help-28

[torn jolt]

What have you tried

[idle scroll]

this is my working out so far

[torn jolt]

"dy/dx of" is bad notation

[idle scroll]

wdym?

[torn jolt]

dy/dx means derivative of y wrt x

Anyways

[idle scroll]

oh right i see

is the working out right so far?

[torn jolt]

That seems about right

[idle scroll]

not sure how to properly simplify this

[torn jolt]

Factor 3(2x-1)²

[idle scroll]

how do you factor that?

and its to the power of 3

[torn jolt]

Let 2x-1 = z

3z³+6z²(3x)

= 3z²(z+6x)

Now replace z with 2x-1 and simplify

[idle scroll]

oh i see thanks so much

makes it much easier

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[void crystal]

Please provide the solution for the 2nd part
actually, I have already solved it, I just want to check if i made some calculation errors
and I would appreciate if you could design some problems for me too, as when I do it alone, there is a huge risk of me making a mistake and not being able to find it

[void crystal]

my answer is (c1+c2(n))(2^n) + n - 6

I am gonna solve it from a book too
but I want to make it interactive so I can get some insights on where I should focus more,
the area I am lacking that is

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[robust slate]

Yes

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[primal warren]

damn dedication

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[sturdy fulcrum]

Using the multinomial theorem I keep getting -252 a^2 b^3 c^4, what am I doing wrong here

[sturdy fulcrum]

lemme show my process

∑[9!/(2!3!4!)] * (-1) a^2 b^3 c^4 * x^2 y^3 z^4

[true gale]

Yeah, that's what you do.

So how are you getting it wrong?

[sturdy fulcrum]

oh nevermind seemed to be a calculation error from my side

mb

[eager obsidian]

yeah

[sturdy fulcrum]

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[void crystal]

unsolved question
please do

i am gonna ask in a new channel

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[idle spear]

How do you find the new upper and lower bounds in spherical coordinates

[stiff musk]

the screenshot asks for cylindrical, not spherical coordinates

[idle spear]

💀 fuck me

Thanks

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[distant bolt]

this is just pythagorean theorem right?

[spare owl]

yes

[distant bolt]

WOOOOOO TYY

[spare owl]

same as saying you walk 3050 feet to the north and 400 feet to the east

[distant bolt]

ahhh got it tyy

another similar question

but without numbers

hold onnn

[stiff musk]

well if they're all equal then p + q + r = p + p + p, yes?

[distant bolt]

uhhhhhhuhhhhh

YES

[stiff musk]

and p + p + p = ?

[distant bolt]

3p? 🥲

[stiff musk]

yea

probably you know how to draw 3p given p?

[distant bolt]

WOOOOOOO

uhh, is it just going to be longer?

[stiff musk]

yea

3 times as long

pointing in the same direction

[distant bolt]

just around 9 units higher?

[stiff musk]

well currently it is (-1,3) where -1 is the x coordinate and 3 is the y coordinate

so just multiply those by 3

[distant bolt]

ohhhhhhhhhhh

i had to read that around 4 times

but i got it 💪

THANK YOUU 🙏

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[sturdy mango]

for a triangle with the endpoints (0,0), (0,9) and (9,0) how do you find the equations of each of the 3 sides?

[sturdy mango]

for t in [0,9]

[pallid coral]

the equations of the lines?

[sturdy mango]

like the equations for the sides

the boundaries

nvm

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[thick hedge]

I don't know how much more math I need to know to solve such problems but I'll ask anyway

[thick hedge]

A particle performs harmonic oscillations along the x axis accoridng to the law $x=acos(\omega t)$

[glossy valve]

ƒ(Why am. I here)=I don't know

[thick hedge]

assuming the probability density dP/dx depends on x find this probability density 's dependence on x

assuming the probability of the particle to fall in the interval -a to a to be 1

source:- Problems in general physics by IE irodov

where do. I even start

[leaden nebula]

Uh ie irodov

[thick hedge]

A physics problem book

[leaden nebula]

I know

[fluid jacinth]

the solutions are given on the internet I suppose

[thick hedge]

yeah just realised

thanks

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[muted ruin]

can anyone explain this? I can't find any information on this

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[gilded tapir]

We got city A and city B the distance between them is 108km. From A to B came a motorcycle and after 1 hour from B to A came a bicycle they will meet 24km away from B. If they came at the same time they would have met 72km away from A need to find the speed if both

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[neat nest]

how do i get help

[supple sail]

911

[neat nest]

i need help with this

oops wait

[supple sail]

wow i was tryna solve it

💔

[hollow summit]

just say it

[neat nest]

i was looking for it sorry

can u help me with this im a kinda struggling with the last question

this one

hello?

can anyone help me ?

