help-13

[still hedge]

and then I plug it in

[cosmic steppe]

Yeah so now you do $\frac{\sqrt{78} - \sqrt{14}}{-9 - (-1)}$

[wraith dagger]

Umbraleviathan

[crimson sedge]

wait

i have a doubt

[cosmic steppe]

I graphed the secant

And the points

[crimson sedge]

in the formula u gave y2 1st

[cosmic steppe]

Doesn't matter

[crimson sedge]

signs do matter

[cosmic steppe]

If you switch the top and bottom

[crimson sedge]

oh ok

[cosmic steppe]

If you switch one but not the other it won't work

If you switch the order of both it doesn't matter: -1/-1 = 1

[crimson sedge]

is that -1

[still hedge]

-0.636

is the answer?

[cosmic steppe]

-1/-1 is 1

[crimson sedge]

bruh

root 78 - root14

is root 64 which is positive

so 8 / - 9 + 1

[still hedge]

so the answer rounding up to the nearest hundredth is -.64 right

[cosmic steppe]

root(78) - root(14) is not root(64)

[crimson sedge]

then?

[cosmic steppe]

The hell you getting root 64 from

[crimson sedge]

then how did u even do?

[cosmic steppe]

$\sqrt{b} - \sqrt{a} \neq \sqrt{b-a}$. This violates exponent laws.

[wraith dagger]

Umbraleviathan

[cosmic steppe]

Calculator

[cosmic steppe]

Yeah

[crimson sedge]

wait what

bruh

[cosmic steppe]

If you let b = 25 and a = 16

Well that's a bad example

[still hedge]

that was right

[cosmic steppe]

If you let b = 64 and a = 4

[still hedge]

WOOOOOOOOOOOOOOOOOOO

LETS GO

thank u umbra

[cosmic steppe]

Would sqrt(64) - sqrt(4) = sqrt(60)?

[still hedge]

now I do not have to redo the entire thing

[crimson sedge]

no

its 8 - 2

i messed up!

[cosmic steppe]

If you're done, close the channel

[still hedge]

how?

[slow thicket]

do .close

[crimson sedge]

dot close

[cosmic steppe]

.close

[cedar kiln]

Channel closed

Closed by @cosmic steppe

Use .reopen if this was a mistake.

[crimson sedge]

.

[still hedge]

.close

[cosmic steppe]

@slow thicket you have perms to close it now :))

I closed it for you

[slow thicket]

i just realized omg

[cosmic steppe]

Like

.reopen

[slow thicket]

that will come in handy

[cosmic steppe]

Try it

[cedar kiln]

✅

[still hedge]

.close

[slow thicket]

.close

[cedar kiln]

Channel closed

Closed by @still hedge

Use .reopen if this was a mistake.

[slow thicket]

bro

[cosmic steppe]

.reopen

[cedar kiln]

✅

[still hedge]

LMAO

[cosmic steppe]

Lol here try it

Again

[slow thicket]

.close

[cedar kiln]

Channel closed

Closed by @slow thicket

Use .reopen if this was a mistake.

[slow thicket]

yay

[cosmic steppe]

Powerful

Now waiting for us to have !lock

[slow thicket]

now that is powerful

.reopen

[cedar kiln]

✅

[runic garnet]

Wait kefir are u the yogurt thing?

[cosmic steppe]

Yeah idk if Tropo and Rat or gonna let us

[slow thicket]

.close

[cedar kiln]

Channel closed

Closed by @slow thicket

Use .reopen if this was a mistake.

[slow thicket]

yeah

[cosmic steppe]

Yeah just close the channel

Don't play around anymore

Fun time's over

[slow thicket]

yeah I was just seeing if i could reopen

[cosmic steppe]

The bot's gonna have a meltdown

[slow thicket]

fun time is over, agreed

[runic garnet]

U love that yogurt?

@slow thicket

[slow thicket]

maybe

fr tho let this channel close

[cedar kiln]

Available help channel!

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[summer igloo]

So, I got this whacky math question that says a kid on a swing can be represented as a sinusoidal function or graph. Man, that is hard to visualize considering they really only go back and forth (changing directions) over a half circle path.

[full trail]

going in a circle is not what defines that specific motion

think what a revolution would be defined as in this situation

[vapid pewter]

I think it is saying that the height of the person on the swing can be represented as a sinograph

[summer igloo]

He starts at 270 degree full stop, he pushes back to 180 to build up energy, he releases and swings up to 0 degrees which represents a half cycle and he follows same path back to 180 degree for a full cycle.

[slow thicket]

time is the x axis

height is the y axis

[vapid pewter]

what that guy said

[summer igloo]

But you still gotta use sine or cosine in the final formula

[slow thicket]

well yeah

draw it out

[summer igloo]

But how would I know what angle the kid is at when they say he pushes back and he is 1m away from center? That doesn't tell anything of an angle.

He is 1m away from center at all times, no?

He doesn't get any further or any closer by swinging on a swing.

[slow thicket]

yes

the straight line from the kid to the center is the same

but the height is differen

i dont even know what the question is

[summer igloo]

Yes, that I can see in my head but it's bizarre how they tell me he's 1m away from center as he pushes back.

