help-42

[hybrid vale]

log laws

[chilly wigeon]

right -3 mb

[hybrid vale]

do you know log laws?

[chilly wigeon]

i dont remember all of them

[hybrid vale]

well as long as u remember some

u can know this

or u could simply do ln both sides

[chilly wigeon]

the second is the inverse right?

[hybrid vale]

so you would have $ln(2^{x}) = ln(3)$

[potent lotus]

Sarro

[hybrid vale]

and then from log properties

$ln(2^{x}) = xln(2)$

[potent lotus]

Sarro

[hybrid vale]

no

same thing just different variable names

[chilly wigeon]

isnt this log_2(3)=x

[hybrid vale]

yes

[chilly wigeon]

-2^x=-3
2^x=3

[hybrid vale]

i was showing u a different way

cus i thought u didnt remember all ur log properties

[chilly wigeon]

i was taught this way

[hybrid vale]

yep that's right

[chilly wigeon]

i started learning them like a day ago lmaoo

[hybrid vale]

fair enough well try to commit them all to memory

for the inverse do the same process

let x =0

to find the y intercept

and let f^-1(x) = 0 to find the x intercept

[chilly wigeon]

couldnt i skip the work by just, yk, inverting it?

switch the domain and range, etc

[hybrid vale]

yep

that works

i just assumed u were stuck on it haha

[chilly wigeon]

hm well when i plug in x=0 for the inverse
log_2(3) so shouldnt my vertical asymptote be 1.58

[hybrid vale]

no that's not an asymptote

[chilly wigeon]

then how do i find the VA of the inverse

[hybrid vale]

log_2(0) dne right

[chilly wigeon]

yea

[hybrid vale]

so what makes -x + 3 = 0

[chilly wigeon]

3

-(3) + 3 = 0

[hybrid vale]

yes so that's ur assymptote

[chilly wigeon]

3?

[hybrid vale]

yep

[chilly wigeon]

so i set the argument equal to 0 to find the asymptote?

[hybrid vale]

yes

[calm coral]

@chilly wigeon Has your question been resolved?

[calm coral]

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.

[tight sphinx]

just a quickie but what does the upside down delta mean?

[tight sphinx]

im guessing gradient?

or is it a vector field?

.close

[calm coral]

Channel closed

Closed by @tight sphinx

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.

[thick fog]

Did i do this correctly ?

[thick fog]

is the answer d ?

due to the fact that the answer i got is 0

[faint sequoia]

i got 2 as a critical point

[thick fog]

what did you get for f'(x)?

well it must be (c) anyways right cause it must have one critical point

[faint sequoia]

i didnt use that method but i just made both equations denominator and numerator equal to 0, and got 2 critical points 2 and 3 then i just tested whether their ranges are positive or negative and found out that only 2 matters

not sure how reliable is that

but i will try to find f'(x) also

[thick fog]

maybe i was supposed to simplify f(x) first ?

giving me 1/(x-2)

then derive it ?

[faint sequoia]

wait actually kinda yeah because the derivative for me became very complicated

either way you still would arrive at the same derivative because

$-x^2 +6x -9 \over (x^2-5x+6)^2$ \
is the same as \
$-(x-3)^2 \over (x-2)^2(x-3)^2$ \
$f'(x) = -1/(x-2)^2$

[potent lotus]

Scythed

[thick fog]

ye thats what i got

so you will end up with -1 = 0

so no critical points

so the answer is (c) right ?

[faint sequoia]

isnt x = 2 a critical point because f'(x) at x=2 is undefined

one critical point?

oh wait im so dumb

since 2 is not in the domain in the function

there is no critical points

[calm coral]

@thick fog Has your question been resolved?

[calm coral]

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.

[naive estuary]

I’m sad

[polar jetty]

Go to #chill. Should elevate your spirits.

[wooden gyro]

Try to not waste a help channel for nothing please

[zealous spear]

[calm coral]

@naive estuary Has your question been resolved?

[polar jetty]

.close

[calm coral]

Channel closed

Closed by @polar jetty

Use .reopen if this was a mistake.

[naive estuary]

.reopen

[calm coral]

✅

[polar jetty]

I am not sure if that's allowed.

.close

[calm coral]

Channel closed

Closed by @polar jetty

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.

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

[deft flax]

oh my god i keep messing up pasting

[calm coral]

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.

[novel aurora]

need help

[novel aurora]

.close

[calm coral]

Channel closed

Closed by @novel aurora

Use .reopen if this was a mistake.

[calm coral]

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.

[plush leaf]

can you help me pls

in the figure, NB ⊥ ABC, BL ⊥ AC. Which of the following is correct?
A AN ⊥ AC
B BL ⊥ AB
C BC ⊥AC
D NL ⊥ AC

[remote mural]

so you have to choose between a b c and d?

and this doesn't make any sense how is NB perpendicular on a triangle

[plush leaf]

to be honest, im not good at math at all, i need to do this assignment, but i don't know how to do it 😭

[remote mural]

do you have any other data ?

[plush leaf]

no(

[remote mural]

OK so you mean NB ⊥ AB and BL ⊥ AC right?

[plush leaf]

NB ⊥ ABC and BL ⊥ AC

[remote mural]

how the*

[plush leaf]

i dont know 😭

[remote mural]

none of these are right

you sure those are the only datas?

[plush leaf]

ohhhh, okay, maybe you can help me with another task

In the figure MA ⊥ (ABC), MC ⊥ BC, AC = n, AB =m.
Write a formula to find the length of the segment BC

√n²-m²
√m²+n²
√m²-n²
(m-n)2

[plush leaf]

yes

[remote mural]

MA is a segment right?

[plush leaf]

yes

[remote mural]

and abc is a triangle? or what

[plush leaf]

maybe yes

[remote mural]

maybe?

[plush leaf]

photo

[remote mural]

oh lord why didn't you send it

[plush leaf]

sorry(

[remote mural]

m²-n²

ez

but don't follow the pic the proportions are totally wrong

[plush leaf]

this?

