help-23

[rose thorn]

it's like

nvm

[hazy elbow]

join centre of the three circles

and try to find height of the triangle so formed

[lean otter]

What's the general formula for area of the rectangle?

[safe radish]

@trail oriole Has your question been resolved?

Channel closed

Closed by @trail oriole

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[inland hawk]

Hello

[inner current]

[inland hawk]

I had this question where there was a graph drawn, and they ask which graph matches, with 2f(x+1)+1 does the “2” mean a scaling or compression im not sure?

I though the function scaled

and by the way f(x) was just drawn not given

[versed wave]

show the original graph

and the whole question

[long shore]

please

[inland hawk]

well i have an example because i dont have the direct questions

it was like this but

2f(x+1) + 1

and other function

the questions is which transformation (given) matches the graph

[long shore]

it depends on the function

like 2 * x^0.5 vs 2 * x^2

[inland hawk]

it was sometving like this

the f(x) given

not x^2

[long shore]

try taking an x value and multiplying it by 2 and see what it would do

[inland hawk]

uhm but I dont have the function

as it was drawn and not given like f(x) = ..

[long shore]

when its a parabola, 2 x the parabola compresses it

so it goes closer to the line

[inland hawk]

it went like that

and they just give this drawing as f(x)

[versed wave]

this seems like a piecewise functions where the middle part is a parabola

so scaling/compressing should be the same, scale if k<1, compress if otherwise

[inland hawk]

hmm so it was scaling

compress*

?

(not very accurate) but this is what I thought

[long shore]

well if you think about it, y = α for all x values at a certain y point

[safe radish]

@inland hawk Has your question been resolved?

[safe radish]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[hushed mantle]

guys help wtf is this symbol

[lean otter]

Lambda

[hushed mantle]

bruh whats a lambda

[analog kelp]

its like x

u can use any symbol

[hushed mantle]

and how does it probe that these two equations have infinite solutions

[desert juniper]

lambda means "this is any number of our choosing"

you prove that these two equations have infinite solutions because they are equivalent, so you only have one equation and two variables

[hushed mantle]

what can you explain slowly

[lean otter]

Is this subject about lagrange multipliers

[desert juniper]

no, what? this is just a system of two equations

[desert juniper]

you have two equations and two variables.
Since the equations are equivalent (the second is just twice the first), you only have one non-redundant equation

which means that any pair of values (x, y) that satisfy the equation are a solution

let's say you choose whatever value of y. You choose y=lambda.
If y=lambda, then x=(6-3lambda)/2

so any pair of values of the form stated satisfy the equation

[safe radish]

@hushed mantle Has your question been resolved?

[safe radish]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[pale isle]

What tf man how they except me to find this shi

Wait

[lean otter]

do u have working

[pale isle]

I got it

Kind

A

I think

Wait

Is this correct

@lean otter

[lean otter]

yea

[pale isle]

@lean otter HELP

This shit got no label

Do I do it myself

Q5

[lean otter]

Yes actually you can find them all

[pale isle]

How

[lean otter]

Do you know where AB is

[pale isle]

Yes at the 2 points where the hexagon and pentagon meet

But idk which is which

[lean otter]

ABP belongs to the hexagon

[pale isle]

Huh

[lean otter]

It says that ABPQRS is a regular hexagon

[pale isle]

Ye

[lean otter]

So ABP is an angle belonging to the hexagon

[pale isle]

But the a and b are interchangeable

Up and down

[lean otter]

Do you think there's a difference between ABP and BAS without knowing the points

[pale isle]

Yes

[lean otter]

Sorry I meant BAS but anyway it's a regular hexagon so all interior angles are the same

[pale isle]

I don’t understand

@lean otter

Is this right

[lean otter]

Yes

[pale isle]

Ok

Wait how tf do you do this again

[lean otter]

Basically, if you swapped P and S or any letter in the hexagon the angle measure would still be the same
ABP = BAS = BPQ etc.

[pale isle]

Yes it’s regular

[pale isle]

Q6b sum random shit

[safe radish]

@pale isle Has your question been resolved?

Channel closed

Closed by @pale isle

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[covert kiln]

For question 5

I took moments of the middle 5g

And I got the anwser to be .34

[earnest olive]

you sure you took moments about the hinge?

[covert kiln]

Yh from the centre I’m sending a pic rn but it’s not loding

[earnest olive]

centre of the rod?

[covert kiln]

Yh

[earnest olive]

nah for hinge questions you need to balance the moments about the hinge for an equilbrium

[covert kiln]

Wdym

So I can’t take moments from the centre of the rod

[earnest olive]

no because of the rotation is taking place about the hinge

[covert kiln]

I’m confused

So u can’t take moments of rotating pivots

[earnest olive]

because this rod would rotate about the hinge

[covert kiln]

Yh but i don’t seee why u can’t take moment from the centre

[covert kiln]

Wdym about the hinge

Do u mean the hinge that x amount away from the centre

[earnest olive]

thing is that the vertical force on the hinge doesn't rotate the rod, it's just a force balancing the weight of the rod and the other 5.5g force

[earnest olive]

yes

[covert kiln]

Oh so u can only take moments of pivots

Like the supports

[earnest olive]

correct

[covert kiln]

Okay thank you

[earnest olive]

remember this concept, i struggled too when i was in high school

the horizontal and and vertical force at the hinge just balance the other forces

[covert kiln]

When u say hinge do u mean pivot

[earnest olive]

https://tenor.com/view/hinge-gif-18937057

basically something like this, the triangle is a hinge

[covert kiln]

Cause so far we’ve been doing questions based on rods

[covert kiln]

Oh ok we called it a pivot for some reason

The triangle

[earnest olive]

ah that's the same thing

[covert kiln]

Yh

Again ty for the help

[earnest olive]

anytime mate

[covert kiln]

.close

[safe radish]

Channel closed

Closed by @covert kiln

Use .reopen if this was a mistake.

