help-10

[obtuse pebble]

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[timid silo]

is this matrix correct ?

[tardy epoch]

Do you have any math work to show

[timid silo]

yes

do you want a picture ?

[tardy epoch]

This is a math server, not a python server

If you have a question about python, go to a python server

[timid silo]

this is math ?

[tardy epoch]

What's your math question then

[timid silo]

is my answer correct ?

literally was my question

[tardy epoch]

There's no math steps here

[timid silo]

this is my answer

[tardy epoch]

.

[timid silo]

I dont think we are understanding one another'

[obtuse pebble]

Channel closed

Closed due to the original message being deleted

[timid silo]

.reopen

.close

[brave bramble]

Is this matrix correct... for what? What is it you're trying to do?

[timid silo]

I accidentally deleted the question part

[obtuse pebble]

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[fresh fractal]

whats the integral of cuberoot of 2x?

[grizzled shore]

What have you tried?

[fresh fractal]

Its for a much bigger problem. Currently stuck in

To find the area under the curve

[shy swallow]

How else can we write cbrt of 2x

[fresh fractal]

I also had this. But idk how the one underlined as an answer

[obtuse pebble]

@fresh fractal Has your question been resolved?

[brave bramble]

I see on your first page, you said that:
(2)^1/3 * (4)^4/3 = (2 * 4)^4/3

Which isn't true

They should just be kept separated, there's no great way to combine powers with different bases and exponents

[fresh fractal]

yeah, I tried figuring out ways to make it work based on the integral calculators answer

I just settled on cbrt 2 x 3/4 x^(4/3)

[obtuse pebble]

@fresh fractal Has your question been resolved?

[obtuse pebble]

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[obtuse pebble]

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[wheat kindle]

i’m not sure if i’m on the right track

but i tried the problem with a 1 card deck and 1 black 3

you have an 8/208 (1/26) probability of getting 1 black 3

[verbal niche]

shouldnt you do 1-the chance of not getting a black three?

[wheat kindle]

hmm i am not that well versed with this topic

[wheat kindle]

but i think this should be accurate at least

[grizzled shore]

How many ways can we get 2 black 3’s?

[verbal niche]

1

[grizzled shore]

This is a hypergeometric distribution that I missed on my exam 😦

[grizzled shore]

There’s 4 decks combined

[wheat kindle]

and a 13 card hand would have a 13/26 (1/2) chance of getting a black 3

[verbal niche]

oh..

[wheat kindle]

yeah that’s where the 208 came from if you were unsure

4x52

[verbal niche]

so then 4?

[grizzled shore]

No

We want to look at the first line

And the letters have meanings on the side

[verbal niche]

amount of defective is 200 right?

[grizzled shore]

Yes

[verbal niche]

could i do

nCr(200,8)nCr(8,5) ?

[grizzled shore]

Where’s the bottom part

[verbal niche]

nCr(208,13)

is th amount of successes wrong?

[grizzled shore]

Wait no

We are looking at a selection of 13 cards

Total is 208

Defective is 13-2

[verbal niche]

oh

uh

so nCr(11,2)*nCr(208-11,13-2) ? @grizzled shore

for top

[grizzled shore]

Yes

[verbal niche]

thn bottom is 208,13?

its still off

[grizzled shore]

,w (11choose2)(197choose11)/(208choose13)

[warm shale]

Failed to get a response from Wolfram Alpha.
If the problem persists, please contact support.

Jun 22, 2023, 3:49 AM

[native inlet]

https://www.wolframalpha.com/input?i=(11choose2)(197choose11)%2F(208choose13)

[grizzled shore]

12% sounds a bit high actually

Hmm

We have here N = 52*4 = 208

K = 8, there are 2 black 3’s per deck

n = 13, size 13 hand is being considered

We observe exactly k = 2 successes

@verbal niche is that correct?

[verbal niche]

yes

[grizzled shore]

I’ve tried doing the derivation for this but it was very messy

And I also don’t have the derivation with me atm

So you can either just try remember this, or try derive this yourself

Oh wait the derivation I did was for something else nvm

You basically just want to see the number of ways to pick 2 successes from 8 successes

Then the number of ways to pick 11 failures from 200 failures

Then divide it by the number of ways to pick 13 cards from 208

@verbal niche does that make sense

[verbal niche]

i think so

ill leave it for now

i'll get back to distribution later tn

.close

[obtuse pebble]

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[obtuse pebble]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[verbal niche]

oh

why isnt it 0.3*0.3?

[rich silo]

The fish are rested when they are about to jump the first log, so they have a 0.6 probabiliy of success

But then, when they are about to jump the second log (without resting), they have a 0.3 probability of success

Therefore 0.6 * 0.3

[verbal niche]

but it says first two without resting

ugh i hate when its so badly wordedd

[rich silo]

Without resting between the two jumps

It's mentioned above that they are rested when they are about to do the first jump

Right before (a)

[verbal niche]

would b be 0.3*0.3*0.6*0.6?

[rich silo]

Yes, correct!

But chronologically, I mean in order, it's

0.6 * 0.3 * 0.6 * 0.3

[obtuse pebble]

@verbal niche Has your question been resolved?

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[verbal niche]

b and c im lost

[hidden garnet]

Two weeks later

Oh wait

First case says that

Pedro won. Right, so that's active. Now what's given? He has a 60 percent chance of winning if he won the game. But, he won't win this week, and also the next week.

