help-26

[prisma saddle]

That has nothing to do with this problem tho

.close

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[distant linden]

?

how to do

[woeful drift]

differentiate and equate to 0

[distant linden]

oh ok

.close

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[wispy acorn]

Do I use the Second Deriv Test?

since g'(x) = f(x) and g''(x) = f'(x)

[glacial adder]

you most definitely can, or just use the first derivative test

[topaz sinew]

@wispy acorn Has your question been resolved?

[wispy acorn]

so whenever f(x) = 0, and it goes from + to -

So only once at x = 1

[glacial adder]

yep that’s correct

[wispy acorn]

got it, thanks

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[distant linden]

how do i do this? 3

[robust ocean]

!original

[topaz sinew]

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

[robust ocean]

Are you using the functions from 1. Thus a,b,c and d as the graphs or there are some other graphs?

[stray lava]

Which are the graphs?

[topaz sinew]

@distant linden Has your question been resolved?

[agile harness]

what have you tried

[topaz sinew]

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[bright ice]

how would I solve this?

[bright ice]

,rotate

[bright ice]

So yeah how would i solve this lol

Thats the thing I dont know 😭

pie r squared right?

[thorny flame]

faiyrose

[bright ice]

So what would I do for that sector then?

Wait

so i would find the area of the circle

then I would find the precent 40 degrees is of 180

then just do the area times the precent?

oh wait my fault lol

11%?

yeah

thats what i got from 360

40 degrees is 11% right?

idk if I know how to find a precent but i just did 40 divided by 360

is that how you find a precent?

ok!

i forgot how do I convert decimals to fractions?

1/9?

is the answer 27.20?

[thorny flame]

faiyrose

[bright ice]

wait I kinda prefer using a decimal so does it matter?

[bright ice]

cause I got this from using a decimal

[thorny flame]

Result:

27.991590543485

[bright ice]

yeah then I just rounded the hundreth

[thorny flame]

Result:

28.274333882308

[bright ice]

hmm ok. Do you think a teacher would accept it using a decimal though?

btw what makes a fraction more accurate>

?*

Ohhh ok! Wouldnt a decimal not rounded be more accurate since it has more numbers? Sorry if Im wrong. Dont know alot or understand math that well.

Ok! Thank you :)

Yes I do think so. Thank you for the help!

I actually do need help with 1 more thing though

I hate the circles unit lol

,rotate

[bright ice]

How would I find the lenght?

No I dont. I learned it but I just forgot it. Im not really good at math because my memory sucks 😭

to be honest I forgot that too

[thorny flame]

faiyrose

faiyrose

faiyrose

[bright ice]

Wait real fast before you tell me the right way lol. I think I might have a way to do it

and i just want to see if it would work lol

so the whole of the circle is 360 right

oh wait

nvm

my fault lol. Keep going. Sorry though I was onto something

[thorny flame]

faiyrose

faiyrose

faiyrose

[bright ice]

Its still loading the image lol. My wifi sucks

ok it loaded

ok so would it be

wait how would I find that?

[thorny flame]

faiyrose

[bright ice]

so 360 equals 2 pie r right?

thats what i dont know how to find out

what would I do to find it?

I dont know

division

Oh ok

[thorny flame]

faiyrose

faiyrose

[bright ice]

How much or how would?

0.14?

[thorny flame]

faiyrose

[bright ice]

so now we just multiply it by 45?

[thorny flame]

faiyrose

[bright ice]

ok!

thank you for all the help!

[thorny flame]

faiyrose

[bright ice]

Ok!

i have a math test tomorrow so im just trying to learn everything 💀

anyways i have to go

Have a great rest of your day!

[topaz sinew]

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[bright ice]

.close

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[acoustic pecan]

a quiz huh

a timed test

[rapid wyvern]

is this a graded exam

[acoustic pecan]

what to do what to do

<@&268886789983436800> my friend here needs some invigilation

[half edge]

delete that rn or im reporting you to the moderators

[worthy storm]

set a snooze button for 57 minutes

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[half edge]

,w invigilations

[thorny flame]

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[half edge]

wow

[worthy storm]

nice word of the day

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[topaz sinew]

@earnest badge Has your question been resolved?

[topaz sinew]

@earnest badge Has your question been resolved?

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[quartz yoke]

Element X is a radioactive isotope such that its mass decreases by 87% every year. If an experiment starts out with 610 grams of Element X, write a function to represent the mass of the sample after t years, where the daily rate of change can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage rate of change per day, to the nearest hundredth of a percent.

