help-28

[agile holly]

what is (-1)^{n-1} * (-1)^n

[crystal ibex]

1?

[agile holly]

huh

[crystal ibex]

we plugging 1 for n right

[agile holly]

in general

it should be -1

[crystal ibex]

so whats wrong on mine

[agile holly]

every (-1) is paired up with except 1

it should just be - 7^n x^5n /n

[crystal ibex]

-summation (-1)^n-1 7^n x^5n all div by n

so i am right till here right

[crystal ibex]

thats the right answer damn i was so close yet so far but explain rq

[agile holly]

nah ur not right here

[crystal ibex]

where did i mess up

[agile holly]

think about it

(-7)^n * (-1)^{n-1}

[crystal ibex]

well for me i thought the negative would cancel out with the (-1) to get positive

but it alternates so i forget but i still dont see how the (-1)^n-1 is not needed or the -1

we are saying it doesnt alternate

[agile holly]

mhm

[agile holly]

it would

but we would have a negative remaining

[agile holly]

we have (-1)^n * (-1)^{n-1}

[crystal ibex]

but if we do it through there and i plug that in

the alternate sign is still there no?

[agile holly]

no

[crystal ibex]

thats like a template

[agile holly]

ez

think about it

every -1 has a partner -1

except one of them

[crystal ibex]

hold on

my brain goes fk mode when ln is anywhere in equation

so because there is a negative in front of the summation the (-1)^n disappears? @agile holly

if theres a negative in front we wont have that correct?

i see the derv of that is always neg when we plug for x

ty for help

.close

[full forum]

Channel closed

Closed by @crystal ibex

Use .reopen if this was a mistake.

[full forum]

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 nymph]

,rotate

[sturdy nymph]

I actually dk

I'm good with these usually but I'm stumped for this one

[lime ether]

fire illustration bro

[sturdy nymph]

idk man

[lime ether]

so you’re looking for the initial velocity yea

[sturdy nymph]

yeah

[lime ether]

which formula do you think will be helpful here

[sturdy nymph]

initial velocity of x or y

usually s = ut + 1/2at² is useful

[lime ether]

that’s useful for time it takes to hit the ground

[sturdy nymph]

v = u + at
then but idk what time or initial is

[lime ether]

which part are you referring to

and in which direction

[sturdy nymph]

wym

[lime ether]

^

x or y direction

and what are you looking for

[sturdy nymph]

y I guess

is there enough information to solve this

[lime ether]

ok well we know vx = ux = v cos(40)

uy = usin(40)

[sturdy nymph]

yeah

no

[lime ether]

we also know vy = 0 at its maximum height so we should find that maximum height

[sturdy nymph]

uy = usin40

[lime ether]

yea i’m used to using vo my bad

[sturdy nymph]

yea genuinely I thought abt all this but there's not enough information to plug into any of the formulas

[lime ether]

usin(40) = gt

you’ll have to use some system of equations i believe

[sturdy nymph]

sorry I gtg

[lime ether]

oh

[sturdy nymph]

yea mb mb

.close

[full forum]

Channel closed

Closed by @sturdy nymph

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.

[distant swan]

I'm just curious on a homework

[distant swan]

given an orthonomral set = {u_1, u_2, u_3}

actually, much better to just send the photo

[nimble crane]

you can quickly verify that {u1, u2, u3} is ON by checking that each of the vectors has norm 1, and are all OG to each other

as for the second part, it should just be a standard system of equations you can solve

[distant swan]

yup, i've already done the orthonormal set

scalar is what i'm having trouble with

i've figured out 2 and 3

lambda_2 is give which is -3

lambda_3 i've gotten which is 3 / sqrt(2)

but lambda one, it says the answer should be 1 / sqrt(2) but I keep getting 2 / sqrt(2)

[nimble crane]

can you show me your work?

you should get 1/sqrt(2)...

[full forum]

@distant swan Has your question been resolved?

[full forum]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[full forum]

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.

[fast marlin]

How did he find these new bounds?

[full forum]

@fast marlin Has your question been resolved?

[fast marlin]

<@&286206848099549185>

[granite shore]

let's make sure you understand this part first

do you know how we get this diagram?

[fast marlin]

No

[granite shore]

take a look at the bounds of your double integral

[fast marlin]

0->3

[granite shore]

the dx comes first so we know 3y <= x <= 3 and dy comes second so we have 0 <= y <= 1

so were trying to draw that region first, in case we need to alter the boundary values

[fast marlin]

How do you know 3y is less than or equal to x

[granite shore]

it is the lower bound of the integral when taking it with respect to the x variable

[fast marlin]

Is that because x=3y?

[granite shore]

we will use that idea, yeah. im looking specifically at this part of the double integral: $\int_{3y}^{3} e^{x^2) dx $

[fast marlin]

@glossy valve

It’s down

[granite shore]

ah dang

[fast marlin]

Oh now it’s up?

[granite shore]

$\int_{3y}^{3} e^{x^2) dx $

[fast marlin]

Give it a min maybe

[granite shore]

this part:

[fast marlin]

Yeah that makes sense

[granite shore]

so basically if we can do this integral first, then do the dy one next, we gucci.

but this integral has no antiderivative, so we look to integrate wrt y instead

so we try to figure out whats going on with x

x is always bigger than 3y but less then 3 according to the bounds

once we know that, we can look at the y bounds, which say y is between 0 and 1

now our goal is to draw all four bounds: (1) x=3y, (2) x=3, (3) y=0, (4) y=1

the region of integration is bounded by these lines

[fast marlin]

Okay I think I got it

[granite shore]

understanding how they get the picture is the most important part, for sure!

[fast marlin]

Can you give me a practice one to see if I got it?