[supple sail]

statement 3 is false

as temp in F increases by 5/9 it'd be equivalennt to 25/81 increase in C

[neat nest]

i need time to proccess it wait

how did u get 25/81 im confused

can u help me on this next question

i need help with these

7?

5

do i add 4 and 3?

m = 7

and n= 5?

im not sure on that one

8

ohh

4n

[supple sail]

Let F be initial temp
F1 be the final temp
so
F1 = F + 5/9 (according to 3rd statement)

and we know C = 5/9 (f-32)

write F in terms of C

let C1 be final temp

so
C1 = 5/9 (F+5/9 -32)

take 5/9 out
should give the value

[neat nest]

woah

ur like super smart

[supple sail]

im like the dumbest person ever

[neat nest]

thanks im in the 8th grade

[supple sail]

i wish i was in 8th grade 💔

[neat nest]

lol

i need help on one mroe question

this one

[supple sail]

okkies

[neat nest]

im not sure

[supple sail]

5 jars

[neat nest]

but do i js divide 23 by 4

[supple sail]

there's this thing called greatest Integer function
you'll study in higher classes

but yes just divide it

[neat nest]

5?

5 jars

[supple sail]

the nearest integer (number ) should be the answer

[supple sail]

yes '

[neat nest]

so if its half price

do i double it

[supple sail]

its 2 euros

yes

[neat nest]

11?

[supple sail]

no

its 11

yes

23/2

[neat nest]

ohh

one last question

[supple sail]

stfu fairyrose
take the reaction back

[supple sail]

whats 1/6 of 120 ?
whats 120 -50?

[neat nest]

6

divided by 120

is 20?

oops

im wrong

[supple sail]

120 by 6 = 20

[neat nest]

wait

yes

[supple sail]

now whats 120 -50

[neat nest]

70

[supple sail]

add the two things you just got

[neat nest]

90

[supple sail]

right

now are you familiar with percentages?

[neat nest]

is it the final answer?

[supple sail]

not rlly

[neat nest]

yea kinda

[supple sail]

whats 20% of 120

hint : it means
2/10 times of 120

[neat nest]

125 x 5?

[supple sail]

no

0.2 times 120

[neat nest]

ohh

mb

[supple sail]

what you get

[neat nest]

can i use a calculator?

i dont have a book to write on cuz its night time

[supple sail]

its fairly simple but if you are allowed calculators in test then yes

[neat nest]

oh

[supple sail]

wait

whats 120 by 10

quick

[neat nest]

im dumb

is it divide?

[supple sail]

whats 12 times 10 😭

[supple sail]

yes

[neat nest]

120

[supple sail]

so what 120 divide by 10

[neat nest]

12?

[supple sail]

times 2

[neat nest]

24

[supple sail]

so this is 20% of 120

now add 90 and 24

[neat nest]

114?

[supple sail]

right !!

now total time was 120

she spend 114

how much left?

[neat nest]

6

minutes

[supple sail]

thats the answer

[neat nest]

thank you

now i get it

im going to sleep

goodnight

[supple sail]

good night !!!

because

think bout it

you spend 10 minutes being silly

another 40 minutes crying

how much time did you spend?

the question says she played badminton for 50 minutes

out of 120 min she had

💀
FUCK !

YOU'RE RIGHT

she slept on my silly mistake

Rip

why were you just watching while i been doing this error

😭

the final answer would be 26 mins ig

should have interefered

imagine next day she goes to school 💀
all wrong

@neat nest

correction in the last problem

50 minutes played badminton

1/6 of 120 = 20 mins

20% of 120 = 24

50 + 20 + 24 = 94

now total time = 124
she spent = 94

time she can spend in cafe = 120 -94 = 26 minutes

hopefully

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[small reef]

i used this method to try and solve this question but i got the wrong answer

does anyone knwo what im doing wrong

[rancid harbor]

ok what's your values for |A|, |B|, etc

[small reef]

isnt is |A| = 50, |B| = 30, |C| = 20

[rancid harbor]

no, those are the people who only like those genres

[small reef]

so |A| = 50 +10+10-5?

that gives me |A| = 65, |B| = 35+x, |C| = 25+x

[rancid harbor]

seems correct

[small reef]

that still didnt give me the right answer i dont think

150-65-(35+x) - (25+x) +10+10-5

which gives 40-2x = 0

x should be 40

[rancid harbor]

if you substitue this you get 150 = 65 + 35 + x + 25 + x - 10 - 10 - x + 5

,w 150 = 65 + 35 + x + 25 + x - 10 - 10 - x + 5

[glossy valve]

Results provided by WolframAlpha

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

Requested by alshfik

[small reef]

oh i see

i forgot the -x

[rancid harbor]

it's not the right answer?