That's not gonna change anywhere.

[slow thicket]

you really ought to draw it out

270 is vertical

180 is horizontal

[summer igloo]

Yes, I stated that above

[flint plinth]

the sinusoidal thing is only an approximate solution, and it's only valid if the total angle that the kid (pendulum) swings is small

[slow thicket]

that can be safely assumed bungo

[flint plinth]

so it's not really true that if he starts at 270 degrees as stated...

that it would be sinusoidal

[slow thicket]

they swing up to 0 degrees

[flint plinth]

unless they're assuming forces other than gravity and the chain

[slow thicket]

from 180 to 0

[summer igloo]

Let's just assume it's a normal kid and he follows that path, getting above 180 or 0 is dangerous. 🙂

[vapid pewter]

I think the reason the question specifies that the kid is always 1m away from the center is telling you the range of the equation you need to make

[summer igloo]

Okay, thank you for the help on this one. I'll try to figure this out again.

.close

[cedar kiln]

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[cedar kiln]

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[radiant topaz]

what's your work

[hollow kraken]

@radiant topaz

[radiant topaz]

you got a quadratic right

when does a quadratic have one answer?

[hollow kraken]

b^2 - 4ac = 0 ??

[radiant topaz]

i think so

[hollow kraken]

so what do i do now ?

[radiant topaz]

solve for m

[hollow kraken]

how ?

[radiant topaz]

what is b what is a what is c here

x^2 -4x + (2-m) = 0

[hollow kraken]

b is -4 and c = 2-m

[radiant topaz]

go ahed

find discriminant

[cedar kiln]

@hollow kraken Has your question been resolved?

[cedar kiln]

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[high axle]

Can you help?

[radiant topaz]

ask the question

[high axle]

How do I figure this out

[runic garnet]

Know that the greatest angle will be opposite the side with the greatest length

See if u can go from there

[high axle]

Ye I know that but like

How do I know the numbers of the sides

It doesnt show me the value of the sides

[runic garnet]

U don’t need to

[runic garnet]

That’s the point

[high axle]

Y?

[runic garnet]

Cuz this is enough to figure it out

[high axle]

But how do I know what side is the greatest length?

If i dont know what its worth

[runic garnet]

Literally this lol

[high axle]

Oh

So

Would it be

CB CA BA?

[high axle]

?

[runic garnet]

No

That’s incorrect

[high axle]

Hmm

[runic garnet]

What’s the largest angle

[high axle]

90

[runic garnet]

What side is opposite the 90 degree angle

[high axle]

Ba?

[runic garnet]

Yes

[high axle]

So its

BA CA CB?

[runic garnet]

Explain ur reasoning

[high axle]

25 is opposite

Of CA

And 8 is opposite

Of CB

[cedar kiln]

@high axle Has your question been resolved?

[cedar kiln]

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[dusty pasture]

How would I solve this?

[dusty pasture]

Without a calculator*

[tropic oxide]

1 - b = log_60(60/5) = log_60(12)

[dusty pasture]

Oh wait- log_60(60/5) because 1 = log_60(60)....

Ahh.

.Close ty

.close

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[torpid egret]

can anyone please check my answer

I am getting 4

here is my working

[cedar kiln]

@torpid egret Has your question been resolved?

[torpid egret]

<@&286206848099549185>

<@&286206848099549185>

[torpid egret]

<@&286206848099549185>

[magic talon]

I recommend you to screenshot your answer and directly send it here

[torpid egret]

okay

[magic talon]

Question too

[torpid egret]

just a sec

[magic talon]

Because there's a risk when you download something from stranger

[spice granite]

yes

[torpid egret]

oh yeah got that

wait sending the solution also then

<@&286206848099549185>

[crimson sedge]

what

how in the fuck did you get 4

[torpid egret]

18/4.5

is 4

[cedar kiln]

@torpid egret Has your question been resolved?

[cedar kiln]

Channel closed

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[smoky stump]

does anyone know whether this is true or not?

I'm not really sure

I think it is

but I want other people's opinion

[crimson delta]

Do some examples

[smoky stump]

Is this proof even right?

This is from a friend

but like I se a problem with this

beacuse for some reasons, I think it is false

nevermind this proof is right

[crimson delta]

Well it's not greatly worded

You should first define what h and g are and then show that hog is surjective while g is not

Not just "because we defined hog to be surjective"

[smoky stump]

Right, we should defien what h and g are right

[smoky stump]

Is that it?

[crimson delta]

You wrote "as we defined hog as surjective, then (some stuff) so we now see that hog is surjective"

That's just bad wording

[smoky stump]

yeah I see now

[smoky stump]

what should I do to imrpove this>?

[crimson delta]

"let h and g be defined as .... We then see that hog is surjective because... and g is not surjective because ..."

[smoky stump]

Like don't we need to assume hog is surjective to prove that g is not surjective

[crimson delta]

No. You show that hog is surjective and g is not

[smoky stump]

right we do, I understand now thanks

Could you please take a look at this proof

[crimson delta]

Yes

Clean

[smoky stump]

wouldn't we need to explain why b=g(a) is part of B?

