help-0

[glossy niche]

wdym? when I substitute 0 into x or y?

[simple loom]

0 into y

[glossy niche]

if I do that it would become 0 = -5x - 4, which should become 5x = -4

divide both sides by 5

[simple loom]

anddd

[glossy niche]

then I got x = 0.8

[simple loom]

-0.8

[glossy niche]

oh wait 4 is a negative 😭

[simple loom]

😁

[glossy niche]

let me try drawing it again, dunno if it'll help though 🤔

[simple loom]

it definitely will

[glossy niche]

its kind of there no? the answer is -3, 11

[simple loom]

yes!

[glossy niche]

if the line drawing was a bit better it should've intersected properly, but eitherway tysm

[simple loom]

no problemm

[glossy niche]

.close

[lone heart]

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[lone heart]

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[hollow carbon]

Hello

[hollow carbon]

I need help

[lethal belfry]

what's the question

[hollow carbon]

finding the area of the shaded part

[lethal belfry]

cool, what have you tried

[hollow carbon]

I tried subtracting the area of a circular ring from the area of a circular sector but my answer does not match the choices

[lethal belfry]

!show

[lone heart]

Show your work, and if possible, explain where you are stuck.

[hollow carbon]

Wait let me rewrite its messy

wait for me

[hollow carbon]

Here

My answer does not match any of the choices and I need guidance

[weak pike]

How to reverse this function
f(x) = x³ + 3x² -3x + √x

[lethal belfry]

!ocuupied

!occupied

[lone heart]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[hollow carbon]

Oh and pardon my handwriting

It complements my mental health

[weak pike]

0-0

[lethal belfry]

the raidus of the inner circle is 1mm

not 2

[hollow carbon]

Let me try again

[hollow carbon]

The answer is still wrong tho

41 pi/ 3

[hollow vapor]

if you take away the sector, youre losing more than what you need to

[hollow carbon]

So the area of the sector is irrelevant?

What should I do?

[hollow vapor]

its not that its irrelevant

you jist need to make up for the area you subtracted in the smaller circle

[hollow carbon]

Can you give me a hint on how to do that?

[hollow vapor]

you can add the sector area of the smaller circle

[hollow carbon]

If you meant by using the radius of the smaller circle to the formula for the sector and adding it, it gave me 45pi/3 and it still does not match the choices given😢

[hollow carbon]

Hello are you still there?

<@&286206848099549185>

<@&286206848099549185>

[weak pike]

I don't know why I always get 13.75 * pi

maybe it's A cause when u don't calculate that circle sector it's closer to 11.4pi

[lone heart]

@hollow carbon Has your question been resolved?

[hollow carbon]

I cant sleep

[hollow carbon]

How did u get this

Can you show me ur solution?

[weak pike]

I TRIED FOR TIRTH AND I GET THIS SHIT AGAIN

alr wait

Sending...

CamScanner 07-17-2024 17.56 - Page 1

This if for forth time

[hollow carbon]

you actually got it

55/4 is 13.75

[weak pike]

Ow

[hollow carbon]

Though I have trouble understanding your solution

No offense

[weak pike]

Also I tried other ways I get that

[hollow carbon]

But it somehow is correct

Can you break it down a bit like step by step

[weak pike]

All thing u need to find is empty area

[hollow carbon]

The sector yea I got that

[weak pike]

I didn't understand u mean radian?

[hollow carbon]

Oh disregard that I meant still in the fraction form

[weak pike]

165/12

U want I highlight it?

[hollow vapor]

yo is the answer b?

i want to check smth

[weak pike]

CamScanner 07-17-2024 17.56 - Page 1

[weak pike]

165/12

[hollow carbon]

13.75 fraction form should be 55/4 thats weird

[weak pike]

So now can someone solve my question?

[hollow carbon]

So far it is

[hollow carbon]

I thought u went asleep

[hollow vapor]

nah i just died

[weak pike]

How to reverse this function
f(x) = x³ + 3x² -3x + √x

[hollow carbon]

So did you got it?

[hollow vapor]

just do your one formula

the

uh

circular angle one

and multiply it by the sector angle

[weak pike]

I didn't check the options on that moment

[hollow vapor]

divide by 2 as well sorry

cause if you look at the formula

let me write it

[weak pike]

What's your grade

[hollow carbon]

grade 11

[weak pike]

I wish our questions was like this

It's for my grade 9 or 8 I guess

[hollow carbon]

Different curriculum I think

[hollow carbon]

Does this apply to similar problems?

Just change the radians in its respective given?

[hollow vapor]

it should, i dont see why not

i can try other egs and see if it applies

[hollow carbon]

Wait lets continue this tomorrow I gtg

.close

[lone heart]

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[pliant olive]

why is it +37x and not just +x?