[quartz yoke]

doing a deltamath that has been confusing me heavily, gotten a few right, gotten most wrong, im unsure

what is different

[hearty anvil]

Been a while, something like 610*0.87^t

Which is from a formula u should have memorized

[quartz yoke]

should if i actually had a teacher that

knows the subject

had 2 math teachers quit this year

been an absolute mess

heres a screenshot of

so i understand that its decreasing

changed the growth to decay

[hearty anvil]

Does this make sense

[quartz yoke]

i take the 0.87 and do 0.87^1/365

[quartz yoke]

yeah i already understood that part

[hearty anvil]

Oh it’s per day

Yeah I think that’s right

[quartz yoke]

and do 365t in the exponent

[hearty anvil]

No wait

[quartz yoke]

huh

[hearty anvil]

Sorry it’s been a while, I think you multiply the exponent by 365 and divide the lower by 365

[quartz yoke]

found an example of

a question thats quarterly

[hearty anvil]

Forth root feels wrong

[quartz yoke]

ended up getting that question wrong

heres what it shows the steps are

with the final answer

here's my new question

this is what i get from just whats given straight away

[hearty anvil]

(1-0.18)^1/365 according to the given formula

[quartz yoke]

yep got that part

[hearty anvil]

But also it says per month

[quartz yoke]

oh oops

[hearty anvil]

So why would it be 365 and not 12

[quartz yoke]

12 not 365

sorry was mixing that with

example question for reference

got that one right

I think i should have this down now

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[calm burrow]

I need a little help with this

[calm burrow]

Is it write if i prove AC = CE by Triangle ABC = Triangle DCE or am i completely wrong

[vale juniper]

I think so, can you send a photo of the notes

[calm burrow]

@vale juniper

[vale juniper]

Ya

[hollow plover]

This one ?

[calm burrow]

yuh

[hollow plover]

May i help

[calm burrow]

alright

[hollow plover]

You see angle ACE and angle DCE are vertically opposite angles

Angle ABC and angle EDC are alternate angles

[calm burrow]

yuh

[hollow plover]

And the other angle must be equal

So we have proved that triangle ACB and Triangle DCE are similar

[vale juniper]

That makes sense, but why are there no numbers, don’t most of these types of problems have numbers

[hollow plover]

Also now we have DC = CB

Its a proof based only i think

[calm burrow]

wait i thought we had to folloow the angles in their alphabeticcal order guess not

[hollow plover]

yeah ofc i did just that

Now we KNOW BY A-S-A axiom of congruency that the two triangles are congruent

[vale juniper]

Could you also say that because DC = BC and since AB||DE, the triangles are similar

[calm burrow]

yuh

[hollow plover]

Hii sry

I lost the channel

@calm burrow @vale juniper We can say that the side opposite to the equal angles are equal in length when congruency is proven

[vale juniper]

Makes sense

[calm burrow]

ngl im trying to get what youre saying but im not

[hollow plover]

Ok i just mean

The side opposite to

[calm burrow]

aint that little ->- sign on AB and on DE prove that they are equal

[hollow plover]

Angle D and Angle B are equal

Since Angle B and D are equal

[calm burrow]

yea

[hollow plover]

No how length can be negative

[calm burrow]

its not negative

im trying to show the sign

[hollow plover]

Oh okk

[calm burrow]

that looks like an arrow

[hollow plover]

oh

In the figure you mean

?

[calm burrow]

yea

or does it rep sojmething different

[hollow plover]

It symbolizes AB and DE are parallell

[calm burrow]

damn i should really revise on my notes

[hollow plover]

So.that we can use alternate angles

If it werent we coudnt use

[hollow plover]

Np bro you r learning

[calm burrow]

angle A = angle E... alternating and angle B = angle D... alternating?

[hollow plover]

Yeah

[calm burrow]

so thats my answer?

[hollow plover]

What ?

Bro i explained the steps

You need to proof congruency

Angle side angle congruency

Write it on copy

Then proceed to this

Basically showing steps on copy

Thats it

[calm burrow]

im not getting what you mean by this

[hollow plover]

Your proof is done

you can do it yourself ?

[calm burrow]

i think we just went back to step 1

im not getting how you want me to write it

[hollow plover]

So start like this

ACB and DCE are vertically opposite angles

DC = CB ( given)

Angle D = angle B (alternate angles)

From The A-S-A axiom of congruency triangle ABC congruent to triangle DCE

So , the sides opposite to the equal angles are equal

Hence AC = CE (since ..
)

Similarly write for the other side

nd you r done

[calm burrow]

ahh now i get it

damn thank you

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[odd jacinth]

Yo, i kinda need help with an excel thing... Currently working on my work report.... I used to know how to do this but now i am just completely lost lmao

[odd jacinth]

i need to summarize 2 collumns with the x amount into another collumn

[acoustic pecan]

wdym

[odd jacinth]

So uh

Say i type "2" into C19, it should mutiply collumn C10 based on my number then summarize it into D19

That would make D19 a value of 600

am i talking non sense? xD

I just dont know the commands is all...