[crimson delta]

Well g:A->B so where else should it be

[smoky stump]

yeah okay

How about this?

[crimson delta]

Yes

[smoky stump]

so is it algood?

[crimson delta]

Yes

[smoky stump]

any improvements?

[crimson delta]

No

[smoky stump]

.close

[cedar kiln]

Channel closed

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[astral thicket]

Hello

[astral thicket]

Does anyone know how to compute this integral

Beta is constant

[lyric narwhal]

,rcw

[lyric narwhal]

,rccw

[lyric narwhal]

,rccw

[crystal raptor]

(Use the react button to rotate instead of using the commend again)

[lyric narwhal]

ah yes

[lyric narwhal]

is this not just the gamma function?

if you take the B outside

it would become B*gamma(b+1)

[astral thicket]

What is a gamma function lmao

[lyric narwhal]

well

it's an extension of the factorial

to include other types of numbers

$Γ(z) = \int_{0}^{\infty} e^{-t}t^{z-1} dt$

[wraith dagger]

kheerii

[astral thicket]

Beta=z-1

[lyric narwhal]

for positive integer values of z, you just get (z-1)!

[lyric narwhal]

that is correct

but you have an extra factor of B in your integral

[astral thicket]

Can you go to integral with me step By step ?

[lyric narwhal]

what?

[astral thicket]

Help me with this step by step

Because honestly I just discovered what is gamma function

[lyric narwhal]

$\int_{0}^{\infty} Be^{-u}u^B du$

[wraith dagger]

kheerii

[lyric narwhal]

is this your integral

?

[astral thicket]

Yes

[lyric narwhal]

$\int_{0}^{\infty} Be^{-u}u^B du = B\int_{0}^{\infty} e^{-u}u^B du = B \cdot Γ(B+1)$

[wraith dagger]

kheerii

[lyric narwhal]

there really isn't any other way of simplifying it

[lyric narwhal]

unless you have a specific value of B, in which case you can use this

[crystal raptor]

What's the context of the question? Look like you have a pdf there, don't want to XY ourselves

[astral thicket]

Let T be an exponential random variable with rate 1, and let β > 0
be a positive constant. Define a new variable X := T
1/β
.
(a) Find the probability density function of X.
[Hint: For b ≥ a ≥ 0, write P(a ≤ X ≤ b) in terms of the density of T, and change the variable of integration to make
the integration limits a and b. Later we will learn a more straightforward approach.]
(b) Find E[X].
(c) Find Var[X].

This is my part a

[astral thicket]

How do we solve part c then ?

[astral thicket]

.

[lyric narwhal]

I am not familiar with variances unfortunately

[astral thicket]

Ok thanks a lot for your attention

[cedar kiln]

@astral thicket Has your question been resolved?

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[plush token]

how do i find the equation of this or something close to it?

[cedar kiln]

@plush token Has your question been resolved?

[cedar kiln]

@plush token Has your question been resolved?

[cedar kiln]

@plush token Has your question been resolved?

[sand cradle]

Are you allowed to give a piecewise defined function?

[sand cradle]

If so, it looks like about $f(x) = \begin{cases}$
$\frac{1}{x + 1} & \text{if }x \leq 0\ $
$-2x + 1 & \text{if } 0 \leq x \leq \frac{1}{2}\$
$\sqrt{x - \frac{1}{2}} & \text{if }\frac{1}{2} \leq x$
$\end{cases}$

Might be with some stretchings

[cedar kiln]

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[summer quail]

An older type of milk packaging had the shape of a tetrahedon. What is the area of each side surface if the package holds one liter and has a height of 1,76 dm? Round the answer to one decimal place

[summer quail]

Can someone explain this?

And how i am gonna solve it

[tropic oxide]

decimeters used unironically

[crimson sedge]

a tetrahedron is a pyramid made out of equilateral triangles as faces

[tropic oxide]

... hold on tho

isn't this problem overspecified

if we take the tetrahedron to be regular (which they often were, from experience) then we need only know the volume to get its side length

the height is unnecessary, one would think

[summer quail]

Am i not supposed to do a equation like X x 1,76/3

[tropic oxide]

i mean, you're definitely not supposed to use the letter x as a multiplication symbol.

but also, the volume of a tetrahedron really is expressible entirely in terms of its side length.

[hidden osprey]

thats one big milk package

[tropic oxide]

1L is a big package?

[hidden osprey]

height

[summer quail]

Its kinda small right?

[tropic oxide]

17.6 cm is not big

[hidden osprey]

oh wait thats decimeter

[tropic oxide]

what'd you think it was lmao

[summer quail]

It was 1,76

That is kinda small

[tropic oxide]

1.76 decimeters, which i converted to the much more common centimeters

[summer quail]

Oh ok

[hidden osprey]

i thought it was a decameter

[tropic oxide]

because seriously who uses decimeters in their day to day life lmao

[tropic oxide]

dam, if you're into outdated metric prefixes.

what common-use units even use the deca-prefix

anyway

,w regular tetrahedron volume

[wraith dagger]

Results provided by WolframAlpha

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

Requested by Ann#0413

[tropic oxide]

where a is of course the side length

[summer quail]

Yea ok

Was this the solution

?

