[fathom mantle]

if you are practicing you should know what the symbols mean right

[fading eagle]

uhm yes. I got it

[pale kestrel]

Another way to do this is:

You give me a positive e.
I will be able to give you a natural k0 so that
For any k >= k0 you give me
This inequality holds

===
In terms of a more intuitive explanation

[fading eagle]

yes yes I got that

how would I go with the : 8- E ?

[pale kestrel]

???

its literally an imequality

surely u dont need to write the entire thing

in 100% words

eight minus epsilon is ...

[fading eagle]

ahhhhh I see. I was just curious. I think I got it now. You're such a great help

oh forgot to close it

.close

[lone heart]

Channel closed

Closed by @fading eagle

Use .reopen if this was a mistake.

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[opal monolith]

An average of 6000 passengers a day takes the city subway trains at the cost of $3 per ride. The city board is thinking about raising the price to $3.50 per ride in order to generate larger revenue. They talk to a consulting team whose study shows that for each $0.50 increase in price, the number of passengers would be reduced by an average of 1000 a day. The consulting team suggests the city board should leave the price of $3 per ride since it already yields the maximum revenue. Prove that the consulting team is correct.

[shadow warren]

6000 * 3 = 18000
5000 * 3.50 = 17500

[lone heart]

@opal monolith Has your question been resolved?

[pale kestrel]

<@&268886789983436800> ^ occupying 4 channels

[gray isle]

.close

[lone heart]

Channel closed

Closed by @gray isle

Use .reopen if this was a mistake.

[dreamy cedar]

Do not abuse help channels like this

[lone heart]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[pulsar moat]

can someone tell me if im wrong? Im trying to prove to my teacher that angel 5 is equal to 3.

[pulsar moat]

I just put random numbers to prove my point

those aren't the actual measurements

[fallow badger]

do u mean prove 5 is 30?

[gray isle]

wrong use of parallel

[fading eagle]

well, that is assuming that the line segments forming angles 5 and 3 are actually just two lines intersected

[pulsar moat]

im trying to prove that angel 5 is the same as 3

[fading eagle]

if that's the case, you can use the vertical angle postulate

[gray isle]

and not a proper proof

[pulsar moat]

how can i prove it?

am i wrong?

[fading eagle]

Vertical Angles Postulate If two angles are vertical angles, then they are congruent (have equal measures)

[gray isle]

that's circular