You can consider this

Just asking though, did you guys cover Conditional Probability?

[verbal niche]

yeah

[obtuse pebble]

@verbal niche Has your question been resolved?

[verbal niche]

<@&286206848099549185>

[hidden garnet]

Oh nice

So

What's actually given is

Probability of Sasha winning given she won the last game

We gotta also find the probability of winning if she lost last game

Same for pedro

Then we probably can use Bayes Formula or law of total probability

[verbal niche]

i like total

[hidden garnet]

Nice

You might try to find winning probability in general

[verbal niche]

could i do 1-chances of not winning if sasha won + 1-chances of not winning if pedro won

the game before the 2 weeks

so 1-65%*65%+1-25%*65%

[hidden garnet]

I was thinking

Probability of Sasha winning = (Sasha won last game x Probability of winning this game considering Sasha did win) + (Sasha didn't win last game x Probability of winning considering sasha didn't win)

Problem is we don't know the last term

Oh wait

Lmao

[verbal niche]

yeah so why not break it up into cases?

[hidden garnet]

Isn't that exactly what's probability of pedro losing even after pedro wining last match

[verbal niche]

yeah

[verbal niche]

why ddoesnt this work

[hidden garnet]

Probability of Sasha winning considering Sasha didn't win last game = Probability of Pedro Losing even if Pedro won last game = (1 - 60%)

[hidden garnet]

You meant 1 - chances of winning.

[verbal niche]

chanses of winning for sasha

were looking for when pedro wins

[hidden garnet]

Hmm wait let me try this in pen and paper

This clears a) because P(W_P_L) = 1 for that case

For b), I think we gotta apply thos twice

[verbal niche]

but cant you just see chances of sasha winning twice in a row?

because thats the onlyway pedro doesnt win

[hidden garnet]

No wait, no one ever says the probability is absolute

Even if Sasha wins twice, third week can be different

If you want to do that Sasha needs to win 3 weeks in a row

This week, next week, two week later

[hidden garnet]

By that I mean either 1 or 0

The only option is recursion

[verbal niche]

im a bit lost

[hidden garnet]

Okay so what I did is

Calculate the probability of this week.

Now for next week, this week's probability is last week's probability. Use it to calculate the next week's probability.

In the case of the one in two weeks later, - the probability for the one week later match is now last game's probability. Use it to calculate pedro's win probability two weeks later

Starting case is 1 as it's already given that pedro has won last week

Good old recursion, just like a program would do

@verbal niche

[verbal niche]

probability of this week

would be what?

wouldnt it be 2 cases?

isnt it easier to calculate next week?

could i break it up into cases like this?

where the subscripts represent the win before?

im having trouble understanding how you did it

its right though

[hidden garnet]

.

Refer to this one

I used Law of Total Probability

Which gives me an expression for this week using Last Week's probability

[verbal niche]

i dont think i know what that is

i thought that meant just finding the opposite case and subtracting it from the total

[hidden garnet]

Oh my god I thought you knew 😭

My baf

[verbal niche]

can you give me example

instead of general equations

[hidden garnet]

Hmm...

[verbal niche]

then i can apply it here

[hidden garnet]

Okay i think this works

Let me type

Let's say you have two bags with marbles in them.

1st bag has 7 red, 3 green marbles

2nd bag has 2 red, 8 green marbles.

So if I now pick a bag at random, and then pick a marble at random from the said bag, what would be the probability that the said marble ia green

Now if you choose the first bag, getting a green marble has probability 3/(3+7) = 3/10

This is precisely the conditional probability P(G|B_1)

Where G means the event of picked marble being green, and B_1 is the event of first bag being picked

[verbal niche]

so 1/2*3/10+1/2*8/10 ?

[hidden garnet]

Yes

[hidden garnet]

Now look at the fact that

P(B_1) = P(B_2) = 1/2

And

P(G|B1) = 3/10 and P(G|B2) = 8/10

So the thing what you wrote can be written as?

[verbal niche]

so these are like my two bags?

[hidden garnet]

...wait no, not two bags.

[verbal niche]

1/2(3/10+8/10)

[hidden garnet]

Think of it as two things being done at once

[hidden garnet]

nono

[verbal niche]

oh i see

[hidden garnet]

.

P(B_1)P(G|B1) + P(B_2)P(G|B_2)

[barren trellis]

joshi bhai kya doubt hai

[hidden garnet]

This is precisely the law of total probability's expression

[verbal niche]

oh i see

[hidden garnet]

So whenever there is like two or more events going on together which are interdependent, this is how you get there

The example is a simple thing to show why that has been delivered

Now if I go in theory you probably won't understand just now, so I did that

If you like it, later you can read Conditional Probability from Sheldon Ross's Probability textbook

Very easy to read for a first time Probability reader

It's just that it's in English

If you're not comfortable in English that is

So in any ways, can you apply the same idea in case of the problem you were in?

There is also two events

Match of last week, on which this week's match depends

Just like this bag and marbles case

[verbal niche]

so like this?

omg

that made so much sense

thank you so much

i wanna give you a hug

thank ytou

[hidden garnet]

You're welcome

[hidden garnet]

If you have time later, please consider this

It's a fun book

[verbal niche]

i will

[hidden garnet]

[verbal niche]

opening a new ticket :)

.close

[obtuse pebble]

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[marsh juniper]

what does part d mean?

i dont understand when it says "sum of products between x and y"

[trail cloak]

Hmm

Do you understand "product of age and frequency"?