[granite shore]

Sure!

$\int$

[glossy valve]

twitch.tv/pencenter

[granite shore]

$\int_{0}^{2} \int_{2x}^{4} (3x+2)dydx$

see if you can change the bounds from starting with y to starting with x

[glossy valve]

twitch.tv/pencenter

[granite shore]

we may need to alter the upper bound to 4, sorry!

trying to create one in my head at 1:50am is challenging lol

[fast marlin]

Like this?

[granite shore]

yep! drawing looks good, its the upper triangle

i got this:

$ \int_{0}^{4} \int_{0}^{y/2} (3x+2)dxdy$

[fast marlin]

Oh right because we want to change it to x

[granite shore]

yep

[full forum]

@fast marlin Has your question been resolved?

[full forum]

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.

[blissful lichen]

What is your method of thinking during an math exam

[blissful lichen]

Like I believe I learned every concept thoroughly but when I get a question I don't know how to solve it

Im theorising it's due to a problem with the way I analyse it

[hoary ember]

personally id try to skip those at the start and leave them to the last

[blissful lichen]

But idk maybe it's a skill issue

[hoary ember]

true...

[blissful lichen]

Then I'm just skipping the whole exam at the point

[hoary ember]

🔥

[blissful lichen]

They are the questions with the bigger scores

[limpid moat]

give a big skim through the whole text firstly and try to evaluate the difficulty of every exercise so that you can organize the order of the exercise as you please

some exercises could be easy but they could take a great amount of concentration, so I am likely to do them firstly ...or they could be difficult exercises but they just need the right idea to being solved

[full forum]

@blissful lichen Has your question been resolved?

[blissful lichen]

No it isn't cus the thing I wanna know is not how to organize the questions in the paper rather I want to know how I should think in order to solve them

[blissful lichen]

I want to know how I can get into the right idea! That's what I want to know

"depends on the question"

Give me a basic process

[limpid moat]

valentine I think it is pretty much the same thinking way that you use during you practice at home

[blissful lichen]

IT DOESNT WORK

.stop

I wanna close this chat cus I don't think my problem is gonna be solved

Thank you so much for trying

[limpid moat]

I think so

np

[blissful lichen]

How do I stop it

[limpid moat]

.close

[full forum]

Channel closed

Closed by @limpid moat

Use .reopen if this was a mistake.

[blissful lichen]

.close

[full forum]

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 hedge]

so what I was thinking was

[tepid flame]

Are you asking us how to prove ∃n∈N(11 | 2^n -1)?

[thick hedge]

I mean it's trivial to verify that $11 \mid 2^{10}-1$

[glossy valve]

Mr bean is not $\R \setminus \Q$

[tepid flame]

Yes

[thick hedge]

oo

this is what I was wondering how to do

thanks

[timid iris]

i dont think n=1 statisfies bro

neither n=2

🤓 ☝️

[limpid moat]

n msut be s.t. 2^n-1 is at least greater or equal than 11

[timid iris]

yeah i m jk lol

[limpid moat]

ohh 2^0-1=0 and 11 does divide 0

[timid iris]

thats why i didnt say n=0 lmao

and n is Natural

[limpid moat]

0 is not in the naturals ?

[timid iris]

i dont think so

N does not include 0, W does

thats how its defined for us in textbooks

[limpid moat]

I know that -1 for example is not in the naturals ...by I would not take for granted that 0 is not in the natural...I think I can find very quicly an exercise where 0 is supposed to be inside the st $\mathbb N$

[glossy valve]

everg

[timid iris]

ok so if 0 is in N

what differenetiates N and W?

[limpid moat]

what is W ?

[timid iris]

whole numbers

[limpid moat]

so in general I would consider 0 inside N as someone expect that

[timid iris]

damn

im from India and over here we have NCERT

which is like the govt regulated book

and it says 0 isnt so yeah

[thick hedge]

Eh, at my uni we define it to be all counting numbers

so 0 doesn't coun

*count

[limpid moat]

I see...but that is not a big deal .. if it can create some issue, just add a little remark at the beginning of your exercise where you specify that 0 is or isn't inside N

[timid iris]

i think maybe its like country to country thing

[thick hedge]

Cool

thanks

.close

[full forum]

Channel closed

Closed by @thick hedge

Use .reopen if this was a mistake.

[full forum]

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.

[real silo]

f(x)= |5−2x| +3
for 2<=x<=8 Find the range of function f.

guys, is the answer 4<=x<=14?

[leaden ermine]

How did you get there?

also your range should be y not x

[real silo]

oh wait yes i mean y

[real silo]

i substitute x = 2 and x = 8

[leaden ermine]

that assumes though that your function is strictly monotonous

which it is not in that interval

[real silo]

ohh

is there a way where i can find the vertex beside drawing the graph?

can i do completing the square for modulus functions

[leaden ermine]

i never heard of such thing

but what you can do is analyze how the transformations affected the vertex, starting with |x|

[glossy valve]

bacc (unhelpful)

[real silo]

is it translation by vector (2.5 , 3)?

[leaden ermine]

yes

[real silo]

ohh okayokaayy

[leaden ermine]

your interval

was 2 <= x <= 8

[real silo]

yes

[leaden ermine]

so what's the actualy lowest range value

[real silo]

y = 3

[leaden ermine]

ye

[real silo]

i get ittt

thank youuu!

[leaden ermine]

just on a note the transformations caused the function to be stricly decreaing between x=2 and x=2.5 and strictly increasing between x=2.5 and x=8

that knowing plugging in x=8 works for the upper bound

but I would never avoid graphing stuff

[real silo]

ohhh okay okayyy

thank youu so much againn

.close

[full forum]

Channel closed

Closed by @real silo

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.

