help-0

[alpine sable]

We can only have one case

We got 120 by 5!

That’s 5 factorial btw

Like dividing 120 by 120?

So 4 x 3 x 2 x 2

[alpine sable]

No no. That is the total number of combinations for the word PEACE

so this would be our denominator

Oh okie

Yes

[alpine sable]

This is the denominator?

No that is numerator

Because that is the E part

To get probability we need to do: wanted/total

Is that 4!?

Yes 4! x 2

Wait why we multiplied it by 2?

Suppose we put the two E’s in the first two slots. Then, we can arrange the the remaining 3 letters in 3! ways. Now, there are 4 different positions Rick in which to place the first E. Thus, there must be 4(3!) = 4! ways to have a word with the two E’s together as we want

[alpine sable]

Actually ignore this

Okie

Same result with complicated outcome

So final equation is 4! x 2! right for numerator

And divide that by denominator of 120

You get 48/120

Those four different positions are like left of P, in between P & C, and right of A in PCE , did I get it right?

Yes sir

What I did was combination

What you did was permutation

Damn

There is a big difference

Yessir

If you did permutations

Total permutations for PEACE = 5!/2!=60

Now, consider those two E's as a single entity and the resultant permutations are = 4!=24

So, probability = 24/60 = 2/5

Which is the same thing as above

48/120 = 24/60

Multiple ways of doing this question

Awesome. Thanks man. Answer is 2/5. Cool got the concept. You rock sir .

The main assumption is that the two Es are together

Np

🙏

Should I close this now

If you want

And have no further questions

My thirst is quenched.

.close

[lone heart]

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[violet flare]

hey

[violet flare]

could anyone help me out with the idea of cartesian products?

need to do SxT as part of a bigger proof

would I just select an arbitrary number of elements from both S and T and perform the cartesian product?

[mortal trellis]

to do what

SxT consists of elements of the form (4n, 4k+2)

so stuff like (4, 2) or (16, -2) or (1000, 34)

[violet flare]

Yes I see that, but how do i write it

[mortal trellis]

rafi wrote the set builder notation earlier

$S\times T = {(n, m)\in \bZ^2 | n \equiv 0 \pmod 4, m \equiv 2 \pmod 4}$

[ocean seal]

Denascite

[violet flare]

I see

ok much appreciated

another question however

how would i prove that SxT is a proper set of another hypothetical set Z

[mortal trellis]

show that any element in SxT is also an element of that other set

sidenote, using Z is a terrible name

[violet flare]

I have a lot of sets on this piece of paper lol

running out of set names

so a proper set only has to share one element with its super set?

[mortal trellis]

thats not what I said

[violet flare]

I do not understand

can you rephrase it please?

[mortal trellis]

all elements of SxT have to also be in the other set

[violet flare]

Ah ok

so if the set i was comparing it to was ExE

it would be comparing {{4n},{4k+2}} and {{2n},{2k}}

correct?

[mortal trellis]

wrong notation but yes

[violet flare]

how would i continue from there

[mortal trellis]

well show that any (n, m) in SxT is also in ExE

show that both n and m are even

[violet flare]

ah ok cool

how would i express the {{4n},{4k+2}} and {{2n},{2k}} properly?

[mortal trellis]

well what exactly do you even want to say

if (x,y) is in SxT, then (x,y)=(4n, 4k+2) for some integers n, k

[acoustic dew]

How can we show that $\sum^{\infty} \frac{1}{n \log(n)}$ diverges? I show that $n \log(n)$ is equal to $n^{1 + \log_n(\log(n))}$ so the exponent is greater than 1 for $n>e$ which means it should converge by the p-test, but apparently it diverges.

[ocean seal]

triz

[violet flare]

bruh

[mortal trellis]

so (x,y) = (2*(2n), 2*(2k+1)) for the integers 2n and 2k+1 so (x,y) in ExE

[mortal trellis]

read #❓how-to-get-help

[acoustic dew]

My bad, it said to send the question in channel help-0 to claim a channel though

ah no i see now

sorry

[mortal trellis]

the 0 is clearly just a number to keep the channels apart

[violet flare]

hmmm

if i prove that all subsets in SxT are even and all subsets in ExE are even, given that the set is infinite, is that considered proof?

s

[mortal trellis]

no

why do you want to do anything with subsets

and what should it even mean for a set to be even

numbers can be even

[violet flare]

sorry i worded it incorrectly

this is what im trying to prove

[mortal trellis]

yes

I gave you the whole proof

I took an element (x,y) in SxT

then I applied the definition of SxT to get that (x,y) = (4n, 4k+2) for some integers n,k

and then I noticed that (x,y) = (2*(2n), 2*(2k+1)) for the two integers 2n and 2k+1

so (x,y) has the form (2m, 2t) with two integers m, t

which is exactly the form of the elements in ExE

so (x,y) is in ExE

and that's it

[violet flare]

oh i get it now

so you've just defined m,t as some integer where m = 2n and t = 2k+1

clever

thank you

.close

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[alpine sable]

Neither 5/6 or 6/5 worked. Wtf am I supposed to put in here

[stiff mural]

1+1/5 for both

So 6/5 in each box

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@alpine sable Has your question been resolved?

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[placid summit]

Need help with factorizing polymomials

[keen pasture]

Do you need to factor a specific one?

[placid summit]

How can i factorize this

[stiff mural]

U could divide the eq by 2 coz they all have a factor of 2 to make it easier

[keen pasture]

,rotate

[placid summit]

Yes

[placid summit]

I divided it by 2

2(5x^2-11x+2)

But i dont know what to do next

[stiff mural]

Well the factors of 5 is just 5 and 1

So u would have something like

(5x ) (x )

Same with 2, where its factor is just 2 and 1

So to get a sum of -11

U would want to check with the 5,1 and 2,1

So it'll be

(5x-1)(x-2)

[placid summit]

Ohh okay thanks

[lone heart]

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[placid summit]

Sorry can i ask a question again?