[remote mural]

ye

[plush leaf]

thanks

[remote mural]

yea tell me if it's right

but according to my calculations it is

[plush leaf]

okie

[remote mural]

ye

wait

do you know anything about barycenter?

[plush leaf]

no

[remote mural]

ok bye!

[calm coral]

@plush leaf Has your question been resolved?

Channel closed

Closed by @plush leaf

Use .reopen if this was a mistake.

[calm coral]

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.

[hexed ginkgo]

Q12
Why did we take the derivative of this r vector?

[tall mason]

the curve is parametrised by u

this means if you want to know the direction of the curve at any point along the curve

you want to find the tangent vector along the curve

which is precisely the vector found by taking the derivative of the position along the curve with respect to the parametrisation variable

aka dr/du

another way to think of it is to think

if i want to know the direction of the curve at any point

i want to know how does x change as u changes

and the same for y and z

so i change u by du

and check what dx is

and the way to find that is to find dx/du

similarly y and z

so you get a vector (dx/du, dy/du, dz/du) aka dr/du

[hexed ginkgo]

but how is that change giving you tangent??
I am unable to visualize it

[tall mason]

think of the curve

just a random curve in space

[hexed ginkgo]

Okay

[tall mason]

at any point in the curve it has an x, y, and z

[hexed ginkgo]

yup

[tall mason]

this curve in particular is parametrised by u

meaning this curve has x(u), y(u), and z(u)

do you remember the definition for derivative?

[hexed ginkgo]

so changing u changes x,y,z along the curve
And u is changed such that the point is always on the curve originally defined

[tall mason]

yes changing u causes you to follow the curve

[hexed ginkgo]

Yeah
change of one variable with respect to another.
and it gives the tangent
Or rather
The slope of the tangent since the change is very small

[tall mason]

yes but mathematically it is specifically defined

as a limit

[hexed ginkgo]

yeah I am aware of that limit too
Limit h-> 0 for f(x+h)-f(h)/h
We can extend this to two variable, 3 variables as well

[tall mason]

exactly

and so if we want to know how a change in u

causes a change in x, y, and z

[hexed ginkgo]

We gotta take the derivative...

[tall mason]

you can if it is not clicking try to compare it to the 1 variable function

as in f(x)

how that changes as x changes

and that the tangent line can be considered a tangent vector

[hexed ginkgo]

But but
Uhh
Why???
Like
Why is it giving you the tangent though?
The main issue I have is that
u was not a variable that I was able to visualize in this 3D space
So I can't grasp how changing u is somehow giving u the slope??

[tall mason]

you can visualize u as a sort of "time"

[hexed ginkgo]

Ohhh
Wait wait
I think I got it

[tall mason]

oh?

[hexed ginkgo]

Like
If I imagine only a 2d space
A plane of x and u
Then I can get the slope of how x changes with u
Which is simply the derivative
Same goes for y and z
I am getting their slopes (aka direction ratios of the tangent on these planes)
And then I am calculating their net which is simply their addition

Am I thinking in the right direction?

I have a feeling I made a mistake somewhere in trying to say what I meant. . .

[tall mason]

you can plot x(u)

in 2d

in a plane

and find the slope

which is the simple derivative

is that what you're asking?

i think the problem is that u cannot be visualized as a dimension

because you already have x, y, and z

and so in order to visualise it you have to do something else

like make u into some sort of time

[hexed ginkgo]

But how I'll take the slope then?

[hexed ginkgo]

yeah
I tried
It kinda failed

[tall mason]

i think of parametrising a curve in 3d as filling in that curve as i increase the parametrisation variable

aka as u gets bigger

the curve gets filled

[hexed ginkgo]

Filled?

How?

[tall mason]

by a colour or by increasing the diameter of the curve

[hexed ginkgo]

Oh

[tall mason]

it's not part of the mathematics, just for my visualisation

[hexed ginkgo]

So like
It's ever increasing?

[hexed ginkgo]

Yeah I mean
I won't get satisfied with just the formulae
I gotta be able to see where it comes from

I'll show you some text

[tall mason]

yes u is increasing

or maybe decreasing but then you can define another u' that is u'= -u in which case it is increasing again

so yes increasing

and u increasing means the curve gets traced out

gets coloured in

or whatever way you may think of it

[hexed ginkgo]

Here too they seem to be taking the derivative of the r vector to the point where we are taking the directional derivative

s (which is our u in this question)
Denotes the length of the arc of the curve between those neighboring points

[tall mason]

yeah that's the step you take in u

to see how far of a step you take in x, y, and z

$\Delta u$ or $\Delta s$ in their case

[potent lotus]

Katharine

[tall mason]

hold up i'm gonna share a video it's gonna take a lil while

[hexed ginkgo]

So taking a step in u takes a step in x
And taking a step in x means that we've begun inspecting the neighborhood of the point where we are taking the directional derivative in?
Is that correct?

[tall mason]

yes

[hexed ginkgo]

Thank you so much 🛐

I see
I've understood like the original problem I had
Like why we were taking the derivative with respect to u here
But now I'm stuck at a more fundamental question

Oh wait nevermind
It's cleared
It was my mistake

[tall mason]

right

bottom is black cuz my screen is super wide

during this video the blue ball is at a specific value of u in this case starting at 0 and ending at ~10

[hexed ginkgo]

A tangent to the curve always gives a direction
So we're having this unit direction tangential vector at a point on this 3D curve
And then taking the dot product with the curl gives us DD which is perfectly okay.

But what I want to understand is that
In 2D
We were taking this direction to any unit vector on the xy plane
Why are restricting ourselves to only the tangent at that particular point in 3D curve?

[hexed ginkgo]

It's an amazing visualization aid
Thank you

[tall mason]

Can you explain what you mean by "We were taking this direction to any unit vector on the xy plane"

[hexed ginkgo]

Like imagine in the xy plane
I have an arrow
When I take DD
I always take it along this arrow
Now this arrow lies in the plane and I am free to rotate it to full 2pi radians where it basically traces out all the angles at any point

Like in this xy plane

I have 3 arrows here
Which is basically just one arrow which I am rotating about the point where I want to DD at

[tall mason]

I'm not entirely sure what your current question is?

