help-0

[zinc vigil]

and cusp is like a corner

[coral pagoda]

Are you having to write the equation, or just draw a picture?

[zinc vigil]

write an equation

[coral pagoda]

So would you say x^2 has a cusp?

Is that kinda what you mean?

[zinc vigil]

|x| would be an example of a cusp

[coral pagoda]

Okay, so it needs to be a piecewise function

[zinc vigil]

it has to be just one equation

[coral pagoda]

Then you're shit out of luck

[zinc vigil]

yeah

idk

[coral pagoda]

You cannot have a cusp if the equation is not piecewise

|x| is a piecewise function

[stray jacinth]

can someone help me w discrete math

[ionic jewel]

i mean

technically you could just throw a abs in this guys answer

multiply the entire thing by |x| and call it one equation

free cusp

[coral pagoda]

Hmmm

[zinc vigil]

I'm also not allowed to use an absolute

[coral pagoda]

Okay, then you're just fucked

This is a poorly written question that puts you in an impossible situation

[stray jacinth]

can someone help me with 10a) for discrete math

[zinc vigil]

yeah

[coral pagoda]

If these really are the restrictions, then e-mail the professor. This is not a doable question with those conditions.

[coral pagoda]

Have you considered asking in #discrete-math ? You'll have a better shot there.

[stray jacinth]

aight ty bro

[coral pagoda]

You bet. Unfortunately, I'm not entirely sure what undirected or acyclic means, otherwise I might be able to help.

[stray jacinth]

no worries bro

@zinc vigil can u help?

also @coral pagoda i kinda need help w 10c if u know that

if not thats fine too

[ionic jewel]

undirected is the edges go both directions (bidirectional), and acylic means there are no cycles

[stray jacinth]

@ionic jewel ty

[zinc vigil]

that question looks like its above my level of math

cant really help

[coral pagoda]

Can you find a bijection between $\Q \times \Q$ and $\Q$?

Or the other way around works too.

[ocean seal]

dackid (jump king +)

[coral pagoda]

Even better. Can you find a bijection between $\Q \times \Q$ and $\N \times \N$?

[ocean seal]

dackid (jump king +)

[coral pagoda]

That will get you in a good spot.

[stray jacinth]

completely clueless

im new to this stuff my teacher hasnt even throughly taught this

[ionic jewel]

Im not writing a formal proof but it ends up being simplifiable to a tree, and you can just color each level a different color

[coral pagoda]

Here, try a different question first.
Let $f:A\to B$ and $g:C\to D$ be functions. Show that if $f$ and $g$ are bijective, then so is $(fg): A\times C \to B \times D$.

[ocean seal]

dackid (jump king +)

[coral pagoda]

This should not be too hard to do and it deals with the problem really nicely.

[ionic jewel]

oh wait ur doing C

i was so confused how this was related to A

[stray jacinth]

no worries

[coral pagoda]

Yea, this is all about 10c)

He asked for help on that too

[alpine sable]

i think @stray jacinth would be better off if u sent a picture of it on a paper with the work

[ionic jewel]

this is for A

[alpine sable]

@stray jacinth am i right?

[stray jacinth]

yeah honestly that would help a lot

[coral pagoda]

For which one?

I'm not doing the work for you

[alpine sable]

bro just help the guy out i would if i had a paper on me but i’m not home

[stray jacinth]

[ocean seal]

dackid (jump king +)

dackid (jump king +)

[stray jacinth]

discrete math is too hard man

im going to drop out

[coral pagoda]

Math is never easy

[stray jacinth]

theres no point of all of this stress

im already failing all of my other classes anyway

[coral pagoda]

You do what you want

[stray jacinth]

yeah man

thanks for the hints

but it doenst reasllt make sense

[coral pagoda]

What do you not understand?

[stray jacinth]

i cant even spell right

im a failure have a nice day

[coral pagoda]

Get your head out of your ass and stop belittling yourself.

What do you not understand?

[stray jacinth]

any of it. this hw assignment is due at 6 and this is the last question i have and i don't understand any of it. none of this q and countabke stuff was on my study guide and i don't know what to do.

border line failing and i cant even be smart enough to know thi s

[ocean seal]

dackid (jump king +)

[coral pagoda]

This is a definition, and we will make use of it.

[stray jacinth]

what is A set A

[coral pagoda]

"A set A" was just an unfortunate consequence of capitalization. The first A was simply the article "a", and the second is some arbitrary set that I am naming A.

[stray jacinth]

so we have to show that x and y are bijective?

[coral pagoda]

We need to show that there is a bijection from A onto the natural numbers

[stray jacinth]

and A is the set (x,y) R^2?

[ocean seal]

dackid (jump king +)

[stray jacinth]

where did u get Q X Q?

[coral pagoda]

Q is the set of rational numbers

Q times Q is the pairing of rational numbers (x, y)

[stray jacinth]

OHHHH

okok i got u

so we need show a bijection between A and N

[ocean seal]

dackid (jump king +)

[coral pagoda]

This extra step is very important.

[stray jacinth]

gonna put this here again

[ocean seal]

dackid (jump king +)

[stray jacinth]

how?

[coral pagoda]

Well, each element in the rationals can map the the natural numbers one for one. Same for the pairing of natural numbers.

Injective means that each element in f is uniquely represented by the input. (Note: x^2 is NOT injective), and surjective means that every element in the range is mapped by some input. Nothing is left out.

Bijective is the combination of both of these.

[stray jacinth]

ok got i

u

[coral pagoda]

Alright cool. You should be able to take the countability of Q for granted, and we will do just that. If you have not proven N times N, we can do a visual argument later.

[stray jacinth]

okok

[coral pagoda]

For now, let's just treat these as things we can take for granted so we can use it in our problem.

[stray jacinth]

so now we need to see if QXQ is bijective to NXN

[coral pagoda]

I want you to prove this

As you should be able to see, if we can prove this, the result is immediate.

[coral pagoda]

For this I mean.

