help-28

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@willow elk Has your question been resolved?

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@willow elk Has your question been resolved?

[willow elk]

still stuck

[torn jolt]

Well the first thing I don’t understand about this exercice is everyon has to go in a room but it doesn’t say taht the capacity of room is 1

Like basically

Do we suppose

1 room= 1person??

Because I think we don’t suppose that and we suppose that basically they can fit k people into 1 room as well which would mean

Using

Binomial k among m I guess

Yeah that’s it you definitely have to apply
$k!/(m−k)!$

Like here’s how to find it in case you forget about it

Draw four doors, so m=4

Now take a k inferior to m, lets say three

Wait I don’t have the formula lmao

[willow elk]

Well, it seems that any number of people can get in a room. they can either get in 1

or can be 1 person in each

[torn jolt]

Yeah yeah I got it now

Here’s like for m=4 and k=3

[willow elk]

my solution was m * (1 - 1/m) ^k, but im sure its wrong now. But i dont know how to get to the correct path

[torn jolt]

You have basically either 1, 2 or 3 doors left

Why would you have 1-1/m that seems a bit foolish since it would cancel out your entire formula

[willow elk]

i mean, my logic was that 1-1/m is the chance that a room is empty

since for 1 person 3 rooms, a room has 2/3 chance he wont go there

[torn jolt]

Oh oh please write with parentethis

[willow elk]

?

[torn jolt]

Like

1-(1/m)

[willow elk]

o, ok

[torn jolt]

Well I guess it’s my bad bc you didn’t write it WRONG

I’m just bad at seeing math on text

[willow elk]

but yea, I supposed that(1/m)^k is the chance of a room being empty for k people

I then multiplied it by m rooms

[torn jolt]

Hmhmhmh

Lemme think abt that proposition

[willow elk]

but im looking for Expected value, so it seems this is not the way

[torn jolt]

What do you guys call expected value ?

[willow elk]

• Expected value E(X) = x1p1 + x2p2 + · · · + xnpn =Pni=1 xipi, where X is a randomvariable, xi - value (output) of random variable X, pi- probability of xi

[torn jolt]

Okkkk I think I get it

Just give me some time

[willow elk]

I feel like I need to have the number of ways I can distribute the people in m rooms. which would be m^k.

[torn jolt]

This is two years program lol I totally forgot about it

[willow elk]

but something is missing

[torn jolt]

I think it might be combinatorics

Like

[willow elk]

ok, thx

[torn jolt]

(K among m)

[snow hound]

Hey i need help with a school work

[torn jolt]

Go to another channel this one is taken ^^

Good luck tho

[snow hound]

Okay

[torn jolt]

Hmhmhm it sucks that the experience isn’t binomial man

I like applying

Nxp

Lol

[willow elk]

not sure whats that?

[torn jolt]

Just Bernoulli stuff lmao

Let’s see what are the settings of P tho

[willow elk]

potentially, We have E(X) = X1 + X2 + X3....XN

[torn jolt]

No …

[willow elk]

why?

[torn jolt]

$E(X)=x1×P(X=x1)+x2×P(X=x2)+...+xn×P(X=xn)$

[willow elk]

we have rooms, each room can either have some amount people or be empty

[torn jolt]

Is the way I learnt it

[glossy valve]

ಠ_ಠ

[willow elk]

what do you mean by P( X = x2? )

[torn jolt]

Let me try it but what I would do is this :

We put down N such as N= number of doors taken

X=1-N

Then

N=(k among m)

[torn jolt]

It like this:

P is for probability

X is for the discrete variable

[willow elk]

hmm

ok

[torn jolt]

Idk if I’m doing the good thing tho 😭

What year are you in maybe I’m off the wrong path

[willow elk]

uni year?

[torn jolt]

I’m sorry I’m so bad at math in English 😭

Ye

[willow elk]

1st year, probability and random variables atm

[torn jolt]

Ok so I think you guys are doing this kind of thing

So you’ve done Bernoulli experiences no?

[willow elk]

er

i think not

maybe mentioned but i dont recall a formula like that

[torn jolt]

It’s not a formula

Basically

It’s like ah it’s call Bernoulli trial in English

Lemme send you a link

https://stats.libretexts.org/Bookshelves/Probability_Theory/Probability_Mathematical_Statistics_and_Stochastic_Processes_(Siegrist)/11%3A_Bernoulli_Trials/11.01%3A_Introduction_to_Bernoulli_Trials

That

The thing is that it doesn’t feel like Bernoulli trial and we don’t really have settings for it

[willow elk]

hmm

but, it states that trials are independent

but are they?

each time someone enters a room, the num of people goes down

and so the number of free rooms

[torn jolt]

Yeah exactly my point it doesn’t feel like Bernoulli trial

Mb

That’s wrong

[willow elk]

why rooms occupied is same as unoccupied?