[acoustic pecan]

=C10*C19 is the multiplying part, but im not sure what you mean by summarizing

SUM adds values together but you only have one, no?

[odd jacinth]

well

do you want me to show you in stream?

it works for some collumns

kinda

[acoustic pecan]

shouldnt it be you putting a number into C19 then its just D19 has "=C10*C19"

[odd jacinth]

I just wanna put in a number, have it summarize everything for me lol

oh

ye kinda yeah

wait actually

think i am big stupid

uh

how do i do it with the "kr" infront?

right now its just like that

[acoustic pecan]

="kr"& C10*C19

[odd jacinth]

o

Thanks man

🙂

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[terse crane]

why did they do cos 120

and not 60

[unique crypt]

law of cosine uses the angle between the actual legs of the triangle not the vectors

[terse crane]

okkk

[topaz sinew]

@terse crane Has your question been resolved?

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[cloud tapir]

How do you see this simplification, the last two products

[half edge]

shouldnt it be -1 and not + 1

for - e^(-0)

anyways what have you tried @cloud tapir ?

[cloud tapir]

what do you mean?

[half edge]

look at the -e^(-0)

[cloud tapir]

ye

[dark frigate]

its positive

[cloud tapir]

its 1?

[half edge]

u put +1 instead of -1

[dark frigate]

it should be +1

[half edge]

why?

[dark frigate]

the - from FTC and the - in the function cancel out

-e^-2 - (-e^0)

[half edge]

waht, where are u seeing FTC\

[half edge]

we're looking at this right?

[dark frigate]

mb i was lookin at second picture

[dark frigate]

maybe u forgot the negative ion know

[cloud tapir]

i mean the second is what

the answer is pretty much

[dark frigate]

u jst forgot the negative

prob

everything looks right

but you forgot the negative on e^0

[cloud tapir]

ah ye

[dark frigate]

yeah

u put it for the first time

[cloud tapir]

yep forgot it after kind silly

kinda

[dark frigate]

but ur answer is right p much yea

just a type

typo*

[cloud tapir]

anyway what have I tried to simplify

[dark frigate]

u work is right

[cloud tapir]

yes but it needs to be simplified

[dark frigate]

ye

[cloud tapir]

and i dont see how I can do so here

[dark frigate]

u already have 1 - 1/e^2

[cloud tapir]

yes thats as far as I get

[dark frigate]

just common denominator the natural logs

[cloud tapir]

yes idk how

[dark frigate]

well

[cloud tapir]

i did that

i read it from my answers

😢

[dark frigate]

this is what u have

[cloud tapir]

I mean I dont know how I even got there

[dark frigate]

wdym

[cloud tapir]

from this

[dark frigate]

like

where u stuck

[cloud tapir]

to the line below

[dark frigate]

like whats the problem here

2^0 is one

[cloud tapir]

yes

oh

[dark frigate]

ion get whats wron

[cloud tapir]

im dumb

im sorry

[dark frigate]

is allg

[cloud tapir]

i got it now I just didnt think

okie let me look

at the next step u showed

[dark frigate]

cuz all ur work is right

[cloud tapir]

damn

so u just put 1 there, in the shape of 4/4 so u can multiply by 4 and make the denominator 8ln(2)

[dark frigate]

🫃🏻

[cloud tapir]

interesting how that feels so illegal

[dark frigate]

its jst multiplying by 1

technically

[cloud tapir]

yet logical

yeah

[dark frigate]

just doing common denominator

and then same denominator means u can combine numerator

and thats it

[cloud tapir]

yep

i like you as a teacher, ure quick w the latex

🙏👍

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[royal sky]

this means its rotating on the x axis right?

[wary tulip]

rotating about the line y = 3

[royal sky]

then for cylindrical shell should i integral wrt y?

or x in this scenario

[wary tulip]

i don’t know how to do this stuff sorry

[golden blade]

yes

[royal sky]

then would this integral be suitable

for the question above

[golden blade]

why to 3?

[royal sky]

cuz the

its from 0 to 3 here i think

this is the grath x=y^2-1

[golden blade]

it's y^2 + 1

[thorny flame]

𝔸dωn𝓲²s

[royal sky]

yes y^2+1 mb

uhm but the rest of the equation

is it correct?

[golden blade]

so if you have y^2+1

you will notice that y goes from 0 to 2

[royal sky]

oh wiat yeah i

had that idea but i removed it idk why

okay tyty

so is this correct?

[golden blade]

yea that'd be my guess

[royal sky]

thing is its wrong so idk what the mistake it

could it be the 3-y?