[coral pagoda]

By the way, (fg) is going to be the ordered pair (f(a),g(b))

[stray jacinth]

A x C -> B X D is also bijective because for every A will be a B and for every C will be a different D (injective and surjective for both) meaning each (A x C) will always be a unique input for (B x D) and will only have one input since each letter only has one unique input(injective) and

A -> B and the other one is surjective meaning there cant be more than one A linked to a B and vice versa

am i right

?

@coral pagoda

plz

[coral pagoda]

Here is a standard argument for showing it is injective.

[stray jacinth]

so i was wrong?

[coral pagoda]

Yours was more intuition than anything. It was not a proof

[coral pagoda]

Surjective means that for each element in b, there is an element in a so that f(a)=b

What you wrote there is what it means to be injective

[stray jacinth]

right

[coral pagoda]

I provided the proof for injectivity, now do it for surjectivity

p. s. The injective proof was one part of 10b), so I recommend you do that one as well

[coarse kernel]

I completely forgot how to do this

[nocturne sluice]

im not no math expert or anything so dont take my answer serious but i think you have to re arrange the variables using some type of math properties

[rancid girder]

its a parabola

[pearl marlin]

Check formulas of projectile

[coarse kernel]

i havent gotten there

[pearl marlin]

For a take b=0 ,the. Solve for t

For b just put 't'

[pearl marlin]

Do you know derivative?

[coarse kernel]

so for a. id get 5 seconds?

[pearl marlin]

You have to solve the quadretic to find t.

[coarse kernel]

im in algebra 2 so no

[rancid girder]

theyre just doing the axis and x-intercept of a parabola i believe

i didnt read it all tho

[rancid girder]

x-axis=time
y-axis=height

[coarse kernel]

i see

aight thx

[rancid girder]

good luck

[coarse kernel]

👍

[radiant elk]

um does anyone know how to do 10a

[alpine sable]

any one know what

whis simbol means

σ^

[warm phoenix]

That appears to be a sigma - not sure what the ^ is for though.

[alpine sable]

it's a sigma but the ^ is confusing

i have to calculate the "punctual estimate of standard deviation" i don't know if that is the term in English

i've the Σx = 3204.77 and the Σx^2 = 10270529.72 and a sample of 10

plz help

<@&286206848099549185>

[drowsy basalt]

nobody helping this poor dude

[alpine sable]

o sorry i didn't saw that nobody helped him

[drowsy basalt]

lol im busy doing some other stuff so i cant help him either

[alpine sable]

in letter a and b you have to do the Pythagoras theorem c^2 = b^2 + a^2 to find the radius of the circle

[radiant elk]

uh i only need to know how to do 10a

[alpine sable]

Oh sorry i really suck at geometry

[radiant elk]

um its been a while and im trying to get my hw done bfr 11, i hope im allowed to ping <@&286206848099549185> 👀

[signal wolf]

Can someone spot the mistake 😉

ln (-1) = ln (-1)
ln (e^iπ) = ln (-1)
iπ = ln (-1)
iπ = ln (e^i3π)
iπ = 3iπ

Or

iπ -iπ = 0 : 3iπ - iπ = 2

0 = 2

[north fulcrum]

Could someone point me in the right direction on starting this problem out?

[small stag]

Find the slant height of the three upper triangles

Use that to find their areas

Then add that to their base

[earnest copper]

What is the best way to review pre-calculus

Khan academy?

[glad ore]

is this a possible solve?

[radiant elk]

the slant height is 13 right, the thing im stuck on is the base rn, i dont know how to find the area of the base because i dont know which sides of the base are equilateral

[small stag]

Where does the 4th line come from

[signal wolf]

But why, why is it incorrect

[small stag]

And 3iπ - iπ is 2iπ

Oh no I’m just looking for an explanation

[signal wolf]

Sorry, silly mistake from my part. But the point is that 0 = 2iπ

[small stag]

No not the slant height, the height of the upper triangles

You have to assume 13 is the length of the three upper edges

And by the way it is drawn

The bottom triangle is the base

[radiant elk]

oh.

i am still super confused 😭

[small stag]

The bottom triangle is the base

The base is equilateral

What does that tell you

[small stag]

I think it has to do with the periodicity when dealing with pi but don’t take my word for it

Wait no

[radiant elk]

that the base is equilateral??

[small stag]

ln(e^3iπ) won’t reduce to 3iπ it becomes Iπ

[radiant elk]

WAIT

[small stag]

It is given

[radiant elk]

oh this entire time i thought that the base was isosceles and not equilateral

oops

[small stag]

It’s ok now you know!

Go get that problem done!!

[radiant elk]

so i use the pythaogrean theorem to find the area of the base?

[small stag]

You can drop an altitude yeah

And since it’s equilateral

The altitude is also an angle bisector and a median

[radiant elk]

o ok

tysmm

[median kraken]

anyone have a idea on this i tried to do it before with the formula but i messed up badly lol

[glad ore]

can someone who knows matrices tell me if this question I posted is able to be answered as the rows and columns are different

[meager gull]

hi

somebody Can help me with a exercise

pleasee U_u

[alpine sable]

Can someone check my work please

<@&286206848099549185>

[raven valve]

The -1 should be in the power of 0.5

a.r^(n-1)

[alpine sable]

so how much it look like?

Pls someone quickly

[random relic]

[-4, 0]

[alpine sable]

Tysm

Last one

These are the two I were confused with

[obsidian slate]

you would multiply the parentheses by 2, move the Xs to one side and constants to the other n then divide to get your x

are you doing interval notation

[random relic]

-3.6x >= 10 + 2(-2x - 7)
-3.6x >= 10 - 4x - 14
-3.6x >= -4x - 4
0.4x  >= -4
x     >= -10
Or in interval notation: [-10, inf)

[alpine sable]

Ty

[obsidian slate]

may i get help figuring out the inverse function of this, please?

i couldnt figure out how to isolate y

[vapid swift]

start by squaring both sides

[obsidian slate]

yes i did that!