[torn jolt]

That was wrong sorry

Ok wait let me actually think about this now 😭

[willow elk]

ye, im thinking for a couple of hours now

Xi = is likely 1 or 0. Since a room can have ppl or not

X - num of empty rooms

[torn jolt]

So if we have k=1 we have X=m-1
If k=2, X=m-1, m-2

[willow elk]

E(Xi) = x(0 or 1 ) * P(room is empty) ?

[torn jolt]

The link I have my question is basically have do you apply E(X)

It’s gonna be

Something lik

X= m-(k among m) i guess ? But I need to check don’t take this too seriously rn

[willow elk]

ye, im also looking

[torn jolt]

No that can’t be it

[willow elk]

in how many ways we can put k people into rooms so that 1 room is empty?

[torn jolt]

Into k! But we’re not interested into how many ways we can put them or I misunderstood maybe

For me the question doesn’t ask the amount of ways

It’s just asking

How many rooms are left I guess

[willow elk]

how many would be empty

[torn jolt]

And then idk what you guys do for E(x) 😂

So first thing we know is that the maximum amount of rooms we can use is m-(m-k) I think

But again I need to check

Waif what the F did I just say

Lmaoooo

It’s really just m-k lmao

[torn jolt]

I’m thinking reverse so this is pretty much the amount of rooms they are using

Which is k normally

I’m just complicating things stupidly in my mind sorry

[willow elk]

well my brain is melting and i dont know how to go on atm

[torn jolt]

Haha same I’m working on 4hrs sleep premed exams in two days and this is program I’ve done two years ago 😭

Well I did it again with the independent variables last year

But I forgot all abt it

Ngl

I don’t think it’s complicated I think we’re just thinking too much at this point 😂😭😭

[willow elk]

our random variable is a sum of random variables

number of ways to put speople in which ith room is empty

for Xi

how can i write this?

[willow elk]

well I havent arrived at any definite solution, so if anyone can enlighten me would appreciate it

[willow elk]

bump

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[still lance]

Bois i need help

Can you guys help me plss?

I'm not good at math

[torpid raft]

.close

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[charred meadow]

please help sketch

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[stiff swan]

I need help with this I don't know where to start

[hollow herald]

standard integral: substitute t = u/2 and refer to derivative of arctan x

[stiff swan]

v = u^2+4
dv = 2udu but there is no 2u

[stiff swan]

where did you get u/2

[hollow herald]

$I = \frac{1}{4} \int \frac{1}{\left(\frac{u}{2}\right)^2 + 1} , du$

[glossy valve]

Arya

[hollow herald]

that's where

^^"

[stiff swan]

v = u/2
dv = 1/2 du but there's no 1/2

[stiff swan]

can I split the 1/4 into two then put the other inside the integral?

[hollow herald]

sure

[stiff swan]

now i got integral of 1/v^2+1 dv

[hollow herald]

that's the anti derivative of arctan v if you remember the standard integrals?

or you could attempt to substitute v = tan θ

[gritty rose]

,w diff arctan(x)

[glossy valve]

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Requested by riemann#2529

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[torn jolt]

If I have an equation y = x^2 + x
How can I determine the equations of the tangents that cross (0, -1)?

[vast fossil]

Let's say the tangent is at some point x = a, what would its slope be?

[torn jolt]

What do you mean by x = a?

[vast fossil]

Let's take some point (a, f(a))

Where a is just a number

Could be 1, 2, 3.75, anything

The slope at that point would be 2a + 1, right?

Because f'(x) = 2x + 1 in this case

[torn jolt]

Yep.

[vast fossil]

And f'(a) = 2a + 1

[torn jolt]

derivative of x^2 = 2x and the derivative of x = 1

[vast fossil]

So the tangent line at that point is y = (2a + 1)x + c where c is some number, right?

We want this line to also pass the point (0, -1)

So the equation -1 = (2a + 1)*0 + c has to be true

So c = -1

And the tangent line is y = (2a + 1)x - 1

And there's only one thing remaining that we need to make sure of

The line y = (2a + 1)x - 1 has to pass the point (a, a^2 + a)

So we need to solve for a in a^2 + a = (2a + 1)a - 1

Do you need help with that or?

[torn jolt]

so

a^2 + a = 2a^2 + a - 1
a^2 = 2a^2 - 1
a^2 - 1 = 0
a^2 = 1
a = +-1

?

[vast fossil]

Yeah

Meaning there are 2 tangent lines to y = x^2 + x that cross (-1, 0)

It's 3x - 1 and -x - 1

[torn jolt]

Cool, I think I understand everything. But why did you call the point (a, f(a)) and not (x, f(x))?