[golden blade]

oh shouldn't it be 3+y

wait lemme think for a moment

[royal sky]

this is the graph

[golden blade]

I mean the radius should be fine

3-y

also how did you get 16pi

[royal sky]

a calculator

[golden blade]

,w Integrate[2pi(3-y)(y^2+1),{y,0,2}]

[thorny flame]

Results provided by WolframAlpha

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

Requested by adoniszgks

[royal sky]

it was through this

oh wat

[golden blade]

i am just confused as you

[royal sky]

yeah haha weird stuff

anyway ty

.close

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[golden blade]

lol

[topaz sinew]

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[fringe oyster]

I have no idea

[nimble garnet]

looks like they're asking you to complete the angle between two vectors formula?

[topaz sinew]

@fringe oyster Has your question been resolved?

[fringe oyster]

yea

[nimble garnet]

do you know the formula

[fringe oyster]

no

nvm

.close

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[fringe oyster]

I tried F so I thought it was wrong but it required an arrow on top to say that its a vector

even though the other vectors didnt have that notation

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[golden flint]

can someone explain why this is injective?

[rigid ivy]

It's the definition. There's no other reason why

[jade thunder]

That’s a definition

[golden flint]

i get it but injective is every co-domain has at most one domain. How is it possible for a domain to have two co-domains?

[cursive mango]

Reread the definition closely

Idk what you mean

[jade thunder]

It’s saying if you pick 2 same elements of the codomain that is in the image of f, then they have the same preimage

That’s not necessarily easier to understand

[cursive mango]

lol

[golden flint]

oh

shit

nvm

ty

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[neon iron]

https://math.stackexchange.com/questions/3444254/taos-infinite-pigeonhole-principle-all-sequences-have-constant-subsequences I don’t understand how these people are calling it an infinite sequence from a finite set

[neon iron]

they are calling the original poster wrong because the sequences are infinite?

X is finite how would u generate an infinite sequence

shouldn’t it be the other way around?

[jade thunder]

You just pick countably infinitely many elements of X in a specific order

But there’s only so many distinct elements you can pick since X is finitely large

[neon iron]

let me get it straight, so by a countably infinite sequence in X, they mean a function from Naturals to X, but since X is finite theres only finitely many “pigeonholes” so at some point the function generating the sequence has to take on the same value (become constant)?

[jade thunder]

Not at some point

But a subsequence

A function f : ℕ -> X

Then you can find g: ℕ -> X such that g(n+1) = g(n) and g(n) = f(k₁), g(n+1) = f(k₂) for some k₁ where k₂ > k₁

Not sure if this is the best way to talk about subsequences though

[neon iron]

what is that trying to show

[jade thunder]

That every sequence has a constant subsequence

[neon iron]

only in finite X

[jade thunder]

Yes

[neon iron]

let me consolidate this for a bit

what is k from

[jade thunder]

It’s the k from f: ℕ -> X

It sends k ∈ ℕ to f(k) ∈ X

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[ancient valve]

for this type of question how do you solve it (with the 3 sets of numbers)

i only know how to do it with 2 sets

[loud oasis]

expand it with two of them, then take the result and expand with the third one

[ancient valve]

okay and for this one what does the 5 do to it?

[loud oasis]

do the usual expansion then do 5(the result), which multiplies the entire thing by 5

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[cinder oxide]

Do both of these formulas find the same thing?

Distance from point to plane

[raven sparrow]

They are yes

[cinder oxide]

Why use one over the other?

[raven sparrow]

I suppose that if you're given the equation of the plane straight away you could directly apply the first one.

I think the second one is more verbose in terms of what's going on though : we project PQ onto the unit normal vector and the length of that gives the orthogonal distance to the plane

[cinder oxide]

When given equation of plane,is the point x0,y0,z0 always the terminal point of the normal vector?

Or not always..it’s just a point on the plane

Coefficients a,b,c are always normal vector?

I am referring to this formula

a(x-x0) + b(y-y0) + c(z-z0) = 0

Just making sure on P here

[raven sparrow]

x0, y0 and z0 is just a point on the plane.

Any point on the plane will do

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[north bobcat]

In the bowl, we have 3 fair gaming dice and 1 gaming die, which has one dot on each of its six faces. We randomly draw two gaming dice from the bowl and roll them. What is the probability that the sum of the dots rolled is at least 5? What is the probability that we drew two fair gaming dice, given that the sum of the dots rolled is at least 5?

[north bobcat]

Can any help me from this

[jade thunder]

Perhaps it’s easier if you first condition it on getting the rigged dice or not

[modern rock]

yeah he found the probability of getting the dice

[jade thunder]

Ah right

Then just find the probabilities

You kinda just count

[north bobcat]

How

[modern rock]

is P(F) the probability of getting a roll of atleast 5?

[north bobcat]

yes

when you have 2 fair dice

[modern rock]

right

[north bobcat]

But do I have to multiplicate it with the chance of pulling out 2 fair dice?