[pearl marlin]

Getting 6th

[lapis harness]

literally use any online calcualtor

[obsidian slate]

your answer on the calculator wasnt an answer choice, there was no need for that

[obsidian slate]

may i ask how you came to that answer please

[lapis harness]

can't google

and can't even compare answerrs

thats new peak

[vapid swift]

yeah i got 6 too

[obsidian slate]

thank you so much! i appreciate it

[obsidian slate]

its a review for ut austins math assessment so i believe thats why

[lapis harness]

no idea what that means

[obsidian slate]

may i ask what you did to get the function inside the parentheses

[pearl marlin]

Just take the negative out to cancle that on other side

[gleaming warren]

What is the Pythagoras theorem

[obsidian slate]

a^2 + b^2 = c^2?

[raven valve]

Sum of squares of adjacent sides of right angle in a triangle is equal to square of hypotenuse

[gleaming warren]

So $h^2 = ?$

[ocean seal]

TheGameBot

[obsidian slate]

i dont understand where the 4 went from 4y^2 after you square both sides. could you further explain how you got the 4 in the parentheses please

[obsidian slate]

may i ask what the problem is

[pearl marlin]

4-5y^2 is in deno. On other side

[gleaming warren]

I just wanted to know the Pythagoras theorem So I can answer some questions

[raven valve]

h^2 = a^2 + b^2

[gleaming warren]

Ok thankyou

[obsidian slate]

could you explain what you did after you squared both sides? i got confused after that

im not understanding how you got to the next step

[pearl marlin]

Cross multiply

[obsidian slate]

thank you sm!

[merry field]

What is 10 cm to m in sig figs?

[vapid swift]

what do you want to do?

what do you have to find?

there's no question there

no

[merry field]

What is 10 cm to m in sig figs?

[alpine sable]

is this right

[vapid swift]

there are just some measurements....what do you actually have to find?

[obsidian slate]

are you finding area?

[alpine sable]

is it free rn?

i have a few doubt to clear thats all

are the terminating decimals and non-reccuring decimals the same thing

[woeful pulsar]

ln has many branches

[little wadi]

https://cdn.discordapp.com/attachments/409596215697866773/851487244103319612/unknown.png
how does one go aroud solving this. just a quick overview

[lavish depot]

Okay so for an exam they gave a question where they gave | 2^t + 2k | >= | 2^(t+1) - 3k | and then asked to find the largest possible value for t, but in the way I did it I got repeated values for t in the combinations I tried, is this a coincidence or will the repeated values always be there for any given equation when doing it the way I did?

[alpine sable]

Hello

Can someone help me

What is this question asking?

[clever helm]

what are the like terms?

8+13x³-12x-8x²-14x³-x+34

[sullen echo]

7x5+7x6+7x7+7x8+7x9
=7x(5+6+7+8+9)
=7x35
=245

[alpine sable]

Thanks

Can I get help on this one

[rigid smelt]

Seems like a marked quiz

[strong dome]

How do I show it absolutely converges when c>1 ?

[thorn kindle]

Ok

Consider the function 1/(x+c^x)

[strong dome]

Right

[thorn kindle]

For c = 0 this represents the harmonic series, which we know diverges

[strong dome]

I agree

[thorn kindle]

For 0<c<1, c^n tends to 0 as n tends to infinity

Like (1/2)^inf = 0 if you will

[strong dome]

aha so also in 0<=c<=1 it should diverge

[thorn kindle]

Yes.

Converges conditionally, with the alternating series

[strong dome]

Yes

and what if c>1 ?

[thorn kindle]

And now do the case c = 1

[strong dome]

how do I show it in this case?

[thorn kindle]

1^n = ?

[strong dome]

when c=1 it also diverges

[thorn kindle]

Yes

So you get the series 1/(n+1)

Which is merely the harmonic series shifted by 1

Which shall also diverge

[strong dome]

yes

I agree

and how do I prove it absolutely converges for c>1 ?

[quaint trout]

Comparison test with (1/c)^n @strong dome

[arctic fulcrum]

when c>1

[thorn kindle]

Now for c>1 you will compare to the geometric series

[arctic fulcrum]

^^^^

since -1^n/(n + c^n) < -1^n/c^n

[thorn kindle]

1/c^n converges, and 1/(c^n+n) tends to 0 faster

[thorn kindle]

Showing absolute convergence

[strong dome]

I don't understand why it is okay to say it is bigger than that

okay nvm I see that

because we removed positive number

[arctic fulcrum]

yeah

thats why n>1 is important

[strong dome]

nice

thank you

I have another question I struggled with but I don't know if you can help me

[thorn kindle]

Now just for fun consider the case c<0

[arctic fulcrum]

ty for save

[strong dome]

it's okay they asked precisely about only c>1 and 0<=c<=1

just for fun haha

[thorn kindle]

Just for fun consider it

What happens?

[ionic jewel]

absolute convergence?

i haven't done these things in so long :(

[strong dome]

if c<0 then it completely diverges?

[thorn kindle]

Not quite

Consider c = -2

[strong dome]

oh

if c = -2 then after absolute value it converges absolutely

right

[thorn kindle]

Yes

Converges absolutely for abs(c)>1

[strong dome]

it's basically the same mirror case of c>0 about negatives

[thorn kindle]

Converges conditionally for abs(c)<1

[strong dome]

and if -1<c<0 then it completely diverges?

i guess

okay thank you

[thorn kindle]

Conditional convergence

[strong dome]

nope it should completely diverge for -1<c<0 because alternating test won't work

[quaint trout]

AST doesn't tell you a series diverges

If the test fails, that means you can't use the test. It doesn't mean the series diverges. It can diverge or converge and the test can't tell you.

[strong dome]

yea I agree

it's okay that's why they didn't ask about this case because they didnt teach us

I have another question

[thorn kindle]

for -1<c<0, c^n is less than n as n->inf

so this essentially becomes the harmonic series which does conditionally converge

ok next question

[strong dome]

I proved that n!*/(n^n) converges if that helps, but I don't know what to do next or how it helps me

[thorn kindle]

f is positive and increasing

phew that makes things very simple for us

[strong dome]

Why simple 👀

[thorn kindle]

and we are also given f(0) = 0

even easier

as n->inf, 1/n^n ->0.

since f(n) is monotonically increasing this means that f(1/n^n) must go to 0 as n->inf

[strong dome]

yea I agree lim(to inf) 1/n^n is 0

so do what I do need to show?

