help-38

[torpid depot]

and see where that takes you

[wraith hinge]

I am guessing the M is a point I need to add and connect to D, right?

[torpid depot]

yes

it should be on AB

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[wraith hinge]

.reopen

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✅

[wraith hinge]

Wdym?

[torpid depot]

i meant AB

[wraith hinge]

Yeah noticed now, alr will try thanks for helping

[torpid depot]

np, good day to you

[wraith hinge]

Same to you

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[wraith hinge]

If you calculate the value of the following expression on your calculator, you get zero. What is the correct value?

It’s in swedish

[fresh pecan]

a^3 - (a-1) * a * (a+1)

where a = 123456789

[wraith hinge]

Oh okay thank you

[edgy cedar]

Why would you get 0?

[hallow spruce]

Calculator cringe

[fresh pecan]

my calculator gets 1 too

lol

[edgy cedar]

[fresh pecan]

probably memory issues

but im not a computer scientist

[slate cloud]

"Assume your calculator overflows quickly."

[wraith hinge]

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[echo fossil]

did mellow typo the answers? im pretty sure that the -64 at the end of the 2nd spoiler should still be -48 and that 3x^3 should be 3x^2

[echo fossil]

id ask him directly but he had to go to class

[amber python]

,w expand 3(x^2 - 8x + 16) + 8x - 48

[solid kiln]

Results provided by WolframAlpha

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

Requested by 夢雪#2250

[amber python]

possibly typo

[echo fossil]

3x^2-16x is what i got, thanks 🙂 just makin sure. its prob a typo yee

thanks!

.close

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[silver creek]

Hi! When we have a linear equation: y=-4a then x=a right? So the linear equation produces the following point: (a,-4a)

[silver creek]

Someone correct me please 🙂

[rugged latch]

I mean yea that looks right

[silver creek]

there's a question that idk whether it's my fault or the answer's in the book fault. Sometimes, the book

answer is wrong so i'm unsure

[lament jewel]

eh i wld say they intersect at that point

[silver creek]

the question: a linear equation intersect the point (3,5) and has a slope of 3/5. Determine a so that the graph intersect y=-4a aswell

So what I did is I used the k formula.
k = (y2 - y1) / (x2-x1)

We know the following points: (3,5) and (a, -4a)

So we got:
(-4a - 5)/(a-3) = 3/5
right?

I got a = -16/23 but the book said a = -4/5

what did i did wrong here?

@lament jewel@rugged latch

<@&286206848099549185>

[rugged latch]

Put it in point slope

Then change to slope intercept

Then set equal to y= -4A

Wait a sec

[silver creek]

Ehm, I don't really understand what you meant. Sorry

[rugged latch]

Yea looking back at what I said now, I realize I’m not rlly understanding the question

Let’s say we find an a-value

[silver creek]

Yes

[rugged latch]

We get some line y=something

What then? The line that goes thru (3,5) and has slope of 0.6 will hit every x and y

Are u sure this is what the question is asking

[silver creek]

It doesn't goes through (3,5)

It's the graph which have the slope of 3/5 goes through the point y=-4a

but we don't know what a is

oh wait, the line goes through 3,5 too

[rugged latch]

Why’d u say intersect (3,5) here then

[rugged latch]

yea

[silver creek]

sorry my mistake

but the line, it goes through (3,5) and the point (a, -4a), right? and they asked for what a is

then i used the k-formula because if (a, -4a) is in same line as (3,5) , the slope (delta y/delta x) should be the same too

which is 3/5

but what confused me is why is my answer different from the book – i probably did something wrong

[silver creek]

yes

and it needed to hit an y point where y=-4a

[silver creek]

and this is where the line, y=-4a intersect

which is (a, -4a)

I'm confused

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[regal jasper]

How do i get the vertex

[split chasm]

doesn't make much sense to be asked the vertex of this

[edgy cedar]

What vertex?

[regal jasper]

oh

[inland orbit]

What exactly did the question say?

[regal jasper]

Draw a graph

[split chasm]

consider domain restrictions and simplification

[regal jasper]

okk

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[lone mauve]

So 2 is the only even prime number in existence

But is there a name for the 2,4 difference pattern? Light blue text

[torpid depot]

Only even prime number

[lone mauve]

Oops ty meant to say even*

[unreal loom]

I don't think so

since it's kinda useless

[lone mauve]

It’s always 4 and 2?

