help-39

[honest bough]

I find that it's much easier to figure out the values of the relevant quantities in the washer method when I draw a picture first

Though, that also applies to the shells method as well

[upper mango]

Ok one sec

Given these functions and limits, I've shaded the area I'm looking for, how do I determine what k is and how do I know if I need to use it

[honest bough]

Consider a random washer

It's got a thickness of dx, right?

[upper mango]

I'm following

[honest bough]

The volume of this washer is π(outer radius - inner radius)²(thickness)

[upper mango]

Ok so since it is going around the x-axis, k is 0?

[honest bough]

Hold on gimme a sec I think I'm fucking up the volume

π((outer radius)² - (inner radius)²)(thickness)

[leaden wadi]

If the axis of revolution is not on an axis, you want to subtract the axis of revolution from the equation that determines each radius.

[honest bough]

Do you agree that that's the volume of a washer?

[upper mango]

Yes it is(given an integral from a to b is in there)

[honest bough]

Well, we're just looking at a single infinitely thin washer

So we're not integrating rn

[upper mango]

Ok

[honest bough]

Using the graph for help, what's the outer radius of a general washer?

And what's the inner radius?

[upper mango]

The outer radius be the function furthest from the axis of revolution, so 2x+1, and the inner radius would be x+1

[honest bough]

Yep

And since the thickness is dx, you can find the volume of a general washer

Then you can add them all up, which is equivalent to integrating

[upper mango]

Right, but my question was when to use k and how to determine it, granted my example has k as 0 so my bad

[honest bough]

Well, just follow the basic principle of finding the outer and inner radii of a washer using geometry

If the axis of rotation isn't on a coordinate axis, then the equation for the radii will be different as well

[upper mango]

Ok, I think @leaden wadi explained it well. So if the axis of revolution was x=-1, I would subtract -1 from both functions right?

Making it (2x+2)^2-(x+2)^2, yes?

[honest bough]

If the axis of rotation was x = -1, then each of the radii would be increased by 1, which is equivalent to subtracting -1, yes

[upper mango]

Ok thanks. And sorry about earlier legit thought I was in an unoccupied channel.

.close

[pearl pond]

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[honest bough]

I'm not a fan of the whole "just remember you should subtract k from the radii." I much prefer the intuitive geometric interpretation. Whatever works for you though

[pearl pond]

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[inland thicket]

Use implicit differentiation to find y’. I’ve tried using product rule and chain but I keep getting stuck. Thanks

[pearl pond]

@inland thicket Has your question been resolved?

[inland thicket]

<@&286206848099549185>

[honest bough]

Show your work @inland thicket

[honest bough]

,rotate

[honest bough]

The RHS is correct

But you should be multiplying sec²(xy) by the derivative of xy, not just y

[inland thicket]

Wouldn’t the derivative of xy just be 1 and then put (dy/dx)?

[honest bough]

No

You have to use the product rule

[inland thicket]

,rotate

[honest bough]

That's not the product rule

(fg)' = f'g + fg'

[inland thicket]

1(y)+(x)(dy/dx)?

[honest bough]

Yes

[inland thicket]

?

[honest bough]

sec²(xy) is multiplying the entirety of y + xy', not just the first part

Also, the y just disappeared between steps 1 and 2

[inland thicket]

So sec^2xy(y+xy’)

[honest bough]

Yes

[inland thicket]

Then how do you get the y’ out from the sec?

[honest bough]

It's not in the sec

You have sec²(xy)(y + xy')

The y + xy' is not in the sec

It's just being multiplied by sec²xy

[inland thicket]

Sorry. I meant to ask how do you get the y’s on one side?

[honest bough]

Start by distributing, probably

[inland thicket]

The secant to the y and xy’?

[honest bough]

Yes

Then get all the y' terms on one side, factor, and divide

[inland thicket]

Got it. Thank you. Do you mind helping with one more please?

[honest bough]

Maybe. Depends on the question

[inland thicket]

Find the points at which the graph x^2 +2y^2 -4y-6=0 has a horizontal tangent line

[honest bough]

What have you tried

[inland thicket]

I found the derivative which I believe is (-2x)/(4y-4)

Then I set it to zero to find the horizontal and wasn’t sure how to go from there

Rotate

,rotate

[honest bough]

Well, if a/b = 0, what does that tell you about a or b

[inland thicket]

It’s 0. But how did you know that from the function?

[honest bough]

What's 0?

[inland thicket]

A or b

[honest bough]

b can be 0?

So a/0 = 0?

[inland thicket]

a=0

[honest bough]

Yes

Now, we have -2x/(4y - 4) = 0

Therefore?

[inland thicket]

-2x=0 so x=0

[honest bough]

Yep

And you can use the original equation to find y

And then you have the point(s)

[inland thicket]

So 4y-4=0? So y=1? So (0,1) is the point?

[honest bough]

Where'd the 2y² go

[inland thicket]

plug 0 into the original function?