[modern rock]

so we have 2 situations, we get 2 fair dice AND we get a roll of atleast 5 OR we get a fair and rigged dice AND we get a roll of atleast five

[modern rock]

yes

when u see an 'and' in probability it means to multiply and when we see an 'or' it means addition

[north bobcat]

So it's 5/12 for the fair dice + the chance of getting rigged and fair x 1/3

[modern rock]

yeah which u worked out was 1/4 right

[north bobcat]

So the 1/4 is correct?

[modern rock]

hmm

now that i think about it, that 1/4 is off

u could get a rigged dice then get a fair dice, or u could get a fair dice then get a rigged dice

[north bobcat]

I'ts 1/4 to pull the rigged one first

1/4 + 3/4 x1/3 = 1/2?

[modern rock]

yep

and we know its true since when we add those 2 different probabilities together we get 1

it could be useful to know that since there is a 50% chance of getting only fair dice then there must also be a 50% of getting 1 rigged and 1 fair dice since thats the only other possible situation.

[jade thunder]

There’s 4 choose 2 ways to get 2 fair dice, which is 6, and there’s 5 choose 2 ways to get 2 dice, which is 10

[jade thunder]

That doesn’t sound like 50/50 to me

[modern rock]

u sure? i even drew a probability tree myself to confirm

[jade thunder]

that's because im dumb

there's 3 fair dice not 4

[modern rock]

lol

[jade thunder]

There’s 3 choose 2 ways to get 2 fair dice, which is 3, and there’s 4 choose 2 ways to get 2 dice, which is 6

that does sound like 50/50 to me

[north bobcat]

So is this the correct appendix

[jade thunder]

yeah

1/2 for 2 fair dice, 1/2 for 1 fair 1 rigged dice

[north bobcat]

Then i have a problem witht he last question

What is the probability that we drew two fair gaming dice, given that the sum of the dots rolled is at least 5?

[jade thunder]

no

what is the probability the sum is at least 5 given you drew 2 fair dice

P(A|B) ≠ P(B|A)

[north bobcat]

but what is B Intersect A

that is a challenge

[jade thunder]

we want to find P(sum >= 5)

P(sum >= 5) = P(sum >=5 | 2 fair dice) + P(sum >= 5 | 1 fair 1 rigged dice)

P(sum >=5 | 2 fair dice) is simply take 2 fair dice, what's the probability you get sum >= 5

you jsut do it like a normal set up

[north bobcat]

5/12?

idk

i am lost in translation

[jade thunder]

there's 36 ways to roll 2 fair dice

how many of those are >= 5?

[north bobcat]

30

[jade thunder]

where'd you get 5/12 from

[north bobcat]

30/36 x 1/2

[jade thunder]

ah right

what about the other one

P(sum >= 5 | 1 fair 1 rigged dice)

[neon iron]

i think i get what you were saying now, its just literally just picking a convergent subsequence; if theres infinitely many values in X then we cant guarantee a convergent subsequence because we dont know that a specific value is used more than once so we cant create a convergent subsequence out of its countably infinite occurrence

[jade thunder]

not convergence

constant

you can definitely find convergent subsequences in countably infinite sequences

also open a new channel

[north bobcat]

1/2 *1/3

[neon iron]

same thing but 1D

thanks i got it

[jade thunder]

you don't

you can't talk about convergence without a topology or metric

X is a bare finite set with no additional structure

[neon iron]

i know

[jade thunder]

you have no concept of convergence on X

[neon iron]

i used it as an analogy

there’s no convergence

its a selective repetition of the values in X

[jade thunder]

is that right

14 15 16 are the only ways?

[north bobcat]

to get more than 5 It's 3 / 6 right

[jade thunder]

yeah

[jade thunder]

why is there a 1/3 in here

[north bobcat]

it's the same

oh fuck

mb

[jade thunder]

3/6 is not 1/3

lol

[north bobcat]

hahahaha

ups

[jade thunder]

so you can kinda think of this question like a tree diagram

1/2 chance to get 2 fair dice

within that, 30/36 is >= 5, 6/36 is < 5

1/2 chance to get 1 fair 1 rigged dice

within that, 3/6 is >= 5, 3/6 is < 5

now for the next part

What is the probability that we drew two fair gaming dice, given that the sum of the dots rolled is at least 5?

you just look at P(sum >= 5 | 2 fair dice)

and swap it

with the formula P(A|B) = P(B|A)P(A)/P(B)

[north bobcat]

Ohh

Idk why i find this shit so hard to understand

Where can i buy you a coffee?