The tangent vector is for all points that lie on the curve

[hexed ginkgo]

Um
Is the above clear though?
Then I'll explain the question again

[tall mason]

i'm not sure i understand what you mean with the rotating the arrow

[hexed ginkgo]

Like this
Tangent vector here is along a specific direction isn't it?

[tall mason]

yes

the tangent vector along the curve is those two vectors

depending on which one you want

[hexed ginkgo]

Yeah but it's only two vectors.
The other vectors we're not talking about in this 3D case.
In 2D case
We were taking it along any vector

[tall mason]

Were you looking at specific curves to take the directional derivative?

or just take a vector and find the directional derivative?

You could use any vector as your tangent vector

[hexed ginkgo]

Huh?
How?

Tangent vector is supposed to fixed for a given curve and a given point isn't it?

[tall mason]

yes but the curve can be changed it you want

[hexed ginkgo]

sighhh
my brain melted

[tall mason]

the point of 12 is that you have a function F

and a curve

and you wanna know how does F change as you move along the curve

that's the directional derivative

[hexed ginkgo]

This^^^
Why only along the curve?

[tall mason]

that's the question

you're not technically forced to move along the curve

you can pick a different curve

or just a direction

and find how F changes in those cases

[hexed ginkgo]

No I mean in general too
That's how directional derivative was defined here ^^^

That's what's bothering me so much

[tall mason]

i don't think i understand what you mean

can you ask the question

maybe can you give an example of what you did in 2D for comparison

[hexed ginkgo]

If for the function that is in the pinned message
I move along a different direction rather than the tangential one but I am still calculating DD at that point u=0 only.

Is this a contradictory statement?

[tall mason]

then you would have found the directional derivative in a different direction

[hexed ginkgo]

But its not wrong right?
One point can have infinitely many directional derivatives since there are infinitely many directions in which I can evaluate the dot product of the unit vector with the curl of the function

[tall mason]

yes

[hexed ginkgo]

Finally!!!

[tall mason]

but obviously if you are being asked to find it in some specific direction

finding it in another direction would be incorrect

that's very obvious right?

😄

But i think i understand what you are asking

[hexed ginkgo]

Yes I got it now
I just found out that I had completely overlooked that "along the curve" business
That's why this tangential stuff happened
And then I got confused how I am getting a Tangent in 3D to begin with lol

[tall mason]

You can take the directional derivative of a function at any point it is defined and in any direction you would want

[hexed ginkgo]

Brain's a mess
But thanks for making it better

I meant clearer *

[hexed ginkgo]

For some reason
I am overjoyed to hear this despite knowing that it's the very definition of having a directional derivative 😭

[tall mason]

We may have talked past one another for a little bit

[hexed ginkgo]

Yeahh
But all's well that ends well

Thanks once again
I wanted to ask you
Can I possibly tag you if I get stuck somewhere in multivariable again?
I felt your way of explaining was very nice overall

[tall mason]

sure

there are people who are much smarter than me though

[hexed ginkgo]

You're like the top 2 smartest ppl I know here though 😭

[tall mason]

not close, Ann is smarter than me, Ramonov is smarter than me EAC is smarter than me etc etc . 😄

[hexed ginkgo]

I consider you supreme for now 🙏
I have not met them so I will not judge them at all.

Take care <3

.close

[calm coral]

Channel closed

Closed by @hexed ginkgo

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.

[cosmic ravine]

without solving the quadratic equation 3x² + x - 5 = 0 determine the sum and product of its solutions

[cosmic ravine]

I need help with that

[pure kayak]

if a quadratic ax^2+bx+c=0 has roots a and b
then a+b=-b/a and ab=c/a

you can derive those using the quadratic formula

[calm coral]

@cosmic ravine Has your question been resolved?

[cosmic ravine]

What does derive mean

[calm coral]

@cosmic ravine Has your question been resolved?

[cosmic ravine]

.closr

.close

[calm coral]

Channel closed

Closed by @cosmic ravine

Use .reopen if this was a mistake.

[calm coral]

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.

[stiff ingot]

why is this true??

[stiff ingot]

like why does the resulting system of equations follow from the previous equation

[hollow kestrel]

The top equation is an equation of the form Xcos(4t) + Ysin(4t) = 25cos(4t). This can only be true if X = 25 and Y = 0

[stiff ingot]

thank you!

that makes complete sense when you put it this way

[hollow kestrel]

Thank you

[stiff ingot]

.close

[calm coral]

Channel closed

Closed by @stiff ingot

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.

[tall hemlock]

I know that $L(x) = g'(a)(x-a) + g(a)$

[potent lotus]

marco.py

[tall hemlock]

but what would g'(a) be?

what would a be actually

[calm coral]

@tall hemlock Has your question been resolved?

[tall hemlock]

.close

[calm coral]

Channel closed

Closed by @tall hemlock

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.

[paper quartz]

does anyone know the proof for this, its ramanujans summation formula for diverging sums

[calm coral]

@paper quartz Has your question been resolved?

[calm coral]

@paper quartz Has your question been resolved?

[tulip veldt]

@paper quartz I suggest that this question goes into #real-complex-analysis you might find some more help there.

[calm coral]

@paper quartz Has your question been resolved?

[past zinc]

it can be done, but I think that due to the volume and time that would be needed for it, discord is not the best place, the proof can be considered as a bachelor's or master's thesis.

[calm coral]

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.

[inner pine]

I need help finding the bounds for Ix, Iy, and Iz. I will be using wolfram mathematica to calculate everything so the bounds can be in any...cartesian,
cylindrical or spherical coordinates. Thank you!

For Ix, I am think about putting the bounds in the order dz dy dz.
First, in Octant 1 under: z = (2-2x-y)/4 or x = (2-y-4z)/2 or y = 2-4z-2x

(y^2+z^2)xyz, the integrand, can it be viewed as the yz plane? (y^2+z^2) has radius 1?
z goes from 0 to (2-2x-y)/4
y goes from ?
x goes from ?

[calm coral]

@inner pine Has your question been resolved?