[honest bough]

For x, yes

[inland thicket]

Why not the derivative?

[honest bough]

Let's say you're given f(x) and you want to find the point where x = 2

To find y, you find f(2), right?

You don't calculate f'(2)

That just tells you the slope

We don't want the slope, we already know it's 0

We want the y value at the point

[inland thicket]

Ok. Gotcha. I got y=0 and 2

[honest bough]

How so?

That's not what I get

[inland thicket]

2y^2-4y=6

I don’t get that either. Sorry. One sec

Y=1,3

[honest bough]

Again, I have something different

Very close though

[inland thicket]

2(y+1)(y-3)=0. Is this what you get?

[honest bough]

Yep

[inland thicket]

Am I just being dumb? 1 and 6?

[honest bough]

No

If 2(y + 1)(y - 3) is 0, what does that tell you

Remember that if ab = 0, then either a = 0 or b = 0

[inland thicket]

Y=-1,3?

[honest bough]

Yes

So what point(s) do we have

[inland thicket]

(0,-1),(0,3)

[honest bough]

Yep

[inland thicket]

Wow. You are so smart. Thanks so much

.close

[pearl pond]

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[fossil lodge]

how is rank[A|b] and rank[A] different?

[sharp quest]

one is the rank of an augmented matrix, the other is the rank of a coefficient matrix?

[fossil lodge]

i mean, why can they be different

[sharp quest]

because [A|b] has an extra column

[fossil lodge]

what do you mean extra column?

oh, b?

[sharp quest]

if A is a 3x3 matrix, then [A|b] is a 3x4 matrix

[fossil lodge]

consistent only apply with augumented matrix, right?

[sharp quest]

yes

[rustic gate]

consistent refers to the original system of linear equations you're trying to solve

so it only makes sense in the context of having the system

every matrix can be thought of as an augmented matrix

but

without a system of equations you're trying to solve

there's no concept of consistency

[fossil lodge]

Why is the augumented matrix's rank =3 ?

oh, does the b column also count towards the rank

[rustic gate]

an augmented matrix is just a matrix

you can ignore the bar

so yes your conclusion is correct

[sharp quest]

for any matrix (augmented or not) the rank is equal to the pivots in the reduced row echelon form

[rustic gate]

although personally i reckon that's the worst way to think about rank

[fossil lodge]

but why is the augumented matrix rank = 3?

if we do r3 - 2r2, wouldnt r3 be 0 0 0 ?

[rustic gate]

the augmented matrix is a matrix itself

ignore the bar

the last row is 0 0 0 3

[pearl pond]

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[queen ember]

Okay so I've been having issues with something. I can't seem to figure it out.

A venn diagram type question

The question goes as follows: 50 people were asked whether they can paint or sew, 13 of them said they could paint and 14 said they could sew. 6 of them said they could do both

How many of them cannot paint or sew.

Now I've tried multiple ways by placing the remaining people as the answers but can't figure it out.

[cyan heath]

What is 13+14+6?

@queen ember

[queen ember]

33, I tried that method yet it kept saying it was incorrect.

[cyan heath]

Okay, i forgot it was a venn diagram

Yea i didnt read the last party of the question, sry lads

[queen ember]

So 17? Apparently they're asking for the number of people who cannot either sew or paint.

Out of the 50.

[cyan heath]

Yea, i bet 17

[queen ember]

It is incorrect..

It says seek help- Jeez..

[pearl pond]

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[queen ember]

.reopen

[pearl pond]

✅

[queen ember]

Okay so new issue-

It asks that 40 people if they can knit or sew.

11 of them said they could knit and 14 said they could sew. 9 of the people who CAN KNIT said they could also sew.

How many people can neither knit nor sew.

since this is a venn diagram, it's a harder issue.

Being the 9 is removed from the 11.

[pearl pond]

@queen ember Has your question been resolved?

[queen ember]

<@&286206848099549185> I was told to ping and all. Sorry for the ping!

I tried multiple methods but couldn't solve it.

[pearl pond]

@queen ember Has your question been resolved?

[urban raft]

have you tried using the inclusion exclusion principle

[queen ember]

I have, the one to include and remove from one or the one they added to have the number for both.

I just dunno how to answer it.

[urban raft]

just subtract the cardinality of the union of both sets from the cardinality of the finite universal set (40). if S is the set ofd people who can sew and K of people who can knit, then the question can just be rephrased as
|(K∪S)`|= |K' ∩ S'| ( De morgans law)
= |U-K ∩ U-S| ( Removing the complement)
= |U-(K∪S)| (Distributive property)
= |U| - |K∪S| (K∪S is a subset of U)
= 40 - |K∪S|

should be correct rite

hmm

probably

[urban raft]

the answer is 24 right?

