help-19

[lilac seal]

guys i need help with a couple of exercicies number one: What is the dimension of the vector space below?

[tepid pelican]

the shortcut is to count the number of free variables, those are the ones that just belong to R.
the long way is finding a basis

[lilac seal]

so 4?

[tepid pelican]

i meant those

those tell you the dimensions

the long way might be better if you dont have the intuition for that though

try finding some basis

[lilac seal]

ok, tysm i'll try this one and send other later

I- The vector w is generated by vectors u and v.
II- Vectors u and v generate the plane x3=0.
III- The vector equation a1u+a2v+a3W= 0 has a unique solution.
IV- The set {u, v} is a base for the plane x3=0.

I, III and IV? #1021175428326633542 #help-0

[odd edge]

@lilac seal Has your question been resolved?

[pliant latch]

whts the q

[lilac seal]

the ?

is about the image

[odd edge]

@lilac seal Has your question been resolved?

[odd edge]

@lilac seal Has your question been resolved?

[odd edge]

@lilac seal Has your question been resolved?

[dark kraken]

That tells you the maximum dimension, you still need to determine if the basis vectors are linearly independent or not

[odd edge]

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[plain needle]

How do I figure out the semi minor axis of an ellipse if I know the semi major axis, both focus points and a point along the ellipse... drawing a line from on focus point to another makes a right angle triangle at the intersection of the elipse. the length of both of does is equal to 2*semimajor axis

[plain needle]

<@&286206848099549185>

<@&286206848099549185>

[tawny summit]

$$ b^2 = a^2 (1 - e^2 ) $$

[clever fjord]

Quantum

[tawny summit]

$$ where (b) is the semi-minor axis, (a) is the semi-major axis, and (e) is the eccentricity. $$

[plain needle]

how did you get eccentricity

[clever fjord]

Quantum

[tawny summit]

that is the same formula to get eccentricity , major axis and minor axis

[plain needle]

ye but e=
1−(
a
b
​
)
2

​
we don't have the semi minor axis

you need semi major and minor to figure out eccentricity right?

[tawny summit]

yeah

[plain needle]

if we don't have semi minor how did we get it

[tawny summit]

at least two values are needed to figure out the left one

[tawny summit]

tell me what you have ?

[plain needle]

I don't have it

[tawny summit]

bruh

[plain needle]

or you mean the question

[tawny summit]

the question

[plain needle]

at coordinantes 1200,0 lies an object the semi major axis is 1484.46m long the first focus point is located at point 0,0 and the second is at -636.35,0 figure out the semi minor axis

the object is at one end of the ellipse

[tawny summit]

we know that distance between two focus point is 2ae

right

[plain needle]

yep

its just 636 right

[tawny summit]

b is given

ae is given

[tawny summit]

use the formula bor

b2 = a2 - ae2

put the values of b and ae

[plain needle]

just show me the soloution im an idiot

[tawny summit]

bruh

$$ b^2 = a^2 - (ae)^2 $$

[clever fjord]

Quantum

[tawny summit]

$$ ae = 636/2 $$

[clever fjord]

Quantum

[tawny summit]

now do it

get the value of a

[plain needle]

not gona argue bro but you said that b is given b you said is the semi minor axis if I recall correctly

[tawny summit]

yeah b is given , read the question

[plain needle]

oh im really dumb I mean to say major axis not minor

[tawny summit]

bruh

get the value of a quickly

[plain needle]

1484.46 we are told

[odd edge]

@plain needle Has your question been resolved?

[odd edge]

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[indigo crater]

I just taught that few minutes ago to another person lol

so... consider the limit at that point

is each square roughly 1 unit?

then let say I am tracing my function from the left to right, what would my value of that function goes to?

$\lim_{x\rightarrow 2^+} f(x)$ that is

[clever fjord]

#damiforthepresident

[indigo crater]

or am I working on the wrong question?

ok. now let's try tracing the function from like 0 and move it to 2. what is your value of your function as you approaching to 2?

I mean, you are not wrong

the limit $x \rightarrow 2^+$ is infinity (you come from the right)

[clever fjord]

#damiforthepresident

[indigo crater]

but what about the left one? (you come from the left)

no...

when you come from the right, you go up and up.

but what about from the left to right?

again... start from 0

keep your finger tracing from x = 0 to x = 2

what is your y

close but not quite

yeah, but I am talking about another one

oh

it is -2

I should put your image in full screen

yeah, if it is -2 then you are right

[odd edge]

@mystic saffron Has your question been resolved?