[sand cipher]

@pliant olive whats( x-6)^2

[pliant olive]

x^2 - 36

+36

[sand cipher]

-36 or +36

[pliant olive]

+36

im confused, when does the x get multiplied by 37..?

cus u multiply 36 by -3 and add 1 to get -107

and u do -3 times x^2 to got -3x^2

but why is x getting multiplied by 37

idk what im missing

[pliant olive]

im lost, where did the -12x come from

ohhhh

its the same as doing

(x-6) times (x-6)

i got it, nevermind

thank you

my brain just wasnt working, im only just getting back into algebra 2

[lone heart]

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[wet pewter]

how do i simplify this?

im trying to find the first derivative of sinx / e^x

[gray isle]

cancel common factor

[flat roost]

factorize e^x in numerator

[wanton wigeon]

Yo listen

What to do

Here to help

@wet pewter

[wet pewter]

ok so i common factored

[wanton wigeon]

So you got cosx-sinx/e^x

[wet pewter]

yes

[wanton wigeon]

So

.solved

.solved @wet pewter

Close the query if it is solved

[wet pewter]

oh thats the answer?

.solved

[lone heart]

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[wet pewter]

ty

[wanton wigeon]

Welcome

[lone heart]

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[honest juniper]

an ant is on a rubber line 20m long. the ant starts at the begining ant it moves at 5m/s to the right. the line streches 10m/s to the right. what is the position of the ant as a function of time?

[mossy laurel]

relative to what?

[honest juniper]

the start

excuse my english if its not clear i can restate

[mossy laurel]

the start does not move so it would be x = vt where t is the time and v is the speed

[honest juniper]

the rubber band streches and when it does so does the ant

[mossy laurel]

oh

[honest juniper]

if its halfway between the ant would still be halway after the strech

[mossy laurel]

so then the overall speed would be the sum of the ant's and the stretch

15m/s to the right

[honest juniper]

no

for example think that the ant is int the middle when line is 30m

when it expands it would move from 15m to 20m

[arctic lintel]

so ur after the position on the string? rather than the position from the start?

[honest juniper]

think about it like this

there is a number line

ur at 0 at the start

line exist from 0 to 20

[prime badge]

the point is that 10 m/s doesn't do anything at the beginning, and as the ant moves, it contributes more

[honest juniper]

ye

[prime badge]

the total speed grows

[honest juniper]

i found this diffrential equation not sure if its correct

[prime badge]

from 5, and never reaches 15

[honest juniper]

\frac{dy}{dx}=5+\frac{10y}{x+20}

uh how to use latex

$\frac{dy}{dx}=5+\frac{10y}{x+20}$

[ocean seal]

mso

[honest juniper]

i think this is the velocity with respect to time

x=time y=pos

[prime badge]

i would expect 10x + 20 there

[lone heart]

@honest juniper Has your question been resolved?

[lone heart]

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[frozen trellis]

i wanna make sure i did this right!

[exotic canopy]

i don't think that's right..

your side length is longer than the hypotenuse

[frozen trellis]

yeah i dont really know what im doing

[exotic canopy]

show your steps

[flat roost]

did you use trigonometry

[frozen trellis]

no

[flat roost]

what did u do

please show your steps

[frozen trellis]

i dont even knoiw what i did i think i did sin 32 = 13/a

[exotic canopy]

ahh

[flat roost]

the definition of sin is opposite/hypotenuse

[exotic canopy]

it's the other way around

[still herald]

wrong lil bro

[exotic canopy]

a/13

then it works out

[still herald]

that's csc 32 deg

[frozen trellis]

OHHH

[frozen trellis]

so why is that

its cuz its

[exotic canopy]

sin is opposite over hypotenuse

[frozen trellis]

on the hypootenuse right

yeah

[exotic canopy]

what is on?

[frozen trellis]

the c = 13

i got 6.8

[exotic canopy]

yep that's correct

[frozen trellis]

okay thank u so much

[still herald]

,w (sin 32)*13

[exotic canopy]

if you are rounding it should be 6.9 tho

[exotic canopy]

so be aware

[frozen trellis]

yes

[ocean seal]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by anshulyolo121

[still herald]

no.

it says round it to the nearest whole number.

[exotic canopy]

if you are done, type ".close"

[exotic canopy]

oh damn, i didn't see that

[frozen trellis]

yeah so its 7

[still herald]

6.9 isn't a whole number.

69 is

[still herald]

yea

[frozen trellis]

thank u

.close

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[forest jasper]

Does anyone know the answer?

[forest jasper]

@frozen trellis @still herald @exotic canopy

[exotic canopy]

why are you tagging me?

[frozen trellis]

?

what???

[lone heart]

@forest jasper Has your question been resolved?

[lone heart]

@forest jasper Has your question been resolved?

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[uncut aurora]

im confused as to why x+5 = (2𝑥+10)^2 turns into x+5 = 4x^2+40x+100
Where is the 40x coming from?