[inner pine]

If anyone helps me a will venmo $1

[calm coral]

@inner pine Has your question been resolved?

[calm coral]

@inner pine Has your question been resolved?

[delicate barn]

okay so what have u tried so far

u just need to pick a coordinate system, find bounds and then evalute the integrals

So whats a good coordinate system, given this is a tetrahedon?

[delicate barn]

@inner pine

[inner pine]

That is the hard part

Finding the bounds 😩

[delicate barn]

okay well pick a coordinate system

this problem is fairly simple

[inner pine]

Cardteasiome

[delicate barn]

okay good.

now draw the xy projection

what will it look like?

[inner pine]

Um

Circle

[delicate barn]

?

do you know what a tetrahedron looks like

[inner pine]

Nor 🥸

Wait

Triangle

[delicate barn]

yes kind of

okay lets go back to xy projection

how do u draw the xy projection in the first place

[inner pine]

Like the ones in Egypt

[delicate barn]

@inner pine

[inner pine]

But 4 sides

[delicate barn]

or better yet, what are the equations of the lines that define our xy projection?

[inner pine]

Z= (2-2x)/4

Yes

[delicate barn]

?

[inner pine]

Wait

[delicate barn]

xy projection

[inner pine]

I am lost but I have an idea

Yes?

[delicate barn]

i just want the equations that define the xy projection

given its in the first octant

what are two equations you know

[inner pine]

Density

[delicate barn]

what

[inner pine]

2x + y + 4z = 2

d = xyz

[delicate barn]

You have a tetahedron in the first quadrant

in ur xy projection what are the lines that define it

[inner pine]

What

[delicate barn]

if you were going to draw the graph from a birds eye view

there are three lines that define the graph

[inner pine]

Yes

[delicate barn]

given in its the first octant, what are two lines you know instantly

[inner pine]

Y = 0

X = 0

[delicate barn]

yes

[inner pine]

YES

[delicate barn]

okay

now theres a third line

what is z in the xy projection

[inner pine]

About that

Is what I don’t know

[delicate barn]

its a bird eye view

you are looking straight down at the xy projection

[inner pine]

y = mx +b

[delicate barn]

what is z in the XY projection

no

z is a number

[inner pine]

Huh

A number?

But isn’t it a line

With a slope we can find?

[delicate barn]

this is the xy world

there is no z

[inner pine]

0

[delicate barn]

yes

so whats the last equation of the line

[inner pine]

z = 0

[delicate barn]

no

xy world

there is no z

whats the equation of the plane

and then after that tell me the equation of the 3rd line

for the xy projection

answer in order

[inner pine]

🤔

😭

Um

What line

So if I were to graph this

[delicate barn]

answer in order

[inner pine]

It would just be the x y up and down

[delicate barn]

answer this first

[inner pine]

y = 0
x = 0

[delicate barn]

no

the plane

its given

in the question

[inner pine]

Um

Of the plane

[delicate barn]

the equation of the plane given in the question

what is it

[inner pine]

2x + y = 2

[delicate barn]

oh yeah

u skipped a step

[inner pine]

REALLY?!

[delicate barn]

thats no the plane

[inner pine]

Bruh

[delicate barn]

the plane is 2x+y+4z=2

[inner pine]

What is the plane

[delicate barn]

but in the xy projection

z=0

so our 3rd line

is

2x+y=2

[inner pine]

😫

[delicate barn]

now u have all 3 lines

[inner pine]

My clac teacher is going to beat me

[delicate barn]

so figure out the x bounds and y bounds

[delicate barn]

u gotta pay attention in class bro lol

[inner pine]

No but this is from so long ago

This is chapter 14

[delicate barn]

this is basically the end of calc 3

[inner pine]

We are in 15 now

[delicate barn]

wat else is there after this?

like curl and divergence?

[inner pine]

Vector calc

Line integrals we are doing now

[delicate barn]

oh line integrals then curl and divergence then parametric surfaces

then ur done

[inner pine]

I didn’t do very good on the last test….

🥸

Ok

So bounds

[delicate barn]

use xy projection

to figure out xy bounds

[inner pine]

y = -2x + 2

-2/1 is slope

So we have

Points on x and y now

That are

😶

But

That’s not

[delicate barn]

draw the graph

and send a picture

include coordinates of intersection

[inner pine]

How do you find the intersection points

[delicate barn]

its a straight line

u have 2x + y = 2

[inner pine]

🙂

[delicate barn]

well id write it as coordinates but sure

okay now whats ur xy bounds

using the graph

treat it like a simple double integral

[inner pine]

😶‍🌫️

[delicate barn]

your z bounds look a bit weird

why /2?

but yeah, besides that ur correct

now just evaluate

[inner pine]

I got z to one side

Because it’s under that thingy

?

[delicate barn]

your algebra is wrong

is what im saying

[inner pine]

Ope

Yes 4

That’s the hardest part for calc for most

But for me it’s everything

[delicate barn]

but yeah

ur done now

just evalute all 3 integrals

[inner pine]

For Iy and Iz it’s same bounds?

[delicate barn]

yes

[inner pine]

😮‍💨

Thank you so much

It’s been a long semester

And it’s just starting

[delicate barn]

unless the integrals are very ugly with dz dy dx bounds

in which case u might need to change the order

lol

[inner pine]

This is for wolfram mathematica computer assignment so it doesn’t care what the bounds are

[delicate barn]

ah

[inner pine]

Which I also have a question about

If you know any of that stuff

[delicate barn]

using wolfram?

[inner pine]

Yes wolfram Mathematica ?

[delicate barn]

yea wat about it?

[inner pine]

YAA

[delicate barn]

it should be simple to compute integrals with it

,calc integral of 0 to 1 integral of 1 to 2 integral of 3 to 4 of xyz dz dy dx

[inner pine]

It’s for a complete different problem

[potent lotus]

The following error occured while calculating:
Error: Undefined symbol integral

[delicate barn]

oh

maybe not so much then

idk how advanced this q is gonna be lol

i only use it for simple stuff

probs better opening a new thread

[inner pine]

I will

But one question question

When going from a problem, whose density at each point is proportional to the distance of the x y plane

To proportional to the square of the distance of the origin

My integrand is just z

So it would be z*sqrt(x^2 + y^2) ?