No pattern to it

[unreal loom]

not at all

[torpid depot]

No

[lone mauve]

Oh OK

[unreal loom]

it is any even number

[lone mauve]

Just these first few

Ah

[unreal loom]

after the first 1

[lone mauve]

Right

[unreal loom]

yeah the first few are close to each other

[lone mauve]

I guess that would make sense.. odd difference would make it even

[unreal loom]

and it thins out a lot after that

[lone mauve]

So sometimes it’s 6, 8, 14

[split chasm]

prime gaps are a pain

[lone mauve]

Ah ty

prime gaps

I like that wording better

[split chasm]

it can well exceed that

[lone mauve]

2,748,920

The higher up you go?

As of April 16, 2022, the largest known prime gap with identified probable prime gap ends has length 7186572, with 208095-digit probable primes and merit M = 14.9985, found by Michiel Jansen using a sieve program developed by J. K. Andersen.

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[silver parrot]

Geometry: okay so my problem is that idk how to prove A=B and B=C without using the transitive property and I'm trying to prove the transitive property so kinda hard. I'm thinking like subtraction property but I don't know how to do that. I've tried brainstorming for a bit but I can't find anything else.

[atomic tapir]

hers a photo of the pdf in question

[silver parrot]

yeah

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[silver parrot]

<@&286206848099549185>

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@silver parrot Has your question been resolved?

[silver parrot]

helpppp meee

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[earnest breach]

is #40 asking for all the x intercepts for f at x? so like, wouldn't that be all the x-intercepts for the unit circle?

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[proper patrol]

I have a question

[proper patrol]

Let's say f(n) is in O(n)

Can I also say that this function is in Ω(n)

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[wraith hinge]

im having trouble with this question

[wraith hinge]

mcdonald's will constract a wheel chair ramp at their new location, a safe ramp rises 1 inch and must be 12 inches long, if the ramp needs to rise 2 feet how long must the ramp be?

i got 288 feet but i know well that's wrong

can anyone help?

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@wraith hinge Has your question been resolved?

[wraith hinge]

<@&286206848099549185>

ill write it word for word

mcdonald's will construct a wheelchair ramp at their new location

a safe ramp rises 1 inch and must be 12 inches long

ok

I'm lost ngl

ok

Ohhhhh

So I just messed up with the metric system part

Ok

Okay thanks

Also how would I find the perimeter of ice cream?

I cant find the length of the cones side(s)

What about the sides

The cone

Ok

Thanks

Ok

I got 6.85

Cm

Nah hapf

Half

The cone

Yea

Ok

Wait I think I know what I got wrong

I had to sqaure the 35 and 12 no?

I got 37

Then I add up the whole thing

24 plus 37 plus 37

Its 98

Then

I do 3.14 x 24 divide by 2

37.68

135.68cm2

Or is it just cm?

Ok ok

Yea

How do I do this

I dont think 39 and 12 have the same factors tho?

Wait 3

Ok

Does the dominator stay the same?

Ok

Is this right?

First one is -56 + minus 3

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[odd sinew]

0.338514680484 does that round to 0.34?

[fringe minnow]

rounded to 2dp then yeah

[odd sinew]

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[hot fulcrum]

I think this one is 8 but im not positive

would appreciate a second opinion

mommies?

[atomic tapir]

mommies 🤨

[shrewd ridge]

that's 7

[hot fulcrum]

oh shit

smart man

theres my mommy

frownyfrog the goat

[shrewd ridge]

there's a 6

6 looks v. nice

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[coral venture]

Hey everyone, need some homework help

[coral venture]

I tried graphing it out to see how many different points I should expect;

and then take the derivative of cot(x) and set it equal to d/dx of -4x

but the algebra there got me lost, I know I should expect 4 results from [-pi, pi] but IDK how to get there

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@coral venture Has your question been resolved?

[coral venture]

<@&286206848099549185>

bruh

I think I got the answer

I got my 4 points

but idk how to like pre-impetively know there should be 4

before calculating

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[west wolf]

Could someone explain what t hours mean?

I can't not replace the variable

[near remnant]

Its some real number

So some real number of hours

[split chasm]

your answer will have t in it

leave t as t

[near remnant]

Exactly

[west wolf]

oh ok let me try again

[split chasm]

like it would literally the formula you'd be applying in questions a,c
you should already have it somewhere

[west wolf]

I think I got my formula right

it should be f(x) = 300(2^1/4)

300 being the initial value

2 = doubling

and 1/4 because it's every hour

so I plugged 12 giving me 2400 for a

and c I got 8072.605586

I rounded that up to 8072.61

[split chasm]

watch your variables and parentheses

there's no variable in
300(2^1/4)
your equation implies that the amount of bacteria is constant

how exactly are you plugging something into that

[west wolf]

well t should be the 1

because t = time

[split chasm]

yeh, you should have
f(t) = 300(2 ^ (t/4))

[west wolf]

I can't put that in my calculator

[split chasm]

you don't?