[safe radish]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[crude bear]

My teacher said that if H(a) is the quadratic form associated with the hessian matrix at A and H(a) is always positive, then a is a local minimum

[crude bear]

I don't understand

Say f(x,y) = x^2-y^2

Then Df(x,y) = (2x, -2y)

So Df(x,y) = 0 iff (x,y) = 0

Now we have f_xx = 2 and f_yy = -2. Also f_xy = 0

So the matrix is [[2, 0], [ 0,-2]]

What is the quadratic form associated?

[obsidian oracle]

It's 2f

quadratic form of Hessian $H$ is $q(v) = v^THv$

[flat frigate]

rafilou2003

[obsidian oracle]

but $q(x,y) = 2x^2 + 0xy + 0yx -2y^2$

[flat frigate]

rafilou2003

[obsidian oracle]

sorry so 2f not f

[crude bear]

And because this is = 0 for some (x,y), we have a saddle?

[obsidian oracle]

not just = 0, that wouldn't help us conclude

if you let |y| > |x|... it gets negative

so we have a saddle because H can be positive as well as negative

[crude bear]

I think I understand now

[crude bear]

If B is bilinear the quadratic form is g(v) = B(v)(v)

So for matrices, it becomes that?

[obsidian oracle]

yep

[crude bear]

I thought doing something like <(B*v), v>

[obsidian oracle]

ah but Bv is a vector

so you can't multiply Bv and v

exactly scalar product

but the scalar product for vectors of R^n

is exactly $<x,y> = y^Tx$

[flat frigate]

rafilou2003

[crude bear]

Hmm

You're right

Okay, I understand now

I was getting confused because this is different from what we see in calc 3

The second derivative test

Maybe it's the same thing and I don't see it yet

[obsidian oracle]

it is yes

the hessian matrix in one dimension has only one coefficient : the second derivative

and so the quadratic form associated to it is

$q(x) = x^2f''(a)$

[flat frigate]

rafilou2003

[obsidian oracle]

so q is positive <=> f''(a) > 0

[crude bear]

I get it now

Thanks rafilou

.close

[safe radish]

Channel closed

Closed by @crude bear

Use .reopen if this was a mistake.

[safe radish]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[pulsar pecan]

how can I tell if this function is injective or surjective without a graph?

[pulsar pecan]

something about image and dimension of the kernel ?

[safe radish]

@pulsar pecan Has your question been resolved?

[hard crest]

with 5 inputs and 3 outputs it can't be injective, to check if it's surjective do a row reduction

[pulsar pecan]

3 outputs as seen by the fact that the function has 3 rows

[hard crest]

yeah

[pulsar pecan]

and 5 inputs as x1,x2,x3 etc

I did row reduction and got a rank of 3

meaning it should span R^3 right?

since these columns are linearly independent

[hard crest]

mmm well it'll span 3 dimensions

to call that R^3 isn't really right but yeah
(imagine a plane in 3d space. is that R^2? I guess you could call it that but it feels kind of odd)

[pulsar pecan]

yeah ig uess

[hard crest]

errr

no i was backwards

yeah it'll span R^3

[pulsar pecan]

The site says:

colspace(A) = im(f) = R^3

[hard crest]

ye ye i was being silly

[pulsar pecan]

proving it is surjective because it spans all of R^3

but what I am wondering is the connection between image and the surjectiveness

the function is R^5 -> R^3

[hard crest]

oh, if the image of the function is all of R^3 then it's surjective

[pulsar pecan]

image = R^3

[pulsar pecan]

How can that be?

I think maybe I dont fully grasp what the image entails

[hard crest]

image is the reachable points, the range of the function

[pulsar pecan]

right

and so if all of R^3 is reachable

[hard crest]

then it's surjective

[pulsar pecan]

then the image is equal to the co-domain

[hard crest]

yeah

[pulsar pecan]

but this is only true because the domain is R^5

which always can map to all of R^3

[hard crest]

can but might not necessarily

but if the domain were R^2 then it couldn't be surjective

[pulsar pecan]

Right okay

[pulsar pecan]

Wait why not always ?

[hard crest]

well imagine something like um

$\begin{bmatrix} x_1 + 2x_2 \ 2x_1 + 4x_2 \ 7x_1 + 14x_2 \end{bmatrix}$

[flat frigate]

hayley!

[pulsar pecan]

is this R^5 ?

[hard crest]

sure

[pulsar pecan]

but I only see 3 rows

[hard crest]

R^5 input

R^3 output

but it's still not surjective

[pulsar pecan]

Oh okay

[safe radish]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[pulsar pecan]

.reopen

[safe radish]

✅

[pulsar pecan]

But the reason why we are 100% sure that ours is surjective is because of the image

which matches the co-domain

I just wanna like know for sure since its all confusing xD

some easy rule

[hard crest]

yeah where as for this second one if you row reduce it you get some 0 rows

[pulsar pecan]

yeah

[hard crest]

it's row reduction

[pulsar pecan]

row reduction -> Check col / rank -> if dim(col) = dim(co-domain) then its surjective

[hard crest]

yes

[safe radish]

@pulsar pecan Has your question been resolved?