[lone heart]

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[warm garnet]

(x,y,z) = (1,1,0) or (1,0,1) or (0,1, (x,y,z) = (7,-6,-5) or (7,-6,-5) or (-6,-5,7) or (-6,7,-5) or (-5,-6,7) or (-5,7,-6)k= 3 we have 1 solution : (x,y,z) = (1,1,1)k= 10 , we have the solutions (x,y,z) = (1,1,2) or (1,2,1) or (2,1,1) k= 9 we have the solutions (x,y,z) = (1,0,2) or (1,2,0) or (0,1,2) or (0,2,1) or (2,0,1) or (2,1,0)k= 8 we have (x,y,z) = ( 0,0,2) or (2,0,0) or (0,2,0)
k17 => (x,y,z) = (1,2,2) or (2,1,2) or ( 2,2,1)
k = 24 (x,y,z) = (2,2,2k= 27 => (x,y,z) = (0,0,3) or (3,0,0) or (0,3,0)k= 28 => (x,y,z) = (1,0,3) or (1,3,0) or (1,3,0) or (1,0,3) or (3,0,1) or (3,1,0)
k=29 => (x,y,z) = (1,1,3) or (1,3,1) or (3,1,1)
k = 35 we have (x,y,z) = (0,2,3) or (0,3,2) or (3,0,2) or (3,2,0) or 2,0,3) or (2,3,0=36𝑥=1,𝑦=2𝑎𝑛𝑑𝑧=3=>x1,y=2andz=3=>
13+23+33=1+8+27=3613+2+33=18+27=36 k= 36 ,: (x, y,z) = (1, 2, 3) ; (3,2,1); (1,3,2) ; (2,1,3) ; (2,3,1), and (3,1,2)
k= 43 we have (x,y,z) = (2,2,3) or (2,3,2) or (3,2,2)
k = 44 we have ( 8,-7,-5) or (8,-5,-7) or (-5,-7,8) or ( -5,8,-7) or (-7,-5,8) or (-7,8,-5)54 => (x,y,z) = (13,-11,-7) ,= 55 => (x,y,z) = (1,3,3) or (3,1,3) or (3,1,1) (x,y,z) = (10,-9,-6) or (10,-6,-9) or ( -6,10,-9) or (-6,-9,10) or (-9,10,-6) or (-9,-6,10)= 62 => (x,y,z) = (3,3,2) or (2,3,3) or (3,2,3) k =64 => (x,y,z) = (0,0,4) or (0,4,0) or (4,0,0k= 65 => (x,y,z) = (1,0,4) or (1,4,0) or (0,1,4) or (0,4,1) or (4,1,0) or (4,0,1)k= 66 => (x,y,z) = (1,1,4) or (1,4,1) or (4,1,1)k

Someone sent this to me
Want to know
Is this maths
And what is it about

[golden canyon]

It is maths I guess, but it doesn't make sense

it should have something to do with vectors though

[lone heart]

@warm garnet Has your question been resolved?

[warm garnet]

Lol 😂
So is an answer

See the whole thing

[lone heart]

@warm garnet Has your question been resolved?

[warm garnet]

Thanks bro
Loma 🤣

[lone heart]

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[silver axle]

I know to start out I would use the formula for the maclaurin series seen here

the first part of that shows that I am plugging in 0 into the series' derivatives, right?

but if I do that, how am I going to get anything other than 0 for the answer

[tacit arch]

you definitely shouldn't be calculating derivatives

you should just memorize/use macluarin series for cosine

and then plug in x^2 for it

then multiply it by x

[silver axle]

ok so im not using that formula at all for this problem

thats just one i need to have memorized

is it possible for you to do a sample problem using that formula for me

just so I know how it would work cuz its not really clicking

[tacit arch]

https://math.stackexchange.com/questions/4051571/why-is-the-maclaurin-series-for-cosx2-simply-the-maclaurin-series-for-co

[silver axle]

.close

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[keen orbit]

just wondering if this looks good, I'm trying to practice my proofs

[remote heron]

looks fine to me

[granite badger]

you should specify the domain of your variables (N, Z, Q, R, C)

k, j are elements of Z

[lone heart]

@keen orbit Has your question been resolved?

[keen orbit]

I would just use the member of notation?

[granite badger]

yes

€ looks like that ish

[keen orbit]

these are informal btw, this class is

[granite badger]

i don’t have it on my keyboard

[keen orbit]

so I don't have to be super strict with notation don't I?

but still specify domain?

[granite badger]

not sure i’ve always been doing proofs ‘formally’

you still should

[keen orbit]

ah, okay, I'll keep that in mind

[granite badger]

as it states in the question

[keen orbit]

so indicate in my P that n and m are members of Z?

[lone heart]

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[slow sentinel]

I made a formula to find the n-th term of any Arithmetic Progression, but I am not sure if it works 100% for all APS. I've tried the formula on many APs and it has worked so far but I have no proof of the formula.

I just need some help, if someone could help me in how to prove it (if its

correct) and is there a way to write a condensed version of the formula?

In the photo I've attached, I've written the formula, I don't know how to express it more condensed. And I've calculated the n-th term of an AP to show it works.

Is there any other simpilar way of finding the n-th term?

[prime badge]

https://www.youtube.com/watch?v=ORH3TwgvJgI

i don't know if there's something different about yours or not tbh

oh okay it's larger

like you get it unsimplified

[slow sentinel]

Give me a moment please

I saw the video

I'm not sure how to explain it

But I think like with mine i could get the formula that generates the nth term for aby degree of an ap

Like what i was looking for, that i could condense the formula (if there was a way) so that all i need to know is the degree of AP, put it in the formula and get the exact formula that generates the nth term

[prime badge]

but that's the first line?

i don;t get it

[slow sentinel]

Like when we have use the sum sign (Sigma) and it has a lower and upper limit, and we plug every integer inbetween.