[west wolf]

I don't?

[split chasm]

like it would literally the formula you'd be applying in questions a,c
you should already have it somewhere

[west wolf]

well because it's t here

I see fractions and I get really scared

[split chasm]

your answer will have t in it

300(2 ^ (t/4))
is literally all they want for b)

[west wolf]

2^t/4

oh

[split chasm]

and watch your

[west wolf]

I think I got it right

I was worried that the system would not compute a variable other than x and y

[west wolf]

thanks a lot

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[proper plume]

hi

[proper plume]

are these correct

just need someone to check it

anyone

here

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[proper plume]

.reopen

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✅

[proper plume]

someone help?

[rugged latch]

Is that hw?

[proper plume]

ye

why

[split chasm]

show work

[proper plume]

ok

so is it correct?

bruh

[rugged latch]

?

[proper plume]

is my thing correct

my answers

[rugged latch]

Yea they look right…

[proper plume]

alr

bruh

there incorrect

somethings wrong

idk what

can i get someone else here?

[rugged latch]

Did u check decimals

[proper plume]

yea

[rugged latch]

How many places is it

[proper plume]

wdym

[rugged latch]

Tenths? Hundredths? Thousandths?

[proper plume]

tenths

[rugged latch]

So y u got hundredths

[proper plume]

cuz its the answer

what did I get wrong?

??

anyone here to help?

nvm found my mistake

.close

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[wraith hinge]

what angles includes AC?

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[wraith hinge]

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[west wolf]

I'm trying to solve these logarithms. For A I tried to convert to exponential to find x

3^x = 1/27

1/27 is technically 27^-1

3^x = 27-1

I'm not sure if 3^-3 is 27^-1

[glacial karma]

aye nice

yeye

so $x=log_3{3^{-3}}$

[solid kiln]

Springsskateboard

[glacial karma]

and using log prop

what do u

get

yeye

$log_a{a}$ = 1 btw

[solid kiln]

Springsskateboard

[glacial karma]

wassup

[west wolf]

it would be 1?

[glacial karma]

nope

$log_a{a^k}$ = k

[solid kiln]

Springsskateboard

[glacial karma]

so what do

u get

for part a

aye wassup

I think

u needa go to

another help

channel

cuz this one

is

occupied

yeye

peace ✌️

[west wolf]

alright I did my calculations

this is what I got

[hallow eagle]

Second one should be 1/6

Exactly

[west wolf]

should I write 1/16 for simplicity

[hallow eagle]

1/6

[hallow eagle]

Yes

[west wolf]

ok thanks

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[restive shard]

log4(36)

[restive shard]

how would u express this in the given base of 2?

like would it not be

log2(36) / log2(4)

but how is the answer log4(36)

pls help

[inland orbit]

That's true but I don't think that's what you're looking for

Let y = log4(36)

Then 4^y = 36

Can you express this with a base of 2?

[restive shard]

k

[inland orbit]

And then solve for y

[restive shard]

ye it would be

2^2y = 2^5

right?

so would it not be

[inland orbit]

2^2y = 36

[restive shard]

ye

[inland orbit]

2^5 is not 36

[restive shard]

ih

oh

wait oh so we just do 36^1/2?

[inland orbit]

So square root both sides?

[restive shard]

yea

[inland orbit]

Then you have 2^y = 6

[restive shard]

wait but how come it asks us for it in this format?

[restive shard]

and not this one

[inland orbit]

We're not quite done

[inland orbit]

Remember y = log4(36)

That's the thing we wanted to re-write with a base of 2

[inland orbit]

So finish solving this for y

[restive shard]

y=log2(6)

[inland orbit]

Yes

[restive shard]

but why would we want it in this form instead of the other one?

[inland orbit]

So log4(36) = log2(6)

[restive shard]

they are both in bases?

ye

[inland orbit]

Well the way the question was worded, sounded like they wanted it expressed in a single log with a base of 2

[restive shard]

oh

so like just a single one

[inland orbit]

I think so

I guess I'd have to see exactly how the question was worded

[restive shard]

y3ea na it said base of 2

k thx man

[inland orbit]

👍

[restive shard]

yo man could u h elp me with another quesiton?

express log8(27) as a logarithm to the given base

base 64

so 2^3y =27

would u just do 27^2 bc this turns 2 to 64?