[uncut aurora]

im ngl im getting back into math now after years and that does look familiar yeah but i didnt remember thats what you do

wait so not only do you multiply both of the same you also multiply it by the other so 2x times 2x which is 4x^2, and then 4x times 10 which gives you the 40x, before doing 10 times 10 which is 100 ?

sorry if im being stupid i have no idea what im doing im just trying to learn

okay thank you

[lone heart]

If you are done with this channel, please mark your problem as solved by typing .close

[uncut aurora]

-4x^2-39x-95=0
(-4x-19) (x+5) = 0 i know you factorize but what happened with the 39

i cant really think of any im confused

oh wait

ac not ax

4 and 95

but

i dont really know what to do

4 is 1 2 and 4 and 95 is 1 5 19 and 95

39

like idk 38 and 10

is that why

cause 39-38 is 1

or wait

idk

what do you mean

1 2 4 5 10 38 95 380 ?

sorry i didnt look it up should i think harder

oh

190

would make sense

so also 19

and the 95/5 gives you the 19

i know that

OH adds up to be 39

well 1 and 38

20 and 19

[ocean seal]

faiyrose

[uncut aurora]

4 and 19

[ocean seal]

faiyrose

[uncut aurora]

x ?

no wait

okay

[ocean seal]

faiyrose

[uncut aurora]

x+5

so 4x + 19

[ocean seal]

faiyrose

[uncut aurora]

5/4+19

no wait

sorry i got ahead of myself

[ocean seal]

faiyrose

[uncut aurora]

yeah

can you not uhh what do you call it

cross out x

so only if its a fraction ?

or on both sides of the uhh

equation

well cant you switch it out and do x + 4x and 5 + 19 or is that not how it works

so what do you do

yeah i got that but

oh

-5

is x -5

you cant do that

cause 4 and 19 dont have like a

you cant divide 19 by 4

right

unless its not a whole number

so then it would be

19/4

or

-19/4

okay cool

thats so dumb though cause this is the original problem

$5sqrtx+5 = 25^x+5$

[ocean seal]

sebdoes

[uncut aurora]

oh

i thought you could do that

but you get the point

[ocean seal]

faiyrose

[uncut aurora]

was there a simpler way to do that since it just gives you -5 at the end

or is that a coincidence

no wait

the square root was to the power

$5^ \sqrt x + 5 = 25^x + 5$

yeah

[ocean seal]

faiyrose

[uncut aurora]

yeah i know thats what i was thnking the whole time

thats why i said was there an easier way to do that

yes bro but i do need to learn this shit anyway for college

i thought itd be fun idk ive always liked math anyway

yea

[ocean seal]

faiyrose

[uncut aurora]

cool

i came on here cause i put it on a calculator that shows steps and i wasnt getting why that was the process

like the 40x

cause of the binomials

i forgot ab that

but ty

[ocean seal]

faiyrose

[uncut aurora]

what about x = x can you cancel that out

[forest marsh]

Always true

So no need of cancelling

[uncut aurora]

$21/x = /sqrt/sqrt{4x^2}/24$

[ocean seal]

sebdoes

[uncut aurora]

what the hell

how does this work

wait can you only cancel it out if the amount of that is the same

so 4x +2x = 1x can i only cancel out one x on the left

[lone heart]

@uncut aurora Has your question been resolved?

[lone heart]

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[buoyant minnow]

wdym? 4 + 2x = 1 ?

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[granite iron]

I really need some help doing discussion boards i am missing 5 for stats,

[twin nimbus]

<@&268886789983436800>

[clever folio]

Cheating is not allowed here

[real gazelle]

Please don't offer money here, and we can't do your work for you. If you have specific questions, we can help you answer them though.

Otherwise, it's not welcome on this server.

.close

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[tender remnant]

Pre - Calc : Arthmetic Series ( Picture )
Can anyone help me out? I have no idea where to begin on this problem

[slate vortex]

I'm assuming S_n means the sum

[tender remnant]

Yes

[slate vortex]

If so, $S_n = \frac{a_1+a_n}{2} \cdot n$

[ocean seal]

Ari

[tender remnant]

Do I plug in the numbers?

[slate vortex]

yes that would solve for n

[tender remnant]

Ok let me try and I'll send a picture

Is this right?

[slate vortex]

a_n is 96 not n

[tender remnant]

Oh

Ok let me redo it

Is this rignt?

Right*

[slate vortex]

yes

[tender remnant]

Ok, is 12 my final answer?

[slate vortex]

Make sure you understand the formula though

since it's pretty intuitive with arithmetic sequences

[tender remnant]

Ok!

Thank yoy

You

[slate vortex]

[tender remnant]

.close

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[primal galleon]

Determine the minimum distance (how do you know that there is a minimum distance?) from the curve $y=1-x^2$ to the origin a) using a parameterization of the curve b) using Lagrange's method

[ocean seal]

dghf

[haughty flicker]

im just guessing here

cant you treat this distance calculation as a function and find the minimum point of it?

this what i though of

i mean

it worked

[rose sigil]

huh?

[slate vortex]

wait

nevermind I'm throwing

ignore me lmao

I thought you were finding the distance from the origin to that point on g(x) for some reason 🤦

[haughty flicker]

so my solution is correct?