So like is there a similar way inwhich this could be simplified?

Like (x-1)+(x-2)+(x-3)+......(x-10)
Can simply be written as Sigma of r from 1 to 10 (x-r)

[prime badge]

,w C(n-1, 3)

[ocean seal]

Results provided by WolframAlpha

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Requested by frownyfrog#3707

[prime badge]

that's waht you multiply by d

but it would have to expand to these a ,b,c,d,e variables somehow

[slow sentinel]

Ohh okok i got it

[prime badge]

i guess there's some conventional way to do this

[slow sentinel]

Tysm

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[bitter wharf]

Idk why I can’t get answer

[fallen verge]

!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'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

[bitter wharf]

2

[fallen verge]

!show

[lone heart]

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

[fallen verge]

!nosols

[lone heart]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[bitter wharf]

idk how to get the value 78400 cuz 7^3 * 4^2

then i got remainder 25

[fallen verge]

remember that you also have log_10(10)=1

[bitter wharf]

ouh

ik

i mean

[fallen verge]

Factor 78400 into (7^a)(4^b)(10^c)

Also is this a test?

[bitter wharf]

a= 2 b=2 c=2

got it thx

.close

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[royal ocean]

Hi I need help

[tacit arch]

[royal ocean]

you have to use using Pythagorean therom

[tacit arch]

,rotate

[tacit arch]

find the diagonal of the base first. that diagonal will be the base to the triangle with the straw as a diagonal

[royal ocean]

will you please be able to show me by drawing a line on the picture?

[tacit arch]

the base is a rectangle

can you not draw the diagonal of that rectangle?

[royal ocean]

sorry, i was confused

thanks for the help

[tacit arch]

the diagonal will be a variable that you'll solve later

[royal ocean]

Ok.

thanks.

.close

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[wheat isle]

I don’t know how to start. I’m having trouble with visualising the diagram

[wheat isle]

ignore the text on the bottom it didn’t crop properly

[limpid turret]

065?

degrees?

[wheat isle]

Huh ?

Bearing of 065

[limpid turret]

What is the first one 065, but the second is 166°? Why does the first one exclude the degree symbol? And is it standard practice to have a 0 prefix for 2-digit numbers like this?

[lone heart]

@wheat isle Has your question been resolved?

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[dapper echo]

Why is 6 being divided by 49? Shouldn't it be multiplied due to the + sign?

[dapper echo]

Or is this a mistake?

[sour dove]

yeah it shouldn't be divided it should be multiplied

[dapper echo]

That's what I'm thinking

thanks

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[sage talon]

This is finding the indicated real nth root

I’m wondering if this is right with the plus or minus 4

Like will it be a plus or minus or just 4

Even root

[sour dove]

yep that's correct. When you have even nth roots you have a +/- answer

[sage talon]

Thank you, it will always be 1 for the odd roots

3,5 etc

Right?

[sour dove]

not quite.

So if you take the cubic root of -27, for example, the answer is -3. So if you have an odd root, the sign follows the answer

oh wait sorry

[sage talon]

Like no plus or minus

[sour dove]

eyah it's just one answer, but the sign

[sage talon]

Sorry I meant to clarify

Ok thank you!

[sour dove]

man I can't type tonight lol

[sage talon]

Lol no problem

[sour dove]

just make sure that the sign carries through

[sage talon]

Gotcha thank you I have a test tmr so wanted to make sure I have that right

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[sleek sequoia]

whats the easiest way to get the reduced form of a matrix using the gauss jordan method?

[sleek sequoia]

here is an example if needed

[sour dove]

I'm not sure there's a "easiest way", it depends on the matrix.

[sleek sequoia]

oh ok

but is there a formula of some sorts

or no

do i have to do each matrix in a specific way?

or multiple options

like an example would be that most examples I've seen calculate the bottom left side to get the zeros there first

[sour dove]

nah not really. I mean the math will work out no matter what you do but you can rearrange and other stuff to make your life easier.

The guarantee is the bottom left, top right triangle if you're familiar with that

[sour dove]

yeah exactly

[sleek sequoia]

ahhhhh ok thanks man

[sour dove]

but like rearranging/swapping the rows, scaling, etc all will help you

yeah np

best of luck!

[sleek sequoia]

thanks

[last ether]

Gauss Jordan is a paper waster

[sleek sequoia]

lmao

[last ether]

I swear they give you a 3x4 matrix and then it takes 2 pages because each matrix takes 1/16 of the fucking paper

[sleek sequoia]

i agree but my teacher doesnt sooo

....

[sour dove]

bad memories from linear algebra, lol. It's also a slowish process by hand

[sleek sequoia]

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[last ether]

I guess that's one benefit of doing Cramer's rule

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[visual lintel]

someone please explain what the point graphed at 4, 0.25 represents (im thinking it’s the reciprocal of the y-int.) as well, if it is what I think it is, why did they graph the reciprocal of the y-int to begin with?

[visual lintel]

<@&286206848099549185>

.close

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[heady tusk]

i have not started, but i must use u=sin4x for substituition

[last ether]

Rewrite cos^3(4x) as cos^2(4x) * cos(4x)

Rewrite cos^2(4x) using the Pythagorean identity

[heady tusk]

ohh ok, and what answer do you get?

[lone heart]

@heady tusk Has your question been resolved?

[heady tusk]

<@&286206848099549185>

[last ether]

Did you even do what I said to do

Or are you just looking for someone's answers to leech off

[lone heart]

@heady tusk Has your question been resolved?