@jade thunder can you help me with numbers

[jade thunder]

what's wrong with this

[jade thunder]

haha it's fine :p

[north bobcat]

Idk howw can i insert into this P(A|B) = P(B|A)P(A)/P(B)

[jade thunder]

well

what's this P(A|B) that we want have

it's P(sum >= 5 | 2 fair dice)

A is sum >= 5

B is 2 fair dice

[north bobcat]

Yes

[jade thunder]

ok so sub in all the stuff

[north bobcat]

But I don't get how the a|b works

so i can't sub it in

[jade thunder]

wdym

we know what P(A|B) is

[north bobcat]

2/3?

[jade thunder]

oh

i see the proboem

[north bobcat]

hmm

[jade thunder]

so P(sum >= 5 | 2 fair dice) = P({sum >= 5} AND {2 fair dice})/P(2 fair dice) do you agree

[north bobcat]

sure

[jade thunder]

and we said this was 5/12

[north bobcat]

yes

[jade thunder]

ok good

P(A|B) = P(B|A)P(A)/P(B)

is now 5/12 = P(B|A)P(A)/P(B)

do you agree?

[north bobcat]

I don't get it I am sorry

[jade thunder]

P(sum >= 5 | 2 fair dice) = 5/12

do you agree

[north bobcat]

Yes 5/6 X 1/2

[jade thunder]

let A denote the event {sum >= 5}

P(A | 2 fair dice) = 5/12

do you agree?

[north bobcat]

okej

[jade thunder]

not okay, yes or no

okay makes me think you aren't getting it but want to move on

which is fine if you don't want to keep going but don't just say okay

[north bobcat]

I was thought that it works like this:

[jade thunder]

yeah

but finding P(A AND B) is kinda hard here

[north bobcat]

Yes and i Don't know how to calculate the upper one

yes exactly

So i lack the base knowledge it seems

The problem is you have those easy fin exercises in the text book that i solve with my right ball and then i come to the exam and i see this sh?t

[jade thunder]

ok i see what i did wrong

[jade thunder]

this isn't quite right

it bugged me earlier too but it's not the right wording

P(sum >= 5) = P(sum >=5 AND 2 fair dice) + P(sum >= 5 AND 1 fair 1 rigged dice)

it should be this

because we have $P(A) = P(A\cap B) + P(A\cap\overline B)$

[north bobcat]

yes this i cna understand

[thorny flame]

Frosst

[jade thunder]

now, P(A AND B) is hard to calculate

but luckily! we have $P(B)P(A|B) = P(A\cap B)$

[thorny flame]

Frosst

[north bobcat]

waaait what's the P(A\cap B)

[jade thunder]

P(A AND B)

P({sum >= 5} AND {2 fair dice})

[north bobcat]

2/3 * 1/2

[jade thunder]

uh

P(A|B) is actually the 30/36

given you have 2 fair dice, the probability of rolling >= 5 is 30/36

[north bobcat]

yes

[jade thunder]

then the probability of getting 2 fair dice is 1/2

so you have 1/2 * 30/36 = P(A AND B)

[north bobcat]

so that is 2/3

[jade thunder]

,calc 1/2 * 30/36

[thorny flame]

Result:

0.41666666666667

[jade thunder]

doensn't look like 2/3 to me

[north bobcat]

5/12

[jade thunder]

yes

P(A and B) is 5/12

ok we're getting a bit off track

[north bobcat]

divided by 1/2

[jade thunder]

no

no no we are losing sight of the objective here

the first question wants us to find $P(\text{sum}\geq 5)$

[thorny flame]

Frosst

[jade thunder]

so then we went

[north bobcat]

=== 1/2 * 5/6 + 1/2 * 1/2

[jade thunder]

$P(\text{sum}\geq 5) = P({\text{sum}\geq 5}\cap {{\text{2 fair dice}} \cup {\overline{\text{2 fair dice}}}})$

[thorny flame]

Frosst

[jade thunder]

does this step make sense

[north bobcat]

yes i understand

[jade thunder]

then we can split it up and get $P(\text{sum}\geq 5) = P({\text{sum}\geq 5}\cap {\text{2 fair dice}}) + P({\text{sum}\geq 5}\cap {\text{1 fair 1 rigged dice}})$

[thorny flame]

Frosst

[jade thunder]

yeah?

[north bobcat]

yes

[jade thunder]

ok problem

this intersection is hard to calculate

BUT we have a solution

we know $P(A|B) = \frac{P(A\cap B)}{P(B)} \implies P(B)P(A|B) = P(A\cap B)$

[thorny flame]

Frosst

[jade thunder]

and i now claim that this conditional probability is easier to calculate than the probability of intersection

[north bobcat]

okay

[jade thunder]

so let's see what this looks like

$P(\text{sum}\geq 5) = P({\text{sum}\geq 5}\cap {\text{2 fair dice}}) + P({\text{sum}\geq 5}\cap {\text{1 fair 1 rigged dice}})$

becomes

$P(\text{sum}\geq 5) = P(\text{2 fair dice})P(\text{sum}\geq 5|\text{2 fair dice}) + P(\text{1 fair 1 rigged dice})P(\text{sum}\geq 5|\text{1 fair 1 rigged dice})$

[thorny flame]

Frosst

[jade thunder]

ok there we go

[north bobcat]

Ookay

[jade thunder]

now let's look at these individually

P(2 fair dice) we found earlier this is 3C2 / 4C2 = 3/6 = 1/2

yeah?