[small reef]

i missed the -x at the end

thats right thank you

ive been staring at my work for ages and didnt even realise

[rancid harbor]

thank you for providing the relevant theorem btw

[small reef]

i completed missed the last bit

apologies

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[sturdy fulcrum]

I keep getting the answer as (2^n+1)/(n+1), what am I doing wrong?
Procedure:
Σ C(r)/(r+1) = Σ(n+1)C(r+1) = 2^(n+1)

[pearl trout]

Can you post the full assignment?

In particular, what are the values C_i

[sturdy fulcrum]

wdym by assignment

[pearl trout]

The full problem statement

[sturdy fulcrum]

yeah well that's all there is to the problem

[pearl trout]

Then I recommend moving on to another problem

[sturdy fulcrum]

huh why so

[pearl trout]

The problem isn't well-defined

[sturdy fulcrum]

why'd you think so

oh is it because

the author prolly assumes you that the expression extends till the n'th term

?

cus that's what most of the other problems are

[pearl trout]

Can you post the full file containing this problem

[sturdy fulcrum]

instead of going on forever ad nauseum

[sturdy fulcrum]

yeah okay

are files allowed here or do i gotta go to dms

[pearl trout]

You can send it to me in DM

[sturdy fulcrum]

ure thing

sure

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[sturdy fulcrum]

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[hidden harbor]

In how many ways can we generate a 7 letter password with the letters 'a' and 'b' if it has to start with b, end with b or contain exactly 4 b's

[hidden harbor]

I tried 2^6+2^6+7!(4!3!)-6!(3!3!)-6!(3!3!)-2^5+7!(2!5!)

using the principle of inclusion-exclusion

but I did not get the right answer

!status

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What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[hidden harbor]

3

The correct answer is 101 and I got 112

I know I could take cases separately but I want to know what I did wrong

nvm im an idiot

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[digital mountain]

claim

[digital mountain]

Can someone please help me?

Ik we have to set y equal to that but how do we find the intersection?

[dapper light]

Do you know the answer?

Yes or no

?

[hollow spire]

ok so first I want you to expand the quadratic

[digital mountain]

okay let me set them equal

[hollow spire]

By expanding the quadratic equation we can fully understand what we are working with

[dapper light]

There are 1 because that is the amount of “x”s there are

It could be 2 solutions because the solution for “x” is repeated twice

[hollow spire]

@dapper light Nosol!

[dapper light]

???

What is Nosol!?

[digital mountain]

Yes but how do u even find a intersection

[hollow spire]

No solutions. We want the people to work things out for themselves

we are just here to assist that

[digital mountain]

Real

[hollow spire]

So first what I want you to do is expand the quadratic alone

That way we have two functions

[dapper light]

Of eq 1 or 2?

[dapper light]

I’m talking about eq 1

[digital mountain]

Was i supposed to solve for X?

[hollow spire]

Just wait sora, don’t get ahead of yourself just yet

[digital mountain]

Okay

[hollow spire]

so if we expand (x+2)^2 what do we get

[digital mountain]

expand means to solve right?

or

[hollow spire]

Foil

Expand means to uncondense it.

[digital mountain]

ohh

we get x^2+4x+4

[hollow spire]

Perfect

So from that we know. The function of (x+2)^2 is shaped like a U because it’s positive and it’s y intercept is +4

From the second equation -2x-4 what can we tell about that equation in terms of graphing

[digital mountain]

its going down by 2 and its y int is -4?

[hollow spire]

Correct

It has a slope of -2 and it’s y-intercept is -4

Now if we put this into a basic graph. (Doesn’t have to be insanely accurate)

[digital mountain]

okay lemme get desmos rq

[digital mountain]

so plug this

and the second one in?

I got 2 points

(-4,4), (-2,0)

[hollow spire]

Yea

[digital mountain]

Oh shi we got the answer

[hollow spire]

I drew this on my phone

[digital mountain]

Lmfaoo thats sick

But is ther a way u can do this without graphin

[hollow spire]

Yea Desmos will give you the points

[digital mountain]

cause i dont have a graphing calc and i dont think my teacher will let me use desmos or her ti-83

[hollow spire]

Well graphing will tell you how many points to look for

Again the graph doesn’t have to be insanely accurate so a bad hand drawn one like mine works

[digital mountain]

Oh ight

[hollow spire]

so we can see that the two functions intersect at two points

That’s how you get (a)

Very simple very easy

A quick goofy sketch works

now to get part B

[digital mountain]

Wait but didnt we do b

the points of intersection are 2,0 and -4,4 no?

[hollow spire]

Yea

But to figure that out without a calculator

you were correct in setting them equal to each other

-2x-4=x^2+4x+4

[digital mountain]

Is that how we knew there was 2 points?

