help-13

[tropic oxide]

in particular there is a function that you almost certainly know by name whose taylor series contains odd factorials in the denominator

[rugged tusk]

ok thanks, i will check it

[cedar kiln]

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[reef venture]

why is this undefined? shouldn't it be 10^100

[crimson sedge]

10^10= 10x10x10x10x10x10x10x10x10x10 so no not exactly 10^100

[reef venture]

its 10^10^10^(1/5)

[fervent mason]

$\qty(10^{10^{10}})^{\frac{1}{5}}$?

[wraith dagger]

Si Arya

[reef venture]

the question was, what is the fifth root of 10^10^10

so yeah i guess

[dense hornet]

assuming that you are using google to evaluate it, it says undefined simply just because it's such a big number

and also, the fifth root of that is not 10^100

[reef venture]

is it 10^(2*10^19)

[dense hornet]

yes

eh no, sorry misread

10^9

[reef venture]

yes 9 mb

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[quartz vale]

How do I solve $\log_{x}\bigg({\frac{5}{2} - \frac{1}{x}}\bigg) > \bigg(\frac{5}{2} - \frac{1}{x}\bigg) \newline$
I know that the domain is $x > \frac{2}{5}, x ≠1 \newline$
I have to take cases for the base, when $x > 1$ and $\frac{2}{5} < x < 1 \newline$
I am stuck at this point

[wraith dagger]

kinglacto

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[brisk thicket]

I think I may be understanding this question wrong

[reef venture]

What is the relationship between wavelength freq and speed?

[brisk thicket]

If we follow the formula that is λ = v/f, then the answer should be 2, right?

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[crystal mason]

Let (fn) be the Fibonacci sequence given by the recursive rule f0 = f1 = 1 and fn+2 = fn+1 + fn.
Show that the real sequence cn = (fn+1)/fn is convergent and determine its limit.
Hint: First show cn + 2 = 1 + cn/(1+cn) and then that the subsequence (c2n) is monotonically increasing and bounded.

How do you show that it is convergent?

[crystal mason]

<@&286206848099549185>

[weary egret]

Is it (1+√5)/2?

[crystal mason]

im asking how you show that it's convergent

[weary egret]

Well if it has a finite limit it is convergent.

[crystal mason]

obviously, but it is asking me to show that it is convergent

[weary egret]

Yes so do the ratio test.

[crystal mason]

how does that go?

[weary egret]

I'm not very good with convergence problems but if you show that a limit exists you ultimately proved it is convergent right?

[crystal mason]

i dont think so :/

[weary egret]

Why?

That's what convergence means

[crystal mason]

oh wait yeah

[weary egret]

Just use the quadratic equation x²-x-1=0

To prove the limit.

Idk about the 'proof' of convergence tho. Sorry

[crystal mason]

why?

[weary egret]

x²=x+1.
x³=2x+1
x⁴=3x+2
x⁵=5x+3

Observe how the coeff of x is the Fibonacci sequence

And how the constant term is also the Fibonacci sequence just a term behind.

x^n=(F_n x)+F_n-1

I hope i didn't confuse you. Sorry if I did

[crystal mason]

haha dw it can't get any worse

so why are we using powers tho

[weary egret]

Just so we can write x^n where n tends to infinity

Let me send you a written solution

That may help

[crystal mason]

but why do we have x^n

Sure

[weary egret]

You can have x^r or any variable doesn't matter.

It's just the r_th power of the root of x²-x-1=0 related with the Fibonacci sequence

[crystal mason]

sorry, i still dont know where the quadratic equation came from

[weary egret]

Just a method i learnt somewhere.

[crystal mason]

is there a name to that method?

[weary egret]

It's just a unique way for finding the n_th term of the Fibonacci sequence

[crystal mason]

interesting

ill give it a try

also, any ideas on the second part?

"Show c_n + 2 = 1 + c_n/(1+c_n) and then that the subsequence (c2_n) is monotonically increasing and bounded."

[weary egret]

Idk I'm very tired rn. Will try and help tomorrow if i can.

[crystal mason]

sure ok. Thanks

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[sand kayak]

1. Timo regularly puts in money in a bank account with annual interest of 3%. At the start of each year he puts in 5000kr. How much money does Timo have right after the 10th time he puts in money?

[sand kayak]

I got S=5000(1.03^10-1)/(1.03-1)=57319kr

Is it correct?

<@&286206848099549185>

[tropic oxide]

just by eyeballing the answer seems reasonable

...yeah this should be correct

[sand kayak]

Thanks!

Now i need to write a system of inequalities that is the colored area on the paper

Originally i didnt have the equations for each line

So i got them by using 2 points

And this is the system i got as the answer

Is it correct?

[tropic oxide]

seems to check out

[sand kayak]

Okay next question

Joel at 4 weeks after birth had a weight of 4300g. Under the 5th week his weight increased eith 225g. His weight will decrease by 3% each week if he follows the average weight curve the 1st year. How much will Joel weigh when he turns 1 years old?