1/n^n converges

[thorn kindle]

you already did most of the work. you've shown that the sum n!/n^n converges. this means that n^n goes to infinity faster than n!. because f is monotonically increasing, 1/f is monotonically decreasing comparable to 1/n^n. therefore the sum n!*f(1/n^n) must converge

basically because n^n is faster than n!

[strong dome]

because f is monotonically increasing, 1/f is monotonically decreasing comparable to 1/n^n
sorry, why did you use 1/f ?

[thorn kindle]

1/f approaches 0 as n approaches infinity

basically you can sort of say that f(n^(-n)) = n^(-n). and i use that equals sign very loosely

[strong dome]

I understand

that was very helpful

thank you

[noble sinew]

its f'(0)>0 not f'(x)>0 - our function isn't (necessarily) monotonically increasing. It is however increasing at around 0

but assuming the above argument is valid then for k big enough we have sum from n=k to inf it is increasing

and then we just have a finite sum from n=1 to k-1

[thorn kindle]

oof good point. that makes things slightly more complicated. but we can still say that since f(x) is increasing around 0 then as x goes to 0 then f(x) must be decreasing

[strong dome]

thank you both :]

[noble sinew]

but why does this argument even work (maybe im slow) - can't the function we put it in approach 0 super slow

such that n! outweight f(n^(-n))

[thorn kindle]

we are given that f(0) = 0

so as z gets arbitrarily close to 0, f(z) gets arbitrarily close to 0

basically 1/n^n approaches 0 super quickly

f(1), f(1), f(1/4), f(1/27)

and the second derivative exists so it is a smooth curve

[arctic fulcrum]

what if my function was the inverse of x^-x, then the sum would be n! * n

actually derivatives stuff cant let me do that

[thorn kindle]

the inverse of (0,1) is (1,0)

we are given that f(x) goes through (0,0)

that example does not work

ok that's enough reasoning with arbitrary functions

gg

[noble sinew]

so the same argument works if we plugged 1/n^(1.01) through f (and looking at the sum f(1/n^(1.01) )?

couldn't f in a sense make this equal to 1/n and hence divergent

or what

but I guess f(1/n^(1.01)<1/n for n big enough or what?

[thorn kindle]

yes that last statement is true

[proud salmon]

Need help with this

[thorn kindle]

r^2theta/2

when it's in radians of course

or an even simpler argument

120 degrees is 1/3 a circle

Sector = A/3

QED

[pastel jungle]

i have a trig question guys

[thorn kindle]

no

[pastel jungle]

its on graphins sin equations

[thorn kindle]

dear god no

[pastel jungle]

is the period of the curve just one peak and one trough

[thorn kindle]

yeah

so sin(x) from 0 to 2pi is one period

[pastel jungle]

but sin 2x is 0 to pi

[thorn kindle]

yep

[pastel jungle]

ah

thanks, it actually clicked i just wanted to make sure i was understanding correctly

dont like trig AMD? lol

[ionic jewel]

trig has too many triangles

and circles

and ambiguity

[thorn kindle]

I'm ok with it but i dont like explaining it to people

And i dont like pi

Its the wrong number

[ionic jewel]

why's that lol

[thorn kindle]

Pi is only half a circle

The constant should be 2pi

[sullen echo]

The tau fanclub I see

[strong furnace]

tau lover in this chat

[ionic jewel]

ah yes area of a circle is 1/2 tau r^2

[thorn kindle]

Yes.

Take the derivative

Wrt r

[thorn kindle]

Which is just tau * r

We define circles by their radius

Not their diameter

[pastel jungle]

another question lol

unit circle

to go from 0 to 2pi you go counter clockwise right

[thorn kindle]

Yeah

[ionic jewel]

you know i agree Tau is better, too bad everything uses pi

[pastel jungle]

if i was gonna put it on the x axis

[ionic jewel]

also the Tau symbol sucks, it's just a weird T

[thorn kindle]

τ

[ionic jewel]

positive x axis counterclockwise to positive x axis

yes like i said, a weird t

[thorn kindle]

π

That is a p

Looks nothing like a p

[ionic jewel]

trust me if i had Tau in a problem with time t I'd switch then up 100%

[sullen echo]

So the derivative of circle's area is its circumference?

[thorn kindle]

Yes

[sullen echo]

How could I not notice that

[pastel jungle]

hm say that again

[sullen echo]

It's awesome

And it intuitively makes sense

[ionic jewel]

is this wrong?

[ionic jewel]

the angle 0 and 2pi both lay on the positive x axis

or 0 and tau

[pastel jungle]

i just meant for laying out the radians on a graph

[ionic jewel]

yes I think my answer was right

and sufficient

[pastel jungle]

i guess i just misunderstood it

[ionic jewel]

perhaps

[pastel jungle]

when finding asymptotes in a y = tan problem is the -pi/2 < variable expression< pi/2 a constant?

[clever helm]

Simplify 12x²-3x+4-(1+x-x²)

[thorn kindle]

what

take the reciprocal

lol!

A = C/(NY)

so just keep C > NY

[alpine sable]

how do I factor:

$10x^2 + 31x + 15$

[ocean seal]

Bleidorb

[ionic jewel]

quadratic equation

you might be able to guess and check but that's too much thinking

[alpine sable]

I tried this:
10x^2 + 30x + x + 15

[thorn kindle]

@spare vale keep C greater than Y

[alpine sable]

im trying to get it in this form (..x + ...)(...x + ...)

[ionic jewel]

yes

use the quadratic equation

[thorn kindle]

I dont think what you're asking is possible then

Sum of C > C

As you tell it N should have no effect on Y

Your formula is A = C/(NY)

Yes

Wdym

So let Y = C?

I guess you could do that

And then take the average of all A

Or maybe just weigh C more

Make X = 2C/N

Or some other constant

Equivalently weigh N less

[tight rivet]

what is 6/12 as a decimal

is it 0.5

[thorn kindle]

0.5

Lol

[tight rivet]

lol

[ocean seal]

farmaceut

[thorn kindle]

What even is the context

[vale wigeon]

was about to ask the same

[pastel jungle]

where does this come from? a rule?