[heady tusk]

yes but we have to do it by using u/substituition

[last ether]

You do the substitution after

Like bro that should be pretty evident

[heady tusk]

I'm sorry, but I'm really lost

grense=range

[manic wind]

Rewrite cos^3(4x) = cos^2(4x) * cos(4x) using the trig identity sin^2 + cos^2 = 1

then apply u-sub, and don't forget the chain rule

[heady tusk]

@manic wind how would I apply the trig identity now?

[manic wind]

rewrite cos^2(4x) in terms of sins

[lone heart]

@heady tusk Has your question been resolved?

[lone heart]

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[opaque sail]

im not sure how to think abotu this

for both c and d

like visualization

i got 32/3 for c

and 20/3 for d

seems wrong t me

[lone heart]

@opaque sail Has your question been resolved?

[opaque sail]

no

[lone heart]

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[radiant obsidian]

hi, im learning about chebyshev's inequality for my stats final, I see two versions of the equation and is wondering if someone could explain how they are the same

[golden canyon]

It's the same I think since variance is sigma^2, and you can make substitution to get from one to the other

i = k * sigma, so k = i / sigma, 1/k^2 = sigma^2 / i^2 = var[X] / i^2

[radiant obsidian]

oh i see it now, thanks so much for the help!

.close

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[alpine sable]

how does 27 ^1/2 changes to 55?

[alpine sable]

its an improper fraction

27 whole 1/2 becomes 55/2

where did two go then

[vale wigeon]

27 ^1/2

there is no exponentiation going on. this is twenty-seven and a half, not 27 raised to the power of 1/2.

also the second equation had both of its sides multiplied by 2

so 55/2 * 2 = 55

[alpine sable]

thank you very much

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[flat vale]

how do i write the solution

[young tendon]

can someone help me with this math problem i dont get it

im supposed to find the volume

[flat vale]

{() or () or () ... ()}?

[young tendon]

and round to the 2nd decimal

[flat vale]

@young tendon bro

[young tendon]

oooh wait im sorry i thought help 0 was the free channel

[flat vale]

all g bro

nvm

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[drifting narwhal]

L is intersection line of x^2+y^2+z^2 = 1 and x + y + z= 1 ,how can it solve like this

[drifting narwhal]

<@&286206848099549185>

[lone heart]

@drifting narwhal Has your question been resolved?

[nimble fern]

did you mean how the integral I becomes the last line?

the only part I don't understand is that why dx becomes (z-y)/√2 ds

[drifting narwhal]

yep

[nimble fern]

do you know why is this so? because i can explain for the other parts

[drifting narwhal]

same as me , that step is what make me confused

[nimble fern]

hmmmm

[winter vale]

@flat vale did you figure it out?

[nimble fern]

do you recall any relationship between ds and dx? just curious

i really wish i can help, but that part really stops me

[flat vale]

yea i got it bro

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@drifting narwhal Has your question been resolved?

[lone heart]

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[alpine sable]

Let the triangle ABC square at A. The BD is the bisector of the angle ABC
(DE AC), the DE is perpendicular to BC (E = BC).
a) Prove that: Triangle ABD = Triangle EBD
b) Prove that BD is the perpendicular duty of the segment AE.
c) Let F be the intersection of AB and DE. Prove that D is the mind of Triangle FBC.

[alpine sable]

someone help please 🙏

I don’t know how to draw and solve this

[vale wigeon]

@sonic linden channel occupied please move

@alpine sable what does (DE AC) mean?

[alpine sable]

U,m

Let me see

[vale wigeon]

do you maybe have a picture of the problem as stated originally?

[alpine sable]

D e AC

The small e in math

[vale wigeon]

send a picture

[alpine sable]

It in a different language tho

[vale wigeon]

does not matter

[alpine sable]

Here

[ocean seal]

Pro_Hecker

[vale wigeon]

ah, belongs to

[alpine sable]

Ye

[vale wigeon]

and you are having trouble making the diagram?

[alpine sable]

Yeah

Can u help?

[vale wigeon]

ok sure let's go step by step with the diagram

draw a right triangle and label it ABC, such that A is the right angle

[alpine sable]

Ok wait

Can You Draw For Me ?

[vale wigeon]

no

[alpine sable]

It will be hard for me to translate ur text while doing the math problem

[vale wigeon]

i don't have any paper with me right now and it would be pointless if i drew it anyway

and i don't speak Vietnamese so i cannot do anything with the language barrier

[alpine sable]

Ok

I try to draw

[vale wigeon]

a right triangle is not hard to draw. should not be hard to draw.

[vale wigeon]

and label it ABC, such that A is the right angle

[alpine sable]

Oh

What are we gonna do next?

[vale wigeon]

BD is the bisector of angle ABC, where D is a point on AC.

draw this.

[alpine sable]

Okay

Done?

[vale wigeon]

well, the angle doesn't look evenly split, but that's probably okay for now.

[alpine sable]

We finished the drawing?

[vale wigeon]

no

DE is perpendicular to BC, where E is a point on BC.

[alpine sable]

Sorry to intervene but looks like OhZ drew this such that D is the midpoint of AC, which is not what was asked

Unless that's just a coincidence, in which case my bad

[vale wigeon]

botd

[alpine sable]

Ann, we draw DE in the middle of BC?

[vale wigeon]

that doesn't make sense...

we drop a perpendicular from D onto BC. and E is where it lands.

[alpine sable]

E in the middle of BC?

[vale wigeon]

no, i didn't say it had to be in the middle.

E is somewhere on BC.

[alpine sable]

Okay

[vale wigeon]

ok now you have the diagram

[alpine sable]

Ok

You still there?

I Have To do the prove session

@vale wigeon

[vale wigeon]

i can give you some pointers for a
but i don't know what "perpendicular duty" means in b, nor what the "mind of a triangle" is in c

[alpine sable]

It’s okay

[vale wigeon]

triangles ABD and EBD share side BD as well as two pairs of angles

[alpine sable]

Can u present like this one?