[inland orbit]

Yeah. You didn't need to do the 2^3 thing

8^2 is 64

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[earnest breach]

Could I start with just creating a triangle ? When it says solve each triangle, does this mean they want the sides and angles or?

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[slim scroll]

Yeah, I believe so

[earnest breach]

So, I want to say that I could solve the sides with the pyth theorm. For the angles, given that I have two, could I easily solve this one? Should I use an identity?

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[wraith hinge]

Hello

[wraith hinge]

My grp solved this, all we need is an explanation

How do we explain the process??

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[wraith hinge]

<@&286206848099549185>

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[glass tide]

hey, I'm trying to find the modulo of two binary numbers. something like
$$101110010_2 \ \text{mod} \ 101001101_2 = 100101_2$$
is there a way to do this 'easily' without converting to decimal?

[solid kiln]

Sacha

[trim lichen]

long division in binary

[glass tide]

thanks 🙂

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[wraith hinge]

what does the 2 do to the graph

[inland orbit]

Stretch vertically

Double the slope

The original graph had slope 1 on the right of the vertex

[wraith hinge]

slope is 1/1 now

[inland orbit]

Yours should have slope 2 on the right of the vertex

[wraith hinge]

so new slope is 2/1

?

[inland orbit]

Yes

On the right half, -2 on the left half

[wraith hinge]

sorry idk what u mean

[inland orbit]

Nevermind

[wraith hinge]

sorry

i did it

[inland orbit]

Yeah, slope of 2

[wraith hinge]

it worked thank u

[inland orbit]

👍 No problem

[wraith hinge]

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[wraith hinge]

.reopen

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✅

[wraith hinge]

@slate dune

what if slope was 5/4

and it was 2 in front

would it become 10/8

or no thats same thing?

would it be 10/4

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[wraith hinge]

.reopen

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✅

[wraith hinge]

what did i do wrong

i made slope 1/3

and moved right 1 up 1

what does f mean

Y

No x

ok

Domain

btw i got no clue how to do this i just accidentally came into this chat

Wow bruh

sorry

:c

:3

c:

D:<

D:

; )

<3

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@wraith hinge Has your question been resolved?

[warm hearth]

Isn't the graph you made a graph of y=f(⅓x-⅓)+1?

if it would be |⅓x-1|+1 then for x=1
the value would be |-⅔|+1

I think you should move it 2 units horizontally to the right

[wraith hinge]

what is lambda

greek alphabet

okay

idk what u mean

i thought the -1 means i move 1 to the right

and the +1 outisde is up 1

[warm hearth]

I'll be back in 15 minutes, srry

[wraith hinge]

ok

[wraith hinge]

hey

ty

[warm hearth]

I'm writing an explanation rn

[wraith hinge]

ok

ty

[warm hearth]

So you have some function y=f($\frac{1}{3}$x)+1, you want to move it by 1 unit horizontally so you do
y=f($\frac{1}{3}$(x-1))+1 transformation

but that's equal to y=f($\frac{1}{3}$x-\frac{1}{3}$)+1

So to get y=f($\frac{1}{3}$x-1)+1

You gotta do
y=f($\frac{1}{3}$(x-3))+1
Transformation

So you move it by 3, not 1 unit

So you have some function y=f($\frac{1}{3}$x)+1, you want to move it by 1 unit horizontally so you do
y=f($\frac{1}{3}$(x-1))+1 transformation

but that's equal to y=f($\frac{1}{3}$x-$\frac{1}{3}$)+1

So to get y=f($\frac{1}{3}$x-1)+1

You gotta do
y=f($\frac{1}{3}$(x-3))+1
Transformation

So you move it by 3, not 1 unit

[solid kiln]

Lambda

[wraith hinge]

?

is the slope correct

1/3 slope

[warm hearth]

Idk why it's incorrect, that's a graph of an absolute value function, so
for y=f(⅓x-1)+1 it should be y=|⅓x-1|+1, so for x=3 you get y=1, and for x=0 you get y=2, that's exactly what is on the graph

[wraith hinge]

no i5ts not

i didnt submit it

it says correct

i just submitted

it said my last answer was wrong

[warm hearth]

Ok, nice, so I was right, yeah?

[wraith hinge]

yea

ty very much

[warm hearth]

Ok, nice

[wraith hinge]

for ur help i appreciate it

[warm hearth]

Graph transofrmations are pain, I hate em, good luck with that

[wraith hinge]

lol ty

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[indigo storm]

For this geometric proof using vectors what is the purpose of finding the magnitude squared of OB and AC?