[vale wigeon]

@pastel jungle channel busy please move

@spare vale what is the context for this data? what are these N's and C's? what meaning does the metric A = (total of CPC)/(total of N) have, and why does one care about increasing it?

[bold token]

Why do we have to get the antiderivative for an equation? Can I just plug the values in to the equation?

[vague coral]

i need context

[vale wigeon]

energy per electron... okay, and what is this A?

[bold token]

Ill talk at #help-2

[vague coral]

ok

[vale wigeon]

wait wait wait

what do you want A to be?

........

[strong furnace]

every electron in an atom is not equipotential tho , am I misinterpreting something here?

[vale wigeon]

okay so what's X?

A = sum(CPC)/sum(N)?

and what was your issue with it again?

i don't understand

why would you expect sum(CPC)/sum(C) to increase when one of the C's goes up

well we don't know if you don't tell us what the actual goal is

all of this is just abstract number juggling so far

[inner hemlock]

is this false? the question says to prove it true but i think it's false

$tan(90-x)=cot(x)$

[ocean seal]

chicken602

[inner hemlock]

i've tested it out with theta = 30 deg and also drawn out right triangle with side lengths a b c but it doesn't seem to be true at all

[indigo jetty]

try again, it's true

[inner hemlock]

aha i got the mixed up with sin and cos

now it's so clear

man

[strong dome]

Help?

so this is what we need to prove, how do I show that?

[civic crypt]

@strong dome Perhaps add and subtract 1 from the left side numerator

Let me see, you get: 1/(x^2+1)^n - 1/(x^2+1)^n+1.

Hmmm, isnt this a telescopic series.

[strong dome]

you mean like this?

[civic crypt]

Yes, but you missed the first term.

Waaait

These are integrals, I thought they were sums.

[strong dome]

yea integrals

that makes it harder because we can't evaluate the integrals its infinite

[civic crypt]

What do you mean we can't evaluate inifnite, we can

[strong dome]

I mean like if we try to get it integrated on both sides so we'll stay have integral on one part

I don't know hmm

[civic crypt]

I dont understand what you saying

[strong dome]

it's okay don't mind me it was just my thoughts and not any good conclusions

[sudden tulip]

Hi

[strong dome]

another way would be to use the given

but then how do I show this last fraction equals to

[civic crypt]

Well, this is just the proof of I_n+1 + J_n1 = I_n

I dont know why this is given, when it is derivable from first line

[strong dome]

The question was originally this

so after I proved a. I thought putting it in given might be helpful

[civic crypt]

Oh ok.

What if you apply partial integration to I_n

[strong dome]

I can do that if there's no x in numerator?

[civic crypt]

Or to Jn.

[strong dome]

I'll try with Jn

[civic crypt]

Nah, not good.

[strong dome]

like this?

[strong dome]

I mean it's close somewhat to this

[civic crypt]

This is substitutaion, and you forgot one x

[strong dome]

yea my bad

[rigid smelt]

i feel like its got something to do with u=(the whoe thing)^n here

since you would be getting 2n*(something)

which is pretty close, havent quite figure out the best way to do that tho

[jagged garden]

My idea is to try trigonometric substitution

[civic crypt]

BUt if you define dv = x/(x^2+1)^n u=x You have: v * u - INT v * u du

[jagged garden]

Have you done that?

[strong dome]

nope didn't try

I'm not sure I know how to apply trigonometric substitution

[strong dome]

you mean you try to integrate again the last integral by integration to parts?

[civic crypt]

integral (x/(1+x^2)^n)

This is easily calculable

So you have that J_n = 1/(2(n-1)) ( 1 + INT ( 1/(1+x^2)^(n-1)) ) = 1/(2(n-1)) - I_n-1

[strong dome]

one moment

[strong dome]

you did it like this?

[civic crypt]

No

u' = x/(x^2+1)^(n+1)

[strong dome]

but how would you use x/(x^2+1)^(n+1)
J{N} = is x**^2**/(x^2+1)^(n+1)

[civic crypt]

v=x

[strong dome]

okay one moment

[tight rivet]

does the numerator have any effect in determining if a (was a fraction) decimal is recurring or terminating?

[strong dome]

how do you know how to calculate u? the integral of this

what is u?

[civic crypt]

What is wrong with you bro????

[civic crypt]

^

[strong dome]

I'm sorry

[civic crypt]

Gj

🙂

[strong dome]

but I don't know how to calculate u to proceed

[civic crypt]

Wait, why you took J_n+1

Instead of J_n

[strong dome]

because you said ^(n+1)

[austere dock]

Does anyone here knows how to do laplace transform?

[civic crypt]

Oh, ok, that might be good.

@austere dock read #❓how-to-get-help

[strong dome]

what would be the next step?

[civic crypt]

@strong dome Compute INT u' du

[jagged garden]

Dunno if this works but try, use the trigonometric identity:
1 + tan^2(theta) = sec^2 (theta)

let
x= tan (theta)
x^2 = tan ^2 (theta)
d(x)/d(theta) = sec^2 (theta)
dx = sec^2 (theta) d(theta)

[civic crypt]

@jagged garden OK, let's first finish my way.

[strong dome]

how do I continue?

[strong dome]

oh this is u

[strong dome]

okay sec

[civic crypt]

Should just be rewritten as 1/(2-2n) * 1/(1+x^2)^(1+n)

[civic crypt]

Rewrite it as I did in previous comment

[strong dome]

so this is what we got

[civic crypt]

Yes. And the first term can be immediately evaluated at (0, +inf)

Which is 0 - 0 = 0

[strong dome]

oh I agree

and the last part ?

[civic crypt]

And for the second term you can extract the constant term and get rid of the minus.
So J_n+1 = 1/(2n-2) INT 1/(x^2+1)^(n+1) dx

[strong dome]

Right so we get, J{n+1 } = 1/(2n-2) * I{n+1}

[civic crypt]

J_n+1 = 1/(2n-2) I_n+1

[strong dome]

and we need this

[civic crypt]

Now we can just move n+1 -> n

Hmmm.

[strong dome]

wym?

[civic crypt]

You didnt apply the minus to the parentheses on the right

[strong dome]

my bad

[civic crypt]

We got this.