A example of it

Ann, it’s okay if you have to go.

Please answer me so I know that u can still help.

@vale wigeon

[vale wigeon]

no

[alpine sable]

You cant help me anymore?

Thanks a lot for the diagram

I gonna ask someone else

[alpine sable]

Diagram

a) Prove that: Triangle ABD = Triangle EBD
b) Prove that BD is the perpendicular duty of the segment AE.
c) Let F be the intersection of AB and DE. Prove that D is the mind of Triangle FBC.

<@&286206848099549185>

Please Help Me Solve this One

.close

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[wicked yarrow]

Hello I need help

[lone heart]

Please don't occupy multiple help channels.

[wicked yarrow]

Hello

I need help

[vale wigeon]

is it the same one from before

[wicked yarrow]

yes

[vale wigeon]

the one with the clock

[wicked yarrow]

But

[vale wigeon]

okay

[wicked yarrow]

You didn't explain

[vale wigeon]

yeah sorry i had to disappear for a moment

[wicked yarrow]

Why would it be 7

A minute agp

Ago

[vale wigeon]

the minute hand shows 36 minutes

[wicked yarrow]

So?

[vale wigeon]

a minute ago it would have been ??:35

[wicked yarrow]

It could be

01

02

03

04

05

06

07

08

09

[vale wigeon]

no need to spam....

[wicked yarrow]

10

Sorry

I just

[vale wigeon]

the minute hand traverses an hour marking every 5 minutes

when the time is a whole hour the minute hand is on the 12

at ??:05 it is at the 1, at ??:10 it is at the 2, etc.

[wicked yarrow]

Wait

Really?

[vale wigeon]

yes that's how analog clocks work lol

[wicked yarrow]

So if the hour hand was

2/5 of the way

It would be

Umm

Wait

[vale wigeon]

then the time would have been ??:24, and it would be impossible for the minute hand to be where it is drawn to be

[wicked yarrow]

Would it be 4?

If it was 2/5

Of the way?

[vale wigeon]

you are overusing the word "it" here so i cannot tell what you are trying to ask

[wicked yarrow]

So

If the short arrow is 2/5 of the way; is the time 4?

[vale wigeon]

no

[wicked yarrow]

Why not?

[vale wigeon]

if the hour hand is 2/5 of the way from one hour mark to the next, then the time is ??:24.

it is not 04:00.

[wicked yarrow]

04:24?

[vale wigeon]

no

[wicked yarrow]

Why?

[vale wigeon]

it may be 04:24 but it may also not be 04:24

[wicked yarrow]

But you said this here

[vale wigeon]

at ??:05 the minute hand is at the 1
and at ??:10 the minute hand is at the 2

[wicked yarrow]

Yes

So if it were 2/5 of the way it would be 04:24

[vale wigeon]

again with this overuse of "it"

[wicked yarrow]

if they time were 2/5 of the way

So 04:24

[vale wigeon]

.....

wtf are you on about

if the hour hand is 2/5 of the way from one hour mark to the next, then the time is ??:24. the time could be 01:24 or 02:24 or 03:24 etc it doesn't HAVE TO BE 04:24 specifically...

[wicked yarrow]

So then

If the time were 3/5 of the way; how can A be 8?

[vale wigeon]

aaaaaaaaaaaaaaa

do you genuinely not understand the difference between "the time", "the hour hand" and "the minute hand" or are you being dense on purpose here

[wicked yarrow]

The hour hand

[vale wigeon]

should we go over this AGAIN for the fifth time

or does "how can A be 8?" mean "i am absolutely convinced that A is not 8 and cannot be 8 by any means and it's your job to convince me otherwise"?

[wicked yarrow]

Can you explain me how the clock works?

[vale wigeon]

you want an explanation of how analog clocks work in general?

[wicked yarrow]

No I know how to read the clock

[vale wigeon]

well you are having trouble with the concept of "at 35 minutes past the hour, the minute hand points at the 7 mark"

[wicked yarrow]

Because there are no numbers to indicate that it's seven

[vale wigeon]

yes but the point is you RECOVER those numbers because you KNOW that it's 36 min past the hour

[wicked yarrow]

Yes

Explain to ke

Me

That if it's 36 past the hour how can it be 7

Explain the me how to recover them when they say 36 past the hour

[vale wigeon]

if it (the time) were 35 min past the hour then the minute hand would point directly at the 7 mark

do you or do you not understand this?

[wicked yarrow]

No

I do not

[vale wigeon]

:00 => minute hand points at 12
:05 => minute hand points at 1
:10 => minute hand points at 2
:15 => minute hand points at 3
:20 => minute hand points at 4
:25 => minute hand points at 5
:30 => minute hand points at 6
:35 => minute hand points at 7
:40 => minute hand points at 8
:45 => minute hand points at 9
:50 => minute hand points at 10
:55 => minute hand points at 11

the minute hand tells you how many minutes it is past the hour

the clock face has 12 hour marks, and the minute hand traverses them all in 60 minutes, so each hour mark corresponds to 5 minutes

[wicked yarrow]

Yes but on the picture the minute hand it 1 minute past another numbrr

0:

I understand

[vale wigeon]

yes exactly

[wicked yarrow]

Wow I didn't know that

[vale wigeon]

you didn't know that yet you claim you knew how to read analog clocks???

[wicked yarrow]

The time question was like the only one I got wrong

And the next question I will show you now

I dont even know how to figure this one out

[vale wigeon]

i would need some paper to show this

[wicked yarrow]

?

Can you help me solve this?

Hello...

<@&286206848099549185>

[wicked yarrow]

?

[vale wigeon]

sorry, i am running around doing paperwork. i cannot guarantee zero-delay responses on my part.

[wicked yarrow]

Oh ok

Do you know how to solve that question?