[vast fossil]

Because we need one stationary point

x is a variable so (x, f(x)) could mean more than 1 points

Instead I just defined a constant number called a

[torn jolt]

Okay cool, thanks!

.done

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[desert tusk]

Determine a factored expression to represent the shaded area of the circle below.
Would it be π(8x^2+10x+3)

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@desert tusk Has your question been resolved?

[hardy jewel]

yes

correct answer

[desert tusk]

ok thank you

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[torn jolt]

Hello. Could someone please assist me with this question?

[torn jolt]

I have done something but I doubt that it's correct

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@torn jolt Has your question been resolved?

[torn jolt]

Ohh

I saw my mistake in the last line. I hope there's no more mistake. If there is, feel free to reach out to me. Thank you!

I don't think it can be simplified any further

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[frozen coral]

can someone explain where did the (-1)^k go?

[torn jolt]

Factored

It's on the far left

[glass crystal]

that is indeed it

[torn jolt]

Oh hi Benjamin

[glass crystal]

hi

[torn jolt]

Good to see you around

[frozen coral]

but isnt that from here?

[glass crystal]

try to expand the second line

and see what you get

(you should get the first line)

[torn jolt]

Notice how there are brackets in the second line

Meaning it is for both terms

[forest quail]

yeah

[forest quail]

just notice the brackets

[frozen coral]

oh yea i see thanks guys

[forest quail]

can you close

[frozen coral]

ok

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[forest quail]

what more do i need to use cauchy schwarz inequality

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[sharp flame]

That is the most AMGMHM set up I've ever seen tbh

Not sure though

[forest quail]

problem is that i don't know the value of a,b,c

[sharp flame]

Have you tried multiplying it out and seeing if you get a pattern

[forest quail]

tried

[forest quail]

got this

oh yeah

1<=a,b,c<=2

ok found max

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[harsh flame]

|u| - 19 < -11

[harsh flame]

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[wheat talon]

Let $G = (V, E)$ be a 3-regular connected simple graph embedded in the plane, with $f_4$ faces of degree $4$ and $f_7$ faces of degree $7$, and no faces of any other degree.\

1. Show that for any such graph there is a $a \in N$ such that $f_4 = 6 + a$ and $f_7 = 2a$.\
2. Give an example of such graph with $f_7 = 2$. \
3. Give an example of such graph with $f_7 = 4$.\

[glossy valve]

RockLEE

[wheat talon]

I dont know how to get started on 1)

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[proven ravine]

how is a 0?

[unkempt spire]

Try visualizing the integral

Imagine an area with no length. What would the area be?

[proven ravine]

@unkempt spirethank you

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[fluid plover]

tino conducted a survey of all the eighth graders in his high school for his math project he asked each student how much he or she spent on school supplies at the beginning of the year round to the nearest dollar he also calculated the average amount spent and found it to be 15.50 unfortunately it rained on the day he bought the graph to turn it in in the last bar smudged what is the height of the smudge bar

[fluid plover]

Hello

I need help

tino conducted a survey of all the eighth graders in his high school for his math project he asked each student how much he or she spent on school supplies at the beginning of the year round to the nearest dollar he also calculated the average amount spent and found it to be 15.50 unfortunately it rained on the day he bought the graph to turn it in in the last bar smudged what is the height of the smudge bar

I don’t know what to do.

[vapid knoll]

im vorkin on it

[fluid plover]

Oh ok sorry

[vapid knoll]

it is 6.5

[fluid plover]

Ok may you ask on how you got that?

Show*

[vapid knoll]

ok

18 + 20 + 21 + 22 + 18 + 16 + 8 + 10 =

133

there are 8 numbers so I divide it by 8

[fluid plover]

Mmh

[vapid knoll]

an get 16.625

then i ad 6.5

det er 9 nummere så jeg deler det på 9

18 + 20 + 21 + 22 + 18 + 16 + 8 + 10 + 6.5 =139.5

[fluid plover]

Wait how did you get 9 again?

[vapid knoll]

i add 6.5

18 + 20 + 21 + 22 + 18 + 16 + 8 + 10 = 133

but wen i get 6.5 i add it

18 + 20 + 21 + 22 + 18 + 16 + 8 + 10 + 6.5 =139.5

[fluid plover]

Oh ok

[vapid knoll]

139.5 divided by 9 is 15.5

[fluid plover]

Ok

[vapid knoll]

do you understand?

[fluid plover]

Wait but isn’t 16.625+6.5 23.125

[vapid knoll]

yes

but 133 : 8 = 16.625

139.5 : 9 = 15.50

[fluid plover]

Ohh

[vapid knoll]

do you understand

[fluid plover]

Yes ty

[vapid knoll]

np

you shod .close

.close

[fluid plover]

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[autumn anchor]

What is state diagram of 3 inputs and 3 outputs real quick?