[queen ember]

It it, holy hell it was more complicated than I thought-

Thank you so much.

https://tenor.com/view/seungwaniglive-seungwanbow-wendyiglive-seungwan-bow-twice-gif-21424849

[urban raft]

Rather, more simply K∪S = People who can EITHER sew or knit so |K∪S| is the number of people who can either sew or knit. the total number of people is 40
so people who can do NEITHER = total - people who can do EITHER = 40 -|K∪S|

lol no problem

[queen ember]

Gotcha, thanks a ton. I can finally move on to another question, jeez-

.close

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[pearl pond]

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[ocean cobalt]

I'm supposed to find (f^-1)'(1) and i have been trying to get the inverse, i've tried online calculators but they dont make sense and i don't really know what the (1) means and how i would use it, the book i have only confuses me more, basically how do i find the inverse in this case and what is (f^-1)'(1)?

[late sun]

I’ve never seen that notation, I’m guessing it can mean 1 of 2 things, multiply the function by 1, which seems pointless, or find the inverse of 1 which sounds more likely, so I’d guess it’s that

[pearl pond]

@ocean cobalt Has your question been resolved?

[ocean cobalt]

this is the only thing i've found in the book thats similar

<@&286206848099549185>

[pearl pond]

@ocean cobalt Has your question been resolved?

[pearl pond]

@ocean cobalt Has your question been resolved?

[pearl pond]

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[dawn ermine]

Would someone mind looking this over?

[trim mantle]

.close

[dawn ermine]

?

[trim mantle]

If i need help

Do i ask here

[dawn ermine]

See #❓how-to-get-help 🙂

[pearl pond]

@dawn ermine Has your question been resolved?

[dawn ermine]

Helloooooooo? 🙂

[pearl pond]

@dawn ermine Has your question been resolved?

[dawn ermine]

.close

[pearl pond]

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[stuck arch]

okay whats your calculation?

[west yacht]

How is -1 wrong
Cuz
q’x= f’g-g’f
q(5)= -1(3)-0(6)/3^2

wait

Oh i used the /3 from last time instead of 9

Nevermind

It would be -1/3

.close

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[zealous jacinth]

why did the sum start at 1

we needed to make the general power (n + s - 1)

so made n= n - 1

[cinder flower]

some of those look like m's but it's hard for me to read

[zealous jacinth]

now if we put n=0 the power becomes
(s - 2) ?

no there isn't m its n

[cinder flower]

this is an n?

[zealous jacinth]

yeah

[rustic gate]

what are we trying to do here with the sums

[cinder flower]

lol ok

[rustic gate]

i think there arent any ms

just long tailed ns

if you shift the index

you gotta shift everything

including the a_n

[zealous jacinth]

so this is frobenius method

[rustic gate]

yeah okay

the a_n hasnt been shifted properly

the way you can think about it is

just think about the first term in the sum

[zealous jacinth]

yeah i forgot the n-1

[rustic gate]

so when n starts from n=0

the first term is a_0 x^s right

so then if you want to keep the same sum but reindex

[zealous jacinth]

yeah

[rustic gate]

and n starts from n=1

then you gotta have a_(1-1) x^(1 + s - 1)

for the first term

anyway if you want to know why we do the reindexing

its so that you can put the same powers of x together

and that means you can combine the coefficients across the different sums

[zealous jacinth]

so

when we change the index of the sum

we look at the a coefficient ?

[rustic gate]

what do you mean

[zealous jacinth]

wait

since we changed n to n-1

A becomes a_n-1

to make a be a_0

the sum index n=1 ?

okay i think i get it

[rustic gate]

the starting term will tell you everything

so yes originally n=0 so a_n = a_0

now n=1 so we need a_(n-1) = a_0

[zealous jacinth]

Just like this

okay

thank you smmm

[rustic gate]

yes

just like that

[zealous jacinth]

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[jaunty needle]

where do i start for a problem like this

[buoyant panther]

do you know when a function is continuous at some point?

[jaunty needle]

not sure how to find that just with a set of equations

[buoyant panther]

it's not set of equations, just piecewise definition of the function

Can you examine sided limits at x = 0?

I mean

[jaunty needle]

am i supposed to plug in x as 0 for them?

[buoyant panther]

$$\lim_{x \to 0^+} f(x)$$
$$\lim_{x \to 0^-} f(x)$$

[jolly parrot]

Modus

[buoyant panther]

basically, but you need to take a suitable formula

[jaunty needle]

ok so should i be using x as it approaches from the left for the top

[buoyant panther]

ye

[jaunty needle]

so the answer would be the lim=5 for the top right

[buoyant panther]

good

[jaunty needle]

and then for the bottom its 0

so it shows its discontinuous bc the limits are different?

[buoyant panther]

yeah

[jaunty needle]

ok that makes sense

[buoyant panther]

also lim at x = 0 does not exist

now on b) you need to tell me what is f(0)

[jaunty needle]

its continuous from the right

?