[vale wigeon]

anyway like. chart out the movement of A and B during A's first three laps

for a start

[wicked yarrow]

They would pass each other 6 times

In the first 3 laps right?

[vale wigeon]

would they?

i don't know.

[wicked yarrow]

Wait, you don't know?

...

@undone falcon

.close

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[red vault]

How do i do this?

[vale wigeon]

define "do"?

are you asked to expand?

[pine kettle]

@red vault what method do you use to foil

[red vault]

It says “perform the indicated operations”

[pine kettle]

yesss so do foil

or

a grid

whatever helps you multiply them out the bwst

[red vault]

I think its foil

[pine kettle]

then do foil

[red vault]

Idk how because it has 2 different variables

Nvm i got it

Idk how to do this one at all

[lone heart]

@red vault Has your question been resolved?

[lone heart]

@red vault Has your question been resolved?

[lone heart]

@red vault Has your question been resolved?

[zenith viper]

can you confirm the answer to be (100 b^2)/9a^10

This was my method.....

[lone heart]

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[fiery oasis]

I don't know how to solve this

[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'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

[burnt notch]

Cross multiply first, then simplify both the numerators and denominators the furthest you can. After that, you got to use properties of the powers and exponents

[fiery oasis]

I see i got it now

Thank you very much

[lone heart]

@fiery oasis Has your question been resolved?

[inner shuttle]

what are the prime numbers between 90 and 100

numbers that can be divided by 1 and itself

like 2 can be divided by 1 and itself get it?

what

[lone heart]

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[inner shuttle]

ok my school system is diferent from yours

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[fossil ether]

Verify that the line l3: 2x - 3y = -15 passes through A and that the line l1: 5x + 12y = 60 passes through B.

[median dirge]

What is A, and what is B?

[lone heart]

@fossil ether Has your question been resolved?

[autumn sable]

A is the point (0, 5) and B is the point (12, 0).

It's easy ti verify, you need to transform the equation 2x - 3y = -15 to have only y on a member.
You set a function f(x) = y = (the other member of the transformed equation).
And you verify if f(x coordonate of A) = y coordonate of A and f(x coordonate of B) = y coordonate of B.

[lone heart]

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[fossil ether]

Is correct????Similarly, to check if the line l1 passes through point B (12,0), we can substitute x=12 and y=0 into the equation:

5x + 12y = 60
5(12) + 12(0) = 60
60 = 60

The equation is also true, which means that the line l1 passes through point B.

[fossil ether]

To transform the equation 2x - 3y = -15 to have only y on one side, we can rearrange it as follows:

2x - 3y = -15
-3y = -2x - 15
y = (2/3)x + 5

Now we have the equation of the line in slope-intercept form (y = mx + b), where the slope (m) is 2/3 and the y-intercept (b) is 5.

To check if the line passes through point A (0, 5), we can substitute x = 0 and y = 5 into the equation:

y = (2/3)x + 5
5 = (2/3)(0) + 5
5 = 5

The equation is true, which means that the line passes through point A.

[autumn sable]

Yes, it's correct !

[autumn sable]

Yes, it's correct too and you have a really good redaction 😮 !

[autumn sable]

Great job, it just needs to do the same thing for point B and it's good.

@fossil ether (let me know if i can ping you)

[fossil ether]

Ok, thank you for your help

[clever ocean]

é lidar

[fossil ether]

@autumn sable yes

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@fossil ether Has your question been resolved?

[lone heart]

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[vernal basin]

How would be the correct input for geogebra for this limits. I get the limit input is lim = f(x) as x->1
But not the curly bracket part, I do it in two inputs or is there a notation in missing.

[vernal basin]

Geogebra or chat gpt, just trying to get how to input this kind of functions

[lone heart]

@vernal basin Has your question been resolved?

[vernal basin]

<@&286206848099549185>

[lone heart]

@vernal basin Has your question been resolved?

[lone heart]

@vernal basin Has your question been resolved?

[vernal basin]

Both, learning how to solve it but in stucked trying to input this to chat gpt where i study and develop my questions

[lone heart]

@vernal basin Has your question been resolved?

[vernal basin]

.close

[lone heart]

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[ionic sedge]

Can someone help

[lone heart]

Please don't occupy multiple help channels.

[ionic sedge]

Did I do this correctly? J have to find the derivative

[pine kettle]

,w derivative of (cos(t)-1)(2t^3-t^2)

[ocean seal]

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Requested by sills#9713

[ionic sedge]

did i do it wrong

[keen mason]

nope

correct

[ionic sedge]

oh, is it just another way of writing it

[keen mason]

mhm

yours is way better formatted imo

wolframs look horrible

[ionic sedge]

yeah lol

[ionic sedge]

can you check this one?

here is my work:

[keen mason]

derivitvie again?

[ionic sedge]

yep

[pine kettle]

,w derivative of ln(x)/(x^2-4)

@ionic sedge

[ocean seal]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by sills#9713

[pine kettle]

they multiplied by x on top and bottom

[ionic sedge]

did i not?

[keen mason]

your still missing a 2 no?

[pine kettle]

yea they arte.

CHAIN RULE.

[ocean hawk]

as I pointed out in the other channel...

[ionic sedge]

Like this?

@keen mason

[keen mason]

you're still missing a facto of 2

[keen mason]

this has 2x^2

[ionic sedge]

what do you mean, do I need to add 2x^2 to the numerator?

[keen mason]

there numerator has -2x^2

and you need x^2 on your numerator too

[ionic sedge]

so how whould i write that

[keen mason]

coz u times top and bottom by x

you did somethingwrong

you would have to re-do it

[ionic sedge]

okay

[ionic sedge]

How's this

@ocean hawk

[keen mason]

perfect

[ionic sedge]

thanks lol

[ionic sedge]

can you help me with this one?

i think all are correct expept a because you cannot determine from the given information

[vapid shuttle]

.close

[lone heart]

Channel closed

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[tranquil tendon]

only one person in a help channel

[alpine sable]

sam gtfo

[tranquil tendon]

@slender furnace use another help channel.