[autumn anchor]

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[whole dragon]

Will the half-range Fourier Series (sine) of sinax or sinx be 0?

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[severe laurel]

sorry wrong channel

[whole dragon]

Did I do it right?

[stiff musk]

isn't a half range series supposed to be integrated over only half of its period?

[whole dragon]

yeah. but the given limit was that. Did I do it wrong? I am new to this

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[whole dragon]

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[woeful moon]

How would I solve question number 4

[wicked drum]

It's D, sending an explanation, wait

[woeful moon]

Ok

[woeful moon]

Can you explain why the tan turns negative

[clear lily]

tan(-x) = -tan(x)

[wicked drum]

It's a property:

tan(-A) = -tan(A). Looking at the graph of tan x you can verify this

[woeful moon]

Thank you

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[kind siren]

is sec (x) = cos(-x)?

[woeful moon]

No

[kind siren]

why

[buoyant tinsel]

cos(x) = cos(-x)

[woeful moon]

Sec(x) is equal to 1/cos(x)

[kind siren]

alright

what about

1/sin(x) = sin^1(x)

are they equal?

[woeful moon]

Did you mean the - 1 power

[kind siren]

yes

mb

as in the inverse

[buoyant tinsel]

sin^-1 is notation for arcsin

You’d want to wrap it in paranthesis

[kind siren]

alright

but would you say theyre equal to one another?

[buoyant tinsel]

Wdym?

[kind siren]

1/sin(x) = sin^-1(x)

those two values

would they be equal?

[buoyant tinsel]

No, 1/sin(x) = (sin(x))^-1

[kind siren]

its not to the power of -1

its the inverse of sin

its written like

sin^-1(x)

[buoyant tinsel]

Oh well then they are not equal

If it was power of -1, they are equal

[kind siren]

ok

what about

f(x)=-3 csc (3x) + 1

is that an even or odd?

[buoyant tinsel]

You should try doing these yourself first

[kind siren]

i did try

and I got it as neither

but I want to make sure

as im struggling with some of these concepts

I get the method

but this one is a bit tricky

@buoyant tinsel

so am I correct?

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[crude python]

Is this correct so far?

[ivory cairn]

what are you trying to do?

[crude python]

Convert 20 which is 95% to 80%

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[novel apex]

How do I continue to the next step?

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[ocean crest]

P(1/3 ,2sqrt2/3 find cos t ,sin t ,tan t

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[ocean crest]

<@&286206848099549185>

[ocean crest]

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@placid mesa Has your question been resolved?

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[astral sinew]

.reopen

Solve the inequality 1/n! < 1/600

Using the fact that this is a strictly decreasing sequence

This turns into n! > 600, or n>=6

,w sum_k=0^6 1/k!

[glossy valve]

Results provided by WolframAlpha

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

Requested by Mr. Gamer#6658

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[cursive vale]

How they got ast value

They have written direct ans can u pls explain the steps

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<@&286206848099549185> hi

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[whole dragon]

How do I put the limits after this? What's e^infinity?

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[whole dragon]

<@&286206848099549185>

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@whole dragon Has your question been resolved?

[torn jolt]

see that it is e^{-mx}

it becomes 0 when you put infinity

[whole dragon]

oh I see

thank you @torn jolt

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[bitter acorn]

I know the notation [2; 1, 2, 1, 1, 4, 1, 1, 6, 1, 1, 8,...]

<@&286206848099549185>

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[bitter acorn]

oops

.reopen

[timber oriole]

you need a new channel

[bitter acorn]

realised

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[plush nebula]

*10 0 5
0 0 0
5 0 5

[plush nebula]

is this closed ?

if the subgroup = G {0,5} is under multiplication modulo 10

i mean it conatains all the element of G but

[rare dock]

this question is confusing...

[rare dock]

are you asking if this defines a group?

[plush nebula]

closed in subgroup

[rare dock]

subgroup? are you implying it's a group?

[plush nebula]

ye

[rare dock]

is there like an original question lol

[onyx glen]

... there probably is

this is a http://xyproblem.info/ moment

[plush nebula]

well

from what i understand

[onyx glen]

0, 5 ∉ U(10)

[plush nebula]

i need to get the relative prime of U(10) which is <5> and the elements of it is {0,5}

[onyx glen]

no

bad

[plush nebula]

then how

[onyx glen]

"the relative prime of U(10)" is a meaningless phrase

and 5 is not coprime to 10

[plush nebula]

so 7

[onyx glen]

the numbers less than 10 that are coprime to 10 are 1, 3, 7 and 9

you cannot get away with listing only one

[plush nebula]

oooooh

i guess i need to read more

thanks for the help

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[sturdy sparrow]

Need help for i I forgot last proof

[full forum]

Please don't occupy multiple help channels.