[odd edge]

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[cold swift]

what have you tried so far

[old flame]

I was going to take the limit of the sum first

as n approaches infinity

[cold swift]

wdym by that

like the partial sum?

this is already an infinite sum

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Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[old flame]

all good

[cold swift]

happens

all good theres still a few open ones

[old flame]

no

wait

that wouldn't work

[cold swift]

are you trying to take the limit of the sequence?

[old flame]

yeah

[cold swift]

yeah thats not gonna help us here

the problem implies that it converges so

theres no need to use the divergence test

how about lets try splitting fraction up

[old flame]

wym?

[cold swift]

its pretty straightforward once you simplify it

[clever fjord]

y0shi

[old flame]

oh

[cold swift]

try that here and see what happens

[old flame]

ok

[indigo crater]

disclaimer: your expression will be... a bit ugly.

one of them that is

[odd edge]

@old flame Has your question been resolved?

[old flame]

ok

this is taking way longer than expected

[cold swift]

so what do you have after the separation

[old flame]

yeah

I just got the first series

which is 0.02

you have to find common ratio and all that shenanigans

[cold swift]

mhm yep

[old flame]

and I see what dami was taking about...

[cold swift]

well this isnt the bad one

the other one is

[old flame]

the second one is not gonna be pretty

[cold swift]

yeah

[old flame]

I have to use a calculator right?

like ain't no way i'm getting the common ratio without one

[cold swift]

well i mean you dont need a calculator to get the common ratio

you need it to get the sum since it wants it to be rounded

[clever fjord]

y0shi

[cold swift]

thats the second one yeah?

[old flame]

yep

[cold swift]

see how the common ratio there is just e/5

[old flame]

O

nvm.

[cold swift]

all good

just need to get the first term here and thatll be it

[old flame]

cool cool

0.352112494412

this is the answer I got

my equation was this:

[cold swift]

yeah that looks good

can rewrite that as $\frac{e^3}{125-25e}$ if you want

[clever fjord]

y0shi

[cold swift]

easier to put in the calculator

[old flame]

i'm just using Desmos

luckily, our prof allows it for our exam

[cold swift]

alright

thats very nice

[old flame]

ik!

now I add them both right?

[cold swift]

yep

[old flame]

cool!

thank you once again

[cold swift]

ofcofc

yw!

[old flame]

I will see you tomorrow!

https://tenor.com/view/goodnight-gif-5295116536817772197

[cold swift]

see you!

good night

[old flame]

.close

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[analog lichen]

10

.close

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[mystic saffron]

i dont understand the questoin

[tulip niche]

so for example

17 ends in 7

which isn’t 5, and isn’t an even number

[mortal trench]

you can just brute force this

[tulip niche]

so it claims there’s an m such that 17*m ends in 1

[mystic saffron]

right

[mortal trench]

just consider the multiplication mod 10

[mystic saffron]

how

[mortal trench]

1*1

let me pull up excel

[mystic saffron]

wait so n and m, they dont end in 5 and an even number?

[tulip niche]

so n doesn’t end in 5 or an even number

[mystic saffron]

m can be anything?

[tulip niche]

however you’ve placed no such restriction on m

yeah

[mystic saffron]

thats so easy

1 * 1

and 2 * 5 where n = 2

[tulip niche]

uh

n is never 2

[mystic saffron]

oh yh it can't be even number

so 9 * 9 and 1 * 1?

3*7

7*3

[mystic saffron]

yhhhhhhhh

ty

guys

<33

[odd edge]

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[analog lichen]

any shortcut?

[woven kelp]

You can subtract the top row from the bottom two

Then add the new bottom row to the middle and subtract the new bottom row from the top, should give a nicer matrix

[odd edge]

@analog lichen Has your question been resolved?

[elfin zodiac]

Log6 = log3+log2

[analog lichen]

Actually i am afraid of elemantry operators because last time i feelt wrong

I meant operatirs i applied and check in desmos it changed

I would like to know elemantry operations

I meant what row operations is not acceptable

I can multiply any row with scaler and substrcat it?

[odd edge]

@analog lichen Has your question been resolved?

[odd edge]

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[twilit spoke]

When determining the second order derivative of a function: $sin(x^2+y^2)+xyz$ why do we write it as $f''_{xx}$?

[clever fjord]

Merineth

[twilit spoke]

First order derivative i understand would be $f'_x$

[clever fjord]

Merineth

[twilit spoke]

First derivative wrt x

But why do we have to indicate it's wrt x again?