[marsh juniper]

i believe so let me post what i think it is

thats what they used for part b and c

[trail cloak]

Okay

[marsh juniper]

would those be the product?

[trail cloak]

Yeah

$\sum x_i y_i$

[warm shale]

VulcanOne

[trail cloak]

You find the product of one row

Then the product of the next row

You keep doing that for all the rows

[marsh juniper]

of all 15 or whatever it is

[trail cloak]

Then you add up what you got for all the rows

[marsh juniper]

but if that was the case, how did they get a negative number

[trail cloak]

Hmm

[marsh juniper]

yeah there is nothing in my notes or formula sheet remotly close to getting that answer

its okay

[trail cloak]

Hmm

[marsh juniper]

its not used for parts going forward but i was stumped on thsi

[trail cloak]

I crunched the numbers and got 82040

[marsh juniper]

maybe the answer key is wrong lol

[marsh juniper]

you did this right/

[trail cloak]

Maybe yeah

[marsh juniper]

?

[trail cloak]

Yep

Multiplied each row

[marsh juniper]

that probably is it honestly

[trail cloak]

And added all the products

[marsh juniper]

i dont see any way to get a negative

yeah i hate this

[trail cloak]

Hmm

[marsh juniper]

so much tedious math

[trail cloak]

Negative appears when you have negative correlation in the R parameter

[marsh juniper]

but i would agree with your methodology

[trail cloak]

But that's an entirely different process to sum of products

[polar fossil]

hang on this is covariance I think

[marsh juniper]

let me post the formulas i only have

these are the ones we were taught for correlation

[polar fossil]

think they just want this bit

which you could get a negative number from

[trail cloak]

Ooo that explains it

[marsh juniper]

i really dont wanna do the crunching for that

but i believe you

if it comes up on my exam i wil pray and use that

[polar fossil]

it's not really thaaat much harder than sum of squares ig

[marsh juniper]

im not a math guy

this is just a portion of my bio class

of research methodology and stuff

[polar fossil]

well I'd be surprised to see that much data without access to excel/similar

[trail cloak]

Yep crunched them and got the answer key

[marsh juniper]

i think the prof is putting 3 of these and 1.5 hrs to complete

so he expects all by crappy calculator and hand

[marsh juniper]

thank you

im more confident now 🙂

[trail cloak]

Wait which calculator are you allowed to use?

[marsh juniper]

let me show you

its ssad

this bad boi

[polar fossil]

[trail cloak]

[marsh juniper]

too much cheating with any other calculator

at my institute

[polar fossil]

we used to hide notes in our battery compartments

i mean, I didn't but maybe I knew someone who did

[marsh juniper]

someone for my ochem 2 class wrote every reaction in his calculator. this could be the result

[trail cloak]

Giving you a pair scissors to mow the lawn :(

[marsh juniper]

yeah

i appreciate the help on this

exams in 9.5 hours

[trail cloak]

Good luck!!

[polar fossil]

[trail cloak]

Hope you ace it :)

[marsh juniper]

thanks boss and thanks for the help bros

i will!

.close

[obtuse pebble]

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[vagrant rover]

can anybody explain pls

[deft hazel]

What do you need to be explained

[vagrant rover]

idk how to solve

[deft hazel]

Do you know composition is?

[vagrant rover]

ya

[deft hazel]

Ok well

Find f o g

[vagrant rover]

f and g?

[frozen blaze]

.

[vagrant rover]

@frozen blaze that is for this guy

[frozen blaze]

hola

[vagrant rover]

get ur help

jason

@deft hazel pls come back ;c

nvm

i done

[obtuse pebble]

@vagrant rover Has your question been resolved?

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[turbid scaffold]

how do i solve this

[deft hazel]

Sorry was going home cause storm

[vagrant rover]

its ok

[deft hazel]

Possibly apply the property that lim of f(x)^g(x) from x to p is lim x to p f(x) ^ lim x to p g(x)

Or

[wooden cipher]

that creates inf^0 indeterminate form

[deft hazel]

Ye apply exponent rules

[gilded needle]

maybe try factoring out 7^n from the expression inside the brackets

[deft hazel]

And limit chain rule

Mayb

[wooden cipher]

Wanna see something cool?

[turbid scaffold]

i dont know what to do aftr that

[wooden cipher]

Factor out a 7^n from the base

[turbid scaffold]

yes

then?

[gilded needle]

you'll have two factors

7 times (1 + (3/7)^n + (5/7)^n)^(1/n)

[turbid scaffold]

yes

then?

[wooden cipher]

Take the limit now

[gilded needle]

can you find an upper and lower bound for the thing inside the brackets?

two constants

[turbid scaffold]

can i take 1/n as 0

so it becomes

[wooden cipher]

Remember 1^0 is not indeterminate

[turbid scaffold]

7 x 1

[wooden cipher]

:)

[turbid scaffold]

why cant i do this

w/o factoring 7^n out

[gilded needle]

well show how you would do it

[turbid scaffold]

then wouldnt it be ^0

vbut the ans would be 1

[gilded needle]

the whole point with 1 + (3/7)^n + (5/7)^n is that it's bounded

below by 1 and above by say 3

so when you take it to the 1/n power.....

[turbid scaffold]

wait

then it would be infinity raised to 0

which is

indeterminant?