[hollow spire]

but make sure you use the expanded version. It’s easier

[hollow spire]

The graph yes

[digital mountain]

oh okay fs

Do you have time for one more problem?

[hollow spire]

so if we set the expanded functions equal to each other. We can solve for x easier

-2x=x^2+4x+8
0=x^2+6x+8

Then factor
(X+4)(X+2)

Now you have the Xs and then plug them back into one of the equations (ideally the simpler one) and you have your answers

[hollow spire]

Yea

What’s up

[digital mountain]

Do u just set these up equally?

like 6x-2 = 12

and then solve for x?

[hollow spire]

Yes but it’s still an inequality

[hollow spire]

6x-12>=12

[digital mountain]

How do u know if its a open circle or closed circle

and where to put the arrow again?

[hollow spire]

See the line underneath the >?

That means greater than or equal to

Close circle means that the value is included while open means it is not included

so if a value can be equal it is included

and the trick to knowing which way to draw the arrow is the way the > is pointing

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[digital mountain]

Thanks @hollow spire Sorry i didnt respond i was eating dinner

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[lilac rivet]

How do I find MB with this circle??

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[cosmic turret]

i dont understand the part a explanation

if anyone can tell me why c1 can be any number

i get c2 being 0 but then c1 + 0 = 0 should make c1 also 0 no?

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[cosmic turret]

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[paper wedge]

Can I get some help?

not sure how to go about doing this problem

[slate violet]

Let the base of the 45 degree triangle be x

And let the base of the 75 degree triangle be 500 - x

x + 500 - x = 500 and the question says D = 500

[paper wedge]

ok

[slate violet]

So then you can write h in two different ways using the two triangles

That gives you an equation in x: once you know x then you know h

Alternatively, if you know the sine rule you can also do it that way

[paper wedge]

sine rule? opp/hyp?

[slate violet]

Ah you haven't covered that yet right

sin a / A = sin b / B = sin c / C

[paper wedge]

nope not yet

[slate violet]

Okok

[paper wedge]

sorry, so I did x+500-x=500

now what?

[paper wedge]

not sure what you mean here

[slate violet]

Okay so for the triangle with the 45 degrees

What trig ratio do you need to use?

[paper wedge]

cot(45)?

[slate violet]

Yes or just tan

[paper wedge]

yeah either works

[slate violet]

Both work

[paper wedge]

ok ima try rq

[slate violet]

Okok

[paper wedge]

i got

x cot(45degrees) = h

[slate violet]

Yeah so cot 45 = x / h

Yep so x cot 45 = h

[slate violet]

And so now do the same for the other triangle

[paper wedge]

okay

[slate violet]

The angle is 75 degrees and the base is now 500 - x

[paper wedge]

can i use angle 15?

or 75 is better

i got

(500-x) cot(15degrees) = h

[slate violet]

Ah fair enough, if you use 15 then you will have the opposite and the adjacent side

Yeah so cot 15 = h/(500 -x)

h = (500 - x) cot 15 mhm

[slate violet]

So now notice both of those equations equal h

[paper wedge]

yup

[slate violet]

Which means you can write an equation in x

And solve for x

[paper wedge]

thats where im confused

do i set h to 0

and solve for x

[slate violet]

So x cot 45 = (500 - x) cot 15

[slate violet]

No

[paper wedge]

oh ok

ima do that rq

[slate violet]

It's a property that if a equals b and b equals c, then a also equals c

[paper wedge]

ok i see

how should i get x alone here?

[slate violet]

Expand the brackets of (500 - x) cot 15

And then move all the x terms to the left hand side

[paper wedge]

ok

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@paper wedge Has your question been resolved?

[paper wedge]

i think i did it wrong, sorry for taking awhile had to do something

ima try again

<@&286206848099549185>

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[gentle geyser]

Can someone pls help me with this vector q?

I don't rlly understand how to do it?

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[upbeat oar]

What did I do wrong using the slide and divide method?

[lament vector]

im not sure what the slide and divide method is but you did vanish away 3 from x^2

[upbeat oar]

Yeah it looks insane but that's the slide and divide method

[lament vector]

the answer is almost correct just

3(x-4)^2

[upbeat oar]

Huh

Maybe if the trinomial has a common factor, then I need to factor that out first.

Thanks.

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[errant sable]

i need help with this proof, provided the following theorem

[errant sable]

So far I have sn<limsup sn +epsilon/2 and tn<limsup tn+epsilon/2

Adding them I had sn+tn <limsup sn+limsup tn + epsilon

And now i feel stuck

I also just don't know how to start this proof

I think you would have to prove both limsup sn less than/equal to lim sup {sn: n>N} and limsup sn greater than/equal to lim sup {sn: n>N}

to then prove equality

<@&286206848099549185>

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@errant sable Has your question been resolved?