[distant swan]

what am I doing wrong?

i've got lambda 2 and 3

but I keep getting lambda 1 wrong

i got sqrt(2) / 2 instead of 1 / sqrt(2)

[pseudo cape]

Those are the same

$\frac{\sqrt 2}{2} = \frac{\sqrt 2 \cdot \sqrt 2}{2 \cdot \sqrt 2} = \frac{2}{2 \sqrt 2} = \frac{1}{\sqrt 2}$

[distant swan]

oh right

what's the trick with orthonormal vectors as well by the way

suppose we have an orthonormal set containing u_1, u_2 , u_3

and a vector a

if a is written in terms of the vectors in the orthonormal set, then this would be the result

[full forum]

@distant swan Has your question been resolved?

[distant swan]

.close

[full forum]

Channel closed

Closed by @distant swan

Use .reopen if this was a mistake.

[full forum]

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.

[austere jungle]

I keep getting stuck and none of the roots i find are real

[glad hound]

Let me grab scratch paper, but I think your partial derivatives are incorrect

Product rule.

[austere jungle]

lemme see

im still turning up the same partial derivative for x

oh i see now i flipped the sign on the partial derivative for y

.close

[full forum]

Channel closed

Closed by @austere jungle

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.

[grave folio]

How would you get the orange area, but only the part of this area which is above x=0 ?

Top parabole: f(x):=20/3*x^2 -2*x +3/10
Bottom parabole: g(x):=-220/27*x^2 +14/3*x -9/20

A formula, explanation, "GeoGebra" formula, ... would be good. Whatever suits the answer best 👍

Thanks in advance

[pearl trout]

Integrate f(x)-g(x) from 0 to the point of intersection

[grave folio]

You're probably right, but I have tried your idea and this was the result.
What exactly do you mean by "point of intersection"?

This is what i am trying to achieve. Getting the read marked area between the two functions above 0

Ahh, got it! Thank you

.close

[full forum]

Channel closed

Closed by @grave folio

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.

[silver sluice]

Hello

[silver sluice]

Have a problem with the 3.2

(In english) draw the tangent to the curve … in … and … draw the curve between …

And …

[torn jolt]

what is the problem ?

[silver sluice]

All the question

[torn jolt]

For 1) ?

[silver sluice]

No for 2

For 1 have

F’(0)= 1

F’(π/4)= 2

Ok so y = 1 / cos x
When x = 0 or x = π / 4

[torn jolt]

what ?

[silver sluice]

Im not sure 😅

[torn jolt]

it is the y= that i dont understand

u mean f(x) ?

[silver sluice]

In 1 i found f’(x) = 1 / cos x
And y = f(x)

I dont know how to continu

[torn jolt]

ok so f'(x) = 1/cos^2(x)

[silver sluice]

Yes

[torn jolt]

not 1/cos(x)

[silver sluice]

Oh sorry i miss the ^2

[torn jolt]

ok

so for f'(0) ?

[silver sluice]

Have 1

[torn jolt]

ah yes u alrdy wrote

so now u must draw the tangente

[silver sluice]

Yes

[torn jolt]

can u easily understand english ? or should i speak french ?

[silver sluice]

French is better

[torn jolt]

ok

ducoup t'es bloqué ou ?

[silver sluice]

Ba pour les tangente je dois les tracer comment ducoup

[torn jolt]

tu connais la dérivée

[silver sluice]

Oui

[torn jolt]

c'est la tangente

en gros

d'abord tu regardes la valeur de f en 0, et en ce point, tu trace la tangente

ici en 0 c'est une pente de 1

[silver sluice]

Ah d’accord enfaite la j’ai obtenu la valeur de y a des coordonnées x

Donc quand x = π / 4 on a y =2

[torn jolt]

dis plutot f quand tu parles, c'est plus facile a comprendre

[silver sluice]

Ok mais c’est ca ?

[torn jolt]

surtout que la tu parlais de f' non ?

[silver sluice]

Oui

[torn jolt]

oui

[silver sluice]

C’est vrai que j’explique mal mes demande je pense

Merci de mavoir aider et davoir traduit en français 😅

[torn jolt]

t'as compris comment faire ?

[silver sluice]

Oui ca devrait etre bon

[torn jolt]

fais voir apres au cas ou

[silver sluice]

Dac je trace avant

C’est bizarre jobtient une droite

[torn jolt]

pour ?

[silver sluice]

Ba enfaite les tangente jai leurs coordonnés en 1 point mais comment on fait pour les tracer

[torn jolt]

en 0 par exemple

t'as f(0) = 0

et f'(0) = 1

donc pour la tangente en 0 tu fais un petit trait droit avec une pente de 1

et c'est tout, il faut pas tracer plus

la tangente elle est collée a la courbe donc pour savoir ou la placer tu calcule f en ce point

[torn jolt]

ouais t'as juste inversé les pentes

celle en pi/4 elle doit etre plus pentue

[silver sluice]

A ok c’est vers le haut

Merci beaucoup

.close

[full forum]

Channel closed

Closed by @silver sluice

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.

[old blaze]

hello everyone

[old blaze]

How did the ** * Z** become + Z + 1 / 2 ? I don't understand

(It's Algebra Topic)

[torn jolt]

That’s how the operation is defined

[old blaze]

?? it's not multiplication

[spark shell]

x * y = x+y+1/2

[torn jolt]

Didn’t say it was

[spark shell]

your x is (x+y+1/2)

your y is z

[old blaze]

How do you see that?

[spark shell]

(this is what i mean btw)

so then since our operation is defined the way it is, the left hand side just turns into (green)+(orange)+1/2

which is what we get

[old blaze]

but why z = z + 1/2 ?