[deft hazel]

ye

[turbid scaffold]

ah

[gilded needle]

don't take limits directly, sandwich it between things that you can take limits of

1 < 1 + (3/7)^n + (5/7)^n < 3

take everything to the 1/n

1 < (1 + (3/7)^n + (5/7)^n)^(1/n) < 3^(1/n)

what do the left and right sides converge to as n -> infinity?

[turbid scaffold]

o sandwich theorem?

[gilded needle]

yep

[turbid scaffold]

1

[gilded needle]

sandwich it between two things that go to the same limit

[turbid scaffold]

so into 7

ahh

i see

[gilded needle]

yep

[turbid scaffold]

thanks everyone

much appreciated

.close

[obtuse pebble]

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[deft hazel]

also like i said can apply some exponent laws and then limit chain rule it, but the proposed above is faster or at least more yk efficient

[turbid scaffold]

like which?

also i need to reopen

.reopen

[obtuse pebble]

✅

[turbid scaffold]

how are they getting e^0 here

[wooden cipher]

?????

[turbid scaffold]

i found this solution online

i dont understand it

[wild swallow]

tf

[wooden cipher]

I guess you can technically say its ((1+epsilon)^n)^(1/n^2) but thats ugly and stupid

[wild swallow]

that's a weird way to write 1

[turbid scaffold]

where is the epsilon coming from

[wooden cipher]

then (3/7)^n

Ignor that

[turbid scaffold]

maybe i havent learnt that yet

[wooden cipher]

Its a really dumb way of doing it

[wild swallow]

there shouldn't be any e appearing

[wooden cipher]

Yea

[turbid scaffold]

so its not coming from the q

theyre j being quirky

and writing 1 as e^0?

[wild swallow]

yeah

[turbid scaffold]

alr nice

[wild swallow]

just ignore the e

[timber island]

think i get it

[timber island]

yeah

[turbid scaffold]

all this confusion

for a simple 1

damn

alr yeah thats it

thanks once again

[timber island]

i was abt to say '1/infinity is a quantity vey, very,very close to 0 (i.e. as n approaches infinity 1/n approaches 0)'

so the bracket reduces to 1

[turbid scaffold]

which is right no?

meaning once you take 7^n out

[timber island]

yeah

yeah its right

[turbid scaffold]

you can do that right?

[deft hazel]

Well what i was going to say lim x to p f(x)^g(x) = 0^0 or inf^0, 1^(plus or minus inf)

[turbid scaffold]

yeah ok

[timber island]

yes u can

[deft hazel]

can be written as lim x to p [exp(g(x)ln(fx))]

because b^x=exp(xln b)

[turbid scaffold]

?

[timber island]

i dont know that yet 😐

[turbid scaffold]

wait no nvm

[deft hazel]

and then ye blah blah lhopital's rule (aka bernoulli's rule)

do you want me to go into it

[turbid scaffold]

nono i think ive done something similar

i remember doing something like this

thank you

.close

[obtuse pebble]

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[keen knot]

dpm = 60 / (((ReloadPerShoot * Clip - 1) + reload) / Clip) * damage

Is this the proper way to calculate damage per minute on a magazine gun
It works this way: when you shoot, you need to wait ReloadPerShoot seconds and when you run out of rounds in your clip, you need to do a clip reload which is represented by the reload variable
I tried to first calculate how many rounds you will be able to shoot until your clip ends, then add to it the full clip reload, divide this by the amount of rounds (Clip) to get the seconds per shell, so I divide 60 (1 minute) by seconds per shell, and multiply it by damage

So when i put ReloadPerShoot as 2 seconds, Clip as 3 rounds, reload as 20 seconds and damage as 25 this gave me 237, i need this to be accurate sot hats why im asking

[lone dirge]

Looks legit...

You can try to do some more sainity checks

some simple examples

Clip = 31, ReloadPerShoot = 1, reload = 0, damage = 1... You expect to get 31 right?

actually not

[keen knot]

a example like this would never happen cuz this is gonna be a pvp game

[lone dirge]

I know just checking if the formula is right

[keen knot]

alright

[lone dirge]

It doesn't have to be realistic

[keen knot]

60 / (((1 * 31 - 1) + 0 / 31) * 1

[lone dirge]

,calc 60 / (((1 * 31 - 1) + 0 / 31) * 1

[warm shale]

The following error occured while calculating:
Error: Parenthesis ) expected (char 34)

[lone dirge]

,calc 60 / (((31 - 1) + 0 / 31)

[warm shale]

The following error occured while calculating:
Error: Parenthesis ) expected (char 26)

[lone dirge]

,calc 60 / ((31 - 1) + 0 / 31)

[warm shale]

Result:

2

[keen knot]

let me try smth

,calc 60 / ((31 - 1) + 1 / 31)

[warm shale]

Result:

1.9978517722879

[keen knot]

wtf

,calc 60 / ((2- 1) + 0 / 31)

[warm shale]

Result:

60

[keen knot]

oh wait

,calc 60 / ((2- 1) + 0 / 31) * 1

[warm shale]

Result:

60

[keen knot]

,calc 60 / ((31 - 1) + 1 / 31) * 1

[warm shale]

Result:

1.9978517722879

[keen knot]

fuck idfk

[lone dirge]

Let's try from scratch again 😉

[keen knot]

oh wait

[lone dirge]

if ReloadPerShoot = 1

[keen knot]

the paranthesis are wrong

[lone dirge]

you really shoot 60 in a minute right?