Channel closed

Closed by @pulsar pecan

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[tame trout]

which one is correct?
problem on the top of the 1st photo

photo 1: the radicand a has a square
photo 2: the radicand a does not have a square

the answer i got was the same as photo 1

[rustic goblet]

they are the same

the first is a^(2/4) while the second is a^(1/2)

[ruby bolt]

Yes

[tame trout]

ahhhhh, i see

thank you

.close

[safe radish]

Channel closed

Closed by @tame trout

Use .reopen if this was a mistake.

[safe radish]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[lavish blade]

hey i don't understand how to make it

[lavish blade]

i was thinking about Integration by parts

[upper rivet]

are you expecting a "nice" answer in terms of elementary functions? don't think thats gonna happen here

[lavish blade]

Idk how my teacher got away with that

[upper rivet]

kekwhat

[lavish blade]

Do you have any idea how he did it?

[upper rivet]

if the question were integral of e^(x^3) * (x^2) dx it makes sense ig

[lavish blade]

I think he just made a mistake I'll ask him directly, thanks for your help

.close

[safe radish]

Channel closed

Closed by @lavish blade

Use .reopen if this was a mistake.

[safe radish]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[light lark]

i have 2 answers from me and my friend the first one is mine i was wondering why it's kinda different could someone help me see which one is correct

[pale basin]

is there a reason you're trying to calculate using the area of the trapezoid instead of just the triangle?

i mean it would ideally give the same answer but

maybe it simplifies the process a little

[safe radish]

@light lark Has your question been resolved?

[safe radish]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[spring basin]

help

[spring basin]

i need to know how to graph |4x-1| = 3

i solved for it

but idk how to graph it

[obsidian oracle]

You mean graph y = |4x-1| and y = 3?

[spring basin]

no

the question is ecatly this:

|4x-1| = 3

i need to graph it on a number line

[frozen berry]

U get two eqns

[spring basin]

ye

[frozen berry]

2 lines basically

[spring basin]

i got 1 and -1/2

[obsidian oracle]

Just graph the 2 points

[frozen berry]

Both are answers

Just graph them

[spring basin]

no but idk if dot is open or closed

negative is open rihgt

[obsidian oracle]

?

[spring basin]

the negative number is an open dot

[frozen berry]

U need to find the line I assume?

[spring basin]

yes

[obsidian oracle]

2 dots. So both closed dots

[frozen berry]

Cuz it'll be a line

[obsidian oracle]

Idk why they would be open

[frozen berry]

Why dot???

[obsidian oracle]

You have a number line right?

Not a plane

[frozen berry]

Ahh, on Number line yh

On plane we get a line

My bad

[spring basin]

it looks liek this

but with numbers

[obsidian oracle]

Yes

[frozen berry]

Just 2 dots

[obsidian oracle]

So 2 dots

[spring basin]

oka

i closed them both

and they are connected

[frozen berry]

Yes

[spring basin]

also

how do i graph |x| = 4

and |x|≤3

i attempted it

idk if its correct tho

[frozen berry]

Show us what u did

[spring basin]

afk for 5 minutes switching class

[frozen berry]

[spring basin]

back

alright

i cant take a phot

.close

[safe radish]

Channel closed

Closed by @spring basin

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[obsidian stream]

k

[flat frigate]

Da Mucky Boi

[obsidian stream]

yeah

wiat

Integrate it in parts

integrate(uv)

You don't know the uv rule?

k

yeah ofc

nah you won't

integration of e^sinx will be some series

[quiet plume]

i.e. there is no antiderivative in terms of elementary functions

If that's the whole question then not much.

[obsidian stream]

wait

lol

it is due to e^x sinx we can't do this

nah

yeah

[quiet plume]

If it was just e^sin(x) inside then it's simple. The sum screws if up.

[safe radish]

Channel closed

Closed by @timber sapphire

Use .reopen if this was a mistake.

[safe radish]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[dry timber]

Hey, ive got an issue with a math problem I’m completely stuck. I have genuinely no idea what is happening here. This is what I’ve done so far (each square is worth 200m) (the red part in the second pic is the last pic, google translate isn’t very good at translating math terms)

[dry timber]

Im just wondering what all the variables mean

[safe radish]

@dry timber Has your question been resolved?

[safe radish]

@dry timber Has your question been resolved?

[dry timber]

<@&286206848099549185> i could really use some help, I’m very very lost

[safe radish]

@dry timber Has your question been resolved?

[safe radish]

@dry timber Has your question been resolved?

[lyric plume]

Those triangles are "delta" and it means "the change in".
So Delta X means "The change in x"
Delta X / t means "The change in x over time"

the θ looking thing is Theta. It's often a variable used to represent an angle

cos(θ) is just the cosine of the angle.
sin(θ) is the sin of the angle.

if you have other questions about what things means, try to type them out

v is a vector, usually represented as an arrow with an X and Y amount

vx is the x component of the arrow. vy is the y component

[dry timber]

hmm thx a lot this is starting to make sense but it says the v = shell speed so wouldnt v be 250m/s?

[lyric plume]

v is an arrow so it's speed AND direction

e.g. is it 250 m/s north? or 250 m/s east? They give you θ to help you break it down into how much speed is in both x and y directions

[dry timber]

OH

ok ok

[dry timber]

im still kinda lost, u say that V is (250m/s, θ°) right?

so the vector is (speed, angle)

[lyric plume]

you can say that V is a vector with length 250. So imagine drawing an arrow on the map that's 250 long

the angle is θ

But V is actually represented as an X and a Y coordinate

if you imagine the arrow starts at (0,0), then draw a line to (X,Y) then it will be exactly 250 long

and the angle it forms with the horizontal axis will be θ

So you can break V down into Vx and Vy which looks like this

I think in the french, they are using v to be 250 and Vx to be 250 * cos(θ)

because cosine of the angle will give you the adjacent ratio, which we then multiply by the length of V

[dry timber]

ok i get it more but the thing im not sure is how does this help me find at which angle to shoot the cannon, ik from the teacher that there is a quadratic formula somewhere. the cannon has to shoot in a parabola right? u can read the second picture to get the context, i dont get how everything ties up togehter to tell me the angle at which to shoot, im a little slow ngl

[dry timber]

i made this image of the problem

[dry timber]

is it right?