Here i have no idea what to do

[bitter reef]

so from what I understand, at week 5 he has 4300 + 225 g weight right?

[cedar kiln]

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[sand kayak]

Yes

Exactly

[bitter reef]

weight decreasing by 3% means you take 97% (so multiply by 0.97) each year. A year has like 52 weeks so 52 - 5 = 47 weeks where he will be losing weight

but you don't get a nice number

so I'm not sure if I went wrong somewhere in my logic..?

[sand kayak]

I think we are supposed to use the formula

[bitter reef]

what formula?

[bitter reef]

,rotate 90

[sand kayak]

S=a(k^n-1)(k-1)

Idk why on discord my photos get posted the wrong way x)

This formula is for succesive addition

You can use it for counting % in a bank account if you keep on putting money in it yearly and so on

[bitter reef]

not sure how it applies here tbh

[sand kayak]

Yea but i dont have any other ideas

[bitter reef]

from what I can see all you have to do is $(0.97)^{47} \cdot 4525$

[sand kayak]

These questions are from chapter 4 and in chapter 4 we use that formula

[wraith dagger]

Doggo

[sand kayak]

Okay

The answer for that would be 1081g

If you put it in the calc

But is it realistic for a one year old to weight 1081g?

[bitter reef]

nah that's why I'm confused

[sand kayak]

Yea i think we are wrong

[cedar kiln]

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@sand kayak Has your question been resolved?

[cedar kiln]

@sand kayak Has your question been resolved?

[quiet sinew]

I think there's a word missing from the problem: if instead we take it as saying that his weight gain decreases by 3% each week then you can use that successive addition formula and get an answer around 10kg, which is reasonable for a 1 year old

[cedar kiln]

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[steel ivy]

$(5^x)-2+(5^x)-1=150$

[wraith dagger]

Bioleve

[upper abyss]

Channel is closing

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[steel ivy]

x = ln(72) / ln(5)

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[dire geode]

.close

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[proud remnant]

Can anyone tell me where the +1/3 and -5/3 came from all the way at the end

[cedar kiln]

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[proud remnant]

Please anyone

My gpa is gonna be so bad tomorrow after this test 😭

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[rocky wave]

0 <= Theta <= 360

[rocky wave]

When -8 + 4tan theta =0

So tan theta is 2

But what’s the answer to the first part

Nvm I got it

.close

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[modern compass]

@obsidian wasp How's it going?
I'm opening this to get away from that room

[modern compass]

does the factoring method make sense? any questions?

[obsidian wasp]

yeah, it does

im just doing one more question

and ill close the channel and call it quits

alright, you can close this channel if you like now @modern compass

[modern compass]

.close

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[opal sierra]

<@&286206848099549185> what do all the symbols mean and how do i figure this out with question a

[cedar kiln]

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[reef whale]

Have you done calculus before

[cedar kiln]

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[spiral topaz]

Find explicit formula for following sequence an(The n is below the a).

a1= 3

3, -4, -11, -18, -25

I'm using 3+2(n-1) formula.

But when I plug in 3 for n I don't get-4

[celest ledge]

10-7n

[glossy elm]

yes

use symbolab for these kinds of things

everything that isn't like those real life applications or word problems you can look for on symbolab

[crimson delta]

it is also kinda helpful to be able to do some things on your own

like when exams later ask for them

[spiral topaz]

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[cedar kiln]

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[wintry wren]

What does it mean by c and b?

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[rugged tusk]

converges absolutely, conditionally, diverges ?

it converges using alternating test

but i dont know if absolutely or conditionally

[tropic oxide]

the absolute value of the general term behaves as (2/3)^n

[simple shale]

there is ni variable for condition

[rugged tusk]

we are interested in highest power ?

[tropic oxide]

$\sum_{n=1}^{\infty} \frac{2^n+n^2}{3^n+n^3}$ converges by, say, limit comparison with $(2/3)^n$...

[wraith dagger]

Ann

[tropic oxide]

exponentials (2^n, 3^n) outgrow polynomials (n^2, n^3)

[rugged tusk]

ok so, then is ok use ratio test with abs value

[tropic oxide]

well you're checking for absolute convergence so yes

[rugged tusk]

ok thanks

what about this ?

again using alternating test it converges

it converges conditionally

i have tried limit comparison test with 1/sqrt(n)

and its inf

and 1/sqrt(n) diverges

am I correct ?

[tropic oxide]

yes

[rugged tusk]

thx

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[jade sable]

can anyone explain how did we get 2a?

[alpine scaffold]

what

[cosmic temple]

i am not very sure but , the 4a^2 gets to the other side and gets divided by 0. so 2a - x = 0
x = **-**2a

but again, i don't have any idea if i am right.