[keen knot]

,calc 60 / (((31 - 1) + 1) / 31) * 1

[warm shale]

Result:

60

[keen knot]

now its different

[lone dirge]

Yes, that's correct

you expect to get 60 regardless of the clip size

For instance

,calc 60 / (((20 - 1) + 1) / 20) * 1

[warm shale]

Result:

60

[lone dirge]

Now if it takes 30 seconds to reload

You expect to get 30

for a clip of size 30

let's try

,calc 60 / (((30 - 1) + 1) + 30 / 30) * 1

[warm shale]

Result:

1.9354838709677

[lone dirge]

Parenthesis are wrong again

,calc 60 / ( ( (30 - 1) + 1 + 30 ) / 30 )

[warm shale]

Result:

30

[lone dirge]

yep

[obtuse pebble]

@keen knot Has your question been resolved?

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[timid silo]

Hi, I am trying to study math over the summer to prepare for 8th grade. Is it possible I could get some tutoring?

[glossy basalt]

usually help channels are for specific questions

[timid silo]

oh.

[glossy basalt]

if you are preparing for grade 8, I'd suggest you can try free online resources like Khan academy

[timid silo]

okay.

.close

[obtuse pebble]

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[verbal niche]

how many ways can i re-arrange the word "The Beetles" to make a 6 letter word?

[verbal niche]

I know the brute force method with premutations

but i remember theres a moire elegant way with using combinations

<@&286206848099549185>

something more conventionally used would be like "AAAAAABBBBBCCCDDDEF"

[ripe shard]

perms is the easiest way

[verbal niche]

?

it would take the longest

[ripe shard]

say u choose 6

u still have to rearrange it

[verbal niche]

but when you walk the letters that takes forever

its the walking part that takes forever

[ripe shard]

whats the walking part

wait nbm

nvm

u have to do cases with perms

cause u have repeating E's

[verbal niche]

mhm

[verbal niche]

i would also like to do it with this after

[ripe shard]

sorry man i forgot how to do this 💀 , ur gonna have to wait from someone else

i need to really revise

[verbal niche]

alright

i know its similar to prems

[ripe shard]

there was a way to do this using comb

its somewhere in my notes

but its in an old book somewhere in the house

[verbal niche]

while were here tho

i'm also having problems with those probability questions for birthdays

i'm fine with 2 people but when its like 3 people idk what to do

probability of 3 people of 35 sharing the same birthday

like this is 2 people

<@&286206848099549185>

[obtuse pebble]

@verbal niche Has your question been resolved?

[verbal niche]

<@&286206848099549185> original problem

[obtuse pebble]

@verbal niche Has your question been resolved?

[tiny seal]

a valid 6 letter word? or just a 6 letter string of symbols?

if just a 6 letter string, can we only use the number of letters we have? or does having B in the sentence allow us to make the word BBBBBB, for example

when we do not care about the number of occurrences in an arrangement, it is a combination, nCr
when we do care, it is a permutation, nPr

in the perm case, we can just treat the three "e"s as three different objects

if it has to be a dictionary valid word, we do have to brute force, since the spelling of words is essentially arbitrary

[verbal niche]

It's just a string @tiny seal

[tiny seal]

then, do we care about occurrences?

[verbal niche]

Wdym

[tiny seal]

can we do
beetles -> bbbbbbb

or are we restricted to one b

[verbal niche]

One b

[tiny seal]

then we can only use three e's, right?

[verbal niche]

Yes

[tiny seal]

okay

so treat each symbol as a different letter

the beetles
has 10 distinct letters

[verbal niche]

Then just 10p6

[tiny seal]

unless we count the space

but yeah

nPr(10,6)

[verbal niche]

Now what

?

[tiny seal]

do you want to solve it manually?

[verbal niche]

Wdym

[tiny seal]

you should be able to do nPr on any modern calculator

[verbal niche]

But that's not the answer

That assumes that "beetle" "beetle" and "beetle" are different

The e's are just flipped around

[tiny seal]

right

[verbal niche]

So then

[tiny seal]

so then, i would say we have a start

we just need to figure out how many permutations to remove

[verbal niche]

Are you saying to divide by 3 factorial?

Because then it's also not that simple

[tiny seal]

im saying we should subtract

we need to subtract however many times we can permute the similar letters

[verbal niche]

Not really

[tiny seal]

*permute them about their positions

[verbal niche]

That ignores the possibility of getting ttebls

[tiny seal]

not in general

i mean:

permute the e in the three words
beetle beetle beetle

those are the permutations

all of them

[verbal niche]

How would i

[tiny seal]

nPr(3,3), i believe

so, when we consider "the beetles", we have four like e, and two like t

[verbal niche]

Yeah

[tiny seal]

there would also be more than three "beetle"

6

[verbal niche]

I know

[tiny seal]

i believe this answer should be correct

[verbal niche]

I don't think so

[tiny seal]

nPr(10,6) - nPr(4,4) - nPr(2,2)

[verbal niche]

Yeah that's not right

[tiny seal]

do you know the answer?

[verbal niche]

Not exactly but I know you're supposed to break it up into cases

[tiny seal]

only other thing i can think of is

10!/(4!*2!)

10 letters -> 10!
4 e -> 4!
2 t -> 2!

this is incomplete, though

if its not 10!/(4!*2!*6!), 6! for 6 positions, then i need to brush back up on combinatorics

[obtuse pebble]

@verbal niche Has your question been resolved?