[rose sigil]

yes

[haughty flicker]

haha

awesome

[rose sigil]

that’s probably what it’s expecting in part a

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[dusty obsidian]

i was attempting to do this question

(it was dy/dx=(y^2)+1)

and instead of dividing by (y^2)+1

i went dy-y^2-1=dx

[tawdry gust]

You can't subtract

[reef pier]

the expression must be a function of y being multiplied by dy

if you tried integrating both sides of dy - y^2 - 1 = dx

then you don't have a differential for part of the integrand on the LHS

that integral doesn't even make any sense then

[dusty obsidian]

i cant go y-y^3/3-y?

[reef pier]

no

the whole point of a separable DE is that it's written as f(y) dy = g(x) dx

[dusty obsidian]

oh i see

its like im adding up the tiny changes with no tiny changes to add up

thanks for the help :)

.close

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[lapis thicket]

How do I get the quadratic formula for this parabola? I recall it starts with getting the a term using the points, but I forgot the formula, and fhe formula after that. If anyone can point me in the right direction, much appreciated 🤙

[finite flax]

are you sure that is the problem that needs to be solved?

is the problem asking for the equation of the parabola?

@lapis thicket

[finite flax]

oh, you meant 'how do I get the equation of the quadratic'

[lapis thicket]

Yeah

[finite flax]

0. Identify 'h' and 'k'
1. Fill in the vertex-form of this parabola where the leading coefficient factor 'a' is unknown

2. Plug in a known point that doesn't eliminate 'a' (hint: There are two easily-identifiable points like this on the graph)

3. Solve for 'a'

4. expand the vertex form where 'a' is known

[lapis thicket]

Alr gimme a minute

Chowing down a burger rn

Like this?

Oh wait

[lone heart]

@lapis thicket Has your question been resolved?

[lapis thicket]

I'm doing 40=-a(13+11)(13+27)

But still not getting it right

11 and 27 are the x intercepts

Nvm 👏👏👏

Close

.close

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[unborn burrow]

I'm not getting the same answer as my professor, anyone know where I'm going wrong?

[unborn burrow]

answer

[lone heart]

@unborn burrow Has your question been resolved?

[lone heart]

@unborn burrow Has your question been resolved?

[small stag]

one thing you didn't multiply your 1/6 out to the final answer

and I believe your teacher's answer is just yours but using the half angle identity for sine

,w 1/3 * pi * sin(1/2)^2

[ocean seal]

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[small stag]

,w 1/3 * pi * (1 - cos(1))/2

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[small stag]

weird your answers differ by a factor of 4

[alpine sable]

How to find anyone?

[lone heart]

@unborn burrow Has your question been resolved?

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@unborn burrow Has your question been resolved?

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[ruby elbow]

soda OR water

[novel remnant]

Man I hate these🥲 halp

[ruby elbow]

so AuB?

[ruby elbow]

channel occupied

[novel remnant]

Thief!🤣

[ruby elbow]

breh

AuB?

notation

how do I find the intersection or do I even need to

wait is it just

total soda sales + total water sales/400

340/400

I have a different problem I want to check but can someone check this one

.close

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[warped topaz]

This is part of the solution to the question ^^

They say I dont need to square it?

I thought I had to do integral between b and a of g(x)^2 - h(x)^2 right?

Oh wait its not a solid of revolution 💀

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[dusty sluice]

Guys So I Am Confused By The Rules Of Algebraic Expressions? I'm A Kid Tho, Can You Help Me Understand....

[hollow vapor]

kid?

a kID?

how old are you

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[dusty sluice]

It's Just YouTube 💀💀

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[abstract prawn]

why this will be less than 0

i mean look at the equation, it should be more than 0

[uneven isle]

is ab a positive

if not

then the 2nd diff should eb engative for alpha = 2pi/3

i think

[abstract prawn]

oh i forgot that lmao let me check

[uneven isle]

-sin(2pi/3) is negative, 2sin(4pi/3) is also negative

if ab is positive then what you have is correct

[abstract prawn]

yup both are positive @uneven isle

[uneven isle]

.

[abstract prawn]

alrightyy

thanks

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[lapis goblet]

when it says determine p2 = f(.5)

i can solve p2 using p2,3 pretty easily

but is that just the answer

i feel like thats too simple

because it would just be P2 = 4

im just confused why is there a different f(.5) when the original was f(.4)

<@&286206848099549185>

wait im actually stupid

it just saying f(x2) where x2 = .5

way simplier than i thought

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[upbeat pilot]

A box contains 4 white, 4 blue, 6 red and 6 black balls, identical except for the color. Without looking, balls are removed one by one from the box, without returning, until the first white ball is removed.

What is the probability that, among the balls that came out before the first white ball, there is exactly one red ball?

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@upbeat pilot Has your question been resolved?

[gaunt tendon]

there are siz red balls ye ?

and total of 20

but u had taken away 1

so 19

6/19;-; ?