[alpine scaffold]

4a^2(2a-x) = 0 => a^2(2a-x) = 0

either a = 0 or (2a-x) = 0
2a - x = 0 => x = 2a

[cosmic temple]

so, i think it might be better if u showed the full problem :)

[wispy talon]

When you're multiplying 2 terms and their product is 0
Then either the first term is 0 or the second term is 0, or both
So using this, you'll get a=0 and (2a-x)=0 => x=2a

[jade sable]

Thanks

h

How did we substitute here to get -16 A3/ ( ....)2

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[jade sable]

Not yet

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[sleek sundial]

Please help me with this problem

[tropic oxide]

this is not a problem

there is no question here

[sleek sundial]

brah, wait

[sleek sundial]

that's all I got during the quiz ·_·

[tropic oxide]

so no written instructions?

[sleek sundial]

nah bro

[upbeat basin]

weird

[sleek sundial]

·_· ik

[tropic oxide]

please do not call me bro.

[sleek sundial]

..sis

[tropic oxide]

so, you haven't been given a question, yet a solution is still being demanded from you?

[gleaming cloud]

Ah, oily macaroni

[sleek sundial]

Ig so

[tropic oxide]

like it's one thing if you were asked to, say, prove that the limit exists

but you have confirmed you have not received any written instructions whatsoever

thus that cannot be the case

[sleek sundial]

Wait, ima ask if there are some written instructions or not

[tropic oxide]

well go ahead and do that...

[ionic dragon]

dont ask, submit it blank, you have vacuously aced the assignment

[sleek sundial]

Ayy, ig that's the answer they need

XD

[violet flume]

not chill

[rare schooner]

A quiz??

[rare schooner]

😂 😂

[sleek sundial]

Yup, a school maths quiz

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[teal topaz]

Could someone send their asnwer to this question

I keep getting $13883 but the textbook asnwer is $13949.62

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[dim kayak]

Can anyone help me with this?

[thick cliff]

i might be wrong but is that even possible? it doesnt have any right angle, degrees or something thats not unique?

[fair hare]

it's possible

[elder pewter]

you can calculate angles using cosine rule

$a^2 = b^2 + c^2 -2bccosA$

[wraith dagger]

IntelligentCake

[thick cliff]

yeah but doesnt cosine only apply to the adjecent divided by hypotenuse

it dont have an adjecent

[elder pewter]

that is not cosine rule

[thick cliff]

oh

my bad

[elder pewter]

I have quoted cosine rule above

this works for any triangle

[thick cliff]

cool

[dim kayak]

There's a specific formula for this case but I forgot it all :(

[elder pewter]

use the formula I have quoted

you can find angle ABC

then use that to find d

[dim kayak]

Haven't reached cosine yet

[elder pewter]

I don't see how you can do it then?

[dim kayak]

Oh

Finally

Use Stewart's theorem

Ty y'all

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[vivid void]

Hi, maybe a complex question, but is there a way to calculate every possible Euler path of this graph. Bad example, just imagine it has one 😅

[fair geyser]

but it doesn't look like it allows one?

all 4 dots have odd number of lines, 4 is not 0 or 2

[vivid void]

Yea, i just noticed. That might have been a bad example 😅. Is there a general way to calculate the amount of possible Euler paths for any graph tho?

[fair geyser]

apparently no

[cedar kiln]

@vivid void Has your question been resolved?

[vivid void]

Thank tou

You

[cedar kiln]

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[torpid cargo]

determine a 4x4 matrix F which satisfies this vector

[torpid cargo]

This is the given information.

In a computer game - such as Asteroids (Atari Inc, 1979) - the player controls a triangular spaceship in
a 2D coordinate system using the arrow keys ←, ↑ and →. Purely graphically, the spaceship looks like
as in the figure below. From a mathematical point of view, the position of the spacecraft is in the coordinate system
determined by the position of two points: the center of the spacecraft C = (c1, c2) and the tip S = (s1, s2).

.

At the start of the game, the spaceship is placed as in the figure above, ie. C = (0.0) and S = (0.1).
The effect of pressing the arrow keys ← (Left rotate), ↑ (Forward) and → (Right rotate) is:
• Pressing ← / → rotates the spaceship around its center a certain angle θ counterclockwise / clockwise.
• By pressing ↑, the spaceship is moved in parallel by the vector # »CS (the vector from C to S).

Now assume that the center and tip of the spacecraft have coordinate sets resp. C = (c1, c2) and S = (s1, s2). We
introduces the following designations:
(c
L
1
, c
L
2
) and (p
L
1
, s
L
2
) are the coordinates of resp. the center and tip of the spaceship after pressing ←
(c
F
1
, c
F
2
) and (p
F
1
, s
F
2
) are the coordinates of resp. the center and tip of the spaceship after pressing ↑
(c
R
1
, c
R
2
) and (p
R
1
, s
R
2
) are the coordinates of resp. the center and tip of the spaceship after pressing →
We collect the four numbers c1, c2, s1, s2, which determine the position of the spacecraft, in one vector (c1, c2, s1, s2) ∈ R
4
.

[cedar kiln]

@torpid cargo Has your question been resolved?

[cedar kiln]

@torpid cargo Has your question been resolved?