$f''_x$

[clever fjord]

Merineth

[twilit spoke]

Isn't this more correct?

[dawn scarab]

We have to indicate it's wrt to some variable because the function contains 3

(considering y and z are also variables)

[twilit spoke]

oh alright i see

$sin(x^2+y^2)+xyz$

[clever fjord]

Merineth

[twilit spoke]

Specifically my question asks for the second order partial derivative of this function

so i have to derive wrt x twice, y twice and z twice?

[dawn scarab]

Does it mention which variable to differentiate with respect to? Also you can write the second order partial like this which imo is pretty clear: $\pdv[2]{f}{x}$

[clever fjord]

𝓲𝓶𝓣𝔂𝓹𝓞

[twilit spoke]

it just says all partial derivatives

$f'_x = 2xcos(x^2+y^2)+yz$

[clever fjord]

Merineth

[twilit spoke]

So this would be the first partial derivative wrt x?

$f''_{xx} = 2xcos(x^2+y^2)-4x^2sin(x^2+y^2)$

[clever fjord]

Merineth

[twilit spoke]

Seems right?

[dawn scarab]

I don't think you put two x's in the subscript

also your first derivative seems right

[twilit spoke]

$f''_{xx}$

you mean this?

[clever fjord]

Merineth

[dawn scarab]

Yeah, I'm pretty sure it's just written $f^{\prime\prime}_{x}$

[clever fjord]

𝓲𝓶𝓣𝔂𝓹𝓞

[twilit spoke]

No, that's what is unclear to me because the book gives me several answers

[dawn scarab]

Ah, well if your book tells you to do it that way, sure, go with that

[twilit spoke]

$f''{xx},f''{yy},f''{zz},f''{xy},f''{xz},f''{yz}$

[clever fjord]

Merineth

[dawn scarab]

I just think personally that it's repetitive notation and that this conveys the message "differentiate twice wrt x"

[twilit spoke]

These are all the answers that it says are correct

[viscid flint]

usually just $f_{xx}$ etc

[clever fjord]

sobpilled crymaxxer

[viscid flint]

without the '

[twilit spoke]

Well

$sin(x^2+y^2)+xyz$

[clever fjord]

Merineth

[twilit spoke]

Couldn't i technically just write this as a gradient the first time?

This would be the partial derivatives wrt x, y and z

creating a gradient

and then i derive each one of those wrt x y and z?

wouldn't this create 3 different gradients out of 1 gradient?

.close

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[viscid flint]

you end up getting a matrix if you take all of the second derivatives

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[floral surge]

if x = 2,32 (32 is repeating)
99.x + 1 = ?

[floral surge]

this is what i have done:

232 x 99 = 22968
229,68 + 1 = 230,68

but the answer is just 231 without decimals

what im doing wrong? it must be with repeating numbers

[nimble blaze]

99.x + 1 = ?
where's that coming from

[floral surge]

thats the question

[soft cloak]

2,32 = 2 + 32/99

[nimble blaze]

ok, you'r issue is that $2.32 \redneq 2.\overdot{3}\overdot{2}$

[floral surge]

so i find 230,68 but the answer is 231

[soft cloak]

what do you mean 99.x

what does . mean

[floral surge]

multiply

[nimble blaze]

ok, your issue is that $2.32 \redneq 2.\dot{3}\dot{2}$

[clever fjord]

ℝαμΩℕωⅤ

[floral surge]

ik but i still cant get the logic behind these repeated numbers

[nimble blaze]

consider the value of 100x

[floral surge]

i cant find how to type on my keyboard but

32 has a line above

let me draw

[nimble blaze]

dot is alternate notation

consider the value of 100x

[soft cloak]

so look

[floral surge]

soo

[soft cloak]

since x = 2 + 32/99

then 99 * x is simple

[floral surge]

sorry

i didnt understand

i mean

oh

so

100x is 232

then why it's -1

to reach 231

i mean i dont understand

[nimble blaze]

your forgetting the repetition component

[floral surge]

yes but i dont know what do with that. how im expected to do operation with a number thats not clear

[nimble blaze]

$2.\overline{32}$ represents $2.323232323232\overline{32}...$

[clever fjord]

ℝαμΩℕωⅤ

[nimble blaze]

after multiplying by 100, you'll have 232.(still repeating 32s)

100x = 232.323232...
x = 2.323232...