[prime badge]

it's stars and bars

well it would be if there was 3 colors

ok so there's 10 red or white

you just mix 10, 4 and 6 and then mix the 3 white and 5 red freely

[pallid scarab]

What we're interested in is only white and red balls.
white balls serve as bars and red balls serve as stars.

so you have x1+x2+x3+x4+x5 = 6

[pallid scarab]

and you're looking for the probability that x1 = 1

so the answer can be found with stars and bars formula (only remove the spoiler if you cannot see how to apply stars and bars) ||(4+5-1)C5/(5+6-1)C6||

||thus 8C5/10C6 = 4/15||

[upbeat pilot]

@pallid scarab sorry for the delay

actually i don't know this formula

stars and bars

[pallid scarab]

https://en.wikipedia.org/wiki/Stars_and_bars_(combinatorics)

[alpine sable]

I did it till the general term I didn’t substitute the calculation,am I still allowed to send that?

It should be this as per my know

[alpine sable]

You need to divide the final value of the summation by 12 factorial

That should be it

[pallid scarab]

I really don't understand why you only consider 1 white and one red

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[alpine sable]

Cause I’m just looking for ideal cases

[alpine sable]

Because I need the probability of that case

[fallen verge]

whats going on here?

are yall working on samuels problem?

you dont need stars and bars

just look at all possible arrangements of WWWWRRRRRR that start with RW

[pallid scarab]

same conclusion

[fallen verge]

but less involved solution

[pallid scarab]

sure that's another way to look at the problem

[alpine sable]

What is stars and bars

[alpine sable]

That doesn’t include a lot of cases

[fallen verge]

like?

[alpine sable]

What if r and w aren’t together

[fallen verge]

doesnt matter

[pallid scarab]

we don't care about blue and black

can be added afterwards wherever

[alpine sable]

But you don’t know in which order they will be picked so u need to include them

[pallid scarab]

wherever you pick blue and black, place them aside

and only put R and W in a row

[fallen verge]

no, because for every picking of blue and black, each arrangement of R and W will have a corresponding one

[pallid scarab]

in the order you placed them

!occupied

[lone heart]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[alpine sable]

So what are you going to use to solve it

Sorry my WiFi died

Are you still there?

[fallen verge]

(8C3)/(10C4)

thats it

[alpine sable]

So the 8c3 is for?

[fallen verge]

RW--------

[alpine sable]

You combined both right

Or did I misunderstand

[alpine sable]

?

[fallen verge]

(number of cases with RW--------, dashes are 3W+5R)/(number of cases 4W+6R)

[alpine sable]

So you’re looking at all the ways the whites and reds can be arranged?

[fallen verge]

yes

[alpine sable]

What I’m trying to say is if you do that ,you’re just selecting the position there are various arrangements for those positions

[fallen verge]

all cases have equal probability

[alpine sable]

Like it could be let’s say w is at the 4th position
It could be
R B BL W
OR
R BL B W

your method accounts for only one case

[alpine sable]

But that still increases the total cases

[fallen verge]

why?

[alpine sable]

Cause you need to select and arrange

Not just select

[fallen verge]

what happens is you get
((RW-)*(whatever method to add B and BL)/((all)*(same method to add B and BL)

it cancels out

[alpine sable]

You can try it with an easily quantifiable example,like calculate probability of getting one white ball before a red one if there are 3 red balls 1 white ball and 2 green balls

Try applying what you said,I’m pretty sure there will be missing cases

[fallen verge]

we get (2C0)/(4C1) = 1/4

have fun listing the 60 cases, but i assure you there are 15 that you want

GGWRRR
GWGRRR
GWRGRR
GWRRGR
GWRRRG

WGGRRR
WGRGRR
WGRRGR
WGRRRG
WRGGRR

WRGRGR
WRGRRG
WRRGGR
WRRGRG
WRRRGG

[alpine sable]

Hmmm maybe you’re right

Ahh shit I just realised op said they are identical

I’m sorry😭😭😭

[alpine sable]

I’m sorry,the solution I sent has an error I solved for n distinct balls so because they are identical you’ll have to divide by their factorials so that cases don’t repeat which just ends up being the other method mentioned

[upbeat pilot]

np

Can I close this channel @alpine sable

[alpine sable]

Yeah sorry again

[upbeat pilot]

Don't worry

Have a great day

.close

[alpine sable]

You too!

[upbeat pilot]

Oh, this channel turned to be your now

[alpine sable]

How do I close it?

.close

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[wanton wigeon]

@forest marsh

[wanton wigeon]

Yaku

Yo

Yaku

.close

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[blissful lotus]

hello

ok

safe channel

but LATEX wont work in an offline channel

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[toxic fable]

hi

[toxic fable]

can someone help with this?

[mental finch]

What have you tried so far?

[toxic fable]

does winning strategy mean they are guarenteed a win

[mental finch]

They have a strategy to win guaranteed

Mike could ignore the strategy and still win or lose, but there is a strategy that would guarantee a win

[lone heart]

@toxic fable Has your question been resolved?

[mental finch]

@toxic fable

[toxic fable]

so i know

that

[scenic crystal]

Hold on for this question

would there be 75 optiosn

[toxic fable]

n 2,3,4,5 works

[scenic crystal]

options*

[toxic fable]

?