[buoyant panther]

nope, since f(0) isn't 0 (it's not equal to the limit from the right)

[jaunty needle]

should i be using the top or bottom equation to derive that f(0) isnt 0

[buoyant panther]

top, because it tells x is less or equal 0

[jaunty needle]

okay

that makes sense

[buoyant panther]

when the another says x is only greater than 0

[jaunty needle]

so in that scenario always use the one that has an equal part to the inequality sign?

[buoyant panther]

we could say that

so

you have

$$\lim_{x \to 0^-} f(x) = f(0)$$

[jolly parrot]

Modus

[buoyant panther]

Hence function is continuous from the left

[jaunty needle]

ok so we know that its not continuous at 0 and at 5 right

or am i wrong about the 5 part

[buoyant panther]

why it's not continuous at 5

[jaunty needle]

because the lim for the top part =5 but not for the bottom at f(0) or is that wrong

[buoyant panther]

the neighborhood of the point x = 5 is included in formula at the bottom

we don't need to analyze top part

or even we can't

[jaunty needle]

ok so then we only know its discontious at 0

[buoyant panther]

yep

[jaunty needle]

so it would be [-infinity,0) and (0,infinity]

for c

?

[buoyant panther]

remember that it's continuous from the left at x = 0

[pearl pond]

@jaunty needle Has your question been resolved?

[pearl pond]

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[midnight haven]

For each $a, b, c \in \mathbb{R}$, prove that:

$a^3 + b^3 + c^3 - 3abc = (a + b + c) * (a^2 + b^2 + c^2 - ab - bc - ca).$

[jolly parrot]

trololol !

[midnight haven]

how ?

I had to solve a similar problem a few hours ago. Due to the help of somebody here, I figured out that I gotta bring terms together in order to form structures like x^3 - y^3 or x^3 + y^3 etc, which can be further simplified. But in this problem, I have really no idea how to group terms together.

[visual light]

do you know how to multiply polynomials

https://www.youtube.com/watch?v=yJzLYa-_Y1k

[midnight haven]

Yes.

But if I multiply the right-hand-side of the equal sign, I'd have 18 different terms.

That's why I try to find another way of solving it.

[visual light]

fair enough

[pearl pond]

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@midnight haven Has your question been resolved?

[pearl pond]

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[oak tulip]

Why is this not being accepted?

[fleet sky]

not quite the answer

what is 4 - 1/2?

wait I'm ture

*tired

have you tried submitting it as $-2y^{\frac{7}{2}}$?

[jolly parrot]

MellowDramaLlama

[fleet sky]

maybe they want it in that form

[jaunty oar]

it says entire radical it should be correct tbh

[oak tulip]

cant submit it as this since its asking for an entire radical

[jaunty oar]

try

$-\sqrt{4y^7}$

[jolly parrot]

imagine

[jaunty oar]

maybe

unless u cant put - either

[oak tulip]

perfect tysm

.close

[pearl pond]

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[jaunty oar]

gg

[midnight haven]

i need help understanding venn diagrams if someone could help me that would be great

[pearl pond]

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[pearl pond]

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[jade kite]

is it possible to find the n+1's complement of a number of base n

[jade kite]

for example the 11's complement of a base 10 number

I found my answer sorry for disturbing

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[wicked yacht]

F(x) = x + cosx, find (f^-1)'(1)

[midnight haven]

let's see your work dawg

[wicked yacht]

I'm just baffled at how to even start ngl

I just need 1 example, and I can probably figure it out from there

I'm currently also trying to find a yt video to help

[pearl pond]

@wicked yacht Has your question been resolved?

[rough stream]

This is called the inverse function theorem

Basically, doing this:

Let g(x) be the inverse of x + cos(x). We want the derivative of g(x).
f(x) = x + cos(x)
x = g(x + cos(x))

Take the derivative of both sides, remembering to use chain rule on the right:
1 = g'(x + cos(x)) • (1 - sin(x))

Sub some value of x that gives a g'(1), then solve for it

[wicked yacht]

That makes sense

Thank you

.close

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[midnight haven]

Help

What is happening

<@&286206848099549185>

Nobody

It’s crazy how 3 questions take hours to get help for In this server

<@&286206848099549185>

.close

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[wary dragon]

trying to find

derivative

getting different result than calculator

[jaunty oar]

do you know the formula for the defintion of a derivative

[wary dragon]

getting 1/2sqrt(x)

yea

f(x+h)-f(x)/h

[jaunty oar]

yeah

so here f(x+h) will become what

[wary dragon]

1/sqrt(x)+h

[jaunty oar]

no

it will be

1/sqrt(x+h)

[wary dragon]

oh

[jaunty oar]

u have to replace the x with x+h

[wary dragon]

h is in sqrt as wel?

oh yea

ok

[jaunty oar]

yeah

[wary dragon]

ok

[jaunty oar]

try it with that?