[tropic oxide]

??

did i give away the answer to the problem? no.

[cedar kiln]

@summer quail Has your question been resolved?

[cedar kiln]

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[calm lagoon]

I need help with a "easy" physic problem! I think its related to kinetics

[violet flume]

do you not need an assumption about the bouncing?

i am bad at physics tho

[calm lagoon]

I was thinking that would be necessary — but I was using a kinematics approach so i didn't know if conservation of energy would apply as an assumption

[calm lagoon]

no worries - i am also bad (definitely worse) at physic

physics*

[violet flume]

okay so

if you can figure out how much energy it has when it hits the ground

damn im gonna have to remember a lot about physics lol

if you know how much energy it has when it hits the ground

then you can break that off as a separate problem

a ball is launched from h=0, when does it have no kinetic energy

[calm lagoon]

theres no kinetic energy at the way start? when it is held at 2.2m

but in the part i crossed off, i said theres no K.E. when it strikes the ground?

i said that all the K.E. will turn into Ug (gravitational P.E. at the apex)

but idk if i have to consider thermal energy in addition to Ug

[violet flume]

nah i think thats an assumption

[calm lagoon]

oh okok

do you think i should use a kinematics approach to this?

[violet flume]

i would just split it, determine the kinetic energy when it hits the ground, and take that as your starting energy in the other direction

[normal void]

just watching your convo is shivering my bones im def not taking physics next year

[calm lagoon]

i feel like my professor expects us to us kinematics eqn for this problem

[violet flume]

you should its fun

get a group of friends and order pizza annd all be dumb together

[calm lagoon]

i am traumatized by physics

[normal void]

but alas carry on

[calm lagoon]

I am a lifesci major and this is a prereq which i unfortunately despise

[violet flume]

i gotta see if i can find my hand of god sheet

you give me a sec to rummage

i swear i have a cheat sheet for this stuff from phys

[normal void]

im going to take life sci too

[calm lagoon]

i mean i have like an eqn sheet but i still dont really know how to approach this problem

[calm lagoon]

exciting :)) love everything besides physics

[normal void]

im joining the navy/military after highschool so i think knowing some biology will help

[calm lagoon]

that's sickk - learning any type of science is always helpful and interesting

but physics... it kills me

[normal void]

all sciences are my best subjects but im somehow garbage at math

[calm lagoon]

no same tho

[normal void]

it baffles me tbh

[calm lagoon]

i realize this is like such high school level stuff but ive never taken physics in my life

[normal void]

lol i was exposed to trigonometry a few days ago and im still traumatised

where did all the numbers go

[calm lagoon]

bro make sure you actually understand everything loll

[normal void]

where is my plus symbol

i need everything back to simpler times

[violet flume]

heres what i think

[calm lagoon]

someone in my professor's office hours admitted they had no idea what the unit circle was, and my professor was astonished

[violet flume]

lets start at the first half

so, you have a ball

[calm lagoon]

our school system has failed us

[violet flume]

you throw it in the way described

it hits the ground

how much kinetic energy does it have when it hits the ground

its a combination of the energy from being thrown, plus energy it picked up from gravity

[calm lagoon]

i said 0.9N

1/2(0.8kg)(1.5m/s)^2

[violet flume]

N? newton?

[calm lagoon]

yes?

[violet flume]

newtons are force

[calm lagoon]

i think o_o

[violet flume]

[calm lagoon]

oh my am i gonna fail my final

[violet flume]

nah youre good

[calm lagoon]

JOULES

[violet flume]

and this is only the gravitational part?

no,

its only the htrown part

[calm lagoon]

is there an additional energy for the first part (ball going down?)

[violet flume]

dangit

[calm lagoon]

lol nice

[violet flume]

https://media.discordapp.net/attachments/903430334681608232/1087407386240757811/IMG_143BAC186408-1.jpeg?width=1271&height=701

so a good hint you have more to do

you havent used all the information in the first sentence

we also have h_i = 2.2m

you do pick up energy from gravity right?

or maybe im just being dumb

like the ball starts with some potential before its thrown

[calm lagoon]

no i think youre right but i have a feeling this problem has to do w kinematics

[violet flume]

dont we gain that as potential in the fall?

im not 100% sure what you mean

its been 4 years since physics lol

kinematics?

[violet flume]

oh man

no no

energy is always easier

well i guess it depends what you are comfortable with

[calm lagoon]

you're completely fine but my professor said that kinematics should be used if you want to know displacement, angles, and/or direction

and energy approach for speed

[violet flume]

okay

so we use YIII to start?

and lets call it like

$v_g^2 = v_0^2 + 2g(y-y_0)$

[wraith dagger]

jan Niku

[violet flume]

_g for ground

no...y is 0 isnt it

so it simplifies

$v_g^2 = v_0 ^2 -2gy_0$

[wraith dagger]

jan Niku

[violet flume]

tell me if i lose you or am being dumb

[calm lagoon]

wait but i thought it was starting at 2.2m?

im sorry i'm quite slow lol

wait also, i tried your energy approach considering Ug (gravitational P.E. in the first part) and got the same answer using kinematics

[violet flume]

was gonna leave it general for a bit

[violet flume]

ah, okay

then youre done ?

haha

[calm lagoon]

does it make sense that the height is greater than the initial height?

oh sorry wait that the same pic

[violet flume]

think of the energies in the initial part

[violet flume]

say you had the same assumptions

but you just dropped the ball=

instead of throwing it

what would the height be

[calm lagoon]

should be less than the inital height?