I don't see that

[spark shell]

x * y = x+y+1/2 right?

instead lets just say a*b=a+b+1/2, same thing

just so we dont mix up the variables

well what if a=x+y+1/2, and b is z

then a*b = a+b+1/2 = (x+y+1/2) + (z) + 1/2

[old blaze]

Ok but then they are the ones who present the exercise badly? Because they use the same variables

[spark shell]

the exercise is presented just fine, im using the a and b values to explain it to you

(x+y+1/2) is treated as a whole number, just as it should b

it looks like a whole expression because we are so used to the traditional definitons of the + and * signs (and the other ones, of course) but when you define a new operation you have to keep in mind that the same rules dont apply

(x+y+1/2) * (z) in this context is just (x+y+1/2) + z + 1/2, since thats how we defined the * operation

[naive hamlet]

If it's easier for you, you can think of an operation as a function

x#y = f(x,y) = x + y + 1/2

(x#y)#z = f(f(x,y),z) = f(x+y+1/2,z) = x + y + 1/2 + z +1/2

where # is *

[old blaze]

ok

thank you

for your help

[full forum]

@old blaze Has your question been resolved?

[full forum]

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.

[placid oak]

Why is the Laplacian of a field represented in a matrix, instead of a vector-of-vectors (no, they're not the same)?\
A matrix $M$ is equivalently a vector-of-covectors, $(M_\mu)^\nu$, and a covector-of-vectors, $(M^\nu)\mu$. The Laplacian, $L$, is a "vector-of-vectors", where each component is the second order differential of the field.
$$L{\mu,\nu} = \frac{\partial^2}{\partial x^\mu \partial x^\nu}$$
So why do we write it in a matrix?
$$L = \begin{pmatrix} \frac{\partial^2}{\partial x_1^2} & \frac{\partial^2}{\partial x_2 \partial x_1} & \dots \ \frac{\partial^2}{\partial x_1 \partial x_2} & \frac{\partial^2}{\partial x_2^2} & \dots \ \vdots & \vdots & \ddots \end{pmatrix} \qquad\mbox{giving}\qquad L_\mu^\nu = \frac{\partial^2}{\partial x^\mu \partial x^\nu}$$

[glossy valve]

Shuba

[full forum]

@placid oak Has your question been resolved?

[full forum]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[full forum]

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.

[compact sail]

The solution is the one that’s typed. My work is handwritten. Could someone please tell me what I’m doing wrong so far to get the incorrect determinant?

[thin flint]

have you checked if your inverse is actually an inverse?

nvm i think the problem is in your determinant calculation

i got -1/4

[compact sail]

I made my left side look like the right

Idk where I could have gone wrong

[thin flint]

try to do the determinant calculation again

[compact sail]

Oh

i got 5/16 ;-;

Could you please point out to me what I did wrong? @thin flint

[thin flint]

lets go to your determinant calculation

you write down the three 2x2 matrices

and their factors in the first row

what is the value you get from the first one of those?

[compact sail]

-1/4

[thin flint]

i mean with the factor included

[compact sail]

Oh dang

[thin flint]

for the determinant yes that is correct

but you have another factor in front

[compact sail]

It should have been -1/8

[thin flint]

no

[compact sail]

1/8?

[thin flint]

$-\frac{1}{2} \det \left( \begin{bmatrix} \frac{1}{2} & 0 \ \frac{1}{2} & -\frac{1}{2} \end{bmatrix} \right) $

[compact sail]

The formula is ad-bc

Right?

[glossy valve]

Katharine

[thin flint]

what a terrible formatting job texit has done

jeez

anyway

yes for 2x2

ad - bc

so the correct answer is 1/8

as you said with a question mark

now second one

[compact sail]

yup

Now I got -1/4

[thin flint]

for the second one?

[compact sail]

Because 1/8-3/8

I got 3/8 for the second one

[thin flint]

ye

no

the second one is 0

the third one is -3/8

[compact sail]

oh

my bad

I misspoke

but yeah I did get 0 for the second one

[thin flint]

you got it though

[compact sail]

I crossed it out rather than writing it down

[thin flint]

1/8 - 3/8 is correct

the way they did it is using the fact that the determinant of a matrix is the multiplication of the determinants of the factors

so

$\det(ABC) = \det(A) \det(B) \det(C)$

[glossy valve]

Katharine

[thin flint]

and using the fact that the determinant of I is 1

[compact sail]

What does that mean?

[thin flint]

this

[compact sail]

What is our ABC?

[thin flint]

$A A^{-1} = I$

[glossy valve]

Katharine

[thin flint]

and so

$\det(A A^{-1}) = \det(I)$

[glossy valve]

Katharine

[thin flint]

$\det(A) \det(A^{-1}) = \det(I)$

[glossy valve]

Katharine

[thin flint]

$-4 \det(A^{-1}) = 1$

[glossy valve]

Katharine

[thin flint]

$\det(A^{-1}) = -\frac{1}{4}$

[glossy valve]

Katharine

[thin flint]

that make sense?

that's what they did

[compact sail]

What is A, B, and C tho?

[thin flint]

A = A

B = A^-1

C doesn't exist

or is I

if you will

[compact sail]

How are we multiplying determinants together?

[thin flint]

what do you mean

[compact sail]

Here: #help-28 message

[thin flint]

Do you know about $f : A \rightarrow B$?

[glossy valve]

Katharine

[compact sail]

I guess not

What does that mean?

[thin flint]

it's a way of writing down functions

[compact sail]

Oh because A is the input and B is the output?