[wary dragon]

let me try doing now

could wait around for a sec

ill just try rq

ok am at sqrt(x) - sqrt(x+h)/h * sqrt(x+h)*sqrt(x) not sure how to continue

writing math stuff on discord is a pain lmao

[jaunty oar]

honestly lmaoo

[jaunty oar]

can you send me ur working to how you got there

just click a picture

it would probably be easier

[wary dragon]

ok

im on computer

so photo booth

😄

half of it is from the past

@jaunty oar ya still there

[jaunty oar]

yeah 1 sec im tryna simplify it

[wary dragon]

k

[jaunty oar]

how did u get h in the numerator im confused

[wary dragon]

where

i multiplied

by this

[jaunty oar]

but then dont u get

,rotate

[jaunty oar]

how did u get h in the numerator

[jaunty oar]

the denominator here is wrong i forgor

but still numerator is right

[wary dragon]

thinking

1s

yea not sure

teacher does it that way

like that type of way

in those circumstances

[jaunty oar]

no i get the multiplying

but how did u get h in the numerator

[wary dragon]

wherer

[wary dragon]

leave that

that was before

i realized

[jaunty oar]

oy

oh

[wary dragon]

h waas under the sqrt as well

lol

[jaunty oar]

ohh

[wary dragon]

my bad

[jaunty oar]

ok then 1 sec 😭

[wary dragon]

i think my numerator is still wrong tho

cuz its not that

need to change

[jaunty oar]

lemme try to solve it from the start

[wary dragon]

ok

end of book answers says f'(1/4)=-4

just wanna know how to get to there

like get the derivetive

[jaunty oar]

i think i got it

1 sec

[wary dragon]

lets go bro i was on this problem for an hour

[jaunty oar]

yeah i got it

klemme send pic

i didnt write lim everywhere but u get it

@wary dragon

u had to rationalize

sorry fr taking so long 💀

[wary dragon]

wait

#help-39 message

this wouldnt work then tho

[jaunty oar]

send graph f

[wary dragon]

i dont have no graph

[jaunty oar]

oh

oh wait

i misread

[wary dragon]

ill just post this again

[long wind]

Does it mean the limit definition?

[wary dragon]

yea

teacher

specified

to use

it

he said not to use other theorems

[long wind]

$\lim_{h \to 0} \frac{\frac{1}{\sqrt{x + h}} - \frac{1}{\sqrt{x}}}{h}$

[jolly parrot]

Olly

[jaunty oar]

this is correct

with the thing i found

@wary dragon

it works with the derivative we found wdym

[wary dragon]

oh yea it

flip

ok

1s

ok well tysm

[jaunty oar]

np

u understood right?

[wary dragon]

appreciate it

going thur it rn

wai

why u write otherway

[jaunty oar]

wdym otherway

[wary dragon]

waited

[jaunty oar]

yeah

[wary dragon]

can u send the pic

again

but from the start

[jaunty oar]

alright

[wary dragon]

to end

thks

[wary dragon]

alr

[jaunty oar]

$\frac{\frac{\sqrt{x}-\sqrt{x+h}}{\sqrt{x}\sqrt{x+h}}}{h}:=:\frac{\sqrt{x}-\sqrt{x+h}}{h\sqrt{x}\sqrt{x+h}}$

[jolly parrot]

imagine

[wary dragon]

dumb question

but

how did u get the later part

nvm

that works

[jaunty oar]

did you get it or should i explain

[wary dragon]

yea i got

[jaunty oar]

alr cool

[wary dragon]

@jaunty oar will the other h not get cancelled as well?

[jaunty oar]

it will

[wary dragon]

in the denominator

[jaunty oar]

all 3 will

i crossed it out i think it just didnt show in the picture

[wary dragon]

kk

[jaunty oar]

i crossed it lightly

oof

[wary dragon]

all good

oh yea

how would i find the slope

[jaunty oar]

that is the slope

the derivative is the slope

[wary dragon]

oh right

[jaunty oar]

plug in a value for x and u will find the slop at that point

[wary dragon]

for graph of f i just plug in some values in 1/sqrt(x)

correct?

[jaunty oar]

yeah

[pearl pond]

@wary dragon Has your question been resolved?

[pearl pond]

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[limber belfry]

does this type of cone always have a radius of 1 ?

[old geyser]

Cones can have different lengths of radii

[limber belfry]

mhm, so basically if you get this function, it is a cone shape but you don't know how long the distance from the centre to the outer point is?

[old geyser]

I guess?

I mean it's true regardless of the height

All it would really affect it height and slant height

[limber belfry]

what is true regardless of the height? and sorry this question is really out of context

i can send you the question i am applying it to if you want but i think what you have said is helpful

[old geyser]

z = sqrt(x^2 + y^2)

But I think I would need context

Sadly I don't have time

[limber belfry]

thats ok i appreciate the help!