[vestal pilot]

it might help if you fix the formatting of your message

[cedar kiln]

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[steel ivy]

Anyone knows what I am doing wrong on my calculator?

[steel ivy]

The result is supposed to be 10800

[upper abyss]

I don't see a result. What's it giving you?

Just those [][]?

Does it need to know the variable it is solving for?

[steel ivy]

Yes

[steel ivy]

I dont think so, because I need to know T

So it would defeat the purpose

I think

[upper abyss]

Like if you typed solve(x = 1), what does it give you?

[steel ivy]

let me see

1

[upper abyss]

Maybe try the earlier equation with x? Lol

I am guessing, I don't know these calculators

[steel ivy]

I appreciate it

Same thing

grrrr

[upper abyss]

No like x instead of t

It just might be confused with t

[steel ivy]

oh ok

worked

lol

calculators are dumb

thanks I hope you become a billionaire

[upper abyss]

I will not I spend too much time on discord

But thank you I'll try

[cedar kiln]

@steel ivy Has your question been resolved?

[cedar kiln]

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[night mural]

hello

[night mural]

can I get help with this question please?

[deep heath]

If k is a root of a polynomial p(x) then (x-k) divides p(x).

[night mural]

thank you

.close

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[keen tree]

its 7.6 right? its for our practice but there is no andwer key

[leaden notch]

Alr lemme check rq

yeah

ur right @keen tree

[keen tree]

thank you

so much

/close

[leaden notch]

yea dw bout it

.close

[keen tree]

wrong command?

ooo

.close

[leaden notch]

yea

[cedar kiln]

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[desert copper]

Help

[fair hare]

,w solve help

[wraith dagger]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by Chunkin#4952

[desert copper]

My math homework needs me to explain how something increasing with 10% and then decreasing with 5% will end up with the start value, I don't know how that works (Change factor)

[fair hare]

well lets call the intial value x

increasing it by 10% would be

1.1x

to decrease it we multiply by .95

so in theory

,w .95(1.1x)

[wraith dagger]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by Chunkin#4952

[fair hare]

maybe I misread the question

how exactly does it decrease value

[desert copper]

That doesn't make sense with my homework saying that it should end up with x again (start value) but maybe it might be a trick question?

Something is being sold and the price is raised 10% and then decreased 5%

And I am supposed to calculate with "change factor"

[fair hare]

would dat be 1.045?

[desert copper]

A change factor equation here would be "1.1 × 0.95 × 1" It think

Which is the same I think

Yeah 1.045

[fair hare]

yeah I just included x instead of 1

since you are looking for the change factor I guess you can just write
1.1 × 0.95

[desert copper]

Yeah but Idk how they mean when they say that I am supposed to explain how it ends up at the start value again, maybe a trick question?

[fair hare]

can you get a picture of the question itself

maybe it's worded slightly different and means somthing slightly different

[desert copper]

I don't have a picture, I wrote it in notepad in swedish but I can translate it exactly

[fair hare]

ok

[desert copper]

Explain with change factor why it will remain the same sum when something is being raised 10% and then lowered 5%

[fair hare]

bro idk

oh wait

maybe they are rounding 1.045 down to 1 💀

[desert copper]

Oooh yeah maybe

But it's supposed to be a tough question apparently but maybe it's kinda easy

[fair hare]

<@&286206848099549185>
"My math homework needs me to explain how something increasing with 10% and then decreasing with 5% will end up with the start value, I don't know how that works (Change factor)"

,w .95(1.1x)

[wraith dagger]

Results provided by WolframAlpha

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

Requested by Chunkin#4952

[fair hare]

any idea what is going on here

we think it may be a mistake in the question or these dumbos are rounding 1.045 down to 1

[desert copper]

Yeah

It would just be dumb and confusing for them to round it down

[cedar kiln]

@desert copper Has your question been resolved?

[desert copper]

Help

[desert copper]

Auggh

[cedar kiln]

@desert copper Has your question been resolved?

[cedar kiln]

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[spare rover]

Is my solution correct? Integration by parts

[crimson sedge]

looks good

[spare rover]

Thank you

.close

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[crimson sedge]

so I graphed this, and did the math and the limit is -3 and 3

then I found out y=12-x^2 is the greater value equation (dont know if thats the correct term)

so my integral is thje limit of -3 to 3 of 12-x^2-(x^2-6) dx

so my question is, do I distribute then solve the integral?

well distribute, simplkfiy then solve the intgral lol

helpppp^^^

[crimson delta]

well not that much to distribute

[crimson sedge]

the negative size

sign

then combine like terms

I wasn't sure if to do that or not

[crimson delta]

well you don't have to but it's definitely easier

[crimson sedge]

alright so when I distribute it and ciombine like terms I get 6-2x^2 x

[crimson delta]

yes

wait no

12-(-6)

[crimson sedge]

oh yeahhh

18

I knew I was doing something wrong lol

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[hushed grail]

Hello I am doing some linear algebra but I saw this:

[hushed grail]

The reasoning for why (Q,R) is not a vector space is not consistent for the reasoning (R,Q) IS a vector space. Both of them return a rational number. But in one case it is a vector, while in the other case - it isn't.