[verbal niche]

You do

[barren trellis]

the beetles has 6 unique words

and provided that there is no say on wether we can repeat the word or not

the combinations are

6^6

because there are 6 letters to fill each digit

[obtuse pebble]

@verbal niche Has your question been resolved?

[timid silo]

can i help? i have just entered standard 11 so i might be wrong😅

this question can be solved by making cases

[verbal niche]

mhm

[verbal niche]

@timid silo please feel free to help

[hidden garnet]

I think in the end both boil down to the same thing

are we counting spaces?

[verbal niche]

no

[hidden garnet]

as letters I mean

[verbal niche]

but i know premutations purely takes too long after 6 letters

[hidden garnet]

count how many distinct letters are out there

i also think repetition is allowed here

[verbal niche]

wdym?

[verbal niche]

<@&286206848099549185>

[timid silo]

whats the question?

[timid silo]

so you want to choose six letters from "the beetles" to make a word

[verbal niche]

yah

[timid silo]

and you want to find all of them

ok

i assume the space doesn't matter?

[verbal niche]

no

[timid silo]

so you have ten letters and six choices.

its a good idea to choose one letter at a time.

so how many choices are availible for the fist letter

[verbal niche]

10 but 4 of them r e's and 2 are t's

[timid silo]

oh yeah

that will compicate things

lets move on and pretend that the e's and t's are unique, i think i can clear that up later

[verbal niche]

i dont think that will work

but 10P6 thn

[timid silo]

it should work. if we get a word with three e's it, we will get 3! of them

so we can divide the number of words with three e's by 3!

[verbal niche]

why

[timid silo]

if we have three e's that is a group with three elements, so there are 3 * 2 * 1 ways of arranging them right?

[verbal niche]

what about the t's tho?

you're supposed to break them into cases

[timid silo]

ok

there are 15 cases

a word has 0-4 e's.

a word has 0-2 t's

we can do those individually i guess

[verbal niche]

theres a quicker way with combinations

i just forget how

[timid silo]

yeah

i may be a sec im helping someone else as well

for now, lets pretend that the duplicate letters don't matter

so our first letter has 10 options

the next one will have 9

then 8

then 7 etc.

since we have 6 letters theres 10* 9* 8* 7* 6* 5 combinations

[verbal niche]

yeah

[timid silo]

ok

sorry i may be slow because im tired

if a word has n e's in it, there are 6!/(6-n)! ways to place the e's.

which means that there will be that many duplicate words that have n e's in them.

[verbal niche]

i figured it out

cases:
1 all different
1 double 4 different
1 tripple 3 different
1 quadrouple 2 different
1 quintouple 1 different
1 sixtupple
etc...

[timid silo]

nice

[verbal niche]

then you would account for stuff like 2 double 2 diff

[timid silo]

i think so

[verbal niche]

.close

[obtuse pebble]

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[supple quest]

I mean how can I know which function's power series this is?

[tardy epoch]

you can enter the sequence into oeis

https://oeis.org/

does your sequence really start at n=0?

[obtuse pebble]

@supple quest Has your question been resolved?

[obtuse pebble]

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[halcyon jewel]

how do you find the degree of
20x(x+7)(x-7)(x+2)^2

[timid silo]

ok

how many x terms are there in the form (x + n)?

[halcyon jewel]

ig 9 altogether

or 2

[timid silo]

the first one is (x + 0)

just an x by itself

the next is (x + 7)

right

[halcyon jewel]

im following

[timid silo]

whats after that?

[halcyon jewel]

well its that cool x-7 right

[timid silo]

yep. what are the last two?

[halcyon jewel]

x+2^2

[timid silo]

yes

how many were there

all together

[halcyon jewel]

regardless of signs

like 4

[timid silo]

you need to count (x+2) twice

since its squared

[halcyon jewel]

oh cuz its squared

[timid silo]

yeah

[halcyon jewel]

okay so my degree overall is five

[timid silo]

exactly

[halcyon jewel]

i dont get functions

but thanks bro

[timid silo]

np

[halcyon jewel]

.close

[obtuse pebble]

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[timid lodge]

I am having trouble understanding my teacher's work for solving a specific problem. They seem to cancel some values out but I do not understand how it works. They seem to cancel the 5/x^6 with the 1/x^3 + 1/x^2, which confuses me as I don't understand how any of those cancel with each other.

[marble ibex]

As x goes towards infinity those terms go towards zero

[timid lodge]

Oooooh that maks way more sense now. thanks!

.close

[obtuse pebble]

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[ripe swan]

So AB=AD=BC
CBD=60°
Compare the A angle with the C angle
Find x

[obtuse pebble]

Please don't occupy multiple help channels.

[ripe swan]

I understand that the A angle is equal to the C angle

And so is ABD angle to the BDA angle

But im unsure how to bring the DBC into play

[obtuse pebble]

@ripe swan Has your question been resolved?

[ripe swan]

<@&286206848099549185>

[obtuse pebble]

@ripe swan Has your question been resolved?

[obtuse pebble]

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[zealous harness]

hello hi yes, so i have this equation and i have to find the equation of the perpendicular line that goes through the point (-1 , 5/4) and calculate the coordinates in which they intersect how do i do this?

[teal turret]

First find the slope of the perpendicular line

Do u know how to get from the slope of ur current line to the slope of the perpendicular line?