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[devout siren]

I dont get it

Why $\overrightarrow{OB} = \overrightarrow{OB}^2$?

[solid kiln]

Noone

[indigo storm]

Yeah I have no idea either

[fathom folio]

What?

[devout siren]

See the working

[fathom folio]

Looks like crank to me

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[trail pike]

could someone help me w integration

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[trail pike]

<@&286206848099549185>

[edgy cedar]

Part I)

What have you tried?

[wraith hinge]

Hint: Something something substitution

[trail pike]

first and second

third cant seem to get me

[trail pike]

which part sorry

[edgy cedar]

Show your second part

[wraith hinge]

alright that's kind of a hard integral to find

but

substitute in u = x+1, du = dx

and solve for x, too, so you would have u - 1 =x

this means (u-1)/u^3/2

do you have an idea of where to go from here? @trail pike

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[junior gull]

70% of the vehicles driving on a street are cars, 30% are buses. the probability of parking for a car is 0.1, for a bus 0.2. what is the probability that a vehicle taken at random will stop?

[junior gull]

0,7* 0,1+0,3* 0,2
Am I right?

[shrewd ridge]

yes

[junior gull]

thanks

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[umbral dirge]

How do I use simpsons method on this integral?

[umbral dirge]

n=10 and the answer should have 8 decimals

[twin hornet]

Its usub

[umbral dirge]

did u read my question

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[night hill]

Here is what I've done so far. Not sure if I am doing this right though.
We have the set {0,1} within Z mod 2. Take the cross product of itself to get {0,1} x {0x1} = (0,0), (0,1) (1,0) and (1,1).
In order for these to be valid subspaces, they must be (1) closed under addition, (2) closed under multiplcation, and (3) contain the 0 vector.

[night hill]

The four results above satisfy the criteria correct? Would that be all the subspaces or am I missing something

[trail pike]

.reopen

[marble wharf]

so Z_2^2 = {(0,0), (0,1), (1,0), (1,1)}, that is correct

and now what is your list of subspaces?

[trail pike]

no sorry i dont quite follow

[night hill]

Would it not just be those four? [0,0], [0,1], [1,0], [1,1]?

@trail pike could you open another chat?

[marble wharf]

those are not subspaces

[trail pike]

but i believe u re supposed to infer from the first two parts of the question in order to integrate

[marble wharf]

are these supposed to be vectors?

[trail pike]

sorry

[marble wharf]

or what do you mean with the [] brackets

[night hill]

Yeah vectors

[wraith hinge]

ah i see, you still can do it manually

[marble wharf]

vectors are not subspaces

[wraith hinge]

the extra stuff might be more confusing all in all

anyways this isn't our chat

[marble wharf]

subspaces are (certain) sets of vectors

[wraith hinge]

open another help channel

[night hill]

What do you mean by that? Like multiple vectors? So all the combinations of [0,0], [0,1], [1,0], [1,1]?

[marble wharf]

you do know what sets are, yes?

[night hill]

Provided they meet the 3 criteria

Yeah, it's a collection of elements

[marble wharf]

[0,0] is a vector. {[0,0]} is the set containing the vector.

and {[0,0]} is in fact a subspace of Z_2^2

the trivial subspace

[night hill]

ah ok I see, so just wrong notation I was using

and are the others in the subspace of Z_2^2? {[0,1]}, {[1,0]}, and {[1,1]}

[marble wharf]

none of these sets contain the zero vector [0,0]

so they cant be subspaces

[night hill]

oh I see. If I changed them to include it, for example: {[0,1], [0,0]} then is it included?

[marble wharf]

does that satisfy the other axioms you listed?

[night hill]

Believe so, addition and multiplication are within it and it contains the zero vector

[marble wharf]

ok

so how many subspaces do we have now

[night hill]

{[0,0]} and {[0,1], [0,0]}. But then I would do that with the others. Like all the combinations of those like {[0,1], [0,0], {1,0}}, {[0,1], [0,0], {1,0}, [1,1]}, etc?

[marble wharf]

well is {[0,1], [0,0], {1,0}} a subspace?

[night hill]

Yes?

or I guess not since it's Z_2^2

[marble wharf]

is the sum of two elements again in the set?