[lyric plume]

yes you have it set up correctly

Assuming there is no gravity

well wait a moment

Reading the original question

I see yes, so this is asking for the vertical angle

Is there gravity involved or not ? (is this physics class?)

If it's algebra class, this is probably correct. if it's physics, they'll want you to add in the effect of gravity on the shell

-9.8m/s I believe is the usual value

[dry timber]

its math there shouldnt be gravity

[lyric plume]

yeah then this is right

[dry timber]

wait but look a the last formula in the last pic ("et" means "and" in french)

i need to use that to find the angle at which to shoot

because it says it loses 4.8m/s i think

[dry timber]

to form kind of a parabola?

i mean we use the quadratic equation so it has to have a parabola?

[dry timber]

(idk where we use it, i just know we do somewhere in the problem)

[dry timber]

also idk how to find: t, Vx, Vy and θ

so i cant rly advance

[lyric plume]

Sure you can

Now it's trigonometry.
Things you know:
The Adjacent of the angle distance (4000)
The Opposite of the angle (150)
What trigonometric function can you use to get the angle?

||using the numonic SohCahToa, we can remember that the Tangent of the angle equals the Opposite over the Adjacent. So just divide 150/4000 = Tan(theta).||

[dry timber]

i dont think this is the way to find the angle at which to shoot the cannon because why would there be 2 whole formula to find the angle if its just sohcahtoa

[dry timber]

the final question is whats the angle at which to shoot the cannon

so

yk what i mean? why would there be two formula with t if we dont use it so find the angle

the last formula indicates that the shell loses 4.9m per second squared so we do have to shoot in a parabola

[lyric plume]

the last formula is
Vy = v * sin(theta)

that's just socahtoa

Oh

[lyric plume]

Ok yeah, so you are using gravity then

apply some algebra

replace Vy with 250 * sin(theta)

the delta y is the change in y. We know the height is 150 meters from the ground

you also need t so you need to know how many seconds it will take to reach the target in the horizontal direction

that's the first formula

Here's a diagram which might help show what you're trying to do

[dry timber]

isnt gravity 9.8? 4.9 is half of it

[lyric plume]

yeah I don't know why they are using 4.9

it's a war on the moon

maybe

[dry timber]

most likely a random number cuz he didnt want us to use a website that calculates

[dry timber]

so do we just take 250 as Vx for the first formula too?

[lyric plume]

no, 250 is the total speed

use 250 for v

[dry timber]

so how do i find t with the first formula?

[lyric plume]

but Vx is based on multiplying v by the cos(theta)

it says
vx = v * cos(theta)

the first formula is 2 equations

vx = delta x / t where vx = v * cos(theta)

you know delta x

it's just the distance to travel

[dry timber]

yes

[lyric plume]

so v * cos (theta) = 4000 / t

Different angles will give you a different amount of time to take to reach that distance. That makes sense

try to work it out from there

[dry timber]

yes but only one angle will make the shell land exactly on the target? i dont get what you mean here, how am i supposed to find the angle necessary to hit that point exactly

[dry timber]

how can i find an other variable here? i only have one number all the others could be wtv

[dry timber]

well

apparently this works

if i make g=9.8

but i cant exaplain why

so it doesnt rly matter in the end

if anyone can help me understand that

[covert yoke]

g = 9.8, but the formula that finds position from time is 1/2 a t^2 + v0 t + s0

Notice that 1/2 a is 4.9 m/s^2 in this case.

[safe radish]

@dry timber Has your question been resolved?

[safe radish]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[obsidian jacinth]

Permutation (a1, a2, a3, a4, a5) from (1,2,3,4,5) is called ‘bingo’ if a1 + a2 <= a3 + a4 + a5

Find how many ‘bingo’ permutation

[versed nacelle]

Well the inequality is false only when LHS equals 8 or 9

So find the number of permutations for LHS = 8, 9 and then subtract from total number of permutations

Note that permutation of either side does not affect the result

[obsidian jacinth]

so find when a1 + a2 = 8,9?

[versed nacelle]

Yes, there are only two possibilities

[obsidian jacinth]

Total number of permutation is 5!

?

[versed nacelle]

[obsidian jacinth]

(a1,a2) = (3,5) (5,3) (4,5) (5,4)

so 120-4 = 116 permutation?

[versed nacelle]

No

You have to account for RHS permutations as well

[obsidian jacinth]

5P3?

[versed nacelle]

??

Yes sorry thats correct

Wait no its actually 3!

Because the RHS is seperate

[obsidian jacinth]

so 3! + 5! - 4

?

[versed nacelle]

No, you multiply 4 by 3!

[obsidian jacinth]

Oh

120-24=96

[versed nacelle]

Yes sorry

I hope that's correct anyways

[obsidian jacinth]

Ok thx

.close

[safe radish]

Channel closed

Closed by @obsidian jacinth

Use .reopen if this was a mistake.

[safe radish]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[hushed minnow]

Given $EX=5$ and $VarX = 4$ how to bound $P(X \geq 10)$?