[errant sable]

I think I did the first proof?

But I'm lost on the second proof for question 16

I just don't understand how we would go about starting the proof

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@errant sable Has your question been resolved?

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@errant sable Has your question been resolved?

[hollow spire]

<@&286206848099549185>

[sleek hazel]

What happened??

[deep trench]

i don't quite understand the notation lim sup sn (they differ from one country to another, i guess)

Oh nevermind i get it

But it appears they want you to prove the very definition of lim sup ...

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@errant sable Has your question been resolved?

[errant sable]

Yeah I saw that

I don’t know how to make for@al proof

I might ask my prof

[sly sail]

I think they the point is to show that the two definitions are equivalent, so you assume the theorem is true and show the statement in the definition holds

or... did they give a definition of lim sup that they intend u to use

[errant sable]

This is the definition of lim sup they gave me

[errant sable]

That’s what I thought but I couldn’t quite write a proof on whether the definitions are the same

I almost wanted to just say that it was the definition of limit superior but I feel like my professor would smite me

[sly sail]

what is the definition of a subsequential limit?

[errant sable]

Let me pull it up

Well actually it’s the same as the definition of a limit of a sequence

But there is a theorem that states that if a sequence were to converge it, it’s subsequences would converge as well

[errant sable]

I think

i have a proof ish?

take sup {sn: n>N} to be a sequence. As N goes to infinity and the sequence reindexes itself, the sequence increases, so the sequence would be monotone. We also know the sequence to be bounded, so the sequence is to converge, and it would converge to limsup sn, otherwise it would contradict the definition of it being the lowest upper bound for the set of limits of sn.

i dont know if this is ok

i dont have the quantifiers for epsilon and whatnot so its far from a formal proof

but are my ideas ok?

[errant sable]

Nvm my professor just said a solid nope

[errant sable]

He said to use this theorem to help prove it

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[fair moat]

I need help with the last two blanks, not sure what to do

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@fair moat Has your question been resolved?

[proven mango]

so which series above does the second one most closely resemble?

[fair moat]

the third series?

[proven mango]

yep

so what x value do we have to choose to make it 1/6^n

[fair moat]

1/6

or is that wrong

[proven mango]

yep exactly

thats right

[fair moat]

and then I just plug in 1/6 into the third series?

[proven mango]

yeah

[fair moat]

okay gimme a sec

[fair moat]

I got 12/125

[proven mango]

yeah thats right

now the second one might be a little less obvious

any ideas?

[fair moat]

no not at all

[proven mango]

alright so we see that it has the n^2 term

and we have a 2^n in the denominator

which x value do we have to plug in to get that 2^n in the denominator?

[fair moat]

1/2?

[proven mango]

yep

so if we do that

[glossy valve]

y0shi

[proven mango]

if we separate that into two fractions

we have this extra bit that we dont really want

$\sum_{n=1}^{\infty}\frac{n^2}{2^n}-\frac{n}{2^n}$

[glossy valve]

y0shi

[proven mango]

so we essentially just have to add that n/2^n part back to get what we want

can we use one of our other series above to find out what that sum is?

[fair moat]

the second one?

[proven mango]

yep

[fair moat]

so I would have to plug in 1/2 to both of them and then add the values?

[proven mango]

yep exactly

[fair moat]

I got 4+2=6

[proven mango]

yeah thats right

[fair moat]

okay got it thank you so much

[proven mango]

yw!

[fair moat]

would you be able to help me with that one as well?

[proven mango]

yeah sure

[fair moat]

one sec

the comparison theorem for series

im not sure which one I got wrong

it says getting 5/6 corrects gives you 50% for the question

and I got 50% so im not sure which one is wrong

[proven mango]

you might wanna look over 4 again

if the bigger series converges the smaller one must also converge

[fair moat]

but for example for n = 3

the inequality would be false wouldnt it

1/2 < 1/9 would be incorrect

[proven mango]

oh wait youre right

i thought that the inequalities were guaranteed to be right

alright check number 3

the inequality isnt wrong

but one of the conditions arent met for the direct comparison test

[fair moat]

what do you mean?

if the bigger series converges then shouldnt the smaller series converge as well

[proven mango]

recall that the direct comparison test requires both series to be positive

[fair moat]

ohh

yeah I totally forgot that was a condition as well

the one on the left would equal -2

for n=2

[proven mango]

honestly me too

yeah

[fair moat]

alright got it again

thank you so much

u were a big help

[proven mango]

yw!