[night hill]

Yes

[marble wharf]

what is the sum of [1,0] and [0,1]

[night hill]

[1,1] oh I see that also has to be apart of the set. So that particular one is not

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[silver perch]

My answer is also correct right? This is factoring by grouping

Oh i realized my mistake

My bad i'll try again

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[dense breach]

weird given answer is wrong lol

they just throw a v in there randomly

[silver perch]

Maybe its a typo

[dense breach]

all you have to do is factor a 2 out

[split chasm]

amongus.

[silver perch]

Anyways thank you

[split chasm]

yeh, that v was supposed to be a p

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[short kiln]

im allowed to do this right?

[keen plover]

Yes

[short kiln]

ok thanks

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[upbeat hound]

hi, I'm having trouble understanding the limsup of a sequence of sets..I think from my intuition limsup Ek by this definition must be unique, but the author talks about "points in limsupEk", so I imagine there could be more than one point? How could this be? Can anyone help me come up with a counter-example?

[digital bison]

why would they have to be unique?
E_k = [0,1] - (1/k, 1-1/k), for k>1
lim sup {E_k} = {0,1}
and
lim inf {E_k} = {0,1} as well

[upbeat hound]

oh sorry, I was confused about what the lim sup of a set means. I thought it meant the same as the lim sup of a sequence....thanks for providing the example, it's very helpful

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[fallow verge]

Hey i have a smol doubt
Is it true that if 'x' is some rational number in form of
x = a + b
the 'a' and 'b' must also be rational

[keen plover]

No

Let x = 0 and a = -b

[modern eagle]

No, 0 is rational but 0=pi-pi

[fallow verge]

F is 0 the only exception? 😔

[modern eagle]

Nope, 1=(pi+1)-pi

And so on

[fallow verge]

aha

Aight got it

Thenks

[modern eagle]

👍

[fallow verge]

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[feral hornet]

does anyone know what the name of this theorem is?

[polar goblet]

oh no

[feral hornet]

what?

[amber python]

that just looks like a parametrisation of the surface

[feral hornet]

what is the difference between these two ?

[amber python]

one of them you're integrating f(x, y, z) on the surface S

the other one youre calculating the flux of F(x, y, z) through the surface S

[feral hornet]

i think one of them is for when you get z = g(x,y) and the other is for when you get like an actual vector, right?

[feral hornet]

oh okay, so not what i just said

[amber python]

f(x, y, z) is a scalar function

and integrating basically means "summing up" the values of f(x, y, z) evaluated on the surface S

F(x, y, z) is a vector function

integrating F(x, y, z) . dS means youre "summing up" the component of F(x, y, z) through the surface elements of S

ru x rv is the surface normal

scaled appropriately according to the area element

[feral hornet]

okay i think i get it, does the formula on the bottom here correspond to any of those formulas?

[amber python]

yeah thats the parametrisation of the surface

[amber python]

that integral looks like the top one here

but you can just as easily change it to be the bottom one

[feral hornet]

okay so it corresponds to the top one, and i can use either of those?

[amber python]

like theyre the same formula

you've just gone and subbed in an explicit parametrisation

[feral hornet]

okay great, thank u so much

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[wraith hinge]

When we have a matrix A, with dimensions m x n, where Ax = b where x is a vector, why do we consider R^m in such a case and not R^n?

[fathom folio]

What do you mean by considering R^m

[wraith hinge]

Let me say that in a different way

If A is an m x n matrix with columns a1, ..., an and b is in R^m, in the matrix equation Ax = b

[fathom folio]

What is the dimension of (Ax)

[wraith hinge]

i mean, we can consider 2 x 3 here i suppose

So would it be R^2 or R^3

And why?

[fathom folio]

no, answer my question

What is the dimension of (Ax)

[wraith hinge]

R^m i guess?

[fathom folio]

Under the equality sign can b be any other dimension?

[wraith hinge]

No, if it is consistent, but my question is why do we consider the rows instead of the columns in this case?

[fathom folio]

I don't understand your question

Matrix multiplication just has convention n x m X m x p

Resulting in n x p

[wraith hinge]

okay

just got my answer from google

R^m s true. It is just another way of saying that for each b∈Rm, there exists an x∈Rn such that Ax=b.

R^n is false. The subspace of Rn spanned by the rows of A is at most m-dimensional (as we have only m rows). And we have already seen that we can have n>m.

[fathom folio]

A real space can't be true or false?

[wraith hinge]

this is answering if A spans R^m and R^n respectively

[fathom folio]

We can have $m \neq n$ though....?