[crimson delta]

the product in both cases is a real number

if R is a vector space over Q then a real number is a vector

but if Q is a vector space over R then a real number is not a vector

as the vectors have to be from Q

[hushed grail]

oops, I mistyped that. Ohh

Is this because Q does not contain all possible combinations of R * Q

[crimson delta]

essentially, yes

sqrt(2) * 1 is just not in Q

[hushed grail]

Are irrational numbers the only numbers which do not exist in Q?

[crimson delta]

yeah. per definition the irrational numbers are those that are not rational. irrational

[hushed grail]

Thanks

.close

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[crimson sedge]

Hello! I wish to know what is the value of sin of 11pi/3.

[tight herald]

What?

What have you tried, how your work...

This is a unit circle question isn't it?

[crimson sedge]

Is from trigonometry

[tight herald]

Unit circle, right?

[crimson sedge]

I suppose, yes

[tight herald]

I solved it in a odd way, not sure how your teacher wants you to do it

Do you know your basic unit circle stuff

pi/6, pi/4, pi/3 that sort of thing?

[crimson sedge]

I have done the following thing : wrote sin of 11pi/3 as sin of (2pi + 5pi/3) = sin 5pi/3 (because 2pi is equal to a full circle) then simply calculated sin of 5*180/3 which sin of 300 which can be written as sin of (360-60) which is in the end sin of 60 degrees which is square root of 3/2

That’s how I think is supposed to be solved though I am not really sure

[tight herald]

300 degrees is not the same as 60, not quite

Yes thats how I solved it though

Well, kinda

[crimson sedge]

I’ve got my math final tomorrow and got to revise on trigonometry and functions

[tight herald]

300 degrees is the same as -60

So it would be the negative of your solution

[crimson sedge]

Oh yeah because is in the third

Thingy

Where both sin and cos are negatives

[tight herald]

Actually forth I thought

[crimson sedge]

Wait yeah nvm for some reason considered

[tight herald]

cos will be positive

sin will be negative

[crimson sedge]

The third as being until like 360 degrees

When in actuality is until 270 degrees

[tight herald]

Yes

Til 270

[crimson sedge]

Anywho, you said your way of solving was a bit different from mine

Mind if you can share it?

Or was just the final answer that was different?

[tight herald]

I just did 660 degrees and then subtracted 360 and got 300

Then did -sin(60)

[crimson sedge]

I see

[tight herald]

which was

-sqrt(3)/2 I thinkkk

I hate trig lol

[crimson sedge]

I solved in some other way in my notebook (this is from a pretty old homework) and for some reason I divided the 11 with 3 and got 3pi and 2pi/3

I will try to find an explication to this later until then, thanks for the help!

.close

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[pale ridge]

in elimination does the first cofiecient to the left choose whether im adding or subtracting or does the one that i have the same on both equations choose? does that make since?

[pale ridge]

<@&286206848099549185>

[tight herald]

• After 15 minutes, feel free to ping @Helpers.

Context?

I get that it's elimination, but can you give an example

[pale ridge]

so lets say the x's were to the right of the y's. would i deteremine whether to subscract or multiply based on whether the ys are both postive or negative or the x?

[crimson delta]

Well if you are just blindly doing calculations you go from left to right

Otherwise you can pick whatever order you want

[cerulean onyx]

u think about whether subtracting or adding would eliminate one variable ie x or y

[pale ridge]

ok

thanks

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[long narwhal]

I’m in year 9 and our teacher is giving us year 11 work and on of our homework questions it talks about circles and diameters and radiuses and I have no clue what that means can someone help please

[long narwhal]

What does it even mean

<@&286206848099549185>

<@&286206848099549185>

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[crisp drum]

WELL

[crisp drum]

I need help with this

when i tried to solve my particular integral everything other than the exponential cancelled

[crystal raptor]

Show your work

[crisp drum]

gimme a min

apparently there should be cos2x and sin2x as well

but idk how

[astral crown]

its because you didn't get the form of the particular integral right

bsin(2x) + c cos(2x) is a solution of the homogeneous equation

[crisp drum]

oh

i see

so what would the particular integral be

[astral crown]

usually when something is a solution to the homogeneous equation, you just multiply those terms by x

[crisp drum]

the only time ive multiplied something by x was when the roots of the complementary function was same as the power of the exponential on the other side

so its the same for trig functions as well i guess

[astral crown]

if you know complex numbers, then trig functions are essentially the same as exponentials

[crisp drum]

ight thank you

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[mystic salmon]

hm

[mystic salmon]

i proved that f_n is continuous

so i can say that since f is just the sum of continuous terms f_n then f is also continuous

right?

[lilac crane]

It doesn't have to be, but it might be

When things go to infinity sometimes the normal rules for finite cases don't work

[cedar kiln]

@mystic salmon Has your question been resolved?

[mystic salmon]

is there a proof that uniformly converging series converges to a continuous function?