[modern otter]

I mean you don't have a range for the values, so it's just a never ending cone

[limber belfry]

yeah thats what i was thinking but i wasn't sure

[modern otter]

You're right

A cone is just a lot of circles with increasing radii put on top of each other

[modern otter]

Not sure if this helps, just another way to look at it

[limber belfry]

tysm no that is really helpful

i might send my questions for reference

but they are a huge mess tbh

2 and 3 are the issues for me

i think i have the info i need tbh. tysm

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[worthy ingot]

Hey

[slate thicket]

Ohh @junior pawn sorry but the channel got taken by few seconds

[junior pawn]

Ok

[worthy ingot]

So I’m doing precalc and we have a f(x) equation that goes like this g(x)=(x-3)/(x+2)

And the x to put in is (x+h)

I am currently on e

[slate thicket]

So you put (x+h) in place of x in g(x)

[worthy ingot]

Yeah I did that for the normal numbers

[slate thicket]

So you get $g(x)=\frac {x+h-3}{x+h+2}$

[jolly parrot]

Deep.

[worthy ingot]

I’m on my last check for this problem but I want to make sure it’s a normal X and not x^2

Yeah you were right

Thanks

.close

[pearl pond]

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[slate thicket]

No problem

[pearl pond]

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[sullen hinge]

Im having trouble finding these 2

[echo flint]

Is it asking for an exact value?

[sullen hinge]

no. also I figured out the first question. I only need help wiht 7

the answers should be fractions

@echo flint annything?

[echo flint]

im sorry my man i havent done this stuff in a long time im not a helper

[sullen hinge]

alright

[echo flint]

ping them theyll be able to help u better

[sullen hinge]

who would you reccomend?

someone help me lol

<@&286206848099549185>

[pearl pond]

@sullen hinge Has your question been resolved?

[pearl pond]

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[mellow atlas]

Number 3

I am most confused about number A it should be two equations

[pearl pond]

@mellow atlas Has your question been resolved?

[mellow atlas]

No

<@&286206848099549185>

[pearl pond]

@mellow atlas Has your question been resolved?

[mellow atlas]

No

[pearl pond]

@mellow atlas Has your question been resolved?

[pearl pond]

@mellow atlas Has your question been resolved?

[grim patrol]

#❓how-to-get-help

[grim patrol]

why do u say that

[pearl pond]

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[signal cargo]

In Rudin's book there is statement that segment (a,b) is not open if we regard it as subset of R^2 but it is open subset of R^1... can someone explain why it is not open in R^2

[marble sigil]

open means the tiny neighborhood around every point is still in the set

in R2 the neighborhood is a tiny circle that goes above and below the 1d line segment

[signal cargo]

how can be define a segment (a,b) in R^2

i think (a,b) will be a point in R^2

[marble sigil]

it looks the same, just a line, like {all the points (x,0) for 0<x<3}

here's the picture

[signal cargo]

okie okie

now I understand

i have another question also

is phi (empty set) a point of Z.

?

[marble sigil]

not sure what phi means in rudin

[signal cargo]

empty set

[marble sigil]

oh gotcha, the empty set isn't a point*

it's just no points

[signal cargo]

i thought so

so what do you think.. is set of all integers is closed set?

[marble sigil]

in R? sure

[signal cargo]

in R^2

[marble sigil]

still closed yea

[signal cargo]

how?

closed set is if every limit point of E is point of E

but Z has no limit point so

[marble sigil]

in math that counts as true

since there's no limits points that break the rule it counts as closed

[signal cargo]

okieee

i remeber a time when for me just [a,b] was closed set.. i had never thought that Z is also closed ..why it is so complicated now🥲🥲

[marble sigil]

it's like [a,a] U [b,b] U [c,c] U ... 😛

[signal cargo]

this makes it so easy to understand.. why don't they write this in books

[marble sigil]

🫠

[cinder flower]

but a union of infinitely many closed sets doesn't have to be closed

[signal cargo]

thnx for help

okie

.close

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[midnight haven]

.ask

. ask

[hot vortex]

What am I doing wrong here?

[hot vortex]

Multiply and express improper fractions as mixed numbers

,rotate

[fleet dagger]

so what's the original expression?

[hot vortex]

4 1/4 * 4/6

[fleet dagger]

is x a variable or a multiplication symbol?

[hot vortex]

multiplication

[fleet dagger]

ok so

first of al

there is one thing you can get simple very easily

look at the first part

the

what could easily be done here?

[hot vortex]

https://gyazo.com/8acbb612ed5f9e0bc9aeeadf8b14f84f

[fleet dagger]

yes yes

[hot vortex]

Multiple 4x4+1?

[fleet dagger]

nno, not plus

its a fraction

is 4 multiplied by 1 divided by 4

so first remember, that as it happens with additions and substractions the division is the opposite of the multiplication

so basically divisions undo multiplications to say it one way

[hot vortex]

I didnt do that with any of the other questions?