[zealous harness]

no, by slope you mean the equation?

[teal turret]

No I mean slope

[zealous harness]

oh no the slope oh yes sorry english is not my main

[teal turret]

U find the negative reciprocal of ur current slope to get the slope of the perpendicular line

What language u speak

[zealous harness]

spanish

[teal turret]

a ok

[zealous harness]

dont worry tho i understand 95% of english i just never do math in english lol

[teal turret]

Ta bien

Entendiste lo q dije?

[zealous harness]

un poco

encuentro la negativa reciproca de la pendiente

como haria eso?

[teal turret]

sabes q reciproca es?

La recíproca de $\frac 56$ es $\frac 65$

[warm shale]

northsteve

[zealous harness]

claro

[teal turret]

Así cual es la recíproca de $\frac 13$

[warm shale]

northsteve

[teal turret]

?

[zealous harness]

3/1

[teal turret]

Sip

(3/1 = 3)

[zealous harness]

entonces tengo que usar la formula para encontrar la pendiente y despues con su recriproca inversa que haria?

[teal turret]

Usa la recíproca negativa de la pendiente original para encontrar la pendiente nueva

Asi cual es la negativa de 3?

[zealous harness]

-3

[teal turret]

Bien

Asi -3 es la pendiente de la línea perpendicular

Entiendes?

O no

[zealous harness]

okay lo voy a hacer y vemos si entendi jajaja

[teal turret]

Jaja

Asi ahora tenemos el punto (-1, 5/4) y la pendiente -3. Conoces el forma punto pendiente de las ecuaciones lineales?

Uh

1 momento

Ésta

Sabes como usarlo?

[zealous harness]

espera espera, la pendiente seria la reciproca inversa de 1/3?

hice la ecuacion para sacar m sin saberlo jajaja pero si me dio 3

[teal turret]

Sip, y negativa

La recíproca inversa negativa de 1/3

[zealous harness]

si! ahora que tengo m uso los puntos y1 y x1 para la ecuacion

[teal turret]

Si

Asi

Haz lo q sabes y muéstramelo

Hemos calculado la pendiente y ya tenemos el punto, así podemos averiguar la ecuación de aquí

[zealous harness]

para hacer esta ecuacion uso los puntos -1 y 5/4 o no?

[teal turret]

Sip x1 = -1 e y1 = 5/4

[zealous harness]

i got it

[teal turret]

Bueno

Dime

[teal turret]

Así

En el lado derecho, ha debido sido -3x - 3 + 5/4

Pq x - (-1) es x+1

[zealous harness]

oh si, me olvide que era -3 jajaja

[teal turret]

Bien hecho

👍

[zealous harness]

Gracias!, ahora como encuentro en que punto se intersectan ?

[teal turret]

Igualar las dos ecuaciones

Y resuélvalo pa x

[polar fossil]

y úsalo en cualquier ecuación pa encontrar la correspondiente y

[zealous harness]

asi me qued

[teal turret]

Perdiste la negativa

[zealous harness]

a

me acabo de dar cuenta

[teal turret]

También -3 - 1/3 no es -8/3

[polar fossil]

y mira el división por 8/3
quisiste multiplicar 3/8? te confundió el división

(no será 3/8 ni 8/3 en el solución actual... pero ten cuidado)

[zealous harness]

y ahora?

[teal turret]

Si

👍

[zealous harness]

ese seria el punto donde se intersectan entonces

Muchas gracias!

[teal turret]

Pusiste el valor de x al ecuación para encontrar el valor de y?

[teal turret]

De nada

[zealous harness]

en cual ecuacion deberia reemplazar x?

[teal turret]

Cualquiera

[zealous harness]

asi

[teal turret]

👍

Puedes simplificarlo a (-3/4 , 1/2) pero ta bien

[zealous harness]

ah si tienes razon

[teal turret]

Ciao guey

Q tengas una buena noche

[zealous harness]

igualmente, thxss

[teal turret]

👍

[obtuse pebble]

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[deft hazel]

Well its asking you to find coordinates

The row and column vector matrices is a notational matter ish or well not really as transpose of one gives the other

Refer to coordinate vectors

[tough bolt]

I think the question is asking for the coordinate of the points, not the position vector

[deft hazel]

Transpose probs but thats not involved here

Its asking you to find the coordinates not radius vector

Multiplying two vectors?

As in…?

Youre talking about scalar multiplication

Right

Okay so do you know what a position vector (aka location or radius vector) is?

Ye it represents a point P with respect to an arbitrary reference origin

Now we have something called coordinate vectors

Which is just a representation of vector as a list (where order matters) of n tuples

In terms of a particular ordered basis

Right so lets say we have a point P in a vector space with an origin O and P is the location vector (x_P, y_P, z_P)

Thought the ordered set notation in rectangular coordinates should be expressed as anything but parentheses and commas to distinguish it from coordinates

So angle brackets work if you want

Otherwise matrix notation is fairly common

[obtuse pebble]

@timid silo Has your question been resolved?

[deft hazel]

To denote suffixes (subscripts)

Ye theyre Cartesian

A vector essentially represents the direction and magnitude of that quantity (by definition). A vector is what is needed to "carry" the point A to the point B; the Latin word vector means "carrier".