[flat frigate]

szahu420

[hushed minnow]

From Chebyshev we get $P(X \geq 10 \lor X \leq 0) \leq \frac{4}{25}$, now how to deal with that $P(X \leq 0)$ if we can't assume anything else about X?

[flat frigate]

szahu420

[hushed minnow]

.close

[safe radish]

Channel closed

Closed by @hushed minnow

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[karmic halo]

Can some1 give me proof of these
A and B are invertible matrices

[safe radish]

@karmic halo Has your question been resolved?

[karmic halo]

.close

[safe radish]

Channel closed

Closed by @karmic halo

Use .reopen if this was a mistake.

[karmic halo]

got it

[safe radish]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[hushed anchor]

I am not sure how to approach this

I was thinking like one norm of a vector is the max absolute of its column right so like one norm of v wouod be 6

so inner product of v and w should be 6

but then doesnt hat lead to multiple types of ideas

[light shoal]

"max absolute" - that would be the infinity norm

the 1 norm is the sum of absolute values of the components

[hushed anchor]

oh yeah just realized

wait how do you differentiate then

[light shoal]

differentiate what?

[hushed anchor]

like what wording would mean what i was thinking of

oh shoot its transpose

so 1 norm of v is the max absolute value column

which would mean 1+3+6+2

[light shoal]

no, sum of absolute values

not max absolute value

[light shoal]

yes, this is correct

doesn't really matter that it's a transpose or not

[hushed anchor]

well if it was a matrix

[light shoal]

a vector and its transpose have the same norm

[hushed anchor]

with multiple columns then it would be the max column sum right

[light shoal]

ah, i see what you're saying

yes if you interpret these as matrix norms and not vector norms that's true

but usually for nx1 or 1xn matrices we treat them as vectors either way

so they have the same norms

[hushed anchor]

oh ok

ty

so for second part its saying norm of v without a subscript so would it also be 12?

or does that mean inf norm

[light shoal]

no, i assume that means the 2-norm

usually that's what is meant for a norm with no subscript

unless you have an unusual convention in your situation

[hushed anchor]

you are probably right

so 2 norm would be 1+9+36+4 square root i assume

[light shoal]

yep

[hushed anchor]

is there a correlation with norm and inner products

so basically sum of w elements square will be 1 meaning like inf solutions and sum of abs value of all u elements will be 1

which is also inf

does (v, w)= ||v | |1 * | | w| |

well obvs i am stupid thats how multiplying with 1 work

but then how would you find values thats weird

<@&286206848099549185>

[hushed anchor]

wait but then the solution isnt possible

rip wtv i will yolo lol

ty though

.close

[safe radish]

Channel closed

Closed by @hushed anchor

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[vague parcel]

Hello everyone, I have a question about complex numbers in a problem that has been posed to me.
The problem is the following
I have to find a complex number whose argument is known to be 45º and by adding it to (1+2i) give a complex number of modulo 5. (the modulus is the same as the distance in the Gauss plane)

I have thought that by defining the complex number that we do not know: a+bi
and adding it to the other number that we know should give the module 5, that is:
(a+bi)+(1+2i)=|Z|=5
but on the other hand I have realized that we have the argument, that is, I can solve for the real part or the imaginary part to be able to calculate it later and create a system of equations.

The truth is that I am a little lost and I don't know where to go with the problem, could you advise me or tell me if the approach I have taken is the correct one?

||<@&286206848099549185>||

[proper crypt]

Read #❓how-to-get-help

Don't ping helpers immediately

[unique salmon]

real

[spice grove]

You can just write your complex number as re^(ipi/4)

[proper crypt]

Or just a + ai

[vague parcel]

sorry I'm not used to using this channel

[spice grove]

or that, because the arg is pi/4

[spice grove]

All the more reason to read the rules.

[vague parcel]

yes you're right

[vague parcel]

ok, I'll try it that way

okay, thank you very much, I had not understood that the argument can be pi/4, I only thought it could be in degrees

.close

[safe radish]

Channel closed

Closed by @vague parcel

Use .reopen if this was a mistake.

[safe radish]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[leaden mica]

How dk j do 13?

[safe radish]

@leaden mica Has your question been resolved?

[safe radish]

@leaden mica Has your question been resolved?

[safe radish]

@leaden mica Has your question been resolved?

[safe radish]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[vestal needle]

hello

[vestal needle]

can anyone tell me how can I find horyzontal asymptotes here ?

when it's x-> +inf

I found it when it's - inf but idk how to find it when it's +inf

[tawny knoll]

it doesnt need to have

it may not have

actually it doesnt have when x tends to inf

and there is no problem with that

f(x) = x doesnt have any asymptote, and nothing wrong with it

[vestal needle]

ik but Idk how to calculate it

[tawny knoll]

if f(x) has an H.A

it means that

$\lim_{x\to\pm\infty} f(x) = L$

[vestal needle]

can you help me do this

cuz I don't understand what are you trying to tell me

I switched x with +inf

This is what I get but idk is it correct

if this is correct then there's no X.A

I just need to know if this is correct 🤷‍♂️

[flat frigate]

Aza

[hard crest]

0 * inf is an indeterminate form

[vestal needle]

isn't e^0=1?

[tawny knoll]

it is

[vestal needle]

1*(-1-inf)

[vestal needle]

I know

If that's the case I need to to lopitalh

[hard crest]

it is but where did e^0 come from

[vestal needle]

e^-inf

[tawny knoll]

hayley is lost uwu

[hard crest]

...is not the same as e^0

[vestal needle]

e^1/inf=e^0=1

[hard crest]

where did e^1/inf come from??

[scarlet jolt]

-inf = 1/inf?