[floral surge]

yes

[nimble blaze]

and then subtract the equations

[floral surge]

its still 231.32323232

[nimble blaze]

no

again you're forgetting that both numbers there have repeating 32s

[floral surge]

why does 1 have repeating 32s

its not 1x

just 1

99 * x + 1

[nimble blaze]

wdym

[floral surge]

i mean

multiplyinig 2,32... gives me 232.323232

[nimble blaze]

yes

that's 100x

[floral surge]

but the question is 99x, we're doing with 100x. even if i subtract one

it gives me 231.32323232

[nimble blaze]

no

[floral surge]

we still got another 1 remaining

[nimble blaze]

you subtract x

100x - x = 99x

[floral surge]

so 232.323232 - 2.32323232

[nimble blaze]

100🍎 - 🍎 = 99🍎

should've used ...to imply the repetition but, yeh

that'll give you 99x

[floral surge]

so substracting 32323232 from 32323232 will basically be 0

so it's 230

adding 1 gives me 231?

[nimble blaze]

yes

[floral surge]

ok

thank you

i dont know

how to get used to

this

lol

[nimble blaze]

practice

[floral surge]

yeah

i hope i can learn

thanks again!

.close

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[stuck wasp]

15

[proper shell]

a day is how many hours

[stuck wasp]

25

[stuck wasp]

24

[proper shell]

rightt

so if the entire circle is covered in 24 hours

how much of the circle is covered in 1

[stuck wasp]

how do i find that out? Radius is 200 and a revulution is 2π

Do i put arc length as 1?

[sand horizon]

2pi*radius is the formula for the circumference

[stuck wasp]

but why do i need circumference?

[proper shell]

think of it like this

after one day

we have some area

after 1/24 of that day (one hour)

we have a fraction of the entire area

what is that fraction?

[stuck wasp]

1/24?

[proper shell]

(we're assuming that the pipe is moving at constant speed)

right

so it's 1/24 of the entire circle's area

what is that

[stuck wasp]

1/24 x πr^2

[proper shell]

mhm

just calculate that

[stuck wasp]

5235.987

[stuck wasp]

Oh my bad

i though the pipe went on both sides of pivot point

[stuck wasp]

can you help me with 16 too

[proper shell]

oh i used this reference lol

[proper shell]

split the polygon into triangles

can u see how?

[stuck wasp]

no not really

[proper shell]

connect each side length with the center of the polygon

[stuck wasp]

We draw to middle point of polygon?

[proper shell]

right

exactly

you dont have to draw all of it out obviously js draw out one of the 64 triangles youve made

[stuck wasp]

So its a triangle with 2 equal sides and a base of 3

[proper shell]

yes

[stuck wasp]

if we split the triangle to two we get the radius right?

Since radius is the line that separates the two triangles

[proper shell]

no

hold on lemme make a diagram to show

you see how the line that bisects the triangle isnt actually the whole radius

[stuck wasp]

oh yeah true

[proper shell]

however one of two of the green sides are both the radius

[stuck wasp]

its the hypotenusa of the split triangle

[proper shell]

yep

how would you find the hypotenuse?

[stuck wasp]

Pythagoras but we dont have the middle line

We only have 1.5^2 + b2 =c^2

[proper shell]

we only have one side, so we can't use pythag

two things define a triangle

sidelengths and angles

so do we know anything about the angles?

[stuck wasp]

triangle is 180 degress?

[proper shell]

lets js look at this angle

you see how it's cut out from the circle

[stuck wasp]

It looks like 30 ° but we arent allowed to guess roght

[proper shell]

ye the diagram isn't to scale

it's js to give you an idea of what it looks like

but how many degrees is a full circle?

[stuck wasp]

Wait wouldnt we divide 360 with 64 to find the angle of each section of polygon

[proper shell]

yes

so this angle is 360/64

but we want half of it

do u see why

[stuck wasp]

Yeah then we just divide the result by 2

[proper shell]

mhm

[stuck wasp]

I got 45/16°

[proper shell]

now you have a right triangle with an angle and a sidelength

(if you split the triangle down the middle)

so how do we find the radius

[stuck wasp]

Trogonometry, by using sohcahtoa

[proper shell]

yep

[stuck wasp]

Wait how did it go again? I use Sin but how i do opposite with angle?

Ok i get this

Sin 45/16 = 1.5/ x

I got 30.57

Thanks bro for help

.close

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[royal nova]

What is 2+2

[near hawk]

!show

[odd edge]

Show your work, and if possible, explain where you are stuck.

[royal nova]

Nvm

[pastel orbit]

don't troll please

[royal nova]

Ok

Sorry

.close

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[old flame]

do I just step up the integral of 2 to infinity of 1/n(ln(n))^2?