[delicate barn]

distance to xy plane is z

distance to origin is sqrt(x^2+y^2+z^2)

square of distance to origin is x^2+y^2+z^2

[inner pine]

Thank you

[maiden tartan]

make sure to do .close if your question has been answered

[inner pine]

.close

[calm coral]

Channel closed

Closed by @inner pine

Use .reopen if this was a mistake.

[calm coral]

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.

[tawny maple]

Please help me solve this proof

[pure kayak]

!ss

[calm coral]

Please post images (such as PNGs or JPGs) of the question rather than other filetypes such as PDFs which have to be downloaded. Non-image downloads can potentially contain viruses or other security risks.

[tawny maple]

mb i didnt know it was a heic

!close

/close

bruh

.close

[calm coral]

Channel closed

Closed by @tawny maple

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.

[cold finch]

ok so this is unit 3 for AB Calculus and I know for a fact that the chain rule is involved in this right?

im just confused on this tiny step

[cold finch]

g'(x) = f(x^2-x) * (2x-1)

or would g'(x) be equal to:

g'(x) = f'(x^2-x) * (2x-1)

notice the 2nd one has f'(x) and not regular f(x)

this confuses me because part of the chain rule is like (u) * (u')

but what about the outside?

is it f'( u) * (u')
or just f(u) * (u')

[spare beacon]

There is no (u)*(u')

When you write f'(u) * (u')

you have f'(u), which is the derivative of f evaluate at u, and multiplied by the derivative of u

it isn't f' times u times u'

[cold finch]

sooooo is it the 2nd one?

cause f(x) is still a function from the table

when I said f'(x^2-x) I didnt mean f' times u I literally meant f' of u

f prime of u like f of x [f(x)]
cause this is a table problem

g'(x) = f(x^2-x) * (2x-1)
g prime = f of (x^2-x) times (2x-1)

OR

g'(x) = f'(x^2-x) * (2x-1)
g prime = f prime of (x^2-x) times (2x-1)

[spare beacon]

you want f'(u) * u', the first one

[cold finch]

u mean the 2nd one

cause I put prime on the 2nd one

[spare beacon]

The first one of this

[cold finch]

my fault

thank you

[calm coral]

@cold finch Has your question been resolved?

Channel closed

Closed by @cold finch

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.

[snow jolt]

e=(-1)^1/i(pi)

[snow jolt]

Is this true?

[humble ivy]

$(-1)^{\frac{1}{i\pi}}$?

[potent lotus]

Jelle

[snow jolt]

ya

[humble ivy]

It is true, yeah

[snow jolt]

Thanks

[humble ivy]

Because you can rewrite -1

[snow jolt]

How can i end the help session

[humble ivy]

With .close

[snow jolt]

.close

[calm coral]

Channel closed

Closed by @snow jolt

Use .reopen if this was a mistake.

[calm coral]

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.

[paper bolt]

I am asked to give an example of vector space over R

[paper bolt]

Does that mean R^1 (literal R, scalars) or R^n?

[plain nimbus]

I mean both of those are vector spaces over R but any R^n is the prototypical example for a (finite dimensional) vector space over R

Any vector space has an associated base field / ground field (or just simply field) so this is asking for a vector space where the field is R

[paper bolt]

So, is it R^n then?

[plain nimbus]

It's only asking for one example

pick an n lol

[paper bolt]

Alright that's what I wanted to ask about xD

Sure, I can pick an n

[plain nimbus]

hahaha yup

[exotic falcon]

There’s not just 1 correct answer

It’s asking you for an example

[paper bolt]

That R^2 is going hard 😈😈😈😈

[plain nimbus]

side note - you can have weirder vector spaces over R -> think of the space of continuous functions over the interval! You can add, subtract, multiply by a real number and you're still a continuous function

so there are some spicy examples

[paper bolt]

Oh those sound cool as hell

I gotta read more about that

[plain nimbus]

that's all functional analysis i.e. infinite dimensional vector spaces!

[calm coral]

@paper bolt Has your question been resolved?

Channel closed

Closed by @paper bolt

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.

[sterile mulch]

This is the differential equation and how I solve it, do I need to do anything after the last step?

[upper sparrow]

[sterile mulch]

ohhh is 1/….

But after the last step should I do anything else?

[upper sparrow]

Well you wouldn't really need to - when you correct this one, you get y as an explicit function of x

[sterile mulch]

Would it be like this?

[upper sparrow]

But as for your one, you could just leave it as either form (remove the C from one of the sides in the above line)

[upper sparrow]

The constant +C would be inside the tan, so tan(x^2 + C), but otherwise fine!

[sterile mulch]

Tyvm for the help!

.close

[calm coral]

Channel closed

Closed by @sterile mulch

Use .reopen if this was a mistake.

[calm coral]

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.

[glad drift]

I need help with this question.
"An object is thrown (straight down) from the top of a 220-foot building with an initial velocity of 26 feet per second. What is the position function of this object?"

[old frigate]

Kinematic equations?

x=ut+at²/2

Position is a function of time

[lime valve]

its thrown down, so y i guess

[old frigate]

Yeah I just gave him a clue

[glad drift]

I'm just wondering if it's -16t^2-26t+220 or -16t^2+26t+220... Unsure if it's +26t or -26t

[calm coral]

@glad drift Has your question been resolved?

[calm coral]

@glad drift Has your question been resolved?

Channel closed

Closed by @glad drift

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.