[vestal needle]

wait a minute

[scarlet jolt]

I think you're trying to say that e^-inf = 1/e^inf

[tawny knoll]

$e^{-\infty} = \frac{1}{e^{\infty}} = 0$

[vestal needle]

yeah

mb

[flat frigate]

Aza

[vestal needle]

yup

mb

so I need to use lopital rule here right?

[tawny knoll]

u have to fix things before that

l'hopitals only for inf/inf or 0/0

not for 0*inf

[hard crest]

i think you have inf/inf

[scarlet jolt]

yeah

[vestal needle]

anyone willing to write it down on paper or somethin

[hard crest]

$f(x) = \frac{-1-x²}{e^x}$

[flat frigate]

hayley!

[vestal needle]

God bless

Thanks

yeah it's inf/inf

[hard crest]

if you don't understand why then review exponent laws

[tawny knoll]

$e^{-\infty} = \frac{1}{e^{\infty}} = 0$ || $(-1-\infty^2) = -1-\infty = -\infty$

[vestal needle]

I got it

[tawny knoll]

well, sec

nvm cant split 2 different things on the same command

[vestal needle]

alr so

how do I now get x-> +inf to this

Idk how to bring lopital rule so I don't have inf/inf

[safe radish]

@vestal needle Has your question been resolved?

Channel closed

Closed by @vestal needle

Use .reopen if this was a mistake.

[safe radish]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[ruby oar]

!help

[safe radish]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[ruby oar]

.close

[safe radish]

Channel closed

Closed by @ruby oar

Use .reopen if this was a mistake.

[safe radish]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[mental abyss]

I need help to prove, if $f'(x)$ is even and $f(0)=0$, then $f(x)$ is odd

[flat frigate]

shrödinger

[split needle]

!help

[safe radish]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[split needle]

Translating this for english

That's "Solve the exponential equation"

[sand pasture]

first step get rid of the 3^()

by takeing log base 3

then you have $x^2 + \frac{1}{x^2} = log_3(81) - (x + \frac{1}{x})$ by using logarithm rule of log(a/b)=log(a)-log(b)

[flat frigate]

TRAMPELTIER

[sand pasture]

Are you here

[split needle]

Yup.

[sand pasture]

comprendes?

[split needle]

That's a book about logs

xd

So i don't know log rn

[split needle]

Actually teaching exponential func first

[sand pasture]

I mean log is defined such that it cancels out the exponential

log is defined such that $log(e^x)=x$, or for base $b$, $log_b(b^x)=x$

[flat frigate]

TRAMPELTIER

[sand pasture]

it's the inverse function of the exponential so to say

with that, it grows VERY slowly (exponential grows VERY quickly)

Have you been taught about log or not?

[split needle]

Previously?

No.

But i understand what y're saying.

[sand pasture]

okay

you know the exponentila function right

[split needle]

Yes.

[sand pasture]

$e^{a+b} = e^a \cdot e^b$ holds right?

[flat frigate]

TRAMPELTIER

[split needle]

Yes.

[sand pasture]

okay with that, also if we subtract b, we get $e^{a-b} = e^a \cdot e^{-b}$

[flat frigate]

TRAMPELTIER

[sand pasture]

that is the same as $e^{a-b} = \frac{e^a}{ e^b}$

[flat frigate]

TRAMPELTIER

[split needle]

Ok.

[sand pasture]

dunno where I'm going

[split needle]

Using only exponential, we can say that $x^2+\frac{1}{x^2} = 4-x-\frac{1}{x}$

Wait

[flat frigate]

𝑲𝒊𝒓𝒊𝒔𝒉𝒊𝒌𝒊𝒈𝒖𝒓𝒆

[split needle]

First time on this server

Srry the delay

[sand pasture]

no problem

yes so we applied log()

and got this

[split needle]

Hmm

I tried this without log therefore

But the answer is very

Strange?

[sand pasture]

what do you mean

[split needle]

$x^4+x^3-4x^2+x+1=0$

[flat frigate]

𝑲𝒊𝒓𝒊𝒔𝒉𝒊𝒌𝒊𝒈𝒖𝒓𝒆

[split needle]

Using x^2=d

[sand pasture]

huh yea it's correct

it's what we get if we multiply our current one by x^2

[split needle]

$d^2 + d\sqrt{d} - 4d + \sqrt{d} + 1 = 0$

[flat frigate]

𝑲𝒊𝒓𝒊𝒔𝒉𝒊𝒌𝒊𝒈𝒖𝒓𝒆

[sand pasture]

yea though maybe +- the square root

(both x and -x can be the square root of x^2)

[split needle]

Backed

[split needle]

Hmm

[sand pasture]

$d^2 \pm d\sqrt{d} - 4d \pm \sqrt{d} + 1 = 0$

[flat frigate]

TRAMPELTIER

[split needle]

I got a little bit sucked there

But i had an idea a little time ago

$d^2 - 4d \pm (d+1)\sqrt{d} + 1 = 0$

[flat frigate]

𝑲𝒊𝒓𝒊𝒔𝒉𝒊𝒌𝒊𝒈𝒖𝒓𝒆

[split needle]

"d^2 - 4d"

My idea, in first was like to use

(x+y)^2 = x^2 + 2xy + y^2

Being x = d^2 and y = 2sqrt d

@sand pasture Am i crazy on this all?

xd

[split needle]

The only problem

Is the signal of 4d

[sand pasture]

I'm unsure how to solve polynomial equatinos of degree 4
maybe going with substitution is not a good way, because it's not like we'd have only x^4 and x^2. We also have x and x^3 giving us these square roots, which doesn't help much

Maybe we should stay at $x^4+x^3-4x^2+x+1=0$
What's your background on this? Did you talk about solving quartics in any class?