[fair moat]

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[hollow loom]

2 dice are rolled. a three appears on at least one of the dice. find the probability that the sum of the uppermost faces is greater than seven

[hollow loom]

wouldn't it be just 1/3?

the answer's apparently 4/11

[atomic hare]

these are the standard D6?

@hollow loom ^

[hollow loom]

yea

standard fair die

[latent lava]

so you that there are 36 possible outcomes if you roll two dice

then there are 5^2 ways to roll two dice such that both do not have a 3 right?

so there are 36 -25 = 11 ways to roll a dice where at least one has a 3

[hollow loom]

but at least one of the die have to have a 3

[hollow loom]

ohk

[latent lava]

ok lol

um but yeah.

assume 1 has a three then to get a summ gbigger than 7, the other die has to be 5 or 6

[hollow loom]

yeah

[latent lava]

so the possible outcomes are (3, 5), (3, 6), (5,3), (6,3) right

[hollow loom]

does order matter?

[latent lava]

yeah

theres two dice

[hollow loom]

oh

ok

[latent lava]

they are not the same unfortunatelly

[hollow loom]

alr

ok so u get 4/11

i understand

thx

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[latent lava]

sweet

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[icy creek]

how does this work?

[ocean lark]

$p \rightarrow q$ is defined as $\sim p \lor q$

[glossy valve]

Damian

[ocean lark]

Thus, $\sim p \rightarrow q$ is equivalent to $p \lor q$

[glossy valve]

Damian

[ocean lark]

which is then equivalent to the negation of the third column in ur truth table by demorgans

[icy creek]

huhhhh

p implies q is defined as not p or q

?

why is defined like that

is that just how it is

[ocean lark]

i would put it more as

we want the truth table of p implies q to look like this

for sense's sake, like false implies x should always be true vacuously

and True implies true obviously works, but you dontr want True implies false to work

and ~p or q is a way of writing this table

[icy creek]

hmm

okiee

thanks

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[fair moat]

first two blanks are right

the last one is wrong

not sure what went wrong

[sacred sparrow]

Are you sure -5/27 is ryt

[fair moat]

its wrong

idk where I messed up

[sacred sparrow]

Hm no -5/27 is right for the 6th derivative

that's odd

formatting looks right as well, not sure what they demand

[sacred sparrow]

Ah probably because you ignored the n=0 term :D

and they don't check whether you wrote the Taylor series in order

you have the 2nd and 4th term

but you don't need the 6th since the 0th is nonzero

[fair moat]

is that just the function itself

sorry im a lil confused

[sacred sparrow]

from the Taylor series

the 0th term

you calculated for n=2 and n=4

but overlooked n=0

and the 0th term is nonzero

so you have to write it instead of the 6th

[fair moat]

ah okay yeah I got it thank you

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[hollow loom]

numbers less than 4000 are formed (4 digits, 3 digits, 2 digits and 1 digit) from the numbers 1,3,5,8 and 9 without repetition. how many of them are odd

[acoustic forum]

!status

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What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

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[supple oak]

can someone solve this step by step 🙏

[vapid barn]

First take the reciprocal of both sides

Actually hold on a sec

What are you trying to solve for

[supple oak]

for x

[vapid barn]

Ok

First take the reciprocal of both sides

[sharp thunder]

that works but the traditional method is to make common denominator

[supple oak]

does -3/8 become -8/3 or 8/-3

[sharp thunder]

thats the same thing

i write -8/3 though

[supple oak]

but what if im doing like a proportion

[sharp thunder]

what do you mean

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[prisma panther]

How would i start doing this question?
I looked at the worked solutions and regular answers but couldn't find anything on it. I don't understand what w is meant to be

[twilit leaf]

are you familiar with the concept of a root of unity

[willow sedge]

to start with, you should know that w^3=1

[prisma panther]

oh is that it

bro then thats simple

thx

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[zealous rose]

I need help with question 17

[zealous rose]

so what now?

is it able to be simplified?

[rugged void]

yes

112 = 16 x 7

[zealous rose]

so we simplify it down to 4 and 7?

[rugged void]

mhm

we get

[zealous rose]

like this?

[rugged void]

ah

already

yes

you can cancel a bit more

to get

oops i meant pm

[glossy valve]

ren

[zealous rose]

I'm not taught that yet but thanks

bye

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[restive quiver]

<@&286206848099549185>

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[restive quiver]

mb mb

will som1 please answer tho

[grave elm]

hmmm

Why do I feel like no such number z can exist

at least i cant think of any

oh wait absolute value...

my bad

Well if you divide 2 complex numbers, what happens with the magnitude?

@restive quiver

[restive quiver]

ummm

it becomes less?

[grave elm]

there is a specific relation between |a/b|, |a| and |b|

do you know this relation?