[solid kiln]

草w

[wraith hinge]

I think I am just...really confused with span

which is causing this confusion for both of us

[wraith hinge]

ahh i guess i see now

my textbook defines matrices as m x n instead

what you said just made it click

just was confused with why we are considering b for R^m for A (m x n) in Ax = b

But that was just because i was subconsciously assuming a n x m matrix in my brain

well thanks!

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[storm cave]

used newton's second law on the part with block m1 to find tension but i keep getting the wrong answer

g - T = 0.5*0.65

g - T = m*a

[unborn bone]

the tension of the string?

by mu does he refer to the friction of the plane?

T2 + R2 + P2 = m2.a (R2 is the friction vector)

then you proceed to splitting the equation into an x and y axist

[storm cave]

yes

[storm cave]

but isn't it easier to just find the tension using F= ma on the m1 part

[unborn bone]

i forgot, do they conserve the same acceleration due to the massless and frictionless pulley?

[mental moss]

what did they asked for?

[unborn bone]

if so we can work with that

[unborn bone]

the string's tension

[mental moss]

ye they do

[unborn bone]

ok

so you do m.g - t = m.a (if i remember correctly)

yeah i see your issue

you forgot the first m

weight is measured in newtons, g is Newton/kg, so you need the mass to cancel out the kg

[storm cave]

ohhhhhhhh

ok i got it

thanks

[unborn bone]

np

[mental moss]

that's what we have to do

there is nothing extra to be done

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[pearl stream]

Given is that the closure of A is defined as the intersection of all
closed sets containing A.

Now also given is that if A is closed, A = Cl(A).

How is that correct? Say there exists a bigger closed set that contains A. Then clearly A does not equal Cl(A) if A is defined as the intersection of all closed sets containing A.

[merry bluff]

Isn't A itself a closed set containing A?

So the intersection must be A

[pearl stream]

Oh wait I somehow had union in my mind and got confused. You're absolutely right. Thx

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[wraith hinge]

we have h(x) unknown and we want to get its equation so we do this. My question is why does fIx)-1 occupy the x^2

[delicate jasper]

readable

[wraith hinge]

?

are you trying to find $h$ such that $h \circ f(x) = x^2$ given that $f(x) = \sqrt{x+1} + 1$?

[solid kiln]

kyou

[wraith hinge]

yes

what have you tried?

[wraith hinge]

i did this

i got the answr i needed

[grand rain]

776

[wraith hinge]

but the thing i am annoyed by is that I memorized that h(f(f-1(x))= f^-1(x))^2

what am i allowed to replace the x with f^-1(x)

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[hazy light]

I'm having confusion in the proof of finding expected value of Sample Variance.

[hazy light]

Suppose, $$S^2=\frac{(X_1-\bar{X})^2+(X_2-\bar{X})^2+\dots+(X_n-\bar{X})^2}{n}$$

[solid kiln]

QuantumBee

[hazy light]

(X bar is the sample mean)

[fresh pecan]

no sigma notation

[hazy light]

How did $\displaystyle \sum_{i=1}^{n}X_i$ turn into $\bar{X}$ here?

[solid kiln]

QuantumBee

[amber python]

oh boy

[fresh pecan]

thats wrong so idk

should be nX bar

[amber python]

the ol calculation of sample variance

by definition you have

[digital bison]

yeah, there's a typo in the step between the two images. There shouldn't be an n there yet.

[hazy light]

So that should have been,
$\frac{1}{n} E \left[\sum_{i=1}^n {X_{i}}^2+n\bar{X}^2-2n^{2}\bar{X}^2 \right]$

[solid kiln]

QuantumBee

[hazy light]

Right?

How is that term $\underbrace{2n\bar{X}^2}{\thonk}$ ?

[solid kiln]

QuantumBee

[hazy light]

Alright, that is the typo?

Ok.

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[amber python]

no the typo is the n

it shouldnt be there

not n^2

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[wraith hinge]

okay so i have this question where i need to multiply a number with 1295 which should be 8075

[sudden obsidian]

@wraith hinge whats the problem?

[wraith hinge]

Hello nvx, i need to find a number i can multiply with 1295 and that number should be 8075 but i cant🙄

[sudden obsidian]

can you write an equation that represents this statement?

[jolly pebble]

Use simple linear equation

[sudden obsidian]

call the unknown number x and try to write this as an equation

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[uneven parcel]

The dimensions of a playground are given with width as Y and length as x. Due to construction the size of the playground is reduced by 3 m in length and 4 m in width
the new playground will be 25 m^2. the perimeter of the original pereground is 64m. determine the dimensions of the original playground

[uneven parcel]

how do i write this in standard form

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[gleaming gate]

In order to find these answer, would I input the amount of time before and after 6:45 into d'(t)

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[civic trellis]

hello

[grand ridge]

the domain is every value of x such that f(x) makes sense

is there a particular number to which this function will yield an error?