[thin flint]

yes

basically

the details aren't important

what i want to say is

you can see determinant as a function

$\det : \mathbb{R}^{n \times n} \rightarrow \mathbb{R}$

[glossy valve]

Katharine

[thin flint]

what this means is

it's a function that takes as input

a matrix

nxn

3x3 if you choose

2x2

and gives out a real number

just a value

and so

multiplying determinants

is just like multiplying real numbers

[compact sail]

Oh ok. Thank you for your help! Do you mind if I send you a friend request?

[thin flint]

you can ping me on here if you'd like

[compact sail]

I'm going to try another problem

Could you please help me with problem (iii)? @thin flint

Idk where to start

[full forum]

@compact sail Has your question been resolved?

[full forum]

@compact sail Has your question been resolved?

[full forum]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[full forum]

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 vapor]

Hey can someone please help with this lin lag problem

i tried setting up a system of equations to determine what row operations are needed

to achieve the shown matrix

this solution feels ridiculous though

[full forum]

@karmic vapor Has your question been resolved?

[full forum]

@karmic vapor Has your question been resolved?

Channel closed

Closed by @karmic vapor

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.

[gleaming ether]

I think this may be an issue with the question, becuase as far as I can tell it's already a single logarithm. Answers I attempted were the original given log and moving the negative sign into the log making it log_b(7^(-1)).

[gleaming ether]

I thought maybe it could be that it meant to ask for an expanded log and I got a little tripped up, because I'm shaky on how to use the quotient rule if there's a negative in front of the initial log

[sudden sigil]

you can put it to the power of -1

which flips fraction

[gleaming ether]

yeah, i tried that

[sudden sigil]

so it’s not logb(7)?

[gleaming ether]

no, nor is it is logb(7^-1)

wait what

ohhhh

ok, i see my mistake

[sudden sigil]

glad i could help

[gleaming ether]

should be logb(1/7^(-1))

i was just tossing in 7^-1

thanks!

.close

[full forum]

Channel closed

Closed by @gleaming ether

Use .reopen if this was a mistake.

[full forum]

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.

[south bay]

Estimate the value of f'(50)

[south bay]

i do not know how to do that

I know the point is (50,400)

.close

[full forum]

Channel closed

Closed by @south bay

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.

[versed light]

https://media.discordapp.net/attachments/903430333888884736/1297762326669164604/rn_image_picker_lib_temp_3861179d-5f93-48b2-8dc2-f6f7f6ffd7d9.jpg?ex=67171ad9&is=6715c959&hm=b7bd99a1747903cf4e29b28fc657a906c25099dd5f44ebc3a4ee6addfc5f0c9c&

[versed light]

how do i translate this to an inequality statement?

[full forum]

@versed light Has your question been resolved?

[gritty rose]

did you send anything?

[versed light]

this

[full forum]

@versed light Has your question been resolved?

Channel closed

Closed by @versed light

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.

[dreamy vector]

can someone help me with solving linear and polynomial inequalities
like whats the goal in the end of the process and what is the process

[dreamy vector]

like what am i supposed to do

[peak compass]

can you show what you’re struggling with

for inequalities you are usually supposed to isolate x

like equations

[dreamy vector]

i cant show photo but i can type out the equation if thats okay with you

[peak compass]

sure

[dreamy vector]

x^3-x^2-3x+3>-x^3+2x+5

the ^ means its an exponent

im lowkey gonna fail functions 12 because my mind goes blank whenever i see stuff like that

[rare pine]

its mostly to factorize

[peak compass]

might help make it > 0

[dreamy vector]

so like put all the numbers to one side

variables

[full forum]

@dreamy vector Has your question been resolved?

[full forum]

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.

[fast marlin]

how do you properly prove that the suprema of x^2<2, x in the reals is sqrt 2 ?

[stable nest]

by definition (sqrt(2))^2 = 2

[fast marlin]

but how do you prove that is the suprema?

ig how do you prove anything is a suprema?

[rustic frigate]

Use the definition

[stable nest]

consider the criteria for a suprema

[fast marlin]

the suprema has to be a number that is an upper bound

and it must be less than all other upper bounds

[rustic frigate]

You know that x^2 < 2 is equivalent to -sqrt 2 < x < sqrt 2, then use the definition

Infact you can show that any interval of the form (a,b) has sup = b

[fast marlin]

if theyre in the reals

or ig if you're looking for a real sup

[rustic frigate]

Even if the interval is intersected with rationals points

The sup is by definition a real number

[fast marlin]

right

[rustic frigate]

The subtlety here is if sqrt 2 even exists and if it’s really equal to the sup, which depending on the level of rigor can be taken for granted if you want

[full forum]

@fast marlin Has your question been resolved?

[fast marlin]

Thoughts?

i think 2 could be more concise i kinda changed what i was going to do while writing

i def didnt need to expand out the square

[rustic frigate]

Not clear whats going in 2), e.g. what’s stopping epsilon of being bigger than sqrt 2? Then you can’t get the inequality you’re working with. Apart from that the inequality at the end is also quite confusing

[full forum]

@fast marlin Has your question been resolved?

[rustic frigate]

Hint: points x in S is equivalent to the condition that -sqrt2 < x < sqrt2, since you’ve used the fact that sqrt2 exits

I.e you don’t really need to bother squaring

[full forum]

@fast marlin Has your question been resolved?

[full forum]

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.

[tranquil spear]

ARE MT ANSWERS CORRECT

[tranquil spear]

just the diagrams

[full forum]

@tranquil spear Has your question been resolved?

[full forum]

@tranquil spear Has your question been resolved?

[full forum]

@tranquil spear Has your question been resolved?

[tranquil spear]

<@&286206848099549185>

[full forum]

@tranquil spear Has your question been resolved?

[full forum]

@tranquil spear Has your question been resolved?

[full forum]

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.