[lilac crane]

Yes there is

In fact uniform convergence is the ingredient needed

[mystic salmon]

@lilac crane can u send me a link for it?

[lilac crane]

Yeah sure

https://en.m.wikipedia.org/wiki/Uniform_limit_theorem#:~:text=In mathematics%2C the uniform limit,of continuous functions is continuous.

[mystic salmon]

is the function we're uniformly converging to differentiable too?

[cedar kiln]

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[mystic salmon]

.reopen

[cedar kiln]

✅

[lilac crane]

Not necessarily

But

[mystic salmon]

im my case it does

since the derivative of f'_n(x) is continuous hm

[lilac crane]

Actually, the sequence s_n(x) needs to converge pointwise, and the sequence of derivatives needs to converge uniformly

[mystic salmon]

ah ye

so i calculate the derivative

i do the sum

i check if its normally converging

[lilac crane]

Yeah, take care in your case the sequence you're checking is the sequence of partial sums

So you can in fact check differentiability of each term in the sum

[mystic salmon]

so $\sup|f'n(x)| = \sup |\frac{-n^2}{(1+xn^2)^2}| \leq \frac{1}{xn^2}$ and since $\sum{n \geq 1} \frac{1}{n^2}$ converges, then $\sum_{n \geq 1} \sup|f'n(x)|$ converges thus $\sum{n \geq 1} f'_n(x)$ is continuous

then f is differentiable @lilac crane

[wraith dagger]

alexisreen

[lilac crane]

I think you got it, sorry I'm a little slow

Oh yes

X>0

[mystic salmon]

yes

tysm

[lilac crane]

Yw

Good questions

[mystic salmon]

np

[cedar kiln]

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[mystic salmon]

hm

[crimson sedge]

?

Ur question

[mystic salmon]

let sum n > 0, f_n be a normally converging series and let g_n(x) = x^a f_n(x), a in (1/2, 1)

prove sum g_n is also normally converging over [0, \infty)

f_n(x) = 1/(1+n²x)

[wraith dagger]

alexisreen

[mystic salmon]

@crimson sedge

[cedar kiln]

@mystic salmon Has your question been resolved?

[dire geode]

this isn't a question. ask a question

[mystic salmon]

@dire geode What is this? OwO

[dire geode]

you're the one with the question, how do i know?

[reef whale]

you need to prove this?

[mystic salmon]

no thats my proof

[mystic salmon]

well i just started my sentence with -prove- so thats the demand

[dire geode]

read this @mystic salmon

[mystic salmon]

Let $\sum_{n \geq 1} f_n(x) =\sum_{n \geq 1} \frac{1}{1+n^2 x}$ be a normally converging series, and let $a \in (0.5, 1) , g_n(x) = x^a f_n(x)$ Prove $$\sum_{n \geq 1} g_n(x)$$ converges normally over $[0, \infty)$

[wraith dagger]

alexisreen

[mystic salmon]

@dire geode sounds good?

[dire geode]

You took all that effort to latex but no effort into explaining where you're stuck or even ask a question.

Explain what you've tried

[mystic salmon]

Let $m_n = \sup_{[0, \infty)} | g_n(x)|$ i've bounded $m_n < \frac{1}{n^2}$

[wraith dagger]

alexisreen

[mystic salmon]

so then i've proved that the series of m_n is converging

thus the series of g_n is converging normally

[dire geode]

that and most of your other inequalities are not true for x in [0, 1]

try treating the two intervals separately

$[0, 1]$ and $(1, \infty)$

[wraith dagger]

riemann

[mystic salmon]

its true for x > 1

[dire geode]

right. so this supremum should reflect that

[mystic salmon]

same thing

[mystic salmon]

so what i said up-here is true for x > 1 right?

[wraith dagger]

alexisreen

[mystic salmon]

for x = 0 u just get g_n(0) = 0

u just sum up zero's

so its also converging

@dire geode no?

[dire geode]

how'd you get from $\frac{1}{n^2 x}$ to $\sum_{n\ge 1} \frac{1}{n^2}$ ?

[wraith dagger]

riemann

[mystic salmon]

1/(n²x + 1) < 1/ n²x , now u do infinite series

x is treated as a constant there

[dire geode]

$\frac{1}{n^2 x}$ is not less than $\frac{1}{n^2}$

[wraith dagger]

riemann

[mystic salmon]

doesn't matter

since the series of 1/(n²x) is also converging

[dire geode]

then just use $\frac{1}{n^2 x}$ in the summation then

[wraith dagger]

riemann

[mystic salmon]

yes

but i'd like to say that 1/n² is a riemann sum thats converging

no confusion triggered

so im correct @dire geode ?

[dire geode]

you're triggering confusion by dropping the x dependence

you can trivially justify it by factoring out 1/x from the summation

[mystic salmon]

Yes

[dire geode]

also you need to define what m_n is here

[cedar kiln]

@mystic salmon Has your question been resolved?

[cedar kiln]

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[dire geode]

what is your question

[cedar kiln]

@crimson sedge Has your question been resolved?