[latent zinc]

$T = { A \in \mathbb{R}^{3 \times 3} \mid a_{ij} = 0 \text{ for all } i > j }$ is the set of all upper triangular matrices. \

Let $A$ and $B$ be two arbitrary upper triangular matrices and $c$ be an arbitrary real number. We check if $A + c \cdot B \in T$: \

[
A + c \cdot B =
\begin{bmatrix}
a_1 & a_2 & a_3 \
0 & a_4 & a_5 \
0 & 0 & a_6 \
\end{bmatrix}

• c \cdot
  \begin{bmatrix}
  b_1 & b_2 & b_3 \
  0 & b_4 & b_5 \
  0 & 0 & b_6 \
  \end{bmatrix}
  =
  \begin{bmatrix}
  a_1 + c \cdot b_1 & a_2 + c \cdot b_2 & a_3 + c \cdot b_3 \
  0 & a_4 + c \cdot b_4 & a_5 + c \cdot b_5 \
  0 & 0 & a_6 + c \cdot b_6 \
  \end{bmatrix}
  ]

Since we know that the product or sum of two real numbers is a real number due to the closure under addition and multiplication for real numbers, it is seen that the requirement from lemma 9.32 holds for the subspace of $V$. \

We now wish to show that the span of the canonical basis is equal to $T$: \

[
t_{1,1}
\begin{bmatrix}
1 & 0 & 0 \
0 & 0 & 0 \
0 & 0 & 0 \
\end{bmatrix}

• t_{1,2}
  \begin{bmatrix}
  0 & 1 & 0 \
  0 & 0 & 0 \
  0 & 0 & 0 \
  \end{bmatrix}
• t_{1,3}
  \begin{bmatrix}
  0 & 0 & 1 \
  0 & 0 & 0 \
  0 & 0 & 0 \
  \end{bmatrix}
• t_{2,2}
  \begin{bmatrix}
  0 & 0 & 0 \
  0 & 1 & 0 \
  0 & 0 & 0 \
  \end{bmatrix}
• t_{2,3}
  \begin{bmatrix}
  0 & 0 & 0 \
  0 & 0 & 1 \
  0 & 0 & 0 \
  \end{bmatrix}
• t_{3,3}
  \begin{bmatrix}
  0 & 0 & 0 \
  0 & 0 & 0 \
  0 & 0 & 1 \
  \end{bmatrix}
  ]

[

• t_{3,3}
  \begin{bmatrix}
  0 & 0 & 0 \
  0 & 0 & 0 \
  0 & 0 & 1 \
  \end{bmatrix}
  =
  \begin{bmatrix}
  t_{1,1} & t_{1,2} & t_{1,3} \
  0 & t_{2,2} & t_{2,3} \
  0 & 0 & t_{3,3} \
  \end{bmatrix}
  \in T
  ]

These matrices to the left of the equality sign have a non-zero number in every entry that is necessary to meet the definition of an upper triangular matrix. Furthermore, it holds that any upper triangular matrix can be written as a linear combination of these 6. Thus, requirement 2 in definition 9.14 for a basis of vector space is fulfilled. At the same time, their entries with 1 do not overlap. Therefore, it is seen that the equation with the 6 matrices $c_1 \cdot t_1, \ldots, c_6 \cdot t_6 = 0$ with $c_1, \ldots, c_6$ in the body only holds for these vectors if $c_1 = \ldots = c_6 = 0$. Thus, the requirements are satisfied.

[potent lotus]

bed

[latent zinc]

Is this correct?

[calm coral]

@latent zinc Has your question been resolved?

[latent zinc]

<@&286206848099549185>

[calm coral]

@latent zinc Has your question been resolved?

[calm coral]

@latent zinc Has your question been resolved?

Channel closed

Closed by @latent zinc

Use .reopen if this was a mistake.

[calm coral]

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.

[quick rose]

Show that $2^{n+1} + 3^{n+1} and 2^{n} + 3^{n}$ are coprime. I tried Euclide and induction but didn’t get anything

[potent lotus]

zarblug

[torn gorge]

mhh...let me think

@quick rose are you already offline?

[quick rose]

Getting to bed but still there

[torn gorge]

ok right...

ok..

by induction maybe it is possible

$2^{n+1}+3^{n+1}=2*(2^n+3^n)+3^n$

[potent lotus]

everg

[torn gorge]

so we just need to prove that $3^n$ is coprime to $2^n+3^n$

[potent lotus]

everg

[quick rose]

Okay nvm

[torn gorge]

😉

[quick rose]

Realized how stupid it was when typing it lol

[torn gorge]

but prove that $3^n$ is coprime to $2^n+3^n$, its equivalent to prove that $3^n$ is coprime to $2^n$

[potent lotus]

everg

[torn gorge]

so its not by induction ...but its a direct proof xD

[quick rose]

Yeah

Ended up being not that hard

[quick rose]

I was completely oblivious to that part

[torn gorge]

mh... i think is not totally trivial indeed

[quick rose]

Since 2 and 3 are coprime isn’t there a theorem about how 2^n and 3^n are coprime themselves ?

[torn gorge]

maybe you could use fundamental theorem of arithmetic and see that the first one has only p=3 as divisor

and the second one only p=2

so they cannot have a non trivial common divisor

[quick rose]

I guess by saying d divides 2^n and d divides 3^n we can get to d = 1 no ?

[quick rose]

That must work as well yeah

[torn gorge]

gg

[quick rose]

Yeah thx!

!close

.close

[calm coral]

Channel closed

Closed by @quick rose

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.

[frigid barn]

why is the answer to this 68

[pure kayak]

68% of data falling within one standard deviation of the mean is just a fact you need to know

im not statistical enough to explain why

[frigid barn]

So I can say 69 and its also correct

[calm coral]

@frigid barn Has your question been resolved?

[calm coral]

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.

[modern mural]

where should i start on this question?

[weary wyvern]

net change theorem

[modern mural]

thanks thats much simpler than i thought

.close

[calm coral]

Channel closed

Closed by @modern mural

Use .reopen if this was a mistake.

[calm coral]

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.

[narrow spear]

I've determined all solutions of the differential equation : $y'' + 4y = sin(2x)*e^x$ and now I need to find all solutions of : $y''' + 4y' = sin(2x)*e^x$ I don't know how to do that is there a trick because it's the derivative of the first solution ?

[potent lotus]

phoestaclies

[coral osprey]

Let w = y'

then y''' = w"

[narrow spear]

oh so it's the primitive of w that give the good result

is it this ?

[coral osprey]

Should be

[narrow spear]

oh ty a lot I thought of that but wasn't sure

👍

.close

[calm coral]

Channel closed

Closed by @narrow spear

Use .reopen if this was a mistake.