[civic trellis]

0

on bottom

[velvet bolt]

yes

[civic trellis]

then domain?

[velvet bolt]

x+13 cant be 0

so x cant be -13

right?

[grand ridge]

don’t give him the answer man, let him figure it out

[civic trellis]

oh

i love you

[velvet bolt]

ok ur right

[grand ridge]

but yes

the denominator can’t equal zero

[night zodiac]

You were a helper, weren't you? So you should already know that

[civic trellis]

okay

[velvet bolt]

yeah mb

[grand ridge]

alright no worries it’s the past now

@civic trellis

the denominator of a fraction can’t equal 0

since you have x + 13 on the bottom

there is a number for x which makes x + 13 = 0

[civic trellis]

-13

[grand ridge]

yes.

so the domain of this function would be…

[civic trellis]

(-infinity, -13)?

[grand ridge]

not quite

[civic trellis]

oh

[grand ridge]

so it’d be every number with the exception of 13

[civic trellis]

-12?

[grand ridge]

how would you write that?

[civic trellis]

(-12, infinity?O)

[velvet bolt]

how do you write "every number"

?

[civic trellis]

infinty

[velvet bolt]

no

infinity isnt a number

[civic trellis]

what

[royal prairie]

Hello

I could lend a hand here

[velvet bolt]

ok...

[royal prairie]

In this situation

[grand ridge]

the set of every real number would be (-∞, ∞)

[civic trellis]

yes

[grand ridge]

but that set includes the number in which this function is not defined

namely, -13

[night zodiac]

You're writing it in interval notation if that terms makes more sense

[civic trellis]

yes

so

is it

[grand ridge]

you were half right* the first time when you put (-infinity, -13) but you forgot about all the numbers greater than -13

[civic trellis]

?

[grand ridge]

that’s correct but you could also write (-∞,-13) U (-13, ∞)

[civic trellis]

oh

[grand ridge]

they’re the same thing but this is more concise

[dire charm]

Not quite correct, the three-interval solution was missing 0

[grand ridge]

actually they’re not the same

because 0 is on the domain of this function

[dire charm]

It would be simpler just to write R\{-13}, though.

[civic trellis]

?

[velvet bolt]

yes

[grand ridge]

if x = 0 then (0) = 12/13, so x CAN be 0

[royal prairie]

Oog

[velvet bolt]

(-inf,inf) is R

[royal prairie]

Hello

[velvet bolt]

and the domain is

R-13

[civic trellis]

you are all very smart

i love you all

[grand ridge]

it would be but they probably wouldn’t understand that because they were using interval notation, not set notation

[dire charm]

Please stop making random posts like these in help channels.

[royal prairie]

Sorry

Hello

[civic trellis]

yes

[dire charm]

I said stop it.

[civic trellis]

lets kiss

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[dire charm]

.close

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[scarlet escarp]

i'm solving an eigenvalue problem $\begin{cases}\frac{d}{dx}(x\frac{dy}{dx})+\frac{\lambda}{x}y=0\ y(0)=0, y'(1)=0\end{cases}$
since this is a cauchy-euler, we can let $y=x^m\implies m(m-1)+m+\lambda=0\implies m=\pm\sqrt{-\lambda}$\
if $\lambda=0$, we get $y=c_1 \ln(x)+c_2$, but $y(0)=0$, so do we throw away the case of $\lambda=0$?

[solid kiln]

maximo

[scarlet escarp]

or do we take c_1 = 0, c_2 = 0?

which i guess amounts to throwing away lambda=0 anyways

and for $\lambda = -k^2 < 0$, we get $m=\pm k \implies y=c_1x^k + c_2x^{-k}$\
using the initial conditions, $y(0)=0c_1 + 0c_2=0, y'(1)=kc_1 -kc_2=0$, what do we do from there?

[solid kiln]

maximo

[scarlet escarp]

are the pairs $(\lambda_k,\phi_k), \lambda_k=-k^2,\phi_k = c_1x^{\sqrt{-\lambda_k}} + c_2x^{-\sqrt{-\lambda_k}},k\in(-\infty,0)$ eigenpairs?

[solid kiln]

maximo

[scarlet escarp]

omg

i've been using the wrong boundary conditions

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