"Multiply and express improper fractions as mixed numbers"

[fleet dagger]

but dont you have to multiply those fractions to get a result?

[hot vortex]

For all of them i've been doing 4*4+1 giving 17

so 17/4 x 4/6

[fleet dagger]

yeah, but that's incorrect

you cant do that because there is no plus symbol

there is only multiplications and divisions

[hot vortex]

https://gyazo.com/a9c85246b17d58910c805f4735a2b744

That's what is showing me?

[fleet dagger]

hmm i see, but that's not what you did up there

[hot vortex]

Thats an example

[fleet dagger]

because there it's not adding the 3 to the one or to the two for example

yes i know

[hot vortex]

2*3+1 is 7

[fleet dagger]

so ok let's proceed with that technique

[hot vortex]

shows 7/2

I can show you more

Also in this video, https://www.youtube.com/watch?v=5tv4vRNQqHk&ab_channel=TheOrganicChemistryTutor

But this one question is playing with me lol

[fleet dagger]

ok so

umm

your sheet is not well expressed

because for that to be true it should be this:

while it's showing this

[hot vortex]

I understand, but why would it show in my pdf, and a video?

That's how hes solving it xD

[fleet dagger]

well idk, but that syntax is not correct for what they are doing

they are doing a different thing than what they are expressing

ok, so let's assume that what's written in the sheet is correct

[fleet dagger]

then following that, this would be correct

indeed

but

i don't really get why you are doing a square root

ah its a division

[hot vortex]

I can show you another question

[fleet dagger]

ok go ahead

[hot vortex]

https://gyazo.com/aa58d16818c660b28864fa2020ca8398

I will solve it rn

,rotate

[hot vortex]

But the one I solved before isnt simplified enough

[pearl pond]

@hot vortex Has your question been resolved?

[pearl pond]

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[minor shell]

7 couples are sitting in a circle, Each Partner must sit exactly across from each other in the circle. John Cannot sit with Mary. How many sequences can this be done?

[minor shell]

Im not sure if I am doing it right but I drew a circle and set John as the reference point

then theres 12 options for whoever sits next to John because it cant be mary or his partner and 11 on his other side

then just fill in the rest of the number

Heres what I got

12x11x11x10x9x8x1^7

1^7 is because half are partners which only has 1 spot for them since they have to be sitting exact opposite

can anyone tell me if I got this question right or if theres anything Im missing

This is Data Management class btw and its permutation unit

[pearl pond]

@minor shell Has your question been resolved?

[pearl pond]

@minor shell Has your question been resolved?

[minor shell]

<@&286206848099549185>

[vestal tapir]

why it cant be mary's partner i dont get it

oh John's not Mary's

you can say that there's 11 options for John's left but you can't tell how many is left for his right, it could be 9 or 10

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@minor shell Has your question been resolved?

[pearl pond]

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[viscid cape]

Hi

[viscid cape]

So Basically

Uhm I'm having a bit of difficult with some things

what kinda of graoh has 2 vertical asymptotes

Please ping when u respond

[hot stone]

Generally, you get a vertical asymptote from division with zero

1/x has a vertical asymptote at x=0

1/(x+1) has an asymptote at x = -1

Sometimes you can have more than one way to make zero in the denominator

These functions might have 2 or more vertical asymptotes

E.g.

1/(x^2 + 3x - 4)

The denominator can be factored into

(x-4)*(x+1)

This expression equals zero when x = 4 or -1

So this function ends up with vertical asymptotes at x = 4 and x = -1

That should give a pretty decent hint at what kind of strategy you can follow

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[weak surge]

Anybody using professor Leonard’s diamond method for factoring?

[weak surge]

Can’t believe I just found out about this…

It will save me a ton of time

[mental violet]

oooo diamond method??

nvr heard of it

[coarse dawn]

That's a very common method to factor

It's just a difference variation of it

[old geyser]

This is what I got when I googled it

Uh

Ice cube from NWA??1?1?1?1?

[weak surge]

Bottom half

[coarse dawn]

Like I stated, it's a very common factoring method, it's just a variation of it

[weak surge]

Who taught you this method? Just curious

I haven’t heard about it before.. wouldn’t say it’s a very common factoring method imo

[mental violet]

only heard of box and cross method

[coarse dawn]

It's common

[mental violet]

maybe it’s not that common in my sch

maybe vv common other places tho

[coarse dawn]

There are many different names to it

[mental violet]

ooooo icic

we just use a calc now HAHAHA

[coarse dawn]

X box method, AC factoring method, etc

[mental violet]

the list goes on

[weak surge]

https://tenor.com/view/diamond-hands-gif-24678515

.close

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[wintry musk]

yo

[wintry musk]

how ya do this

[midnight haven]

what do u think it is

[pearl pond]

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[grand birch]

help

[wintry musk]

help this man

[tawny jolt]

@grand birch wouldnt it be the opposite of points?

since it's inverse

i think u'd just flip the points, ex. (-6, 0) would be (0,-6) as an inverse

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[opaque hearth]

What is the purpose of the absolute value around z? Why couldn’t it just be z^2?