[torn jolt]

I am working on the following problem: Find a convex function $f:\mathbb R^n \to \overline \mathbb R$ such that $\partial f(0)=[1,2]^n$

[glossy valve]

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

[torn jolt]

Oops TeX didn't compile correctly, lemme fix

I am working on the following problem: Find a convex function $f:\mathbb R^n \to \overline {\mathbb R}$ such that $\partial f(0)=[1,2]^n$

[glossy valve]

ken

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

[torn jolt]

Here $\partial f(0)$ denotes the subdifferential of $f$.

[glossy valve]

ken

[torn jolt]

I know for other reasons that we have $\partial \lVert \cdot \lVert_1(0)$ is just the unit ball of the dual norm to $\lVert \cdot \lVert_1$, which happens to be $\lVert \cdot \rVert_\infty$. This gives us the hypercube $[-1,1]^n$. So morally, all we need to do is compose this with a linear transformation that transforms the unit cube $[-1,1]^n$ to $[1,2]^n$. I am trying to use the chain rule for subdifferentials to do this, but haven't been able to get it to work out correctly so far.

[glossy valve]

ken

[torn jolt]

Definition and possibly helpful chain rules for subdifferentials

I also solved this problem in the $n=1$ case. It is given by a piecewise function $$f(x)= \begin{cases} 2x, x \geq 0 \ x, x\leq 0. \end{cases}$$ Then our subgradient is just the collection of slopes of lines that lie below the graph of $f$. This is evidently $[1,2]$. However I can't see how to generalize this to higher dimensions.

[glossy valve]

ken

[full forum]

@torn jolt Has your question been resolved?

[full forum]

@torn jolt Has your question been resolved?

[torn jolt]

I'll restate the problem for clarity amongst the other messages: Find a convex function $f:\mathbb R^n \to \overline {\mathbb R}$ such that $\partial f(0)=[1,2]^n$.

[glossy valve]

ken

[full forum]

@torn jolt Has your question been resolved?

[full forum]

@torn jolt Has your question been resolved?

[full forum]

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.

[sharp stratus]

I need help to start this off

[remote zealot]

u can use the identity: a² + b² = (a + bi)(a - bi)

[sharp stratus]

ok if I do that

(x^2+8i)(x^2-8i)=0

[remote zealot]

yes

[sharp stratus]

so x^2=-8i or x^2=8i

how do i go on from there?

[remote zealot]

actually no

[sharp stratus]

oops

[remote zealot]

why is x still squared

recheck the formula

[sharp stratus]

but it is x^4 in original problem

[remote zealot]

oh wait really

[sharp stratus]

yes

[remote zealot]

oh my bad im a dummy

[sharp stratus]

ur good

so what would I do now?

[remote zealot]

well js do smt classic

Nvm that wont work too

Only choice is to use the identity a⁴ + b⁴ = (a² -sqrt(2)ab + b²)(a² + sqrt(2) + b²)

[sharp stratus]

whoops

I'll use quartic formula

but thanks!

[remote zealot]

yk

there was an easier way

[remote zealot]

This was literally easier

This mean eacg factor is equal to 0

[sharp stratus]

I know

[remote zealot]

and just find your 4 solutions

[sharp stratus]

I got 2 solutions 😭

x=2sqrt(2i)

x=2isqrt(2i)

[remote zealot]

x² + 8i = 0

Means x² = -8i

x = ± 2isqrt(2)

u forgot ±

[sharp stratus]

ohhhh

thank you

[remote zealot]

np

Same with other solution

±

[sharp stratus]

.close

[full forum]

Channel closed

Closed by @sharp stratus

Use .reopen if this was a mistake.

[full forum]

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 hedge]

so I'm trying to prove that every set of the form [a,b]. or (a,b) or [a,b) or (a,b] has a least upper bound

[thick hedge]

By definition it follows that for [a,b] and (a,b] b is the least upper bound

for (a,b) by definition it is the set of all elements strictly less than b, so the least upper bound must be eactly b

similarly for [a,b)

How do I formalise this further?

My definition of upper bound is an element is an upper bound of A if it's greater than or equal to every element of A

[devout valley]

And of the least upper bound?

[thick hedge]

We haven't defined it in class, but I'd assume it's the least real number $M$ , such that $M \geq a \forall a \in A$

[glossy valve]

Mr bean is not $\R \setminus \Q$

[devout valley]

Sure anything [strictly] less than, in this case, b, should not be an upper bound (which should be easy to formalise what not being an upper bound means)

(analogous statements for the [greatest] lower bound and all )

[thick hedge]

so for half closed and closed sets the existance of a least upper bound is fairly easy to prove formally

but how do I formalise it for open sets

[devout valley]

For where the end we're considering is "open", it's a tiny bit more work, but not the worst: prove that b is an upper bound (that one is immediate by definition), and prove that it's the least upper bound, so as before, anything [strictly] smaller than b is not an upper bound

[thick hedge]

So a bit of epsilonics would be required, I suppose

hmm

[devout valley]

In other words, if you have any c < b, you wanna find some x between a and b (exclusive) such that x > c

[thick hedge]

hmm

[thick hedge]

Could I have a hint

[devout valley]

You may wanna consider the cases where c >= a, and where c < a

(drawing a picture of those situations may be a bit enlightening as well!)

[thick hedge]

I'm just wondering If I'm overdoing it

because we used way simplier proofs by contradiction to prove that sets don't have lower or upper bounds

Eh, this is easier once proven tbh

So just to be clear , what I want to prove is

If there exists a $c \in \R$ such that $b>c implies $c \in [a,b)$

right

[glossy valve]

Mr bean is not $\R \setminus \Q$
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[thick hedge]

wait, I want $b$ to be the least upper bound

[glossy valve]

Mr bean is not $\R \setminus \Q$

[hollow saddle]

Isn't this trivial in the field R?