[torn jolt]

hi

B = 180 - A + C

A + B1 = D
C + B2 + D = 180

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[iron skiff]

i need help understanding this

[tight glen]

do you know how to isolate x?

[iron skiff]

like slove for x

[tight glen]

yes

[iron skiff]

?

[tight glen]

okay so

[iron skiff]

yes for other questions

[tight glen]

have you tried anything so far?

[iron skiff]

i was do 1.2 times

the 6

[tight glen]

what is the specifically difficult for this one?

[tight glen]

ye, what did you get?

[iron skiff]

it has 1.2

7.2

[tight glen]

ye

so, you have x-0.8=7.2

right?

[iron skiff]

do 0.8 on both size?

[tight glen]

add 0.8 on both sides

yes

[iron skiff]

is it adding

nvm

it sub

i got 6.4

[onyx glen]

do you have work to show or did you attempt to do it in your head

oh, wait, no, that's that one step you screwed up

7.2 + 0.8 is not 6.4

[tight glen]

they subtracted

[onyx glen]

bad work layout => mistakes

[iron skiff]

the answer is 8?

Is this correct

[digital needle]

Yes

[iron skiff]

what about my other on

[iron skiff]

this one

not same question tho

[digital needle]

Umm

Can you send the original question?

And your answer?

[iron skiff]

my answe is x=96

[digital needle]

$0.2x-1.8=21/+1.8$

$22.8=0.2x/:0.2$

[glossy valve]

Doctor beak

[digital needle]

Did I miss anything?

[iron skiff]

no

[digital needle]

Well then I believe you are wrong

Let's retrace your steps

[iron skiff]

yes pls

[digital needle]

What's the first thing you did?

[iron skiff]

okay that hard for me explan

in text

but in vc is easy for me to tell what i did

[digital needle]

Ok

Let's enter vc then

[iron skiff]

which one

[digital needle]

#8kbps

[iron skiff]

ok

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[kind ledge]

When does rolles therom not work?

[kind ledge]

I'm confused about if f(x)=x^(2/3)-x^(1/3) works.

[torn jolt]

Rolles theorem does not work when the function is not continuous and differentiable.

[kind ledge]

so if you can't turn it into a derivative?

and it does not go on forever?

[torn jolt]

Rolles theorem can be applied to the function f(x)=x^(2/3)-x^(1/3) as it is continuous and differentiable.
If the function cannot be turned into a derivative and does not go on forever, then Rolles theorem cannot be applied.

[kind ledge]

How would you solve for C then? since the numbers it gave for A and B are [0,1]

[torn jolt]

like the usual way

we are bothered about the differentiability in (0,1)

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@kind ledge Has your question been resolved?

[kind ledge]

so c would = 1/8?

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@kind ledge Has your question been resolved?

[kind ledge]

Does A and B have to be the same?

[torn jolt]

no lol, else its meaningless

[torn jolt]

yea

[kind ledge]

so you do not need to find the min and max?

[kind ledge]

I mean try to find a amount between the min and max that makes it 0?

[kind ledge]

I kinda get it right now

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[jade timber]

I need to make password with 6 signs it can have {2 3 5 8 e f v}

How many password there are with letters or numbers not repeating or with last sign being number

[jade timber]

I tried doing
7x6x5x4x3x2 + 7x7x7x7x7x4 - 7x6x5x4x3x2
But I had few similar and i think its wrong

I think my way of thinking about what to remove is wrong

[wild sleet]

you just need one term

[jade timber]

I am not sure I understand

[wild sleet]

like, 4×6×5×4×3×2

[jade timber]

Okay but could you elaborate why if possible i would like to understand

I think i do but would like to be sure

[wild sleet]

last one must be number, so you start with 4, and then the rest is normal

[jade timber]

Okay

[wild sleet]

like, it doesn't matter that the condition is on the last character

[jade timber]

Yeah makes sense thanks

[wild sleet]

if it said second character must be number or fifth character, it's the same result as first

[jade timber]

Okay but why would i take from 6x5x4x3x2 and not 7x6x5x4x3

Okay i got it you take it right away and that 7 basically becomes 6

Thanks a lot for help

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[clear lily]

is there an argument for 2 dimensional?

is there a base such that it is 2 dimensional

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[rustic coral]

I have a math test in a few hours anyone willing to help me? <@&286206848099549185>

[spice orchid]

Help you on the test while you're doing it?

[rustic coral]

No help me prepare for the test

Sorry for wording it wrong.

[spice orchid]

If you have specific questions, send them

[rustic coral]

Do we just multiply straight across and then simplify if possible?