[restive quiver]

no sorry i have no clue bout it yet

[grave elm]

What about division in polar form?

Do you know how that works?

If you really haven't heard about any of this, you can just try plugging in z = x+iy, and trying to get the real and imaginary component oz (z-5i) / (z+5i)

but it will be a lot of work

with something like this it would be much easier

[restive quiver]

imaginary reflection?

[grave elm]

specifically the division part of that

[restive quiver]

wdym subtract angles

can you articulate

[grave elm]

First of all, have you ever heard of the fact that if 2 complex numbers a and b get multiplied, their arguments (angles) add, and their magnitudes multiply

If not, then i think we cant work with this, which is kinda shame, but its possible to do it without it

[restive quiver]

can you do the part in which you said that it is gonna be a lot of work

[grave elm]

Okay nvm, if you've never heard of these intuitive meanings, then just plug in z = x + iy, and try to simplify the expression as much as you can

[restive quiver]

i can do a little bit of hardwork

then waht

[grave elm]

You should be able to get real and imaginary component of (z-5i) / (z+5i)

then you can get expression for magnitude

and basically get an equation

then you can find the relation between x and y, that would satisfy it

and thats your answe

it might be too much of a work though

[restive quiver]

idk the other things too tho

the 'intuitive meanings' haha

@grave elm can you type th solution in the way you originally intended to?

just type it here I'll try to understand it later

[grave elm]

Okay so

when 2 complex numbers a and b are divided, the magnitude of result corresponds to |a| / |b|

meaning that |(z-5i) / (z+5i)| = |z-5i| / |z+5i|

and if |z-5i| / |z+5i| = 1

then |z-5i| = |z+5i|

now this should be fairly simple to either imagine, or solve

@restive quiver this is the outline to the 2nd solution

solving |z-5i| = |z+5i| should be trivial enough, it's basically just writing z as x+yi, and then comparing the magnitude expressions

[restive quiver]

@grave elm im getting y equal 0

[grave elm]

thats correct

[restive quiver]

that means x axis?

[grave elm]

mhm

[restive quiver]

right?

[grave elm]

yes

[restive quiver]

okeh lemme check it real quick

wow

@grave elm

you're correct

thank you so much bro

[grave elm]

yw

[restive quiver]

and i also understood it

[grave elm]

cool

[restive quiver]

the above solution

[grave elm]

this also works for multiplication btw

|a*b| = |a| * |b|

[restive quiver]

yea yea i just recalled it

[grave elm]

cool

[restive quiver]

i had learned these

i jusr forgot

hehe

thanks again

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[fresh vessel]

If there are N people who give ratings on a scale of 1-10 (inclusive, non-integers allowed), what is the largest possible difference between the arithmetic and geometric means?

[fresh vessel]

Just based on intuition, I would assume the ratings would contain only ones and tens, and at least one of each.

Largest I could find by just guessing at some values was with the ratings 1, 10, 10. Means being 7 and ~4.642, with their difference being ~2.358.

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@fresh vessel Has your question been resolved?

[fresh vessel]

Doing a brute force search of every possible combination of ratings up to 10 people gave me a better solution of 1, 1, 10, 10, 10, with a difference of ~2.419.

And for every N up to 10, the highest possible difference for that N is by using only ratings 1 and 10.