[scenic crystal]

I noticed that as n-2,n-3,n-4,n-5 re all wining

[mental finch]

What happens if n is greater?

[scenic crystal]

thats where I am stuck

I have gotten to this base winning position

but between 6 to 100 I am confused

[mental finch]

Suppose n = 6

What are the possibilities? I.e is it even possible to find a guaranteed win for Mike?

[toxic fable]

im lost

[mental finch]

Maybe we can reduce n somehow to the previous cases when it’s Mike turn

Then we win guaranteed

[toxic fable]

2,3,4,5,8,9,10,11,14,15,16,17,20,21,22,23,26,27,28,29,32,33,34,35,38,39,40,41,44,45,46,47,50,51,52,53,56,57,58,59,62,63,64,65,68,69,70,71,74,75,76,77,80,81,82,83,86,87,88,89,92,93,94,95,98,99,100

?

i used python

[mental finch]

Play around with n = 6 basically is what I’m asking

[mental finch]

Why?

[toxic fable]

at 6

its losing since

regardless of what mike picks the other guy can pick the rest

[mental finch]

Yup

[toxic fable]

what bout 7

[mental finch]

Mike will still lose here, as we can flip the game and see it from the perspective of the other player

No matter what Mike picks, it will either be 5, 4 or 3, which we knew was a winning move for Mike when it was their move

But since it’s the other players turn they can always win, and so Mike will lose

Makes sense?

[scenic crystal]

is there like a formula to get to this part

[toxic fable]

yeah

[mental finch]

Now what if n = 8, then Mike might be able to reduce the case down to a previous winning one?

[scenic crystal]

any ideas to get to this formula

[mental finch]

We know now that if a players is meet with case n=6,7 then they can lose

[toxic fable]

yep by picking 2

he makes it losing for ian

[mental finch]

Yup!

[toxic fable]

but how do i repeat this pattern for higher ns

oh its recursive

[scenic crystal]

bingo that seems it

[mental finch]

Yeah

[scenic crystal]

whats the recursiveness

[mental finch]

It’s good to play with the low ones, as we just did

[scenic crystal]

of the formula

[mental finch]

You’ll sense the pattern in such case

So try now n=9 etc and see if you can find the pattern!

[scenic crystal]

hold on a minute if every possible value entered does the n value at the end has to equal something? Bit complicated I know im confused

[mental finch]

Notice how 2 + 4 = 6, and as we saw 6 is a losing number for whoever is playing on it, and we have that 3 + 4 = 7, so there is a sort of periodicity going on here, we can see that 8 + 4 and 9 + 4 are also losing numbers for Mike etc

It’s worth going through each case, as we did.

[scenic crystal]

like all of them

[mental finch]

Not needed

Just the base ones

I guess you could attack this differently, but the intuition you gain from playing with the lower base numbers is so easy it’s hard not to go that route

[scenic crystal]

like what is considered the base ones

[mental finch]

By starting from the start, i.e n=1 and then up we establish a few base cases when it’s clear Mike will win

As we do so we might also caught the pattern and can reason the way we did above

[scenic crystal]

from earlier what are the base cases

[mental finch]

Go up and read

[scenic crystal]

ok so between 1 to 8

[mental finch]

If we instead consider the numbers 1 up to 7, then 1 and 6,7 are losing numbers. We can shift all these by 6, then we might notice that the ones in same place from before are still losing numbers, we have 7 and 12, 13 as losing numbers, and this pattern continues

[scenic crystal]

ooh i see it now

but how are things like 75 a loosing number

[mental finch]

Hm, why?

If you can subtract 6 until it lands on 1,6 or 7 then it’s a losing number

[scenic crystal]

wait is that it

take all posibilit subtract 6

and if its a 1,6,7 uts loosing

[mental finch]

Yeah

That’s the pattern I see atleast

It makes sense if you play the game for low n

[scenic crystal]

but explain how things like 9 would work

it works but it doesnt follow that rule

[mental finch]

This is due to way we can pick 2,3,4 which is just shifting

[mental finch]

As in?

9 is not a losing number

[scenic crystal]

like 9-6=3

[mental finch]

Yeah so it didn’t land on 1, 6 or 7

So it’s not a losing number

[scenic crystal]

how did we lead to this then

[mental finch]

That’s all the winning n apparently

[scenic crystal]

than i guess it not right

[mental finch]

We wanted to find all n for which Mike wins, I just gave a way to find for which n Mike does not win

And that’s just equivalent

[toxic fable]

how do i approach this

?

[mental finch]

So you can just exclude all losing numbers

[toxic fable]

ik that sin x has a range from -1 to 1

[mental finch]

This question is not even remotely close to the previous one, you should open a new channel for it

[toxic fable]

ok

can i close this then

?

[mental finch]

Yeah if you feel done, btw isn’t that question basically the help channel above this one?!