[flat frigate]

TRAMPELTIER

[sand pasture]

https://en.wikipedia.org/wiki/Quartic_function#:~:text=[edit]-,Nature of the roots,-[edit]

[split needle]

Nah.

[sand pasture]

So, looking at wikipedia, there is a very complicated formula that solves this

[split needle]

With complex numbers?

lmao

[sand pasture]

It's no complex numbers, but a bunch of calculation

Where did you get this task from?

[safe radish]

@split needle Has your question been resolved?

[safe radish]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[tender meteor]

hi

[tender meteor]

how can i solve : lim as n->infinity (n^3 • [ cos(1/n) - 1 ]) , i thinked that (cos(1/n) * epsilon(n)) / epsilon(n) --> 1

but i cant do n^3 * 0

[empty gyro]

$\lim_{n\to\infty} \left(n^3\left[\cos\left(\frac{1}{n}\right)-1\right]\right)$

[flat frigate]

SWR

[tender meteor]

yes

thanks!

[empty gyro]

Can you use L'hopital?

[tender meteor]

nope

[empty gyro]

Can you use $\lim_{x\to 0} \frac{\sin{x}}{x}=1$?

[flat frigate]

SWR

[tender meteor]

yes

[empty gyro]

I believe it diverges

[tender meteor]

$\lim_{n\to\infty} \left(n^3\left[-(-\cos\left(\frac{1}{n}\right)+1)\right]\right)$

[flat frigate]

alee

[empty gyro]

What does that do for you?

[tender meteor]

$\lim_{n\to\infty} \left(n^3*-1/2 * 1/n^2)$

[flat frigate]

alee
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[tender meteor]

$-infinity$

[flat frigate]

alee

[tender meteor]

eeeeeeeeasyyyyyyyyyyyyy

.close

[safe radish]

Channel closed

Closed by @tender meteor

Use .reopen if this was a mistake.

[safe radish]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[fiery mural]

how do I simplify 3(2)^3-2x

[light shoal]

well what's 2^3

[fiery mural]

8

[quiet cypress]

Have you learnd PEMDAS

[fiery mural]

yes

[quiet cypress]

so now you have 3(8)-2x

what is next

[fiery mural]

mutiply

[quiet cypress]

are you trying to solve for x?

correct. So what is next step

[fiery mural]

just to simplify it

[quiet cypress]

24-2x right

so you have options. You can solve for x and set the equation 24-2x=0

[quiet cypress]

what?

okay, I see

[fiery mural]

can you come back?

[light shoal]

what's up

[fiery mural]

how do I simplify it?

[sand pasture]

$(h \circ k)(x)$ is defined as first applying k to x: $k(x)$ and then applying h to the result: $h(k(x))$

[flat frigate]

TRAMPELTIER

[fiery mural]

yeah

so 3(2)^3-2x

[sand pasture]

yea with parenthesis

[fiery mural]

how I simplify tho

[sand pasture]

$3(2)^{3-2x}$

[flat frigate]

TRAMPELTIER

[fiery mural]

ye

but I needa simpify it somehow

[sand pasture]

Yea now simplify it

i mean what is 2^x saying

we do 2 times 2 times 2 .... x times

right?

[fiery mural]

yeahhh

[sand pasture]

yea

if we do it 3 times

we have 2 times 2 times 2 is 8

[fiery mural]

mhm

[sand pasture]

then you multiply with the other 2s

which are $2^{2x}$ many

[flat frigate]

TRAMPELTIER

[sand pasture]

and don't forget the 3

so $3 \cdot 8 \cdot 2^{2x}$

[flat frigate]

TRAMPELTIER

[sand pasture]

can simplify with 24 in front

[fiery mural]

didn't work

[sand pasture]

okay another thing we can do

is

when you have $2^{2x}$

[flat frigate]

TRAMPELTIER

[sand pasture]

that is the same as $2^x \cdot 2^x$

[flat frigate]

TRAMPELTIER

[sand pasture]

right?

[fiery mural]

ye

[sand pasture]

and now we can group the 2's from both of the $2^x$ into 4's

[flat frigate]

TRAMPELTIER

[sand pasture]

so it's $4^x$

[flat frigate]

TRAMPELTIER

[sand pasture]

cause 2 times 2 is 4

[fiery mural]

it still didn't work

[sand pasture]

yeah

we can simplify a bit more

[sand pasture]

I mean what is a way to write 24 in terms of 4's

?

[fiery mural]

4*8

[sand pasture]

nah

[fiery mural]

wait

4*6

[sand pasture]

yea

so what can we do?

[fiery mural]

ummmm

[sand pasture]

squeeze it somehow into the 4^x

[fiery mural]

idk

[sand pasture]

we have $6 \cdot 4\cdot 4^x$

[flat frigate]

TRAMPELTIER

[sand pasture]

it's the same as $6 \cdot 4^{x+1}$ (VERY MUCH SIMPLIFIED INDEED!!)

[flat frigate]

TRAMPELTIER

[fiery mural]

it still didn't work

[sand pasture]

they're just dumber than us

[sand pasture]

oh wait

we forgot about the minus

try $24 \cdot 4^{-x}$

[flat frigate]

TRAMPELTIER

[fiery mural]

nah

[sand pasture]

doesnt work?