[north bobcat]

yes

correct

[jade thunder]

let's sub that in

we also know then P(1 fair 1 rigged dice) = 0.5

[north bobcat]

yes

[jade thunder]

$P(\text{sum}\geq 5) = 0.5P(\text{sum}\geq 5|\text{2 fair dice}) + 0.5P(\text{sum}\geq 5|\text{1 fair 1 rigged dice})$

[thorny flame]

Frosst

[north bobcat]

okay i understand that

[jade thunder]

ok now if i give you 2 fair dice

and ask you what is the probability you roll >= 5

what would you say

[north bobcat]

5/12

[jade thunder]

no

there's 36 ways to roll 2 fair dice

how many of them are >= 5

[north bobcat]

30

[jade thunder]

so 30/36

[north bobcat]

i mean 5/6

yes

[jade thunder]

well same thing

[north bobcat]

yes

[jade thunder]

so P(sum ≥ 5| 2 fair dice) = 30/36

because that's what this notation means, suppose you had 2 fair dice, what's the probability you roll a sum ≥ 5?

[north bobcat]

yes

and then for the other one. N = 6 and m = 3 right

so it's 1/2 for the 1 fair 1 unfair

[jade thunder]

yep

so P(sum ≥ 5|1 rigged 1 fair dice) = 1/2

let's put that in

$P(\text{sum}\geq 5) = 0.5\cdot 30/36 + 0.5\cdot 3/6$

[thorny flame]

Frosst

[north bobcat]

yes

[jade thunder]

ok put that in your calculator

or use your brain

it gives you 2/3

[north bobcat]

yes

[jade thunder]

ok good that's part 1

[north bobcat]

yes i did that

but then

[jade thunder]

ok now we need part 2

[north bobcat]

yes

[jade thunder]

we want to swap them around

find $P(\text{2 fair dice}|\text{sum}\geq 5)$

[thorny flame]

Frosst

[north bobcat]

Ooo okay

so

[jade thunder]

bayes theorem

we know that $P(A|B) = \frac{P(B|A)P(A)}{P(B)}$

[thorny flame]

Frosst

[jade thunder]

so then $\P(\text{2 fair dice}|\text{sum}\geq 5) = \frac{P(\text{sum}\geq 5|\text{2 fair dice})P(\text{2 fair dice})}{P(\text{sum}\geq 5)}$

[thorny flame]

Frosst

[jade thunder]

do you agree?

[north bobcat]

yes i do

[jade thunder]

ok but we actually know everything on the right side separately

[jade thunder]

here

[jade thunder]

here

[jade thunder]

and here

let's sub that in

so then $\P(\text{2 fair dice}|\text{sum}\geq 5) = \frac{\frac{30}{36}\cdot\frac{1}{2}}{\frac{2}{3}}$

[thorny flame]

Frosst

[jade thunder]

put that in your calculator what do you get

[north bobcat]

5/8

[jade thunder]

that's the answer to part 2

[north bobcat]

Thank you so much for your time

[jade thunder]

👍

[north bobcat]

.close

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[regal charm]

Hi, anyone know how i would do this?

[topaz sinew]

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@regal charm Has your question been resolved?

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@regal charm Has your question been resolved?

[sour hull]

i thought you were only a helper

hee hee

[regal charm]

yes i'm a helper

helping myself lol

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@regal charm Has your question been resolved?

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[foggy ingot]

Did I compose these correctly?

[foggy ingot]

<@&286206848099549185>

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[neon iron]

guys

[neon iron]

if all output values of function x are greater or equal to 0 then absoluting the output values of the function x will be equivalent the output values of the function x

how to read this

[keen venture]

fx is ugly. f(x) all the way.