[calm coral]

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.

[gritty moss]

How did they get this answer?

Where did the -1 come from?

[pure kayak]

so, 1/2 + 2x-x^2/2 - 2 + 1/2

nope wait i did an oopsie

there

1/2+1/2 -2=-1

[gritty moss]

ah ye

thanks mate

.close

[calm coral]

Channel closed

Closed by @gritty moss

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.

[twilit crag]

Ive gotten this far with the problem XD what do I do next? qvq

[brazen elbow]

whats the relation between 2^a and 2^-a?

[calm coral]

@twilit crag Has your question been resolved?

[calm coral]

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.

[rich tree]

I'm bieng told this is doable by u substitution, but I'm a bit rusty on that. What u would I use?

[swift laurel]

we want to simplify the inside of the square root as much as possible so we'll set u = the inside of the square root, i.e. u = 3x + 5

[rich tree]

Yes, of course.

I did try exploring that

But I got stuck with handling the x in the numerator

So I figured I picked it wrong?

[swift laurel]

if u = 3x + 5 we can solve for x

[rich tree]

OH

Hold on

.close

[calm coral]

Channel closed

Closed by @rich tree

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.

[jovial sentinel]

The propeller of a boat at dock in the ocean will rise and fall with the waves. On a particularly wavy night, the propeller leaves its resting position and reaches a height of 2m on the peaks of the waves and -2m in the troughs. The time between the peak and the trough is approximately 3 seconds. Determine the equation of a sinusoidal function that would model this situation assuming that at equation , the propeller is at its resting position and headed towards the peak of the next wave.

[calm coral]

@jovial sentinel Has your question been resolved?

[calm coral]

@jovial sentinel Has your question been resolved?

[calm coral]

Channel closed

Closed by @jovial sentinel

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.

[signal shadow]

i have found the complex number x which is -1±i√3/2 what is a faster way to find the value if you input it in the exponents? qvq

[marble escarp]

roots are omega and omega^2

Do you remember omega^3n =1, 3n+1=omega,3n+2=omega^2

[remote mural]

ig u could convert it to polar form and then use demoivres

its also a root of unity of 3

so all the exponents that are a multiple of 3 will result in 1 when the complex number is raised to said power

[remote mural]

if you are unfamiliar with demoivres theorem

[alpine stone]

Looks like an overkill

You can simplify x^49 + x^50 + x^51 + x^52 + x^53 to just -x^51 by factoring

Then you observe that (x - 1)(x^2 + x + 1) = 0, x^3 = 1

And use the fact that 51 is divisible by 3

[calm coral]

@signal shadow Has your question been resolved?

[alpine stone]

Was anything unclear in the suggestions?

[signal shadow]

How djd you simplify -x^51?

[potent lotus]

A Lonely Bean

A Lonely Bean

[remote mural]

wow thats clever

[signal shadow]

Sorry if Im being irritating rn but why did you -x^51 and how did you get 0 after the factorization? qvq

[alpine stone]

So that you could have those (1 + x + x^2)'s once you factor out

Alternatively you could just do this

[ x^{49} + x^{50} + x^{51} + x^{52} + x^{53} = x^{49}(1 + x + x^2 + x^3 + x^4) ]
[ = x^{49}(1 + x + x^2(1 + x + x^2)) = x^{49}(1 + x) = x^{49}(-x^2) = -x^{51} ]

[potent lotus]

A Lonely Bean

[alpine stone]

The 0 appears because I got 1 + x + x^2 inside the parenthesis

And we are told that 1 + x + x^2 is zero

[remote mural]

hope this helps

you also could have written it as a sum of a geometric series a1(1-x^n)/(1-x)

and have gotten the same thing

remember x^3n where n is any integer will always equal to 1 since the root is a 3rd root of unity

lmk if theres something you dont understand i dont mind explaining

[calm coral]

@signal shadow Has your question been resolved?

Channel closed

Closed by @signal shadow

Use .reopen if this was a mistake.

[calm coral]

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.

[astral jasper]

Find the function for a secondary function, that crosses y-axis in 2 and only has one zero point 2

[calm coral]

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

[astral jasper]

.close

[calm coral]

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.

[glad fossil]

I am struggling with question 3C

I am thinking that R stands for real number?

[calm coral]

@glad fossil Has your question been resolved?

[glad fossil]

<@&286206848099549185>

[leaden thunder]

,rotate

Hmmm

Upload the question image again

[glad fossil]

Give me a moment

[calm coral]

@glad fossil Has your question been resolved?

[cunning veldt]

try to find x and y such that h(x, y) = (1, 0)

[calm coral]

@glad fossil Has your question been resolved?

[calm coral]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[calm coral]

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.

[sweet briar]

help plz with #21 ty

[pure kayak]

whats the problem?

[sweet briar]

i need to find the domain and range

[pure kayak]

yeah, where are you struggling with it

[sweet briar]

im confused?

i dont know where it is

😭

[pure kayak]

do you know what domain and range are?

[sweet briar]

yes

the x and y

[pure kayak]

kinda, what specifically

[sweet briar]

domain is all possible inputs and range is all possibe outputs

[pure kayak]

nice, what do you think the domain of 21 is?

[sweet briar]

the 1??

[pure kayak]

i mean in question 21

[sweet briar]

[-1,1]?

[pure kayak]

what makes you think that?

[sweet briar]

because it is across from eachother

[pure kayak]

im not too sure what you mean by that

but i can see there are points on that line outside of [-1,1]

in terms of x values

so the domain cant be [-1,1]

[sweet briar]

oh

is it 0

[pure kayak]

im afraid not

thats not a set

[sweet briar]

right

sorry

[pure kayak]

no problem

[sweet briar]

i dont understand the graph

[pure kayak]

what about it confuses you?

[sweet briar]

it look zigzagity

[pure kayak]

it is indeed zigzagity

i wouldnt focus too much on the shape

[sweet briar]

ok ill try

is the range [1,-1]?