[gritty rose]

Correct

a/b * c/d = (ac)/(bd)

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[iron skiff]

help

[tight glen]

what have you tried?

[iron skiff]

i was to the times'

fo like

so like i mean is 2 time 5.25

then add 1.7

do the same on both sides

then divid

.colse

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[sterile swift]

do I need separation of variables here

this is occupied but if you open a new channel I can answer it for you

[timid zealot]

i swear i clicked help

sorry

[sterile swift]

or not because the x is multiplied by the dy/dx

ur good haha

happens

[cold quarry]

add 3y to both sides

then multiply both sides by dx

[sterile swift]

but don't you have to integrate?

like wouldn't it be xdy and 3ydx

[cold quarry]

divide both sides by x and both sides by 3y

then integrate

[sterile swift]

ah I see

so then I have 1/3ln(y) + c1 = ln(x) + c2

I can probably solve that more fully

thank you!

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[rain vapor]

May someone tell me if B is the correct answer? The answer sheet said A was the correct answer. However i dont understand how they got A.

[rain vapor]

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[cold quarry]

i get B

[rain vapor]

thank you

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[weary mountain]

I got a bit of a dumb question, but its confusing me, so I gotta ask it.

I need to find the derivative of g(v) = av + b/v, to get the derivative of the term on the right is simple enough, but for the term on the left, I am thinking that I should be using the product rule. However, the solution appears to just keep v and trash a, can anyone fill me in as to why just v is the correct derivative of av?

[weary mountain]

(any help would be greatly appreciated, as my brain is already melted)

[clear lily]

no need for product rule

theres only constants

you could write $g(v) = af(v) + bh(v)$

[glossy valve]

Gijs

[clear lily]

where f(v) = v and h(v) = 1/v

[weary mountain]

so that does kind of help, but the derivative of a constant is supposed to be 0, no?

so wouldnt one of those constants turn into 0 and basically cancel out the other? (0*v or a*0)

[clear lily]

if you used the product rule nothing would go wrong exactly

but you dont need to

[weary mountain]

ah, okay sounds good. Maybe I'll just do that and stick to what I know then. Thank you @clear lily, I appreciate your help

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[bronze sigil]

I'm not sure what im doing wrong here

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[latent hinge]

on the first line you need to take sin(46.4) instead of dividing by it

[bronze sigil]

yeah i just didnt write sin by accident

the calcualtions account for that

358sin(46.4)/534

and then i took the inverse of that to find angle B

so arcsin(.4855)=29.044

[latent hinge]

yeah and use that to work out angle c, which would be 180 - 29.044 - 46.4

then repeat the process for the distance AB

[bronze sigil]

then I subtracted angles A and B from 180 to find angle C and then did 534sin(104.355)/sin(46.4) to find the lengt

but the answer is still not correct

534sin(104.355)/sin(46.4)=714.37

but that isnt correct

[latent hinge]

one of your sin arguments is wrong i think

104.355 should be 104.555

so try 534*sin(104.355)/sin(46.4)

[bronze sigil]

I got it.. so stupid

[latent hinge]

hope that helps :)

[bronze sigil]

thank you

[latent hinge]

easily done dont worry lol

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[versed shell]

How do I prove this identity?

[versed shell]

b, c is a d-dimensional vector, X is m*d matrix

I tried d/dX_ij b^T X^T X c = d/dX_ij sum(sum(b_j * X_jk * X_ki * c_j)) but I'm not sure how the dimensions will work out

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[tribal dune]

dont really know if im setting this up correctly

[tribal dune]

cuz when i cross multiply i dont see how i should continue (10x=12h+xh)

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[old tendon]

Hello Everyone! I got this question on my physics homework that I do not understand how to do, however I was able to get the answer. Can someone explain to me what I need to understand to solve this problem? Any equations, theorums, laws?

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[frosty geyser]

yes

[celest quiver]

proof ?

[frosty geyser]

yes do it

[celest quiver]

how?

[frosty geyser]

what have you got

[celest quiver]

I was thinking about the rearrangement inequality

I think i got it

If I supposed a≤b≤c then 1/c≤1/b≤1/a then is it possible to show a/b≤b/c≤c/a ?

<@&286206848099549185>

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[ivory moon]

Tried some vector stuff

[ivory moon]

Didn’t work

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[hollow zenith]

so why does the series diverge if the first time is n^5, but not if its n^4
I thought it would only diverge if the numerator has the same highest power as the denominator?