[dire geode]

it's not a function

doesn't pass the vertical line test

share the whole problem

screenshot or picture of the original

[cedar kiln]

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[obsidian wasp]

$\sqrt[3]{\frac{8x^3}{27}}$

[wraith dagger]

Leaky

$\sqrt[3]{\frac{8x^3}{27}}$

[obsidian wasp]

what are the steps required to solve this?

[foggy merlin]

8=2^3
27 = 9x3 = 3^3

so it should be easy to take the cube root of this

[obsidian wasp]

very nice

thank u

.close

[cedar kiln]

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[cedar kiln]

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[cedar kiln]

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[fossil topaz]

can i ask for geometry?

[kindred orbit]

dont ask to ask

[fossil topaz]

Let ABC be an acute triangle (AB<AC) inscribed in (O).Draw,BE,CE are tangent to (O),xy is tangent to (O) at A, draw EP//xy(P belongs to AB) ) and EP intersects AC at M, BM intersects PC at I. a) Prove that BCMP is incircle and determines the center of the circumcircle BCMP b) Prove that I belongs to (O).

help me

[cedar kiln]

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[spice latch]

can someone explain to me what rounding continuous values is? the teachers explanation is very confusing and only spent one day teaching us this

[spice latch]

is what she wrote

<@&286206848099549185> sorry for ping but it’s urgent i have my final exam tomorrow

[cedar kiln]

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[gentle lintel]

∠ 4 = ∠ 8

[wheat comet]

Someone teach me find measurements measurements

Hmm

That was fast wow

[wheat comet]

Is that measurements?

[gentle lintel]

a hint

according to your labels

[wheat comet]

Idk how to find it doe

[gentle lintel]

you have labelled

every angle

consider my hint

you’re not far honestly

[wheat comet]

No my teacher labeled it

[wheat comet]

Pls tell me how

[gentle lintel]

i did

[wheat comet]

Where

[gentle lintel]

.

give some thought into it

that reads ‘angle four equals angle eight’

[wheat comet]

Tell me how to find it

[gentle lintel]

are you expecting people to just give you the full solution lol

[wheat comet]

Yea

[gentle lintel]

well sorry your expectations cannot be met

we dont do that here

[wheat comet]

Then teach me

[gentle lintel]

we can give hints and you can learn

[gentle lintel]

i gave you a hint already :v

[wheat comet]

Ok ty

Bye

.close

[cedar kiln]

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[wheat comet]

.reopen

[cedar kiln]

✅

[wheat comet]

Teach me pls

Teach how you find it so fast

[gentle lintel]

experience mostly

just try to bring the angles tgt

[wheat comet]

How

[gentle lintel]

i gave you a hint

angle four equals angle eight

use that

[spice latch]

bruh why are u guys talking as if i’m not even her

here*

[wheat comet]

Is there a video that you can find that teaches MD it?

Me it

[gentle lintel]

this particular problem??

[wheat comet]

Yea

[gentle lintel]

we never just hand out the solution like that

[wheat comet]

Then teach me it

[gentle lintel]

i gave you a hint

do you not understand the hint lol

[wheat comet]

No

[gentle lintel]

you know where angle four and angle eight are

[wheat comet]

Yea

[gentle lintel]

i assume m and n are parallel lines

[wheat comet]

Wait there's no 8

[gentle lintel]

there is

[wheat comet]

Where

[gentle lintel]

the 8 is terribly drawn lol

[wheat comet]

Oh I see it

[still granite]

Above (8x-3)?

[gentle lintel]

angle eight IS 8x - 3°

[wheat comet]

How does this help me?

[gentle lintel]

think

use your head

[wheat comet]

Idk what to think

[gentle lintel]

are you familiar with angle properties

like do you at least know what they are

[wheat comet]

No

[gentle lintel]

no wonder

let’s just do a quick review ig

you know parallel lines

?

[wheat comet]

Yea I think so

Yes

[gentle lintel]

yea so

these are parallel lines

[wheat comet]

Ok

[gentle lintel]

they’re usually denoted by >> or a big bold triangle

[wheat comet]

Ok

What's next

[gentle lintel]

ok so

i am sending a picture

worst internet in existence

[wheat comet]

Ok I wait

[gentle lintel]

this purple line is called a transversal

to begin with some terminology

it cuts through these two lines

[wheat comet]

Ok

[gentle lintel]

so it has some properties

[wheat comet]

Ok

[gentle lintel]

obviously, if you copy-paste the green squares on each other, it’s the same thing

[wheat comet]

Ok

[gentle lintel]

right

you understand

[wheat comet]

Yes

[gentle lintel]

then a = b

whenever you have a transversal, and two parallel lines, the corresponding angles between them are the same

[wheat comet]

Ok

[gentle lintel]

this is called the corresponding angles property

not hard

[wheat comet]

Ok

[gentle lintel]

next up, a circle is 360°

this should go without explaining

[wheat comet]

Ok

[gentle lintel]

then consequentially

if we have some number of lines that go through a same point

and add all the angles between them up

we should also get 360°

[wheat comet]

Ok

[wheat comet]

Ok

[gentle lintel]

right

this makes sense to you?