[civic crypt]

So in terms of n+1. We can write it in terms of n

[strong dome]

hmm like this?

[civic crypt]

But something is fishy here.

[strong dome]

yea for sure haha

[civic crypt]

No

J{n+1 } = 1/(2n-2) * I{n+1}

n+1 = m

n = m-1
J{m} = 1/(2m-4) I{m}

And rename m as n.

[pliant lotus]

can somebody help

[civic crypt]

J{n} = 1/2(n-2) I(n)

[civic crypt]

read #❓how-to-get-help

[pliant lotus]

ok

[strong dome]

n+1 = m
n = m - 1
so n-1 = m-2
2n-2 = 2(n-1) = 2(m-2) = 2m-4
right okay I'll write it like you said sec

[civic crypt]

I think we should try to apply

on J{n+1} = 1/(2n-2) * I{n+1}

Like from a) you have I_n+1 = In - J(n+1)

[strong dome]

right

[civic crypt]

So J{n+1} = 1/(2n-2) * [I{n} - J{n+1}]

[strong dome]

I agree

[civic crypt]

J{n+1} (1 + 1/(2n-2)) = 1/(2n-2) I{n}

J{n+1} ((2n-1)/(2n-2)) = 1/(2n-2) I{n}

J{n+1} = 1/(2n-1) I{n}

Hmmmm

[strong dome]

wow

[strong dome]

I didn't understand this step sec

[civic crypt]

Put it on common denominator left side

[strong dome]

J{n+1} = 1/(2n-2) * [I{n} - J{n+1}]
not like this?
J{n+1} = (I{n} - J{n+1})/(2n-2)

[civic crypt]

Its the same

You move J{n+1} to the left

[strong dome]

oh okay

[civic crypt]

So you can get rid of them

[strong dome]

J{n+1} = 1/(2n-2) * [I{n} - J{n+1}]
J{n+1} + (J{n+1} / 2n-2) = (I{n})/(2n-2)
J{n+1} (1 + 1/(2n-2)) = 1/(2n-2) I{n}

[civic crypt]

Wait, we made mistake before

[strong dome]

what did you do here?

[strong dome]

really? I didn't see

[civic crypt]

=>

[strong dome]

oh

[strong dome]

that makes things easier I think

sec

[civic crypt]

It immediately makes it over it seems

So just integration by parts and game over.

[strong dome]

yea so just integraion by parts and thats it

[strong dome]

I don't know how you could prove it that way too XD

[civic crypt]

You just need to find the correct stuff to integrate

[strong dome]

that was my main struggle

[civic crypt]

You know how to solve this integral?

[civic crypt]

^

[strong dome]

it's by doing t = 1+x^2, then dt = 2x dx right

yea I made it

[civic crypt]

yea

gj

🙂

[strong dome]

It was really tough question

thank you 😄

[civic crypt]

With these recursive integrals, integration by parts should be the first idea to try

The only problem is to find what is u' and what v

[strong dome]

yea and then like magic everything disappears and you get what you need

[civic crypt]

ok, have a good day

[strong dome]

thank you, you too 🙂

[viscid harbor]

How many miligram in one gram??

[strong dome]

There are 1,000 milligrams in 1 gram.

[signal wolf]

Correct!

[viscid harbor]

Thanks

[lime gorge]

Can I get some help beyond this?

And is it correct?

[alpine sable]

sorry idk what your talking about

[lime gorge]

Class discussion, this is what I got

[lime gorge]

Lol meant this it just uploaded

Slow

[wary stream]

You can't use sine to find BC

[lime gorge]

Ahh ok so how would I find it?

[wary stream]

Different trig function

[lime gorge]

Basically I need BC and BA

[alpine sable]

yes your correct by getting BC using sine just not sure how you got 20

i get 12

[lime gorge]

BRUH

[wary stream]

Unless you meant you used law of sines

[lime gorge]

U just gave me the answer 💀

Why lol I need to learn how to do it

[alpine sable]

so?

you can still find it yourself

i dont see the problem

[wary stream]

Dude, I said not to give answers in a different channel

[lime gorge]

Whatever I can still learn on BA

[alpine sable]

whats wrong with you man i gave him the numerical solution not the whole process which he has to do

[jade sail]

whyd u give ther numerical solution

theres no point

[lime gorge]

THATS THE PROBLEM

[jade sail]

jeff do u know soh cah toa

[alpine sable]

how is that the problem is beyond my understanding

[lime gorge]

Yes

[jade sail]

ok well if ur tryiing to find BA

[wary stream]

Please read #rules before answering people's questions

[jade sail]

first classify BA based on the given angle

like is it opposite adjacent or hypotenuse

[alpine sable]

can you quote me where it says what i did is wrong

[lime gorge]

It is hypotenuse

[jade sail]

yea ok do the same wiht the given side CA

[wary stream]

#❓how-to-get-help Rule 7. Linked the wrong channel

[lime gorge]

Opposite

[jade sail]

yeah so u haev opposite and hypotenuse which matches up with soh for sin opposite hypotenuse

so u can use sin for hte hypotenuse

[lime gorge]

No lol I DONT have hypotenuse

[jade sail]

yeah you can use sin to solve for it

[lime gorge]

Look

[wary stream]

Also under guidelines, 5th bullet point, underlined section

[lime gorge]

No hypotenuse

[jade sail]

sin(degree) = opposite / hypotenuse
sin(68) = 22.6 / x
solve for x for hypotenuse

[alpine sable]

"When asking for help, do not insist on getting just the answer; we are here to help you learn, not cheat. Likewise, if you are providing help to others, try your best to explain and elaborate instead of simply giving away the answer."

I did exactly what this suggests. I told him that what he wrote (using sine, which I interpreted as sine law) is the correct procedure, just that I get a different numerical solution using it. The goal was for him to go over his solution and see if he made a mistake. Numerical solution does not mean anything if he doesn't have the process, almost every math book I've used had numerical solution / sketches of proofs at the end so that you can check whether you were right, but not able to cheat.