[pearl pond]

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[fluid lynx]

hello is this the correct answer here?

somebody told me it was wrong and i'm not sure why

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[safe forge]

am i doing it right? it says to square the expression

[light helm]

what are the exact instructions

word for word,

only the first 4 are expressions,
and if you were indeed asked to just square the expression, you shouldn't be setting those to 0

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[oblique briar]

Hello can someone help me with this factorisation
(2b+3)(-12b+5)+12(2b+3)=(2b+3)(...)
And tell me the way please thank you

[mental violet]

have u tried anything?

[oblique briar]

no

well yes

idk what to say

im stuck

on this

for ages

.close

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[pearl pond]

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[limber belfry]

shouldnt we take the square root to get r?

[limber belfry]

since r^2 = 2rcostheta

so wouldnt r be the square root of the RHS expression instead?

[mental violet]

u can divide both sides by r

[limber belfry]

tyy

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[arctic hamlet]

some explain

[arctic hamlet]

can some one explain this ?

i cant understand

.close

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[arctic hamlet]

.reopen

[slate thicket]

eh

[pearl pond]

✅

[slate thicket]

don’t close and open

[arctic hamlet]

ok

[slate thicket]

also what do you not understand

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[teal yacht]

can someone help me solve this?

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[stuck cargo]

Hello! Is it possible to create "digital" functions? For example, a function that equals 1 when the variable x has a decimal point and 0 when it does not, etc. And if yes, could you provide an example?

[edgy stone]

https://en.wikipedia.org/wiki/Indicator_function

indicator functions are functions that are equal to 1 when the input is in a certain set and 0 when they aren't

so you could have an indicator function for the set of non-integers

[midnight haven]

do you know how to construct piecewise functions?

[stuck cargo]

No, i dont. Im relatively new to math

[midnight haven]

something like this

you can also put an "if" after the comma, maybe that makes it more clear

the top line basically just says that its a real function (you can plug in any real number) and that it outputs either 1 or 0

[stuck cargo]

And what does the \ do?

[midnight haven]

you know R and Z yeah?

[stuck cargo]

I know Z

[midnight haven]

Z is set of all integers and R is set of all real numbers

and R\Z is the set of all real numbers excluding all integers, so it only contains all the numbers with a decimal point

sometimes its also written as R-Z (as in, "minus", to show the exclusion)

[stuck cargo]

And whats the difference between piecewise functions and indicator functions?

[midnight haven]

maybe this is easier

hmm for that one you might want to be a bit more familiar with set theory

basically the indicator function for a set A gives back the number 1 if x is in A and 0 if x is not in A

it is a piecewise function

the term piecewise function is a bit more general

this is a piecewise function too

its just splitting up a function into two or more cases

[stuck cargo]

Thats exactly what i was looking for! Thank you!

.close

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[daring lance]

How does one rewrite this

[sick adder]

Do you remember slope intercept form?

[daring lance]

Yes I do

y=mx+b

[sick adder]

So we're given a function that's all mixed up here, but we can change parts of it to resemble that y=mx+b form

Namely, we isolate the y variable from the rest

[daring lance]

Mhm

I just have never been gave this type of function so I would like help with steps on how to get it to y=mx+b form

[sick adder]

Here, let's start by moving things to the other side of the = sign to get y on its own

If we subtract 18 from both sides of the equation, we can move it to the other side

$-8x + 10y = -18$

[jolly parrot]

lexitorius

[daring lance]

And then you would divide 10?

[sick adder]

Not quite

You could, but that wouldn't get you much closer

We still have to move the -8x term

How would we get rid of -8x and move it to the other side?

[daring lance]

Add 8x?

[sick adder]

Yup

What would we end up with if we added 8x?

[daring lance]

x

?

[sick adder]

Almost; the x can move with the -8 too

[daring lance]

or 1x

[sick adder]

If we add 8x to both sides, one of the sides would get the term 8x

$10y = 8x - 18$

[jolly parrot]

lexitorius

[sick adder]

Think of 8 and x being stuck together, if you move them with addition and subtraction then they move together

[daring lance]

Oh ok so now you divide 10 both sides?

[sick adder]

Exactly

[daring lance]

y=4/5x-9/5?

[sick adder]

$y = \frac{4}{5}x - \frac{9}{5}$

[jolly parrot]

lexitorius

[sick adder]

That's exactly what I got 👍

Just remember that when you have terms that have a number and a variable, addition and subtraction will move them around together

You'd need to use division to split them apart

Otherwise it seems like you know what you're doing, just had to get it started for you

[daring lance]

Ok I get it now I was confused thank you

.close

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[azure pulsar]

just asking a generalized question, but how do you know when to use u-subsution or to use uv-∫vdu