2: 1, 10
3: 1, 10, 10
4: 1, 1, 10, 10
5: 1, 1, 10, 10, 10
6: 1, 1, 10, 10, 10, 10
7: 1, 1, 1, 10, 10, 10, 10
8: 1, 1, 1, 10, 10, 10, 10, 10
9: 1, 1, 1, 1, 10, 10, 10, 10, 10
10: 1, 1, 1, 1, 10, 10, 10, 10, 10, 10
```So I assume I'm correct in the solution only having ones and tens.

A geometric mean can also be calculated by taking an average of the logarithms, so I could alternatively average zeroes and ones for calculating the geometric mean.

So the differences of 1, 1, 10, 10, 10 and 1, 1, 1, 1, 10, 10, 10, 10, 10, 10 are the same.

So it's a question of the ratio between 1s and 10s...

[warm abyss]

Assuming we only have k tens and n-k ones we get that if we maximize AM-GM we get k = n * gamma with gamma being a constant roughly equal to 0,6

[fresh vessel]

Looks like something like that, yes.

[warm abyss]

Of course you'd always have to decide if you take 1 less or 1 mor tens

You'd only need to show that the optimal solution does only contain 1s and 10s

[fresh vessel]

Hmm?

I mean, even assuming it does, where'd you find the answer?

[warm abyss]

The one with the ratio?

[fresh vessel]

You said the constant is roughly equal to 0.6, but what is it exactly?

[warm abyss]

Something disgustingly irrational, if I didn't make a calculation error

0,592

[fresh vessel]

Hmm

[warm abyss]

This tends to happen a lot though

[fresh vessel]

I think showing that the optimal solution only includes 1s and 10s is to show that for any set of ratings that includes other ratings, the difference could be increased by changing a rating to a 1 or a 10.

[warm abyss]

Yes

Mhhh, why did it autocorrect that 🤔

[fresh vessel]

But I think I'm happy with just a vague understanding that it is so.

[warm abyss]

Where is this question from?

[fresh vessel]

I just made it up.

[warm abyss]

Cool idea

It might be interesting to know the maximum difference, too

[fresh vessel]

Can't wait for it to be e or something.
Trying to figure out the formula of the difference if I know the ratio right now.

[warm abyss]

From my calculations we get about 2.41 as the limit

If we only have 1s and 10s

And I didn't do any algebra mistakes

[fresh vessel]

1, 1, 10, 10, 10 was already >2.4189

[warm abyss]

lol

2.4189 is the continuation

[fresh vessel]

I mean, wouldn't you round your answer to 2.42 then, especially if talking about the upper limit.

[warm abyss]

Oh, now I realize

0.592 is probably the gamma, which is already incredibly close to 0.6, which it is here. Therefore, the values are so close

[warm abyss]

My mistake 👍

[fresh vessel]

With the optimization of it only being 1s and 10s, I can brute force check a very large number of participants.
I might arrive at it eventually, but I'm curious how you arrived at 0.592?

[warm abyss]

I made the formulas for AM and GM in terms of k (number of 10s) and then simply took the derivative

[fresh vessel]

Oh yeah.

That makes sense.

[warm abyss]

Setting it equal to 0 I got k = n*gamma where gamma was a disgusting term containing some logs

Cool question 👍

[fresh vessel]

Yup, I arrived at the same result, and brute forcing it got me a difference of 2.4195910495294894 with 57554 ones and 83519 tens. (As far as I checked. I know it gets more precise later.)
Cool.

.close

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[wicked cliff]

why is 0.5?

[granite torrent]

the intervals are of length 0.5

[wicked cliff]

why

[granite torrent]

because the differences of the interval endpoints 3 - 2.5 = 2.5 - 2 = 2 - 1.5 = 1.5 - 1 = 1 - 0.5 = 0.5 - 0 are all the same value

[wicked cliff]

How i can integrate that?

[granite torrent]

you don't

the problem asks you to find the riemann sum

[wicked cliff]

but supponse i want find

that function

[granite torrent]

have you been taught how to integrate yet?

also it is a coincidence that the riemann sum happens to equal the integral in this case; generally, this will not be true

[wicked cliff]

this

[sharp vortex]

but this is not what question asks you to do

[rugged void]

dam

[wicked cliff]

I know but i want find that rieman sum

[rugged void]

*Riemann

[granite torrent]

it looks like you are integrating

a riemann sum over 6 intervals is not the same as what you are doing

you see the limit n --> infinity you wrote

that is indicative of infinite intervals (so you are effectively making an attempt to fully integrate)

[wicked cliff]

yes

i want use that method

but i wrong because is 9/2

[sharp vortex]

it is not a method for that question

riemann sum does not equal to integration

[wicked cliff]

I know, I'm just practicing Riemann sum, I want to apply that method

[wicked cliff]

wdymn

[rugged void]

...?

[wicked cliff]

What did I do wrong in that integration? I'm not get 9/2

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@wicked cliff Has your question been resolved?

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[quick summit]

I don't understand part b and c

I hope the image is clear!

!status

[full forum]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[quick summit]

2

[glacial pasture]

where are you stuck

[quick summit]

part b

[glacial pasture]

have you done anything

[quick summit]

i tried

equating

y=-3x+7

since curve c intersects with the line

but that just 0=0

[glacial pasture]

equating?

[quick summit]

so im thinking about integrating but not sure

[quick summit]

y1=y2 yeah

f(x) = g(x) basically

[glacial pasture]

finding C has nothing to do with the straight line or integrating

[quick summit]

so integrate>

?

[glacial pasture]

i said no integrating

[quick summit]

oh

[glacial pasture]

two words : vertex form

[quick summit]

uh

sqaure it?

[glacial pasture]

?

what is 'it'

[quick summit]

idk what the vertex form is

[quick summit]

(-3x+7)^2

[glacial pasture]

y=a(x-h)^2+k, vertex is (h,k)

[glacial pasture]

it has nothing to do with the straight line

[quick summit]

whats a

vertex

like the midpoint

?

[glacial pasture]

its the extremity of the parabola, its max/min point

[quick summit]

oh

so i plug in the values of Q

into the formula

whats a tho