[toxic fable]

apparently i cant have more than one channel open

what the flip

[mental finch]

Uh this question is the same as in #help-39

[toxic fable]

ok thanks

ill close this now

[scenic crystal]

yeah go there

[toxic fable]

.close

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[scenic crystal]

no dont

[lone heart]

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[limber pulsar]

The point P lies on circle with equation x^2 + y^2 - 6x - 16 = 0 and the point Q has coordinates (8,1). Find the minimum length of PQ giving you answer in the form k(root2)

[limber pulsar]

been confused for a while cz idk what p is.

[arctic lintel]

P can be any point on the circle

but they want the point on the circle closest to Q so that the distance between them is at a minimum

[lone heart]

@limber pulsar Has your question been resolved?

[limber pulsar]

i got it thanks x

got some help from another chat thing asw lol

.close

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[feral shore]

Can some one please help in this question'

[feral shore]

<@&286206848099549185>

[tribal axle]

Sure! What do you need?

!status

[lone heart]

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

[feral shore]

2

[tribal axle]

Could you show the progress made so far?

[tribal axle]

Thanks!
So at this point you need to show when
x(2x+5) > 0
Remember that
a * b > 0 if:

1) a and b are positive
2) a and b are negative

Try using this fact to continue the equation.

[cobalt vine]

You are confused. This is not like solving equation

[feral shore]

I have to find the answer in form of Range. So how shall I do that?

[cobalt vine]

As Woomy has said

[tribal axle]

nvm lol

i had a confusion

[cobalt vine]

Basically, you need to check sign of x and (2x+5)

[feral shore]

i think there is also some concept of Domain to solve it

[tribal axle]

Yes, after solving the equation you need to make sure that your answer is within the domain of the logarithm

as whatever is inside the log cannot be negative, you also need to check when 2x^2 + 5x + 1 is negative, and remove that from the range

[feral shore]

so like for domain i keep this?

[tribal axle]

yes

[feral shore]

oh alr i think i got it

[cobalt vine]

We had the inequality $2x^2 + 5x + 1 > 1$, tho

[ocean seal]

Closer

[feral shore]

yes? i solved that

[tribal axle]

thats only after exponentiating both sides with a base of 1.5

[feral shore]

I got it

i got the answer

thanks

[cobalt vine]

I mean solving that will ensure the thing inside log greater than 1 so we don't need to check the domain

[feral shore]

also there one other ques, can i ask that too?

[tribal axle]

yw :)

[tribal axle]

go ahead

[tribal axle]

if its less than 1 but greater than 0 its still fine even inside the log

sin(pi/6) is 1/2

so log_0.5(pi)

i'd just use a calculator to see if its positive or negative, for irrational or rational idk how you would show that

[feral shore]

i think its +ve and rational

[tribal axle]

how can you say its rational?

[feral shore]

hmmm it will be positive that i am sure

but yeah how can i prove it rational or irrational?

[tribal axle]

Use a calculator to make sure

[tribal axle]

I would say its irrational, since pi is irrational

ohh i see how to prove its irrational

[feral shore]

how pls tell

[tribal axle]

actually nvm i dont think its possible to straight up prove it

since a and b are both not integers

but intuitivly its not rational since pi is irrational and iirc log is closed under irrationals

[feral shore]

I did this

[forest marsh]

,wa solve pi = \frac{1}{2^x}

[nocturne pasture]

,w solve pi = \frac{1}{2^x}

🙂

[feral shore]

Lol

[forest marsh]

Clearly not rational then

[tribal axle]

log being ln?

or log_10

[ocean seal]

Results provided by WolframAlpha

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[nocturne pasture]

,w what is -(log(pi)/log(2))?

[ocean seal]

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[nocturne pasture]

Ok log is just log ig

[feral shore]

so it is irrational?

but i dont think the value will be Negative?

[cobalt vine]

You can use change of base: $\log_{1/2}\pi = \frac{1}{\log_\pi \frac{1}{2}}$

[ocean seal]

Closer

[cobalt vine]

pi is irrational so pretty sure it is irrational

and pi is greater than 1/2

[reef pier]

unfortunately that's not enough to know

https://mathoverflow.net/questions/40145/irrationality-of-pi-e-pi-pi-and-e-pi2

[cobalt vine]

so the denominator it is negative

[feral shore]

this cant be in negative though

no matter what value we put for X it will come close to O but not negative

[cobalt vine]

But x can be negative, tho

and you set x = ...

[feral shore]

but if x is negative then it will become this

[cobalt vine]

2^x = pi is valid, tho

[wise oyster]

any help?

🙏

[feral shore]

i think its fine, thanks for all your help!

.close

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[unborn burrow]

I got zero for divF

[lone heart]

Show your work, and if possible, explain where you are stuck.

[unborn burrow]

isnt the integral of 0 always zero

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[tardy stag]

hmm yeah i get divF = 0

oh

where x > 0

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[quick oyster]

how do I solve this, I don't get this formula

[reef grove]

do you know how to find the area of a rectangle?

[quick oyster]

b times h?

[reef grove]

yes, does this make intuitive sense for you?

[quick oyster]

kinda, is it 5 times 10?