[violet flume]

i dont think with our assumption

[calm lagoon]

oh then it would be the same height as initial

but then since a force was added, the final height is >> than initial height?

[violet flume]

yea

which you can sum the energies loosely

[calm lagoon]

ah okok

[violet flume]

you have some potential

that gets you where you were

[calm lagoon]

hopeuflly this is the correct answer

[violet flume]

then youre adding some kinetic

[calm lagoon]

okok

[violet flume]

your assumptions dont give you a way to lose energy

[calm lagoon]

thank you for your help!

[violet flume]

np good luck on your final

[calm lagoon]

thank you :)

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[oblique prawn]

so you know like when you’re trying to reference an element of a matrix with the notation $A_{ab}$

[wraith dagger]

Jash

[oblique prawn]

and a, b are digits

how do you say it when a and b are more than 1 digit

[dire geode]

you just leave it as $A_{ab}$ and write $a=12, b=34$ later

[wraith dagger]

riemann

[oblique prawn]

oh

ok ty

.close

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[crimson sedge]

why is the top answer wrong but the bottom answer is right

[crimson sedge]

isnt the first term (8+x)^1 = (8+x)

is the first question meant to be for the same series?

[blissful glade]

yes

however your problem is that your common difference is (8+x)

so (8+x)/(1-(8+x)) is your sum

dividing top and bottom by (8+x) gives you:

1/((1/(8+x))-1)

taking out -1 gives you the sum shown

[crimson sedge]

but they have different values, im confused now

[blissful glade]

additionally the sum to infinity is different than a set sequence

[cedar kiln]

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[fleet terrace]

does anyone know?

[tame wraith]

im acc curios

,w integrate cos(x)/(x^2 + 1)

[wraith dagger]

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[tame wraith]

yh, i thought not

[fleet terrace]

from -inf to inf

the answer is pi/e

how to solve it

[tame wraith]

@fleet terrace it has something to do with contour integrals

[fleet terrace]

do you know how?

[tame wraith]

That's out of my area of expertise

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[tranquil mason]

where did the 3

circled in red in the image come from

how did they have that 3 there

[digital spade]

It's from deriving f^3(x)

[tranquil mason]

how?

[digital spade]

What's the derivative of f^3(x)

[tranquil mason]

i'm not sure how to find that

[digital spade]

You haven't done derivatives?

[tranquil mason]

i have

but

how do i get that from a graph

[digital spade]

Ok what's the derivative of x^3

[tranquil mason]

3x^2

[digital spade]

Yup

[tranquil mason]

ohhh

okay yea i see now

[digital spade]

This is what they did but with f(x)

[tranquil mason]

.close

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[untold raptor]

Im not sure if I’ve done this correctly can someone check if it looks right

The wording of the question is kind of putting me off thinking I did this right

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[spark rune]

i wasnt in class so im just not sure how to do this

if someone could help explain

[cedar kiln]

@spark rune Has your question been resolved?

[spark rune]

<@&286206848099549185>

[spark rune]

<@&286206848099549185>

[idle bane]

You should check if all the angles are the same

If not then they're not similar

[spark rune]

in this case they would not be similar then?

[idle bane]

Correct

[spark rune]

Alright here is another question I have

what is angle y congruent to>

?

@idle bane

[idle bane]

Let me see

[spark rune]

i dont see one it could be other than y again

[idle bane]

Yeah is was thinking that too

[spark rune]

and yzx would be congruent to?

z?

[idle bane]

To U

Id say

[spark rune]

first one is correct

U is wrong

its not U or Z

[idle bane]

Oh lol

Oh oops

I read it wrong

Shouldn't it be W

[spark rune]

yeah it should be

[spark rune]

how about this one?

[idle bane]

Well U and R are congruent

And S and T are also

[spark rune]

how do you know?

[spark rune]

Next question i need help with

@idle bane

if you can

[idle bane]

BCG right

[cedar kiln]

@spark rune Has your question been resolved?

[spark rune]

yes

[cedar kiln]

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[static fern]

all i did was try programming it in python and we got 109

[cedar kiln]

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[static fern]

<@&286206848099549185>

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[crimson sedge]

how do you do (c) and (d)?

[crimson sedge]

indices

[cosmic steppe]

The easiest way is to take the natural of both sides and isolate x

[crimson sedge]

how do i take it away tho

[cosmic steppe]

Show me your work

[crimson sedge]

im not sure how to even start it

[cosmic steppe]

didn't I just say to take the natural log of both sides...