[pure kayak]

right numbers, wrong order

[pure kayak]

also just a note

when you use infinity in set notation

use ( and ), not [ and ]

do you know the difference?

[sweet briar]

[.] is for the included sets?

idk

my teacher said to use it

[pure kayak]

yeah pretty much, [2,3] would mean 2<=x<=3
(2,3) would mean 2<x<3

when using infinity you have to use ) or (

since you cant '=' infinity

[sweet briar]

ohh ok

but how about if, for example 2, infinity

do u use (.) or [.]

[pure kayak]

for the infinity, definitely )

for the 2 it can be either

just depends if its included in the domain or not

eg [2,infty) would mean x>=2

(2,infty) would mean x>2

[sweet briar]

oh ok

is the domail all real numbers?

[pure kayak]

in this case, yes

[sweet briar]

OH TYTY

[pure kayak]

no worries

[sweet briar]

.close

[calm coral]

Channel closed

Closed by @sweet briar

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.

[calm token]

The homogeneous system, Ax = 0, has a unique trivial solution if and only if
λ=/=0 is an eigenvalue of A.

why is this statement true?

[analog pike]

i'm not sure how to interperet λ=/=0 is an eigenvalue of A.

do you mean that 0 is not an eigen value of A

[pure kayak]

think its just lambda is non-zero

[warm wren]

I think it is that there exists a nonzero eigenvalue?

[analog pike]

if it's just that there exists a non-zero eigen value then it's not a true statement for $\begin{matrix}2&0\0&0\end{matrix}$

[potent lotus]

Willow

[analog pike]

since it has an eigen value of 2, but anything in the span of (0,1) is a solution

if it's instead that all eigen values are non-zero, you can use the relationship between det(A) and it's eigenvalues

[calm token]

well

[calm token]

this is how i interpret it

i thought it was false

and i tried to prove it this way:

its possible my logic was just flawed

i was confused with the wording of the statement

[analog pike]

yeah, if you interperet at there exists a non-zero eigen value then your logic holds

[calm token]

my professor did not seem to like my answer

so maybe im misinterpreting

[analog pike]

It's possible your professor meant all eigenvalues are non-zero

[calm token]

in which case its true?

[analog pike]

yes

the statement would be true if all eigenvalues aer non zero

have you learned that the determinant of a matrix is equal to the product of it's eigen values with multiplicity?

[calm token]

i believe i just recently learned that, but not sure, different terminology for the same thing possibly

where you can use determinant with like A-lambda*identitymatrix to find the eigenvalues?

[analog pike]

this is how you find eigen values, but we also have that if A has eigenvalues $\lambda_1,...,\lambda_n$ that $\det(A)=\lambda_1\cdot\dots\cdot\lambda_n$

[potent lotus]

Willow

[analog pike]

so effectively, det(A) is only zero when 0 is an eigenvalue

so if 0 isnt an eigenvalue, then A is invertible

[calm coral]

@calm token Has your question been resolved?

[calm coral]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[calm coral]

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.

[remote mural]

hello

[remote mural]

finnaly

[glacial lily]

What is your question?

[calm coral]

@remote mural Has your question been resolved?

[calm coral]

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.

[sinful lion]

i dont understand why its not accepting it as an answer

[stoic oyster]

idk ask your prof or something

the program is clearly screwed up, it accepted your previous thing

or maybe you need to put r*x

it looks like that's what you did in the 1st prompt

@sinful lion

[sinful lion]

but it seems right to you

?

yeah it is idk why i asked that

related to that, i was fucking around and i just got it right by accident but idk how to solve it fr

[stoic oyster]

just plug sin(kt) in the DE

[sinful lion]

ik y''=-2ksin(kt)

[stoic oyster]

why 2k

you mean k^2 surely

[sinful lion]

oh

woops lmao

[calm coral]

@sinful lion Has your question been resolved?

Channel closed

Closed by @sinful lion

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.

[sturdy willow]

is this right?

[sturdy willow]

and how do I find the relative min?

[potent igloo]

lgtm

[crimson cliff]

@sturdy willow evaluate the function at those critical properties

and check which has a relative min

[sturdy willow]

wdym evaluate?

.close

[calm coral]

Channel closed

Closed by @sturdy willow

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.

[mellow summit]

How can i simplify this multiplication problem with the grid method?

[nimble crag]

Put all terms of the first polynomial in the first row of a grid, the terms of the second in the first column of the grid and fill the grid with the multiplication

[calm coral]

@mellow summit Has your question been resolved?

[mellow summit]

Can you show an example or write down smth like that? Kinra contused and never done anything like thos

[nimble crag]

sorry, I can't write down, but you can take a look at this guy https://www.youtube.com/watch?v=c5xS-Rig8E4

I used this method a couple of times, but then I simply multiply polynomials "in line" to waste less paper

[mellow summit]

Oh thanks, but what if theres more than two numbers in one polynomial like in that question i sent

[nimble crag]

in your question you have 4 terms for the first polynomial and 3 terms for the second, so you have to create a 4 x 3 grid

[calm coral]

@mellow summit Has your question been resolved?

[calm coral]

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.

[chilly compass]

!status

[calm coral]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[storm wedge]

consider u = sinx

[calm coral]

@soft orbit Has your question been resolved?

[calm coral]

@soft orbit Has your question been resolved?

[calm coral]

@soft orbit Has your question been resolved?

[calm coral]

@soft orbit Has your question been resolved?

[soft orbit]

1

[tulip veldt]

hi @soft orbit id start like this

[soft orbit]

Ohh let me do it

Someone deleted?

[tulip veldt]

nope nvm i dont think that will work lol

Ya, sorry, I didnt think it would work

let me think for a few more mins

Have you heard of Weirstrauss Substitution @soft orbit ?

It looks like we may need to do seomthing like this

[calm coral]

@soft orbit Has your question been resolved?

[tulip veldt]

Hi @soft orbit someone mentioned to me that the function is odd around the middle of the interval you're integrating one so we can use integral properties to solve

My friend convinced himself that $f(\pi/4 + x) = -f(\pi/4 + x)$ if that makes sense.

[potent lotus]

twitch.tv/pencenter