[reef grove]

we define this green area with an area of 1 because you can go 1 unit of length in each direction.

If you want to calculate the area of the whole rectangle you are just asking the question, how many times can I fit this green area inside the rectangle

[cinder aurora]

Yo any help😭

[reef grove]

!occupied

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Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[reef grove]

and that turns out to be the same as multiplying, because you can put this green area 10 times from left to right and 5 times from bottom to top

so that means 5 * 10

this concept always applies you just try to check how many small rectangles or cubes you can fit in your geometric object

if you still need helping with finding the surface just ask or if anything was unclear

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[calm tulip]

how would i go about even solving this

[alpine ore]

If you can convert that tan(-x) into smth•tan(x) then you'll have a common factor

and then you will have (tanx)(stuff) ≥ 0

...which will be easier to solve

[calm tulip]

idk if this is right but

-tan^2x-2tan(x)?

[alpine ore]

Yes correct

[calm tulip]

wait so how does that work

moving the negative from inside to outside

[alpine ore]

tan(-x) = -tanx

It's a property of the tan function and sin function

[calm tulip]

but not cos

[alpine ore]

yup

[calm tulip]

so then i get tan^2(x)+2tan(x) <= 0 -> tan(x)(tan(x)+2) <= 0

[alpine ore]

Yeah

[calm tulip]

now im stuck

idk what all the interval stuff is

[alpine ore]

As a starter

Let's get rid of the "or equals" part in ≤

[calm tulip]

ok

[alpine ore]

A ≤ B means two cases,
1: A = B
2: A < B

We'll take case-1 for now

[calm tulip]

tan(x) must be -2 or 0

[alpine ore]

Remember, we're solving for x

if tan(x) = -2, then x = ...
if tan(x) = 0, then x = ...

[calm tulip]

sin(x)/cos(x)=0 therefore sin(x) must be 0 and for sin(x)/cos(x) to be -2 then its a diff number

for the first one isnt it pi and 2pi

[alpine ore]

sin(π) = 0, true

There's another solution you're missing

[calm tulip]

are you referring to the tan(x) = -2

[alpine ore]

No I'm still referring to sin(x) = 0

[calm tulip]

OH 2pi

i mixed up the things

i thought pi was -pi and 2pi was pi for a moment

[alpine ore]

solution set of sin(x) = 0 is {..., -3π, -2π, -π, 0, π, 2π, 3π, ...}

But we discard any that aren't in our interval

So we get three x values out of this, x = 0, π, 2π

[calm tulip]

uh huh

[alpine ore]

As for the tan(x) = -2 part, I think the solution's gonna have to stay in terms of arctan

[calm tulip]

which is arctan(-2)?

[alpine ore]

Now we'll take case-2

[calm tulip]

im confused because if arctan(-2) is -1.107 that doesnt fit

[alpine ore]

Yeah we'll just offset it by 2π

[calm tulip]

ohh

what do you call that?

[alpine ore]

It's the periodicity of the trigonometric functions

(If "periodicity" is even a word, lol)

[calm tulip]

ohh thank you

so you add it by whatever the period is?

in this case 2pi

[alpine sable]

Isn’t tan pi periodic ?

[alpine ore]

tan(x) is periodic

[alpine ore]

Do you know how to solve ab < 0 ?

[calm tulip]

im afraid not

[alpine ore]

Just think of it like

How can I multiply two numbers and get a negative?

[calm tulip]

ohh

[calm tulip]

so like coordinates in quadrant 2 and 4?

[alpine ore]

I think that's skipping too many steps

[alpine ore]

ab < 0
implies
either: a < 0 AND b > 0

or: a > 0 AND b < 0

tan(x)(tan(x)+2) < 0
implies
either: tan(x) < 0 AND tan(x)+2 > 0

or: tan(x) > 0 AND tan(x)+2 < 0

[calm tulip]

ohh thank you

[alpine ore]

Does the "or" part make sense?

[calm tulip]

yes

[alpine ore]

tangent is bigger than 0, but also at the same time less than -2

[alpine ore]

Does this make sense?

[calm tulip]

that does not

[alpine ore]

exactly

That's why we will discard it

So we'll just have to solve
tan(x) < 0 AND tan(x) + 2 > 0

[calm tulip]

so tan(x) is between -2 and 0

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[still dove]

Why is the point G, where the horizontal line drawn from point F intersects, the orthocenter of triangle ABC?

(Red line means same length)

[trail jewel]

Do you know the meaning of orthocenter

[trail jewel]

Cuz this picture literally proves it

[still dove]

.

i want to know, Why and how does horizontal line from point F create point G, the orthocenter of triangle ABC

This problem focuses on points F and G

[still dove]

not this 👎

[still dove]

This is just evidence proving why it is the orthocenter. in case you might not believe it.

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@still dove Has your question been resolved?

[still dove]

Please use my ggb to solve this problem...

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@still dove Has your question been resolved?

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@still dove Has your question been resolved?

[soft bridge]

hi

can you explain me mre about your question?