I mean like coordinate is a vector ish as it has a direction from the origin lets say we’re working on Euclidean 3-Space (the linear space) and we have our origin O, the canonical bases and whatever

If its a vector

It can be expressed as however a vector is denoted as

That could be the ordered set notation

Im writing on phone so its rather uncomfortable and i wont be able to LaTeX things so ill redirect you to some pages

https://en.m.wikipedia.org/wiki/Standard_basis

https://en.m.wikipedia.org/wiki/Vector_notation

https://en.m.wikipedia.org/wiki/Position_(geometry)

https://en.m.wikipedia.org/wiki/Coordinate_vector#:~:text=In linear algebra%2C a coordinate,the axes of this system.

https://en.m.wikipedia.org/wiki/Matrix_(mathematics)

Pick up a linear algebra book

Or go over your high school text book there should be some lin alg ib there

Well ye many

Thats fine highschool books are usually crap

Get an advanced highschool-undergrad book on linear algebra if you want to

Not really necessary at this stage but i typically buy field specific maths books

If youre gonna do maths or something involving maths after highschool its common to study linear algebra

So calculus (also multivariate calc), mathematical proofs, set theory, abstract algebra, linear algebra, and ye

For the maths/physics majors at least and maybe computer scientists

No?

R u sitting GCSEs

I use both dont matter

No

I used to be in the british curriculum

[obtuse pebble]

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[obtuse pebble]

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[dim topaz]

Would I rewrite the equation inorder to have the denomaintor be 1?

Would it be x^2(x^1/2+x)?

[deft hazel]

So they just want you to use the elementary/polynomial power rule?

[deft hazel]

What

Use your exponent laws

To get rid of the fraction

And rewrite the root as a fractional exponent

Then distributive property and ye superposition rule of differentiation and youre done

[dim topaz]

Ohhhh Ok I see

[timber island]

whats superposition rule of differentiation..?

[deft hazel]

Linearity of differentiation

[timber island]

ah k

[deft hazel]

Or linearity rule however you call it

[dim topaz]

.close

[obtuse pebble]

Channel closed

Closed by @dim topaz

Use .reopen if this was a mistake.

[obtuse pebble]

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[mellow basalt]

any hint on how to calculate that integral 0-1 1/3-x+sqrt(x^2+9)

[normal oracle]

can you type to see better which integral you're refering to?¿

[mellow basalt]

i don't know how

[sage geode]

$\int_0^1\frac{1}{3 - x + \sqrt{x^2+9}}\dd{x}$?

[warm shale]

alonelybean

[normal oracle]

is that one?

[mellow basalt]

it's this one

[sage geode]

I thin conjugate works

[hearty flame]

Maybe substituting x as 3 tan(theta)

[mellow basalt]

k trying rn

[normal oracle]

rationalize first

[mellow basalt]

i got 3+x+sqrt(x^2+9)/-6x

i'll split in more integrals and see where it goes

[normal oracle]

i think that's wrong

[sage geode]

You should have something like this

[normal oracle]

yes, that one is correct

[mellow basalt]

yea mb i used wrong conjugate i used + instead of -

i think it's -6

[sage geode]

I sacrificed that -1 and flipped the signs in the nominator

[mellow basalt]

and now how i calculate integral sqrt(x^2+9)/x

bcs the other ones are ln and x

[sage geode]

Integral of sqrt(x^2 + 9)/x from 0 to 1 is undefined, so instead we have to integrate (sqrt(x^2 + 9) - 3)/x

As unconvincing as it may sound, we use the conjugate again

Well, at least that's what I did, and it worked

So, it becomes this

[mellow basalt]

i got a x^2

up

x^2/sqrt(x^2+9)+3

[sage geode]

Yes, but you forgot about the x in the denominator

And x^2/x = x

[mellow basalt]

you're right

nah i think i took the wrong way

this is the ex

c)

i tried to build the integral like 0<x<1

and then calculate the integral it usually works

[sage geode]

What does the text say?

[mellow basalt]

whatever n is proof that lim n-inf = 0

[sage geode]

Alright

So, on the interval (0, 1)

We have f(x) > f(1)

[mellow basalt]

yes

[sage geode]

Therefore 1/f(x) < f(1) and x^n/f(x) < x^n/f(1)

Meaning $0 < \int_0^1\frac{x^n}{f(x)}\dd{x} < \int_0^1x^n\dd{x}$

[warm shale]

alonelybean

[sage geode]

Now you may apply squeze theorem

[mellow basalt]

yea thd

thx

smart move

@sage geode

why on (0,1) f(x)>f(1)

i calculate the derivate and i got that f'(x)>0 on 0,1

[sage geode]

Yeah, so the minimum value should be either x = 0 and x = 1

That is what you do when f'(x) = 0 has no solutions, you check the values at the bounds

[sage geode]

So you calculate f(0) and f(1) and compare them

[mellow basalt]

and f(0) is greater and f(1)

that means f(x)>f(1)

am i right?

[sage geode]

Yes

[mellow basalt]

and how you got to the integral

[sage geode]

Just took the inequality and integrated both sides

[mellow basalt]

f(x)>f(1) and integrated?

[sage geode]

f(x) > f(1)
1/f(x) < 1/f(1)
x^n/f(x) < x^n/f(1)
integrate

[mellow basalt]

thanks a lot bro

[obtuse pebble]

@mellow basalt Has your question been resolved?

Channel closed

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• Show your work, and if possible, explain where you are stuck.
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[glossy yew]

anyone good at probility