[thick hedge]

I want to prove if $c > x \forall x \in [a,b) \implies c \geq b$

[thick hedge]

Not with my form of the completeness axiom

[glossy valve]

Mr bean is not $\R \setminus \Q$

[devout valley]

It is much easier to show that anything strictly less than b is not an upper bound, than it is to show that any upper bound must be greater than b

[thick hedge]

hmm, okay

[devout valley]

That's this statement here: any c that's less than b, our lub, is not an upper bound, so there must be an element of (a, b) that's strictly greater than c

[devout valley]

Note that c itself needn't be in the interval (a, b) itself though, hence this hint (it just needs to be strictly less than b, it could also be strictly less than a as well, or not)

[thick hedge]

$ \forall c$ st $c<b$ . We now wish to show that there is an element $x\in (a,b)$, such that $x>c$

[devout valley]

(and there do exist elements c that are strictly less than b, this is a forall proof)

[glossy valve]

Mr bean is not $\R \setminus \Q$

[devout valley]

Remember the epsilon-delta proofs and how they started? "let eps > 0 be arbitrary/given" or equivalent?

[thick hedge]

Yeah

Just a minute

[devout valley]

Similar here: let a c be given such that c < b. We now wish to show [what you said]

[full forum]

@thick hedge Has your question been resolved?

[thick hedge]

We first consider the case wherein a>c

In this case all elements of $(a,b)$ are greater than $c$ and we're done

[glossy valve]

Mr bean is not $\R \setminus \Q$

[thick hedge]

now let c>a and c<b

This means that $c \in (a,b)$

[glossy valve]

Mr bean is not $\R \setminus \Q$

[thick hedge]

but we know that $c< \frac{c+b}{2}<b$. and thus it lies in (a,b). This completes our proof

[glossy valve]

Mr bean is not $\R \setminus \Q$

[thick hedge]

How is this @devout valley

[devout valley]

Cool, give me an explicit one if you can

But otherwise, I'm happy, if a <= c < b, choose x = (c + b)/2 and that's in the interval and strictly greater than c as we need

[thick hedge]

. Didn't expect it to be this easy

And I suppose this "b" is what we call a limit point?

[devout valley]

Yep, e.g. you can create a nonconstant sequence in the interval that converges to b

[thick hedge]

sure $\frac{a+b}{2}$

[glossy valve]

Mr bean is not $\R \setminus \Q$

[devout valley]

Perfect

[thick hedge]

And I suppose greatest Lower bound is proved similarly

Thanks charbit!

.close

[full forum]

Channel closed

Closed by @thick hedge

Use .reopen if this was a mistake.

[full forum]

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 hedge]

I'm trying to prove that $\Z$ is not bounded below in $\R$

[glossy valve]

Mr bean is not $\R \setminus \Q$

[thick hedge]

As proven earlier, every interval on $\R$ has a greatest lower bound. Let this lower bound be $\alpha$. $n \in \Z$ so $n\geq \alpha \forall n \in \Z$. But the integers are closed under subtraction. So $n-1 \geq \alpha ; \alpha \in \R $. so $n \geq \alpha +1$. But We've already established that $\alpha$ is the greatest lower bound. We've thus arrived at a contradiction , this $\Z$ doesn't have a lower bound in $\R$

is this fine?

[glossy valve]

Mr bean is not $\R \setminus \Q$

[full forum]

@thick hedge Has your question been resolved?

[fervent owl]

what's ur question?

proof looks fine to me

[thick hedge]

Just wanted it verified

thaks!

:D

.close

[full forum]

Channel closed

Closed by @thick hedge

Use .reopen if this was a mistake.

[full forum]

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.

[ivory lark]

C

[ivory lark]

Yes

[glossy valve]

faiyrose

[ivory lark]

Root of is just the squared divided by 2

No?

I know the rules im just conufsed as if im suppose to root the numerator

Aswell

Beacause if so the answer is 1 and if not it should be -5.5

If im not missing something

So what i did was do the numerator first

Sqrt of that is 3 and 3.5

Added them so its 7.5

Then the top i js did the sqrt

3 then 1.5

So became 5a^1.5/ a^7.5

5 x 1.5 is 7.5

Use the rules

7.5 - 7.5

= 0

Anything up to 0 is 1

Is that correct?

How so

The numerator

(A^6)^1\2 equals 3

Yes

I know.

But its all the same base so it doesnt really matter until the answer

[glossy valve]

faiyrose

[ivory lark]

5a^3? What are u asking

[rugged void]

yes

now you can cancel those with the exponents on the bottom

[ivory lark]

Yeah thats what i did

Isnt it correct 1

[rugged void]

no

[glossy valve]

ren

[ivory lark]

Shouldnt u do sqrt first then minus?

[glossy valve]

faiyrose

[ivory lark]

Yes

So the top would become 5a^1.5? Or 3/2

[glossy valve]

faiyrose

[ivory lark]

So it would become a^1.5 sqrt of 5/ a^7.5

Oh u add before the sqrt

So 6.5

[glossy valve]

faiyrose

[ivory lark]

Sqrt of 5/a^5

I cant use calculator

Wouldnt that become 7.5 though

[glossy valve]

faiyrose

[ivory lark]

Yes i know but wouldnt the answer become different

[glossy valve]

faiyrose

[ivory lark]

3 and 3.5

[glossy valve]

faiyrose

[ivory lark]

Oh i gor confused

Yeah my bas

[ivory lark]

Okay thank you so the answer is this

.close

[full forum]

Channel closed

Closed by @ivory lark

Use .reopen if this was a mistake.