[wheat comet]

Yes

[wheat comet]

So where does this go

[gentle lintel]

then all the angles on one side of the line adds up to 180°

[wheat comet]

Yes

[gentle lintel]

the 360° and 180° properties are, respectively, called ∠s at a pt. and adj. ∠s on str. line

in layman, ‘angles at a point’ and ‘adjacent angles on straight line’

[wheat comet]

Yes

[gentle lintel]

this makes sense also?

like you understand why it’s true

[wheat comet]

Yes

[gentle lintel]

ok so

two parallel lines and a transversal

[wheat comet]

It has some properties?

Corresponding line?

[gentle lintel]

using the properties i said, we can solve this problem

for example

we can solve for ‘?’ using the corresponding angles property

try answer it

[wheat comet]

That triangle should be on the other side?

[gentle lintel]

wdym

[wheat comet]

Idk

[gentle lintel]

where do you see triangles lol

[wheat comet]

The withe bold ones

[gentle lintel]

the >> indicate parallel lines

it tells you they’re parallel

[wheat comet]

Oh ok

[gentle lintel]

that gives us ground to apply whatever parallel lines properties we wanna apply

[wheat comet]

I have no idea how answer this because you did not tell me how

[gentle lintel]

well

i did

[gentle lintel]

i even told you which property to use

[wheat comet]

Yes

I know

But how will I use it

[gentle lintel]

this was the corr. ∠s property

[wheat comet]

Wth is a corr

Just give me solution or teach me how to measure it

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[wheat comet]

Is my mode correct?

<@&286206848099549185>

@eager pier pls help me

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[glass panther]

I am taking linear algebra ——
When solving go check if b is a linear combination of some set of vectors a1, a2, a3, I got a augmented matrix that is reduced to having 0s on the bottom row. This would mean that you would need make free variable equal to some other variable like t but I am not sure if this is allowed.

[gentle lintel]

wdym

[glass panther]

Wait let me send a pic

The second pic is my work

I am trying find c values such that b = c1a1 + c2a2 + c3a3

[gentle lintel]

well

it’s the same thing as solving

c1 + 5c3 = 2
c2 + 4c3 = 3

shouldn’t be that hard

[glass panther]

So uhh would I have c3 = t then solve that way

[gentle lintel]

not really

simply setting c3 = 0 will do

but yea, there are infinite linear combinations that yield b

[glass panther]

Ohhhhhhhh

[gentle lintel]

if you’re looking to represent all combinations then sure, c3 = t

[glass panther]

Ok thank you!

.close

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[fair sandal]

what is the formula for this type of question, ijust forgot it lol

[gentle lintel]

secant secant theorem

[livid hound]

you have two secants,
math names are lazy and many pretty much describe what they supposed to be used for

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[fair sandal]

how do i solve this

[vague gulch]

you could first find the other angle in-terms of x

[cedar kiln]

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[cedar kiln]

Please don't occupy multiple help channels.

[stoic wing]

Send the problem

@crimson sedge

[cedar kiln]

@crimson sedge Has your question been resolved?

[low nacelle]

Use pythagoras

[cedar kiln]

@crimson sedge Has your question been resolved?

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[hybrid solstice]

how would i do this

[cedar kiln]

@hybrid solstice Has your question been resolved?

[hybrid solstice]

<@&286206848099549185>

[cedar kiln]

@hybrid solstice Has your question been resolved?

[hybrid solstice]

<@&286206848099549185>

[cosmic steppe]

What is the absolute minimum and maximum value

[sage forge]

Is it good enough to approximate it with a normal sin function being stretched?

[cedar kiln]

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[azure violet]

What is the probability that seven randomly selected people all have birthdays on the same day of the next time they turns one? Enter the answer as a decimal number, fraction or percentage.

[tight herald]

So the probability all 7 people have the same birthday?

[azure violet]

Yes that they all are born on the same day

in the week

[tight herald]

So, monday tuesday etc

[azure violet]

yes

[tight herald]

I will think about it

It doesn't seem too challenging though

[azure violet]

I know

but the formula is confusing

[tight herald]

Which one?

Is it permutations

[azure violet]

I think

[tight herald]

Yeah the one with the factorials?

[azure violet]

it didn't really specify

[tight herald]

Oh

I usually think of "r" as the number of seats if that makes sense

And "n" as the people

[azure violet]

can you try using numbers

so I understand

[tight herald]

I don't understand sorry

As in, an example?

[azure violet]

The question is:

What is the probability that seven randomly selected people all have birthdays on the same day of the week next time they have their birthday

[tight herald]

Well there are seven days in a week

And seven people

[azure violet]

yes

[tight herald]

So you can find the number of permutations

[azure violet]

but the first shouldn't really matter cuz it's 7/7

but after that

I think the complicated part comes

[tight herald]

?