[lime gorge]

Tysm

[wary stream]

You straight up told an answer, with zero work or anything

[alpine sable]

maybe wasn't explicit and detailed enough for you, i will try to give more details next time

[wary stream]

If you got a different answer from the person, ask them what their work was

[alpine sable]

i said that i interpreted "using sine we get 20" as using sine law to get 20?!

also, i don't see much more that can be said than using sine law in this problem

[wary stream]

Then you said the answer you got, you should have asked to see what they did to achieve their answer

[alpine sable]

ok fine

[bright maple]

i dontn get how u do this

[lime gorge]

Plugged it into Desmos, didn’t get an answer @wary stream

[wary stream]

Use a calculator

[jade sail]

jeff lol solve for x dont plug it in

[wary stream]

Not desmos

[lime gorge]

Ty

[wary stream]

Desmos is mainly used to graph

[gray isle]

(also make sure your calc is set to degrees for this question)

[jade sail]

sin(62) = 22.6/x
x * sin(62) = 22.6
x = 22.6/sin(62)

yeah desmos is normally in radians

[modest fiber]

if $R$ is a rotation matrix, is it true that $mR \vec v \cdot x=m \vec v \cdot R \vec x$?

[ocean seal]

ProphetX

[plucky crow]

Whats the differential of x^sinx? Ping me if you know

[wary stream]

The derivative? There's online derivative calculators

[lime gorge]

Ty

I got 25.6 @wary stream is that right?

[jade sail]

yes jeff

[strong dome]

how do I find for what a values this integral converges?

Here's what I tried

but I don't know what to do next with the last I found

[loud perch]

guys

can help me

with that

[jade sail]

this channel is in use lol

[loud perch]

ok

[alpine sable]

ok, clearly the function has no vertical asymptotes (becasue the denominator is always nonzero) so the only part you need to consider is at infinity, right?

[strong dome]

Right

[alpine sable]

do you know any method for determining whether an integral converges at infinity?

[strong dome]

we do Let b > 1 and do integral from 1 to b
Then we do the limit of that, and if we get something which is defined(not infinity) so the original integral converges

[alpine sable]

Ok yes, that's true. But that is only useful if we actually know how to integrate the function under the integral.

There is another way that doesn't require us to actually integrate

[strong dome]

I agree, that's why I don't know what to do in this case

because I am not sure I know the other method

the other method might be using comparison tests or ratio

right?

[alpine sable]

i'm trying to find something about it online, if i don't find it i'll explain it myself

it actually doesnt use any of it

[strong dome]

hmm

okay

[loud perch]

can anyone help me to use @ocean seal

Question: Solve equations |6-2x| = 8

[rigid smelt]

check #latex-help

theres an entire channel for that

[woven plaza]

[strong dome]

anyone has an idea?

[rigid smelt]

did you integrate first?

[strong dome]

it's impossible to integrate this because it's recursive?

[rigid smelt]

channel is busy

please move

well you can use integration by parts

tho the solution isnt very clear for me

give me a moment

[strong dome]

I think their intention is using something else hmm

like something with tests

[strong dome]

from here

[alpine sable]

<@&268886789983436800> Sussy server invite

amogus

[sly mantle]

b&

[alpine sable]

hey guys, can someone join in a voice chat with me? i need some help in math and i'd appreciate it

[jaunty plover]

Hey

If I have a 5th degree equation, and I solved it and got 2 real solutions, this means I still have 3 imaginary solutions right?

[glass lichen]

no

[vapid swift]

imaginary solutions are always even in number

[glass lichen]

at least depending on the scalars for the co-efficients

if the co-efficients are from R, then complex roots come in conjugate pairs

[jaunty plover]

wait my bad

1 sec

If I have a 5th degree equation, and I solved it and got 3 real solutions, this means I still have 2 imaginary solutions right?
Is this better?

[gray isle]

wording is still a little bad

[jaunty plover]

should I use "complex" instead of "imaginary"?

[gray isle]

yes, complex would be more appropriate than imaginary,
but "solving it" implies that you would have found all the solutions (real and complex)

[jaunty plover]

i think like the way I solved it just wouldn't give me the complex solutions, I guess

[gray isle]

it is also a bit unclear whether you were only able to find 3 of the solutions which happened to be real (and don't know anything about the other solutions)

[alpine sable]

can someone help me out with this in the voice chat?

[jaunty plover]

i just assumed that, since it needs to have 5 solutions, and 3 were real, then the 2 remaining would be complex

[gray isle]

depending on polynomial, it could also have have 5 real solutions

[jaunty plover]

I see, thanks

[gray isle]

you could consider factorisation or graphing to determine how many of each you have

[alpine sable]

can someone help

[alpine sable]

i would say you can use this:

Let $g:[a, \infty) \to \mathbb{R}$ be continuous and let there exist $\lim_{x \to \infty} g(x) = L$.
Then:
$\int_a^{\infty} {\frac{g(x)}{x^s}} dx$:

(a)converges iff $s > 1$

(b)diverges iff $s \leq 1$ and $L \neq 0$.

[ocean seal]

Matejp1

[strong dome]

then do I need to think of g(x) of mine or I can apply this logic immediately on what I got?

if I apply it so on numerator we have 3x^a and on denominator we have x^(3a)
So doing: converges if 3a-a > 1 which is a > 1/2 , and diverges if a <= 1/2

[alpine sable]

could you resend what you got

but i think it's ok because I also got the same result!

[alpine sable]

<@&286206848099549185>

[strong dome]

How did you do it? like this?