[crimson sedge]

so i just remove 6 and 12 and leave x?

[cosmic steppe]

No

Have you worked with logarithms before

[crimson sedge]

No

[cosmic steppe]

Well there's no actual way then to get x other than taking the natural log of both sides

Are you sure you haven't seen things like $\log(x)$ or $\ln(x)$

[wraith dagger]

Umbraleviathan

[crimson sedge]

no, this question is from my textbook on indices chapter

[cosmic steppe]

I see no other way then

They require logs

[crimson sedge]

ok

.close

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[urban quartz]

hey

[urban quartz]

??

[violet flume]

domain so

youre looking for problem values

can you think of a place this function might not be defined

[fair mortar]

write the denominator as factors

[urban quartz]

(x-5)(x+5)

??

[fair mortar]

yes

so

one rule is

denominator can never be zero

so now

$f(x) = \frac{(x-2)}{(x-5)(x+5)}$

[wraith dagger]

bettim

[violet flume]

woah

[urban quartz]

ok

[violet flume]

blue

[urban quartz]

so now what

[violet flume]

do you have the hex for that blue

[fair mortar]

at what values of x does the denominator will be zero?

[fair mortar]

cyan

[urban quartz]

5,-5

[violet flume]

do you have the cyan for that blue

[fair mortar]

#00FFFF

[violet flume]

oh, damn

[fair mortar]

yes

so the domain is all real numbers except -5 and 5

you can represent it as

$x \in (- \infty ,-5) \cup(-5,5) \cup(5,\infty)$

[wraith dagger]

bettim

[urban quartz]

the U

??

[fair mortar]

yes

or you can write it as

[urban quartz]

alrr W man

u a legend

thx bro

[fair mortar]

yw

$\mathbb{R} - \lbrace-5,5\rbrace$

[wraith dagger]

bettim

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[lethal bison]

is g ○ f even possible?

[radiant topaz]

no

[lethal bison]

.close

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[lethal bison]

thx

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[fleet terrace]

Could anyone please solve this integral?

[tropic oxide]

we don't give answers here

[fleet terrace]

But its not homework

Its a hard integral i found online which i found interesting

Its complex analysis or feynman

[tropic oxide]

when you say "Could anyone please solve this integral?" you sound like it is homework you want done for you

[fleet terrace]

Oh

So could you please help me?

[tropic oxide]

how familiar are you generally with complex analysis

[cedar kiln]

@fleet terrace Has your question been resolved?

[fleet terrace]

From 1-10, 3

[tropic oxide]

do you know the residue theorem

or whatever its called

expressing a contour integral of a holomorphic function in terms of residues at the poles inside

[fleet terrace]

Ok

Is there a quick video explaining it?

[cedar kiln]

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[plush token]

how do i find the equation of this or something somewhat similar to this?

[cedar kiln]

@plush token Has your question been resolved?

[buoyant latch]

what is this supposed to be

passes through (-2, -2), (-1, 1), (1, 1) and has an asymptote of x=y as x -> ± inf?

it looks like it passes through 0,0 but that's not a point written

[plush token]

yeah idrk either

im pretty sure its a graph that has many functions multiplied or added together

[buoyant latch]

so first things first then, we want lim x->inf = x and lim x-> -inf = -x

hmm

we also want it to be under for -inf

and above for +inf

,w graph (x^3+x)/(x^2+1)

[wraith dagger]

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[buoyant latch]

ok fantastic

[plush token]

lmao

[buoyant latch]

we want f(1) = 1, f(-1) = 1, f(-2) = -2

hmm we also know f'(-1) = 0

that means if f(x) = g(x)/h(x) that g'(x)h(x) = g(x)h'(x)

ok

,w graph x((x+1)^2-1))/((x+1)^2+1)

[wraith dagger]

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[buoyant latch]

now that approaches from the wrong side though

[plush token]

yea it's supposed to intercept at 1,1 as well

[buoyant latch]

hmm this also does pass (-1, 1) but not as a turning point

[cedar kiln]

@plush token Has your question been resolved?

[plush token]

anything similar is fine?

[cedar kiln]

@plush token Has your question been resolved?

[cedar kiln]

@plush token Has your question been resolved?

[cedar kiln]

@plush token Has your question been resolved?

[abstract shell]

Are you allowed to define it piecewise?

[cedar kiln]

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[heady salmon]

How do you you format the radius of a function in the Shell volume method?

[cedar kiln]

@heady salmon Has your question been resolved?

[dire geode]

are you working on a problem?

[tulip island]

radius should be using like the function right?

[heady salmon]

ya this one

[cedar kiln]

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[tulip island]

OH!

i think i go tit

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[marble ermine]

Hello, I have a question, to solve a first order differential equation such as ty'(t) - y(t) = 2, I need to divide the expression to get $y'(t) - \frac{y(t)}{t} =\frac{2}{t}$ and find the solutions for t != 0, but what do i do when t approaches 0? That part confuses me

[wraith dagger]

lilisworld

[royal loom]

looks like the bot is down right now

$5=5$

[wraith dagger]

AustinU

[marble ermine]

ok then, but you can understand my question

[royal loom]

are you just trying to solve the ODE?