<@&286206848099549185>

<@&286206848099549185>

[abstract plaza]

wait

[old flame]

ok

mb

[abstract plaza]

did u Studied calculus 3

[old flame]

nope

this is Calc 2

[abstract plaza]

numerical series are from calcu 3

[old flame]

wym?

[abstract plaza]

this exercise is from numerical series exactly calculus 3

[old flame]

ok

how would you do it though?

cause Integral Test is something we learned

[abstract plaza]

ok i give u an example

[old flame]

ok

[abstract plaza]

i study math in french so

[old flame]

I understand the first picture

you did the Integral Test

[abstract plaza]

i try to give u the right answer

2 min

[old flame]

ok

[abstract plaza]

1/2

if i didn't commit a mistake

[old flame]

it has to be an integer though

[abstract plaza]

this the result

i dont have a phone on me right now to show u the steps i took to get this unfortunatelyl

[old flame]

it's all good

[abstract plaza]

good luck

[old flame]

thanks!

[abstract plaza]

idk if u understand bit of french but maybe it helps

[odd edge]

@old flame Has your question been resolved?

[old flame]

this kinda helps

i've been looking through it

but it's not exactly what i'm looking for

i'll ask if someone else can help

thank you though!

<@&286206848099549185>

[supple zealot]

!original

[odd edge]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[old flame]

it wants Integral Test

but I really dk how to find the answe

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[placid hamlet]

Hello anyone there

[odd edge]

@placid hamlet Has your question been resolved?

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@placid hamlet Has your question been resolved?

[low locust]

no you are the only person on this discord

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[nocturne chasm]

how do i do the 2nd part?

3. Sketch a graph that has a domain of D:{x∈R} and a range of R:{y∈R,y≥2}. Can you draw one that is a function, and one that is not?

[worn sandal]

Do you remember when something is not a function

[odd edge]

@nocturne chasm Has your question been resolved?

[nocturne chasm]

Yess this is an easy part of the course. I just don’t know, or maybe I’m just lagging from doing math all day. But, Idk how it can not be a function while fulfilling those reqs

Like nothing that is limited to y=2 and not a function can have a domain of all real numbers

Unless again I’m js not thinking hard enough

[dim sandal]

Yes, when a vertical line intercepts the curve twice. In other words there are more than one output of y for an input of x.

[worn sandal]

^ this

[nocturne chasm]

I understand that part, thank you :). I’m just unsure of how to draw a graph out that isn’t a function while still having a domain of all real numbers and a range >= 2

[worn sandal]

you could just draw 2 parallel lines

[nocturne chasm]

Wouldn’t that be two functions then?

[worn sandal]

or just take the function you drew and draw an extra point somewhere

[worn sandal]

You could say it's one function

[nocturne chasm]

How would its equation look like? Or is that not possible

Thank u for your help btw

[nocturne chasm]

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[austere hull]

I have to calculate this limit

[austere hull]

Im not sure what to do next

I could use d'Hopital I think, but that seems like a lot of work

[sullen ferry]

this feels like a polar sub

definitely

[austere hull]

do I have to use d'hopital now?

[sullen ferry]

just start with a polar sub

from the beginning

do you see how this helps?

[austere hull]

without the transformation to e^g(x)*lnf(x)?

Isn't this basically the same thing? @sullen ferry

<@&286206848099549185>

[mellow solstice]

whats the ans?

1?

[austere hull]

yes

[mellow solstice]

So you've done the most of the things

[mellow solstice]

now transform it to e^gx form

[mellow solstice]

why there's Ln?

[austere hull]

f(x)^g(x) = e^g(x) * ln(f(x)), no?

[mellow solstice]

ill send you w8

[mellow solstice]

we write it as this

[austere hull]

Im so confused

I was using this

[mellow solstice]

thats right

we just do some transformation in this

ill try to find the proof for u hold on

[mellow solstice]

Yes

here's the proof

[austere hull]

I see

Interesting

I didn't know that

thank you!

[mellow solstice]

np

[austere hull]

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[still anchor]

(i'm not sure if this is the right place to ask since this is more of a question about the structure of a course than a specific problem)

i'm currently learning ODEs and am mostly just going through a textbook instead of following the lectures since they're pretty low-quality. i noticed that the course goes directly from undetermined coefficients to laplace transforms, but my book has several chapters between them (see photo). is it standard to skip the stuff in chapters 4 and 5 in an ODE class, or should i read them?