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

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[teal badger]

Hi there I am stuck from the line 1 to line 2 would anyone be able to explain the process I king of understand it but im not too sure

[waxen flame]

The two sine functions are the same so its the same as saying 2 times sin(pi/6)

[teal badger]

my guess was 1/3 (2sin 2pi/6 which would give me 60 degrees instead of the 30 i need to get the 1/2 and for the second part i dont get how it would be 2/3 when it was 1/3 if that makes any sense what i said

wait u dont divide the bottom denominator right

[waxen flame]

$\sin{\frac{\pi}{6}} + \sin{\frac{\pi}{6}} = 2\cdot \sin{\frac{\pi}{6}}$

[ocean seal]

Kookiemon

[teal badger]

so the 1/3 (2sin pi/6) 2/3 of sin pi/6 and pi/6 is 1/2 so then it would be 2/3 * 1/2 right?

[waxen flame]

Correct.

[teal badger]

OMG thank you so much ive been at it for 30 minutes appreciate it

[waxen flame]

yw

[teal badger]

.close

[lone heart]

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[surreal meadow]

!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'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

[gritty yacht]

I dont know where to begin

[neat mango]

What does it mean for graphs to intersect?

[gritty yacht]

they cross at one or more points

[neat mango]

Exactly. So at the points of intersection they will have the same (x, y) coordinates

[gritty yacht]

yes

[neat mango]

At the intersection, both graphs will have the same value of y

So, we can rearrange both equations to be functions of y (writing it as y = ...)

Since they have the same values of y at the intersection, both functions of y are equal

Does this make sense so far?

[gritty yacht]

yse

yes

[neat mango]

With both functions of y equal to each other, we can find the solve for the values of x

These values of x correspond to the y-coordinates of the intersections, and thus we find the (x, y) points of intersection

[gritty yacht]

i understand

[neat mango]

Cool! Try to work through it and let me know if you have anymore questions!

[gritty yacht]

thank you

[neat mango]

No problem!

[lone heart]

@gritty yacht Has your question been resolved?

[lone heart]

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[ionic sedge]

cn someone check if i did this correctly

[ionic sedge]

here is my work:

@ocean hawk

[waxen flame]

The math checks out.

[ionic sedge]

so the total distance traveled would be 3 correct

abs value of -3

[waxen flame]

Yes, it travelled -3 feet from its initial position but the total displacement is the absolute value of -3.

[ionic sedge]

here is my work:

oops

rotated

[waxen flame]

,rotate

[waxen flame]

Looks good.

[ionic sedge]

my work:

,rotate

[waxen flame]

Looks good.

[ionic sedge]

part a is:

@waxen flame

[waxen flame]

Looks good.

[ionic sedge]

wait, its asking for 0.1

[ionic sedge]

i got 1.4

[waxen flame]

Sounds good.

[ionic sedge]

this is a review sheet for my exam in 2 weeks by the way, thanks for checking my work

[waxen flame]

yw

One moment, I'm helping someone else at the moment.

What have you tried?

[ionic sedge]

i believe a is (-3,0)U(0,3)

[waxen flame]

And what makes you think that?

[ionic sedge]

because the curve is concave down there

what do you think

[waxen flame]

Sounds reasonable.

What about (b)?

[ionic sedge]

i have no idea how to do b

[waxen flame]

What does the first derivative say about a curve?

[ionic sedge]

it gives the slope of the curve at a specific point

[waxen flame]

And if the slope is positive?

[ionic sedge]

the derivative of the function will also be positive?

[waxen flame]

But what does a positive slope say about the function? Is it increasing or decreasing?

[ionic sedge]

increasing

[waxen flame]

And is a function increasing or decreasing when the slope is negative?

[ionic sedge]

decreasing

[waxen flame]

And what about if the slope is zero?

🤔

[ionic sedge]

no change?

would "b" be (-5,0)U(5,inf)

[waxen flame]

No.

By definition, increasing means that given a < b, then f(a) < f(b).

[ionic sedge]

oh

[waxen flame]

So for some arbitrarily small distance, as long as the y value from one point to the next increases, the function is increasing.

[ionic sedge]

oh

so b would be (-5,3)U(5,inf)

@waxen flame ?

[waxen flame]

On the left side, where is the graph increasing?

[ionic sedge]

-inf,-3?

[waxen flame]

Yes.

And on the right side, where is it increasing?

[ionic sedge]

3,inf

[waxen flame]

And where is it decreasing?

[ionic sedge]

-3,3?

[waxen flame]

Yes. Are they brackets or parentheses?

[ionic sedge]

Brackets on the closed intervals

[waxen flame]

x=-3 and x=3 aren't inclusive of the intervals because the slope changes from negative to positive and vice versa.

[ionic sedge]

okay

so

[waxen flame]

So at those points on the interval, you would use parentheses to show that those values of x are not included on the interval.

[ionic sedge]

okay

going back to the question, so b is (-inf,-3)U(3,inf)

[waxen flame]

Yes.

$(-\infty , -3) \cup (3, \infty)$

[ocean seal]

Kookiemon

[ionic sedge]

and a would be (-3,0)U(0,3)

would c be the same as a?

[waxen flame]

Yes.

[ionic sedge]

so c is (-3,0)U(0,3)

[ionic sedge]

now i have no idea about d and e

[waxen flame]

The second derivative of a function indicates if a curve is concave up or concave down.

If the second derivative is positive, then it is concave up. If it is negative, then it is concave down.

Can you identify the intervals with that information?

[ionic sedge]

by "it" you mean the original function?