[full forum]

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.

[rugged raft]

how can I find A^n ? A is not diagonalizable so I have no idea now

[wanton comet]

whats the charecteristic equation for this?

[rugged raft]

this

[wanton comet]

ok

so (A-I)^3 =0

yeah?

and u need to find A^n

yeah?

[rugged raft]

yesss

[wanton comet]

iok

write A-I=B

B^3=0 yeah?

(since (A-I)^3=0)

so

A^n= (B+I)^n

would u agree?

now binomial expand

A^n= I+nb+ (n)(n-1)/2 B^2 + b^3 +b^4 +...

since b^3 =0

they cancel out

so

A^n= I + nB +(n)(n-1)/2 B^2

[rugged raft]

but we dont know B

[wanton comet]

B=A-I

we know A

we know I

😄

[rugged raft]

lol barin fart

lemme calculate to check

[rugged raft]

I got a pretty complicated result and I checked the soln, they used a different method idk

[wanton comet]

what did you get

and awhat did they get

it should be the samet hing

[rugged raft]

their answer is neater

@wanton comet do you understand this method maybe?

I dont quite get it

[wanton comet]

division algorthim

[rugged raft]

why did they do this

[wanton comet]

what is E

[rugged raft]

identity matrix

[wanton comet]

yeah you should get the same thign only

[rugged raft]

but why did they do this

[wanton comet]

because our method only works if (A-i)^3=0

u can use that anywhere

but its quite more annoying

[rugged raft]

hmm

i dont understand this division algorthim

[wanton comet]

wait

[wanton comet]

can you show the enetire thing

[rugged raft]

sadly it's a one-line hint

[full forum]

@rugged raft Has your question been resolved?

Channel closed

Closed by @rugged raft

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.

[rugged raft]

stat1

[wanton comet]

multiply it by

(1-1/2^2)

and divide it by the same

does taht work?

[rugged raft]

aah yesyes

tysm

.clsoe

[wanton comet]

i dont

[rugged raft]

.close

[full forum]

Channel closed

Closed by @rugged raft

Use .reopen if this was a mistake.

[wanton comet]

think

it does

[rugged raft]

it does

[gaunt oriole]

.reopen

[wanton comet]

its 2^n

so like

u get

(1-2^4)(1+2^4) = 1-2^8

but

ur next thing is

(1+2^16)

[rapid rain]

?

2^(2^3) = 2^8

(1-1/2^2)(1+1/2^2) = 1 - 1/2^4

then * (1+1/2^4) which gives 1 - 1/2^8

then * (1 + 1/2^8)

etc

[wanton comet]

its 1+1/2^2^n

[rapid rain]

yes, so?

[rapid rain]

times 1 + 1/2^2^1

[rapid rain]

times 1 + 1/2^2^2

[rapid rain]

times 1 + 1/2^2^3

[wanton comet]

oh yeah

it checksout

[full forum]

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.

[fathom trench]

hi

[marsh shale]

hello

[fathom trench]

i need help with this question

can anyone help me

[slate violet]

https://mindyourdecisions.com/blog/2017/12/24/tiny-but-not-so-simple-geometry-problem-areas-from-quadrilateral-diagonals/

same question, different numbers

[fathom trench]

thx

.close

[full forum]

Channel closed

Closed by @fathom trench

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.

[slate violet]

oh, arg z is the angle it makes with the positive real axis

like the usual angle in trig

the red angle theta

you want to find the maximum angle then for every point on the circle

also, tangents from the same point to the circle have the same length

so you could find the distance from (0, 6) to the origin

and it's the same over on the other point

for other circles you would just use Pythagoras given the distance from the centre to the circle

[full forum]

@torn jolt Has your question been resolved?

Channel closed

Closed by @uncut wadi

Use .reopen if this was a mistake.

[full forum]

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.

[proven warren]

(physics) Anyone know how you would calculate the error for values in a linear regression model? I have $D^2 vs. n$ in a graph, D has error, n has no error, I'm trying to get the error for the slope but dont want to use standard error cuz its too small 😭 and it doesn't take into account error in D.

[glossy valve]

Hemesfere

[full forum]

@proven warren Has your question been resolved?

[full forum]

@proven warren Has your question been resolved?

[full forum]

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.

[glacial valve]

Can someone please explain me how just considering the order of the first occurences of the numbers is enough for finding the required probability ?

[glacial valve]

Someone please help me with this problem . I have been wondering how this works from last couple of days 😭 😭

[full forum]

@glacial valve Has your question been resolved?

[full forum]

@glacial valve Has your question been resolved?

[full forum]

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.

[stuck storm]

If I have the equation $-\frac{b}{a}=\frac{1}{2}\frac{ka^2}{\omega^2a^3b^2-kb^2}$, how can I solve for the ratio b/a in terms of the constants k and omega

[glossy valve]

The د

[thorny isle]

You can factor in the denominator by b^2

[stuck storm]

ok

[full forum]

@stuck storm Has your question been resolved?

[full forum]

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.

[echo merlin]

I think the answer is E i'm just not sure

[glacial pasture]

explain your reasoning then

[echo merlin]

If you plug in 3 into both equations the answer comes out the same

oh

its only continous

bc when u differentiate u get 2 diff answers

[glacial pasture]

do you?

how?

f is continuous at 3
its derivative is also continuous at 3

no issues

[echo merlin]

So the answer must be B then

[echo merlin]

You have to derivate both functions

Wait

Ur right

I'm pretty sure

[glacial pasture]

I never said you were wrong, i just asked you to explain why you thought that

[echo merlin]

Yeah I realized that

[torn jolt]

continuous bc both functions have same value at x=3