[sharp oak]

No these are not usually skipped

But your course is the ultimate decider. Do whatever you need to for the marks

[still anchor]

oh okay, it's a community college class and a lot of the other classes have been pretty poor quality and skipped a lot, so i figured it's good to ask

since im planning on transferring the credit to a 4 year and i dont want to have gaps

ty!

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[gray parrot]

Can somebody explain why the answer isn't (A)? My understanding is that an inflection point denotes changes in concavity, and the second derivative f''(x) represents concavity where negative numbers mean f(x) is concave down and positive numbers mean f(x) is concave up. I chose (A) because f''(x) = 0 is the point before we go from concave up to down/vice versa. This was marked as wrong and the correct answer is (D), but i'm not sure why.

[still anchor]

f'' can also change signs when it has a discontinuity

[gray parrot]

I heard about that but it says its an inflection point

so doesn't it still have to equal zero

[cold skiff]

you can have an inflection point and the function not need be differentiable

[still anchor]

no not necessarily

[gray parrot]

are you saying that you can have an inflection point but also not be able to differentiate the function to get the second derivative?

[cold skiff]

for y=x^2 f''(x) = 2

and we know f'(x) = 0 at 0

[still anchor]

imagine a function where its first derivative looks like this--the sign of the second derivative goes from positive to negative at the point where there is a sharp corner in f', but f'' is never zero

[cold skiff]

I don't think that function is differentiable

but I think I gave a counterexample

let F(x) = x^2 -- F has a tangent line at x = 0, yet F''(0) = 2

[still anchor]

f is differentiable. it isnt smooth but it is differentiable

because that red line is a graph of f', which is well-defined

and continuous

[cold skiff]

my bad, the graph is for the first derivative, correct

then again im not sold that such function has 2nd derivative

what function would look like that and still be differentiable?

it looks sort of like an abs value graph

inverted

which is continuous but not differentiable

[still anchor]

yeah it would probably be some transformation of abs(x) or the step function

but honestly it's not too important the specific function of y in terms of x. moreso its the idea that even if f is continuous, we can have sharp corners on f' representing a change in concavity

[gray parrot]

i understand now

[gray parrot]

ty

[gray parrot]

ty

[gray parrot]

this picture in particular makes it incredibly intuitive

thanks

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[cold skiff]

but doesn't this sharp corner make F' not differentiable? thus F'' doesnt exist

[still anchor]

f'' doesnt need to exist at the point itself, the condition that i'm using is that for any small epsilon > 0, we have f''(a + epsilon) being a different sign as f''(a - epsilon)

[cold skiff]

yeah this I agree, okay

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[pastel orbit]

hm, I think I need a hint here

[clever fjord]

higher!

[warped grove]

what have you tried so far

which direction are you working on?

[pastel orbit]

I'm thinking that the contrapositive for the => direction might be easier

so assume there is a nonempty open U in X such that U \cap A is empty

I want to show that the closure of A cannot be all of X now

but I am stuck

[warped grove]

alright, then what

[pastel orbit]

hmm

[warped grove]

how are open and closed sets related?

[pastel orbit]

they're complements of each other

[warped grove]

yes

and what's the definition of closure?

[pastel orbit]

so I need to show that X\A is open then?

[warped grove]

no

[pastel orbit]

$\overline{A} = \bigcap {B \subseteq X : B \supseteq A \text{ and B is closed in X}}$

ah

ah, missing braces but w/e

this is the def of closure I am working with

hm

[warped grove]

B is closed* in X?

[pastel orbit]

right, typo lol

sorry

[clever fjord]

higher!

[warped grove]

Okay so how would you show that the closure of A is not X?

i.e. is a proper subset of X

[pastel orbit]

I just need to find one B such that B is a proper subset of X?

cause then the intersection could never be all of X

I think?

[warped grove]

yes!

so you need to find a B such that B contains A and is closed, and is not all of X

you have a U such that U is open and does not contain any of A, and is nonempty

[pastel orbit]

choose B to be the complement of U

[warped grove]

yess

[pastel orbit]

then B is a superset of A, a closed subset of X, but smaller than X

ah, clever!

now the other direction...

repost

if every nonempty open subset of X contains a point in A, I need to show that the closure of A is X

hmm

[warped grove]

you got this!

[pastel orbit]

.<

let me try for a bit and see what I can come up with

okay, my plan is to show that the only closed subset containing A is X itself

then the closure of A is simply X by default

so I should do this by contradiction

I will assume that there is another closed subset containing A which is not X

[warped grove]

alright

[pastel orbit]

now I need to apply my hypotheses in some way

well, if I call this closed subset C, then the complement of C is open and by the hypothesis contains a point of A...