[alpine sable]

the idea is right, yes, but it could be done a bit formally

let me write it out

[strong dome]

oh please I'd like to see it formally 🙂

oh I think I got it formally but I didn't write t

this is our g(x)

[alpine sable]

what you did was consider just the important parts, x's, and it's good enough for quickly finding what a should be, but to really prove it it's good to do it like that

to actually find the g(x)

just as it is stated in theorem

[strong dome]

oo that seems good

nice

[alpine sable]

this is probably conceptually the hardest topic in real analysis 1 / calculus

[strong dome]

I was thinking about doing it differently but close to yours with this g(x)

then doing ratio test of them both

[alpine sable]

yes, i think the idea is similar

[strong dome]

and we got value 0<3<inf so both converge

and for the last to converge we need 2a-a>0 which is the same

[strong dome]

yea I agree

[alpine sable]

that's what my professor was telling us when we were practising this

[strong dome]

he was preparing you for the worst haha

[alpine sable]

yes hahah I had to do probably 20 similar problems before I really got better at it

[strong dome]

same and tomorrow's my final haha

[alpine sable]

hey i'm wondering did you state this theorem

cause i would like to find an english source on it

i cant find it at all on the web

[strong dome]

what theorem?

nope I'm not English sorry

[alpine sable]

this one : Let $g:[a, \infty) \to \mathbb{R}$ be continuous and let there exist $\lim_{x \to \infty} g(x) = L$.
Then:
$\int_a^{\infty} {\frac{g(x)}{x^s}} dx$:

(a)converges iff $s > 1$

(b)diverges iff $s \leq 1$ and $L \neq 0$.

[ocean seal]

Matejp1

[strong dome]

oh so yea

[alpine sable]

yea im not english either

and I can only find it in our book and notes

but not anywhere else

[strong dome]

this is how we learned it from the integral test

and we learned in sums that

[alpine sable]

ohhhh you do it the other way around ok

first series and then integrals

[strong dome]

so this both sums up to this

[alpine sable]

we did it reversed

[strong dome]

yea thats how we did it

[strong dome]

interesting hmm

[alpine sable]

yes we first did this theorem for improper integrals

and then when we were later doing series

we mentioned the integral criterion for series

so that you can check if the series converges by checking if that integral converge

[strong dome]

haha I see

reversed

[alpine sable]

well ok good luck tomorrow!

[strong dome]

thank you 😄 you too :]

[undone tangle]

could someone help me with this?

[stark rampart]

I think you use dot product here

[alpine sable]

dm i need help with a few 8th grade math problems no one dms me ;-;

because you are supposed to post them here

[warm siren]

3b and 4c

[earnest wharf]

<@&286206848099549185> is this right

Or nah

[coral pagoda]

That is right

[deft oriole]

Taxi driver charges 2.50$ for the first mile and 1.40$ for each additional mile

Linear or exponential

Plz help

<@&286206848099549185>

NVM I got it

[arctic zinc]

Hi, I have a question with linear relations. When you are given an equation like: 1/2x + y = 4, how would you solve it and graph it?

[alpine sable]

well you could just find the measure of an interior angle

then subtract 180 by that

[wary stream]

Use (n - 2) *180 to find sum of interior angles

[alpine sable]

You're close but

[wary stream]

Take the abs

[alpine sable]

why 128.8-180

or yeah you could simply take the modulus of that

[wary stream]

The modulus? Why?

[alpine sable]

fyi modulus is also another way of saying abs val

and also modular arithmetics

[wary stream]

What modulus value would you use to make it equivalent to abs?

[alpine sable]

Hm?

what

yeah

[wary stream]

When I see modulus, first thing I think of is remainder, like 5 mod 5 = 0, etc

[alpine sable]

Yeah it's what most people think of

Modulus is a synonym of Abs Val

which is also represents modular arithmetics

yeah

you're right

I mean yeh you could have gotten the value of 1 interior angle then subtracted 180 by that

or simply 360/n

[tranquil helm]

Photo from RM

[tranquil helm]

Can just anyone help me with finding the first part of the question.. I mean just tell me what process to do.. <@&286206848099549185>

[stray finch]

ελληνας εδω, σπανια συνανταω

[warm siren]

i didnt get help yet..

<@&286206848099549185>

[alpine sable]

Υπάρχουν μερικοί εδώ

[jolly hearth]

Can i ask a question

[wary stream]

What language is this?

[jolly hearth]

Its really dum tho

[jolly hearth]

No idea lol

Anyways

My dumb question is

[alpine sable]

Greek

[jolly hearth]

If im playing a game and im fighting a boss with a 5% drop chance if i fight the boss 20 times am i confirmed to get that drop

[vale wigeon]

no

[acoustic shadow]

Make cases of lambda, kinda like what the domain of lambda is

[vale wigeon]

you have an approximately 64.15% chance of getting your drop @jolly hearth

[tranquil helm]

Yup.. Those are the roots thanks.. But the coefficients?

[acoustic shadow]

What roots did you get ?

[glossy galleon]

Can someone help me

[gray isle]

where are you stuck?

[glossy galleon]

The entire thing I don’t know what to do it’s so confusing

I never learned this before

[gray isle]

have you started trig?

[glossy galleon]

This is a review for finals and it’s like 40 points

[gray isle]

that doesn't answer my question

[glossy galleon]

Yeah

Sorry I wasn’t paying attention

[gray isle]

do you know about special triangles and ratios?

[glossy galleon]

Uh I forgot all Bout it

I just remember 30 60 90

[gray isle]

i recommend reviewing basic right triangle trig before attempting this question

[plucky crow]

hey

can someone explain why

(1+x)^1/2 converges if modx is less than 1?

1+0.5 for example

is 1.5

ahhhhh

never mind

[languid ore]

Sin con tan?

[alpine sable]

m

[fresh fulcrum]

Hello everyone I have got a quick question. I have got a problem in my maths book

(x-4)^3 = x^3 + px^2 + qx - 64
for all x, find the values of the constant p and q

Answers from the book are p = -12 and q = 48 I am finding it hard to see why. Since (x - 4)^3 = x^3 - 64

[gray isle]

Since (x - 4)^3 = x^3 - 64
is definitely not true

[glad ore]

does anyone know a good resource I can use to answer this

[gray isle]

$\fdream$

[ocean seal]

ℝamonov

[gray isle]

consider the definition of exponentiation and do a tedious expansion
or apply binomial theorem

[fresh fulcrum]

ok yes I see it ! Thank you 🙂

[alpine sable]

Hello

Can I get help

With some classwork

I have no knowledge of this

Like none at all

I don't know what I'm doing honestly

Trig ratios

all you need

[short thorn]

Ye Sin Cos Tan

[lilac dove]

Need help

[alpine sable]

I have this

But I don't know what to do with this

[alpine sable]

Just apply pythag