[fiery mural]

nnah

[sand pasture]

maybe $24 \cdot 2^{-2x}$

[flat frigate]

TRAMPELTIER

[fiery mural]

nah

[sand pasture]

$6 \cdot 4^{-x+1}$

[flat frigate]

TRAMPELTIER

[sand pasture]

no way thats not working

[fiery mural]

don't know what to say

[sand pasture]

what trash side is that 😄

[fiery mural]

app.formative.com

my teacher uses it so that you can check ur work and turn it in when ur done with it

[sand pasture]

Write him an email that all simplifications are not possible

[fiery mural]

they are a her but yea

[sand pasture]

nice a her

[fiery mural]

.close

[safe radish]

Channel closed

Closed by @fiery mural

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[oblique leaf]

how do i deal with the abs value in this integral

[devout shale]

Can you show the original problem?

[oblique leaf]

this integral from 0 to 2pi

[devout shale]

Great

Okay, is cos^(2)(x) ever negative?

[oblique leaf]

nope

[devout shale]

So the product of cos^(2)(x) * sin(x)

is only negative when sin(x) is negative

right?

[oblique leaf]

yes

[devout shale]

When is sin(x) negative in 0 to 2pi

[oblique leaf]

pi to 2pi

[devout shale]

Great

so split the integral there

[oblique leaf]

ah ok

and add a negative sign in front

[devout shale]

You know then that from 0 to pi the integrand is |cos^(2)(x)sin(x)|=cos^(2)(x)sin(x) [because it's positive |f(x)|=f(x)]
and the integrand from pi to 2pi is |cos^(2)(x)sin(x)| = -cos^(2)(x)sin(x) [because it's negative |f(x)|=-f(x)]

[oblique leaf]

right, thank you!!

[devout shale]

No problem

[oblique leaf]

.close

[safe radish]

Channel closed

Closed by @oblique leaf

Use .reopen if this was a mistake.

[safe radish]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[ornate osprey]

Quick question regarding calculus limits. When it's 0/0, you have to factor or whatever. What if it's num/0? Would that just be -infinity/infinity or do you still have to factor?

[eternal carbon]

what is "num" here?

if this answers your question, a limit that approaches non-zero-value / 0 ends up diverging

[ornate osprey]

let's say we have something like this

instead of -5 it's -6

it would be -1/0

meaning the answer is -infinity?

[eternal carbon]

yes

[ornate osprey]

I see, okay

That's what I thought, but just wanted to make sure hahaha

[eternal carbon]

well sometimes you say -infinity sometimes you say DNE

in any case it diverges

[eternal carbon]

cool 🙂

[ornate osprey]

that's fair

Thank you! 😄

[eternal carbon]

welcome 👍

[ornate osprey]

.solved

[safe radish]

Channel closed

Closed by @ornate osprey

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[full hazel]

Why did the C become a coefficient?

[eternal carbon]

because of exponential function property, e^C is a multiplicative constant

to be exact, the 2 Cs you see there aren't actually the same; one's C and one's e^C... but, usually when solving differential equations of the first order, people don't mind that

[full hazel]

So e^C is equal to C?

[eternal carbon]

sort of.

whoever wrote that solution simply transformed e^C into C because they are both constant values

[full hazel]

Ohk thanks for explaining

.close

[safe radish]

Channel closed

Closed by @full hazel

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[honest bone]

can someone tell me how we get the 3 formulas from this

[honest bone]

so k is a constant presumably?

in the arctan formula we pull it out

and we're left with dx/(x^2+k)

if k was 1 then it translates to arctan(x) + c

should i take it as a given formula that k is always x/k or is there some kind of arrangement for it

[safe radish]

@honest bone Has your question been resolved?

[plucky elk]

You use inverse function theorem to find the derivative of the inverse trig functions, then FTC

[safe radish]

@honest bone Has your question been resolved?

[safe radish]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[safe radish]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[white flint]

I need help on how to solve inequalities then graph them my problem is 3x-4y (greater than or equal to) -12

[white flint]

Please help

I guess they just skip lower math

Can someone help me..

[safe radish]

@white flint Has your question been resolved?

[safe radish]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[vivid idol]

If f(x) = (x+1)^2. Does a Horizontal dilation by 2 make it (0.5x+1)^2 or (0.5(x+1)^2)?

[vivid idol]

Or (0.5(x+1))^2

[pure agate]

The first one.

[vivid idol]

Ty

[glossy cypress]

np

[glossy cypress]

you should type the command " .close "if you dont have any more questions

[vivid idol]

.close

[safe radish]

Channel closed

Closed by @vivid idol

Use .reopen if this was a mistake.

[vivid idol]

.close

[safe radish]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[steep yacht]

Are all primes, (q + p) - 1. p and q are also both primes

[plucky elk]

p+q-1 is almost never prime

Errr

Sent that prematurely

[steep yacht]

Still doesn't mean all primes can't be of that form

Ok, no worries

[plucky elk]

Oh I misunderstood

Definitely not 2

[steep yacht]

Maybe I should say all odd primes

[glossy cypress]

yeah i was gonna say two breaks that

[steep yacht]

Might be hard answer because it's like simlar to goldbach but for primes.

[glossy cypress]

i cant really generalize it, but 29 and 2 are both prime. adding them and subtracting one you get 30, a non-prime.
wait nvm thats not even the question lmfao

[steep yacht]

Might be able to use dirichlet theorem

I'm not to familiar with tho

[glossy cypress]

not sure but you could maybe use wilson's theorem to prove it??

surely th ere's a number theory nerd that can answer this

[steep yacht]

Right

Would this imply that there a always aleast two primes that a (p' - 1) distance away from each other?

Is that circular logic, or some sort of series? Because let's say you have 11 + (7 - 1) = 17, the gap the 17 and 11 is 7 - 1. Then you get 5 + (3 - 1). So you get, (p1 + p2 + p3) - (terms - 1)