[odd edge]

@pastel orbit Has your question been resolved?

[pastel orbit]

shut up you bot

I'm thinking!

[warped grove]

@pastel orbit Has your question been resolved?

[pastel orbit]

no, I'm super stuck

[warped grove]

you can do it, I have full faith

[pastel orbit]

I got stuck here, and I'm honestly unsure if this was even a valid way to proceed...

[warped grove]

Why wouldn't it be?

[pastel orbit]

cause all I see are ends

but I think I'm missing smth

[warped grove]

Let's say you're proceeding by contrapositive right?

• Assumption: A is not dense
• It follows that there's a C such that A \subseteq C \subsetneq X where C is closed
• ...
• Goal: there exists a nonempty open subset of X not containing a point of A

Fill in the "..."

(Hint: it's entirely analogous to the proof of the other direction)

[pastel orbit]

wait but, I wasn't doing this by contrapositive...

[warped grove]

You basically were

Contradiction, contrapositive... they're equivalent anyways

[pastel orbit]

[warped grove]

This is one of those theorems where you can actually do both directions at the same time I'm p sure, because you only use iff statements in the proof

[warped grove]

But go on, fill in the ... bit

[pastel orbit]

[pastel orbit]

observe that X\C is open because C is closed, and that it's also nonempty because C \subsetneq X. but since A \subseteq C, (X\C) \cap A = empty, so we are done.

I had written down that (X\C) \cap A was empty earlier... but I didn't make anything of it because it didn't give me any tangible contradiction 😭

and that's why contrapositive >> contradiction, folks

[pastel orbit]

I think this works?

[warped grove]

yup!

[pastel orbit]

smh

I'll never do a contradiction proof again

useless method of proof

[warped grove]

well...

contrapositive only works to prove implications

not statements by themselves

[pastel orbit]

(I am being facetious dw)

[warped grove]

[pastel orbit]

I cannot believe I didn't come up with this earlier

[warped grove]

note that you can phrase this as a bidirectional proof:
"A is not dense" <=> "there exists closed C containing A but strictly contained in X" <=> "there exists open U not containing A but nonempty"

and then negating both sides gives you the statement

[pastel orbit]

icic

[pastel orbit]

one last thing I want to ask, about the 2nd point

[warped grove]

yea

[pastel orbit]

C could be the closure of A, yes?

is there any other explicit C though?

[warped grove]

It is just some closed set containing A

It could be the closure, if it's the smallest such set

[pastel orbit]

hm

[warped grove]

but if you start from the right and go to the left here, you can't pick C to be the closure

[pastel orbit]

wait nvm that's obvious too

[warped grove]

it will just be the complement of U, whatever U is

[pastel orbit]

I see

okay, got it

thanks for the help Eric! (and for believing in me!)

[warped grove]

you're welcome, keep it up

[pastel orbit]

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[mellow folio]

how would i answer this?

[spice wagon]

$Pr(4 \leq X \leq 5) = Pr(X=4) + Pr(X=5) = {6 \choose 4} p^4 {(1-p)}^2 , + {6 \choose 5} p^5 {(1-p)}^1 = 15p^4{(1-p)}^2 + 6 p^5 {(1-p)} = (p^4 (1-p)) (15(1-p) + 6p)$

[clever fjord]

oscoface

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[feral void]

Hey, just looking for someone to look over my math and correct me on any mistakes I could have made ( math is not a strong suit) thank you.

[elfin zodiac]

1 is correct

2 a is correct although I can’t read the process, i think i overdid some steps

2 b is correct

2 c correct

[fathom wind]

Wooohoo. 4 in a row

[elfin zodiac]

You made a mistake in d

The result is correct

But there is a misconception

Sqrt(x) * sqrt(x) is not sqrt(x^2)

[feral void]

Ah I see.

[elfin zodiac]

It is (sqrt(x))^2

When you have two things identical multiplying you square the while thing

Because sqrt(x^2) is |x| not x

But sqrtx * sqrtx is x

Ans (sqrt(x))^2 is x

[feral void]

Ohh ok I see what you’re saying.

[elfin zodiac]

Yes, the square outside the root

Let me check the others

I dont see the e result

Ok i see now

That one is correct too

Last one is correct

3 a is correct

Now i have to leave

But looks like u got it

[feral void]

Okay thank you!