[torn jolt]

first one, compare with 1/n

u get like n^6/n^6 something

[hollow zenith]

because eventually I will only add up zeros so why does the limit of the sum diverge

[torn jolt]

second one is same story but compare with 1/n^2

would also get u n^6/n^6

but 1/n^2 is convergent while 1/n isnt

[hollow zenith]

what

[torn jolt]

well, the sequence doesnt necessarily dictate if the series converges or not

[hollow zenith]

but if the sequence is not equal to 0, then the series diverges right

[torn jolt]

the limit of 1/n is also 0

does that mean it converges?

[hollow zenith]

the limit of 1/n^2 is also 0

so why does this converge

[torn jolt]

yes, and it converges

well you are opening another topic of why 1/n diverges while 1/n^2 doesnt

[hollow zenith]

whatever what can I do to solve my current problem?

[torn jolt]

again, compare with 1/n and 1/n^2

using limit comparison test

[hollow zenith]

ok ill try that

[thin pivot]

woa i had no idea this diverges

[torn jolt]

use 1/n for the first series, and 1/n^2 for the second

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[nova wing]

i need some help with reciprocal functions

<@&286206848099549185>

i'm confused with how these work

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[torn jolt]

How to solve for the value of Q here? its a general chemistry kind of question but yes, resorts into mathematics.

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[vagrant linden]

hey im curious why sumation 1/n is convergent and sumation 1/n^1.000001 is divergent, i understand the math says so using integral tests, but like we are still adding numbers in 1/n^1.0000001 regardless if they are small or not, meaning at an impossibly large n we should still aproach infinity, right?

[fast peak]

well but the numbers are getting small fast enough

[vagrant linden]

but why does numbers getting smaller change anything

its still increasing

[fast peak]

do you know that eg sum 1/n^2 converges?

[vagrant linden]

ye

[fast peak]

or sum 1/e^n ?

sure those sums are still increasing

but the numbers you add are getting small really quickly

[vagrant linden]

but like, regardless if they are small, we are adding .0000000000000001 to our total

which is increasing

and we will always be adding

so we should still go to infinity

thats my thought process

[fast peak]

n^1.000..01 is bigger than n

so 1/n^1.000..1 is smaller than 1/n

[onyx glen]

hey im curious why sumation 1/n is convergent and sumation 1/n^1.000001 is divergent
you got that the wrong way around.

[vagrant linden]

oh yeah whoops

[vagrant linden]

why does this matter

[fast peak]

ok maybe I misunderstood what you meant

1/n^2 = 1/n^(1+1) and it converges even tho we "add 1 in the exponent"

more precisly it should be "it converges exactly because we add something in the exponent"

[vagrant linden]

but why does it change anything

just because we add a one, our numbers get small faster

but we are still increasing

.0000...1 is still increasing

[fast peak]

yes but the numbers are getting too small to matter

[vagrant linden]

what

too small to matter

[fast peak]

just because we are always adding stuff does not mean that we have to go to infinity

if the stuff we add is really tiny then we don't get anywhere

[torn jolt]

They are probably asking "why does 1/n diverges while, 1/n^1.0000001, that has a very small change of power converges. How can this small difference in powers change the convergence behaviour of the series". It is hard to explain it intuitively in another way than "it just does" I guess

[vagrant linden]

no regardless if n^99999 gets small fast we are still adding

in sumation

so we should get infinity

[fast peak]

no

I assume you mean the sum 1/n^99999

[vagrant linden]

oh ye

but like we still are adding

[fast peak]

the numbers are getting super tiny

[vagrant linden]

whats the difference of a super tiny number of 1/9999999999 compared to 1/9

they still add

like one is greater than another

but they still add

[fast peak]

have you seen the sum 1/2^k and seen why it converges?

[vagrant linden]

no

why does it converge

[fast peak]

well the numbers are getting small enough fast enough

but ehh I hoped you had seen that sum already

have you not seen a geometric series?

[vagrant linden]

1/n?

[fast peak]

thats not a geometric series

[vagrant linden]

then prob not

[fast peak]

1+q+q^2+q^3+q^4+...

[vagrant linden]

oh

i understand that diverges

what does this help to explain tho?

[fast peak]

it converges for |q| < 1

[vagrant linden]

oh yeah

[fast peak]

so in the case of q=1/2 we have 1+1/2+1/4+1/8+... converges

even though "we are always adding positive stuff"

but the stuff we add just gets too tiny

[vagrant linden]

but then i can ask the same question

why does it matter if its small if we are still adding stuff

why is 1/999999 any different from 1/9

they are still numbers

is the answer really just because math says so, there is no other way to understand it

[topaz valley]

q=1/2

[fast peak]

whoops

like if we have the sum 1+0.1+0.01+0.001+...

you can look at the partial sums

1, 1.1, 1.11, 1.111 and so on

with each new term we are getting bigger, sure

but we will obviously never reach 2 for example

[vagrant linden]

oh

[fast peak]

cause the numbers we add are too small

[vagrant linden]

ohhhh i see

ig that makes sense

[fast peak]

whether there is an intuitive reason why 1/n diverges but 1/n^a converges for every a>1, no clue

[vagrant linden]

and for 1/n^1.0000000001 we just barely cross that threshold of adding .01 to 1.1 (or something similar)

[fast peak]

as in an intuitive reason why exactly there is the breakpoint

[vagrant linden]

so it just kinda happens there?