[waxen flame]

Yes.

[ionic sedge]

concave up at (-inf,-3)U(3,inf) (same as b)

concave down at (-3,0)U(0,3) (same as c)

@waxen flame

[waxen flame]

No

[ionic sedge]

what do you mean

[waxen flame]

Concave up means the open end of the curve is pointed upwards and vice versa for concave down.

The point at which the curve switches from concave up to concave down, or vice-versa, is called the inflection point.

The inflection point will be an endpoint of the intervals for the second derivative.

[ionic sedge]

is that related to crossing the x axis

[waxen flame]

No.

[ionic sedge]

so, what would the interval be

[waxen flame]

One second, I'm making a graph that should explain things better than I can in words.

[ionic sedge]

okay

you there

@waxen flame

[waxen flame]

Yeah.

https://www.geogebra.org/classic/gvvyejbm

So this shows this intervals where the slopes are positive and negative. They correspond with a positive and negative first derivative.

[ionic sedge]

ah i see

[waxen flame]

Hmm, I'm having some difficult making the graph so it shows concavity. This may take about 3 or 4 minutes.

[ionic sedge]

no worries, you can just explain by words

[waxen flame]

Well, here the arrowing is pointing downwards to indicate the open end of the curve.

[ionic sedge]

yeah

[waxen flame]

Here the curve is still pointed downwards. There is an inflection point at (0,0) where the open-end of the curve changes though.

[ionic sedge]

okay

[waxen flame]

The second derivative "determines if that arrow is pointed upwards or downwards" to indicate concavity.

This is for a visual reference only.

[ionic sedge]

yep

[waxen flame]

If the second derivative is positive, then the function is concave up.
If the second derivative is negative, then the function is concave down.

As I mentioned, there is an inflection point at (0,0) where the concavity changes from negative to positive.

That inflection point will be an end point of the intervals.

[ionic sedge]

would it be -3,0

[waxen flame]

No, the interval of positivity for the second derivative will be from (0, +inf).

The inflection point is the endpoint of the interval for the second derivative.

[ionic sedge]

and would the interval for negativity be -inf,0

[waxen flame]

Yes.

[ionic sedge]

this look right

[waxen flame]

It's decreasing from (-3,3).

And the same for (c).

[ionic sedge]

the first derivative?

[waxen flame]

Yes.

a) should be (-3,3)

[ionic sedge]

would i get points taken off on an exam for doing that

doing (-3,0)U(0,3)

[waxen flame]

👍

[ionic sedge]

alright, thanks for the help

[waxen flame]

np

[ionic sedge]

.close

[lone heart]

Channel closed

Closed by @ionic sedge

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Remember:
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[amber plover]

can someone please explain to me how these are wrong

[lone heart]

@amber plover Has your question been resolved?

[amber plover]

<@&286206848099549185>

[exotic belfry]

you missed the brackets after 1/3.

[amber plover]

missed the brackets? I'm sorry not sure I understand

Am i not just supposed to multiply both sides by 1/3 to get rid of it from x

[exotic belfry]

i would write 1/3(x+12pi/6) in a different form as you:

[amber plover]

yeah but i dont think it would change the answer would it

[exotic belfry]

yes, it would. as there should be 1/3 at the 12pi/6 part.

and there is a second thing i do not understand.

[amber plover]

what is it you don't understand

[amber plover]

yes but i did 12 pi/ 6 first before subtracting it from the other side

on a calculator

[exotic belfry]

i would have $\frac{x}{3}+\frac{1}{3}\cdot\frac{12\cdot \pi}{6}$, and the second thing is the transformation to the next line.

[ocean seal]

ThM

[amber plover]

where did the + 1/3 come from though..?

I don't know why im getting these questions wrong i've never had trouble with transformation questions before

[lament forge]

there isn't a + 1/3
there's a sum of two things, which is because of "x-12pi/6", and both of those things are multiplied by 1/3, because initially the sum was multiplied by 1/3 and then we distributed that

[exotic belfry]

exactly. you have multiply x with 1/3 and you have multiply 12pi/6 with 1/3, thats exactly what i did.

[amber plover]

i dont think that's what normally happens though hold on let me send you a screenshot of my notes

the first side with x isnt touched

the number is just switched to the other side

[exotic belfry]

your mixing up things.

first: distributive law says how to expand a multiplicative term before brackets into the brackets.

second: your example shows an additive transformation of an equations. thats just something complete different.

[amber plover]

alright i got it sorry about that

i forgot about a couple things

[exotic belfry]

and btw the example is ambigous. i have seen different interpretations for 1/3y in my life. Some people say it is $\frac{1}{3}\cdot y$, some say it is $\frac{1}{3y}$

[ocean seal]

ThM

[amber plover]

ok this I now understand i got wrong thank you but I'm still confused on the first one

it's really straight forward

1 is the a value 4 is the c value

i've had the exact same questions on other transformation questions from other units and never got them wrong

[exotic belfry]

so, if youre convinced it is the same as ever and it is right, so what can someone do then for you?

[amber plover]

i'm just saying it's the same as i've always done but it's wrong so I'm just confused

[amber plover]

this is from my notes

move the 8 to the other side

divide both sides by -9

[exotic belfry]

again, this is not the case you are starting in this example.

First we have to be clear how you learned this:

[amber plover]

i learned it as 1/3y

[exotic belfry]

ok, lets set y = 2, what is the value of 1/3y?

[amber plover]

1/6

[exotic belfry]

ok, for you it is $\frac{1}{3y}$

[ocean seal]

ThM

[amber plover]

yes it always has been

almost never seen 1/3 x y used

[exotic belfry]

$\frac{1}{3(x+\frac{12\pi}{6})}$

[ocean seal]

ThM

[amber plover]

yes i got it I understand this question now thank you

[exotic belfry]

ok, then we can close this channel?