[marble ermine]

yes

that one

[royal loom]

are you familiar with integrating factors?

[marble ermine]

yes

[royal loom]

what have you found the integrating factor for this to be then?

[marble ermine]

since the bot doesnt work

uhm

the integral of (2/t²)

[royal loom]

no

[marble ermine]

it's -2/t

[royal loom]

for an ODE of the form y'+p(t)y=q(t)

the integrating factor u(t) will be e raised to the power of the integral of p(t) dt

find that for your question

and then let me know what you find u(t) to be

[marble ermine]

yeah

p(t) is -1/t

so the integrating factor is t

[royal loom]

nop

if p(t) was 1/t then sure

[marble ermine]

nope wait it's exp(-ln(t))

[royal loom]

nop

performing your integral will give -ln(t)

yes?

e^(-ln(t))

is (e^(ln(t)))^-1

is t^(-1)

is 1/t

[marble ermine]

ok

[royal loom]

so the integrating factor is 1/t

can you go from there or do you need more help with it?

[marble ermine]

i think the problem is t

if t=0

it's not defined

[royal loom]

what's not defined?

[marble ermine]

i can find solutions for t!=0

[royal loom]

what's the complete question, could you send a picture?

[marble ermine]

it is just asking me to solve ty'(t) - y(t) = 2

[royal loom]

okay

have you found the solution

[marble ermine]

i devide both parts by t to get rid of the "t" in a_1, and then use the integrating factor but only works when t!=0 because cannot devide by 0

[royal loom]

have you found the solution yet

yes or no

[marble ermine]

yes

so it looks like

i mean no because they only work for t!=0

[royal loom]

I'm not sure if this is the help you need but

the original ODE is

ty'-y=2

correct?

when t=0 the equation is then is -y=2

i.e y=-2

which is also what your general solution would give you (if you had found it already) by plugging in t=0

is that what you mean?

[marble ermine]

yes, so we don't need to specify that t!=0?

becase we divide by t when we want to solve it?

[marble ermine]

that works here because there's no denominator but when i need to get rid of "t" in the left and divide by t

[royal loom]

listen, if the original equation is ty'-y=2 and you are concerned about the solution when t=0 then plug in t=0 and it will give you the solution is y=-2. The rest of the solutions can be found by dividing through by t and finding the integrating factor etc...

I'd be most concerned with finding the general solution

have you found that yet?

[marble ermine]

the general solution I found was some constant number C - 2

[royal loom]

that's not correct

[marble ermine]

Ct - 2

[royal loom]

yes

that is it

try t=0 in that

what do u get

[marble ermine]

-2 but for redaction sake

i cannot say 1/t without specifying t!=0

can I?

[royal loom]

formally no

[marble ermine]

so what do i say

[royal loom]

?

[marble ermine]

nvm, i guess it's ok

thanks

.close

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[light pine]

why did they choose c to pick c = -lnA

like why that

out of everything

how do they know to pick that for C

[obtuse grail]

They chose it because it could combine with the other natural logs I think

[light pine]

but like

what if i chose to pick

c = ln(A)

i would get a different answer

so techincally

is there more than one answer?

for the curves of steepest descent

[cerulean sail]

Not really, it might look different but you can always make changes (remember the "absorbing constants" stuff we did that other time)

[light pine]

yhyh

ight kl

thanks

good reminder acc

.close

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[exotic solar]

really dont know where to start, I've only done problems with quotient when x --> inf

[dull oxide]

you can turn this into quotient

Hint: factor out a 1/x from the whole limit

[exotic solar]

hm

let me try

f

i tried doing like this

and its going towards the wrong answer

because the answer is 3, but, by the last expression, is going towards -inf

I've messed up somewhere

[dull oxide]

Oh

I mislead you

Factor out an x, not 1/x

When you factor out x, write it as 1/x in your denominator

[exotic solar]

oh

my friend helped me

he used cojugation

thanks for your time

.close

[cedar kiln]

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[vagrant current]

how do i work out the equation for this curve?

all i know is that y is inversly proption to x

therefore y = k over x

[sharp lotus]

youre on the right track, now pick some helpful points (ones that are whole numbers are good candidates) to work out k

[crimson obsidian]

The general outlook of the graph is similar to that of y=k/x

[sharp lotus]

you see any points on the graph with integer coefficients?

[vagrant current]

i can see only 2 with integer coefficient

only the x value 2

[sharp lotus]

well, 2 on each half of the graph right?

(2, 1), (1, 2), (-1, -2) and (-2, -1) are all on the graph

[vagrant current]

oh yea your correct , didn't spot that

[sharp lotus]

so if you plug in lets say (1,2) into the equation you already said y = k/x, what do you get for k?

[vagrant current]

for k you would get a value of 2

[sharp lotus]

alright, now test the other 3 integer-valued coefficients we mentioned, if you use y = 2/x, does it work for everything?

[vagrant current]

i'll test them now , give me a sec

[sharp lotus]

then also think about the asymptotes, do they make sense as x increases without bound and x -> 0 ?

from either left or right etc?