[fast peak]

yeah

[topaz valley]

theres a kinda intuitive reason why the area under 1/x is infinite

[fast peak]

like you said, you can check it with integral test

[topaz valley]

but why 1/x^1.0....01 is not infinite anymore

[vagrant linden]

when math dealt with finite values it was a whole lot simpliler lol

but i have to say this is a lot more interesting

i appriciate the help this makes sense to me now

ty!

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[trail oxide]

I need help visualizing |z+i| >= |z+1| on complex plane, thanks for helping me

[trail oxide]

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[white jasper]

I don't know how to find the median?

<@&286206848099549185>

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[wild vapor]

https://www.statology.org/median-of-grouped-data/ @white jasper

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[torn jolt]

Hello

[torn jolt]

If we have a 2×2 matrix

And we know the trace of A^2021 =0

And trace of A^2022 = 0

Where A is 2×2 matrix

How can we show A^2=O2

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[ivory cairn]

what is O2?

[torn jolt]

The matrix with all values 0

[eager violet]

Woah, the future is now

[summer jacinth]

To prove that A^2 must be the zero vector we must prove that A^2021 and A^2022 cannot have values in the matrix such that they can cancel out. I think this is because 2021 is an odd power and 2022 is an even power. There's no way to have two positive numbers cancel out so A^2022 makes it such that 0s in the diagonal are the only way the trace will be zero.

By cancel out I'm meaning the sum of all the numbers in the diagonal equals zero. A^2022 makes all those numbers positive.

[torn jolt]

How do you know A^2022 makes all the numbers positive?

[summer jacinth]

A^2022 is arbitrary, it is similar to A^2 since two negative numbers make a positive

All of the other values do not matter other than the diagonal

Only entries ij where i = j will affect the trace and when you are doing the matrix multiplication they are getting multiplied by themselves.

[torn jolt]

If we show the determinant of A^2 is 0 and the trace of A^2 is also 0

It results A^2 = O2?

[summer jacinth]

Does the question ask for a determinant

[torn jolt]

No but I think we can do it with characteristic polynomial

[summer jacinth]

If it is a 2x2 matrix and the determinant is zero then it will have to have only zeros in the diagonal because nothing can cancel a singular value

Because if the determinant is zero there is a repeating row or row of all zeros

[torn jolt]

Thats not true

[summer jacinth]

If you put the matrix in reduced row echelon form only one row would have values if the determinant is zero. How would that value get canceled out when you sum the diagonal.

[torn jolt]

Matrix (1,1)
(1,1) has determinant 0 but it doesnt have any 0

[summer jacinth]

It also doesn't have a trace of zero

So that wouldn't apply

[torn jolt]

You didnt mention the trace to be 0 in this sentence and I understood wrong

So

[summer jacinth]

Sorry I was meaning in context of your problem

[torn jolt]

But if we have (-1,1)
(-1,1)

It has determinant 0

And trace 0

And doesnt have any 0

Hmm

[summer jacinth]

Yea, I didn't think about that. You're right. But, if you were to raise that matrix to the 2022 power you would get 1 and 1 in the diagonal and the trace would be 2

Do you have to use determinants in your proof?

[torn jolt]

So if we know trace of A is 0 and determinant of A is 0

We know A^2=O2

But not A

Cuz of hamilton cayley

[summer jacinth]

What class is this?

[torn jolt]

11

[summer jacinth]

11?

[torn jolt]

Yes why

[summer jacinth]

Linear Algebra 11?

I'm confused 11 what

[torn jolt]

Of course

Also calculus with Banach fixed point theroem, metrices and contractions also in 11

[summer jacinth]

I guess I just want context on how they want you to prove this

[torn jolt]

They say A 2×2 matrix with complex numbers and det(A^k-I2)=det(A^k+I2) for K in {2021,2022} and want to show A^2=O2

And I said if P(X) is char polynomial of A^k

Then P(1)=P(-1)

And we find Trace of (A^k)=0

So trace of (A^2021)= trace of (A^2022)

No?

And they are 0 of course

And here I am stuck

I want to show the det(A)=0 and trace of (A)=0

The trace part I think we can do by some induction on hamilton cayley

[summer jacinth]

Yea, I think you could parameterize this since the matrix is so small

[torn jolt]

Ok I showed determinant of A = 0