[neon iron]

and f(x) is the output right then why do we read it as function of xmaps to etc like wh cant we just say its an output and read it by saying its an output

[neon iron]

wf

wtf

[keen venture]

So |f(x)| = f(x)

[neon iron]

wat

[neon iron]

guys

[merry hill]

f(x) isnt output

[neon iron]

yes it isss

like in here

f(x) = 15

[merry hill]

f(x) is a function of x

[merry hill]

15 is output

[neon iron]

dats how u reas it ig

[merry hill]

not f(x)

[neon iron]

no

[merry hill]

yes

[neon iron]

f(x) is beinf equivalent to 15

so its an output too

[merry hill]

and?

no

[neon iron]

a = b

[merry hill]

f(x) is a function of x

[neon iron]

dats how u reas it

but ir does represent output

[merry hill]

what f(x) outputs is output

f(x) itself isnt output

[merry hill]

no it doesnt

it represents function of x

[neon iron]

@worthy storm

bro

[neon iron]

no

are you trying to learn the entirety of math

you've been asking questions all day

[atomic wadi]

x = input, f(x) is the equation that gives output

[neon iron]

i think she's just trollin

[neon iron]

no it hasnt been all day wtf

cuz she's been in the sub the whole day

[neon iron]

whatthefuck

[merry hill]

what no

[neon iron]

nowhatthefuck

[neon iron]

doesnt f(x) representthe output

bungo said it does

[atomic wadi]

if x=3, f(x)=15, 15 is the output

[merry hill]

f(x) doesnt represent output, it represents a function of x

[atomic wadi]

f(x) is the equation that only makes the output

[merry hill]

^

[neon iron]

true tbh

makes more snese if

ig

[atomic wadi]

like u make dough, put in oven, gives bread

oven is the function

[neon iron]

yea

[atomic wadi]

thats a dum example tbh HAHA

[neon iron]

no

it aint

[neon iron]

so to read this

function of x

bro no

it does represent output values

function of x greater than or equal to 0 doesnt even make sense

huh

[urban grove]

yes that's correct

[atomic wadi]

write f(x) pls

it hurts my eye

[neon iron]

den dont loik

[urban grove]

yeah that's right, it's the output when the input is x

[merry hill]

f(x) itself isnt output tho

wht f(x) will give is output

[neon iron]

😝😝😝😝

[urban grove]

I don't know what you're talking about

[neon iron]

[neon iron]

it is read as function of x but it does represent thr output

[merry hill]

f(2) = 2

2 is the output

not f(2)

f(2) is merely a function

[neon iron]

but irs being equivalejt to to fx

[urban grove]

If f(2) and 2 are equal, then if 2 is the output, then so is f(2) though

By the definition of equal

f is a function, not f(2)

[neon iron]

yeaaaa

frrr

exacrlt

[merry hill]

f(2) is value of function at x = 2

well

[neon iron]

it wasnt the whole day
jus sum hours
and im selfstudyin maths and no teacher so discord is needed ans yt ans gpt

[merry hill]

yeah that's the same

[neon iron]

ok

so

[merry hill]

but how is saying f(x) is output

f(x) is a function in x

if you put x = whatever then it becomes value of the function at x = whatever

[atomic wadi]

f(2) is output, f(x) is not output. done.

[merry hill]

yes

in their question f(x) is written

not f(2)

[neon iron]

and x = 2 is input

[neon iron]

@vernal matrix wtf whats with all thr gotojail reactions wtf u hater bruh

[vernal matrix]

Bad notation

[neon iron]

u just dont fuckwith my handwriting

[vernal matrix]

See here

[neon iron]

my handwriting is good

[neon iron]

ohhh

[vernal matrix]

As for the comments on f(x), I refer to here

[neon iron]

wdym

im right right?

[urban grove]

Don't say stuff like this here.

It's completely inappropriate.

[atomic wadi]

average fortnite players cant blame

[neon iron]

dats u

and fry them and givr tuem to thr djcks

duvks

.cloxe

.close

[topaz sinew]

Channel closed

Closed by @narrow fable

Use .reopen if this was a mistake.

[urban grove]

what?

[neon iron]

ducks

are healthy

[urban grove]

that doesn't make any sense

[neon iron]

yes

.close

[topaz sinew]

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>.
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[hot flame]

i solved and got 11

just wanna check answers

[regal mural]

Divided by what

It is not visible

[merry hill]

x-4

[regal mural]

Ok

Lemme check

[merry hill]

its 17

[regal mural]

11

[merry hill]

11

yes

[regal mural]

11 is correct

[merry hill]

divided by 2 instead of 4

mb

[topaz sinew]

@hot flame Has your question been resolved?

Channel closed

Closed by @hot flame

Use .reopen if this was a mistake.

[topaz sinew]

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.

[lime isle]

Im not to confident in the answer being 1, can someone double check 35 for me?

[noble laurel]

What is the question

[lime isle]

Once I cancel out sin and sec turns to cos, do the cos also cancel leaving me with 1?

[noble laurel]

sin(x)/(tan(x)) = ?

sec(x) = ?

in terms of sine and cosine

[lime isle]

do i fill in ur question marks?

[noble laurel]

Yes

[lime isle]

Oh ok sorry

sin(x)/(tan(x)) = sin(x)/sin(x)/cos(x)

[noble laurel]

https://tenor.com/view/thumbs-up-good-job-ok-okay-fine-gif-14556563

[lime isle]

sec(x) = 1/cos(x)