[vagrant current]

so after testing the other 3 points gathered earlier , they all end up having the same value of 2 for k

and when i subsitute them into y = 2/x they end up getting a value of -2 or 2

[sharp lotus]

yes, so the equation seems to work for all test points

so you pretty much had it from the start, but all you had to do is calculate the value of k using a test point

[vagrant current]

thank you for the help man honestly , and thank you for your time also 😁 😁

[sharp lotus]

you're welcome, cheers

feel free to .close if that's it : )

[vagrant current]

yeah that was all , have a great rest of your day :))

.close

[cedar kiln]

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[cedar kiln]

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• Show your work, and if possible, explain where you are stuck.
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[vagrant current]

how do i integrate this?

[velvet mortar]

What have you tried?

[strong lantern]

Use this formula

[vagrant current]

so i've tried adding 1 to the powers and diving the denominator by the new powers but that didn't work

[vagrant current]

i'll give it a try

i've tried something similar to this earlier but the final answer was inccorect when i subsituted my 2 integral values

[halcyon marlin]

pretty sure you didnt divide correctly

1/2 * 1/4

[strong lantern]

You have to multiply (n+1) in denominator in each term also

[halcyon marlin]

oh you just added 1. you're supposed to divide with the new power

so divide 4 in 2nd term

divide 7 in 3rd

and divide 10 in 4th

[sharp lotus]

to clarify your wording: you need to divide each TERM by the new power, not divide the DENOMINATOR. Dividing the denominator would be equivalent to multiplying each term, the opposite of what you need to do

[vagrant current]

when you say "multiply ( n+1 ) " which value of n+1 are you talking about is it? is it the new numerator value that we multiply with the denominator?

[vagrant current]

oh alright so i understood my first mistake adding 1 to the denominator

as what you and koter said

i would need to divide the new power by the denominator so the first term would be

how would i divide this new value by the denominator tho?

[sharp lotus]

you just slide another 4 in the denominator to divide the term by 4

sry, that's tiny

[strong lantern]

Yup- take term x^3/2.
the "n+1" here is 4

So put it according to formula
i.e x^4/2(4) = x^4/8 after integration

[sharp lotus]

so you're just dividing that whole term by 4, if there is already a denominator that amounts to sliding in another factor of 4 down there

[strong lantern]

yup-

[vagrant current]

ohhh so that's how you'd work out the value of the denominator

[sharp lotus]

so that term just ends up being

[vagrant current]

and then you'd do the same for each other term 🤔

[sharp lotus]

indeed

[vagrant current]

well thank you guys for this

just 1 more questino

whats the exact name of this integral equation?

i've never seen it in my classes

[sharp lotus]

it's the power rule for integrals

it's just the opposite when you do derivatives

[vagrant current]

oh right , i'll take a look into it ... this method is much better than the one i was taught

[sharp lotus]

remember when you do derivatives, the exponent goes down by 1 and you multiply by the OLD exponent, go back and forth on a few examples (integrate once, then do derivative), you will end up with what you started, or do a derivative first then integrate, order doesnt matter

[vagrant current]

noted 👍 , thanks a lot man honestly i think the method you guys showed me saved me so much time from the older method i was shown

[sharp lotus]

Spoiler of the fundamental theorem of calculus: ||derivation and integration are opposite operations||

what was the method shown?

you might have been taught just definition of integration, riemann sums and whatnot and expected to do the problem this way for the first day or so. The shortcuts come soon after, but it is important to understand the geometric intuition of what integration is doing and how it is defined in the first place so hopefully you got some of that.

[vagrant current]

so we'd have to convert the fractions into index form without any denominators and then add 1 to the power and divide ,

but with questions like this one its something we didnt do in class
normaly the denomaintors for questions we did in class would be x or any other algebraic value*

[sharp lotus]

what even is index form?

[vagrant current]

yeah true , we've started integration 2 weeks ago its a rough topic

[vagrant current]

so for example 1/x in index form would be x to the power of -1

[sharp lotus]

I definitely don't think any course would expect anyone to solve this particular problem with riemann sums though...that sounds...painful

[vagrant current]

its a shame because my class is struggling just as much as me on this topic , the teacher is also just a student

( we dont have a fully qualified maths teacher atm )

[sharp lotus]

isn't the problem given already in index form then? all the x's are in the numerators

[vagrant current]

yeah , but here in my school we'd have to remove the denominator and bring it up wait

i'll show an example

[sharp lotus]

that makes no sense when the denominator is just a constant...

[vagrant current]

something like this

[sharp lotus]

if you are not getting good lectures in your class i recommend this teacher's youtube videos, she has good clear writing, speaks clearly and has good understanding of the topics and they are explained in good detail for an introductory level (she's a high school teacher), there is a whole list on AB calculus you can find on her channel, here is the particular video on antiderivatives
https://www.youtube.com/watch?v=xPXnVomKb9w&list=PLLpHa44nPtMs-tmAhYHIEoCjytRii_6Y1&index=54&ab_channel=MichelleKrummel

[vagrant current]

I've never heard of her , i'll check her calculus videos out 🖊️