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[summer trail]

How to check if a real fraction $\frac{p}{q}$ in base m can be precisely represented in base n?\
Is it just checking if $q=n^x$ for any natural number x?

[clever fjord]

Jigglyproff

[low locust]

do you mean like how 1/2 can be written as 0.5 in base 10 but 1/3 needs a period?

[summer trail]

I mean that I can write 3/5 precisely in base 10 but not in base 2

like 0.6 base 10 but 0.5+0.06..... in base 2

[low locust]

0.5+0.06 makes no sense in base 2. you can only use the digits 0 and 1

[summer trail]

if they would be in base 2 I mean

0.1 in base 2 is 0.5 in base 10

cant add 0.01 (0.25), cant add 0.001 (0.125) cause they would go above, the next was 0,0001 which is like 0.625 in base 10

therefore I cannot represent 3/5 base 10 in base 2 precisely, because I will never hit that number

[weary pelican]

so

it has to do with the denominator

[summer trail]

I could represent 5/16 in base 2 just fine

[weary pelican]

see that a number can be written finitely in base b if it can be written as x/b^n

where x is an integer and n is a non-negative integer

but

take the example of b = 2 for example

and p/q = 0.56

[summer trail]

my first guess is that it wouldnt work?

[weary pelican]

we write it in irreducible form 14/25

so given the irreducible form p/q = 14/25

any fractional way to describe this number HAS to be something like (ap)/(aq)

so the denominator has to be divisible by q = 25

but is 2^n ever divisible by 25?

[summer trail]

no

[weary pelican]

so can 14/25 ever be written finitely in base 2?

[summer trail]

no

[weary pelican]

general case:

[elfin zodiac]

Prime factors

[weary pelican]

p/q irreducible fraction

[summer trail]

but wouldnt checking if $q=2^n$ is possible with n as integer?

[clever fjord]

Jigglyproff

[weary pelican]

check if q can ever divide b^n

meaning

if p_1, p_2,..., p_r are the prime factors of q

[summer trail]

oh

[weary pelican]

they need to be prime factors of b as well

[weary pelican]

since 2 is prime

the only numbers that can be written finitely in base 2

are something/2^n

so 3/4, 5/8, etc

as soon as the denominator is not a power of 2

(even if not in irreducible form FOR THIS CASE)

it can't be written finitely in base 2

[summer trail]

okay lets say we wish to check base 10 -> base 12

3/24 base 10 would not work right

[weary pelican]

you just happened not to choose the irreducible form, and it works

because irreducible form is 1/8

2 is a factor of 10 and 12

so no problem

[summer trail]

ah let me check this for a second

ah yeah

its 0.3 in base 12

[weary pelican]

0.125 base 10, 0.16 base 12

[summer trail]

ah yeah mb its $1/12+6*(12^{-2})$ base 12 -> 0.125 base 10

[clever fjord]

Jigglyproff

[summer trail]

alright that makes sense, thanks so much

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[ebon sentinel]

can someone help me with this

[night raven]

Solve both equations for y

And draw those lines

[ebon sentinel]

i dont know how to do that

[night raven]

then find the intersection

[night raven]

You dont know that a line is defined like y = mx + b

[ebon sentinel]

this is a example

i need someone to do it for me

so i can perpare for my test

my teacher is rude to

[night raven]

No you need to do the exercise yourself so you can understand it

[ebon sentinel]

she doest help anyone

i learn by looking

[tulip mica]

x+y=9

What number do you like?

@ebon sentinel

[ebon sentinel]

what do u mea

mean*

[tulip mica]

Between 10 and -10 choose a number

What do you like

[ebon sentinel]

8

[tulip mica]

Nice choice

Now put x=8 in x+y=9

What do you get for y?

8+y=9

What is y?

[thick garnet]

answered in the other chat

[tulip mica]

.close

[ebon sentinel]

.close

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[elder canopy]

Hi I'm not exactly sure where I went wrong here. My teacher's feedback is "There are errors in A, C and D"

[odd edge]

@elder canopy Has your question been resolved?

[elder canopy]

with A, isn't it just taking the integral of p(x) and setting it equal to 30 to get your length?

<@&286206848099549185>

[fallen hound]

yes it is

[elder canopy]

so I'm not exactly sure where I went wrong..... was it the integral part?

[fallen hound]

I dont think so whats the ans given

[elder canopy]

she didn't give the answer 😭

[fallen hound]

damm

let me try it once

[elder canopy]

ty!

[fallen hound]

I am getting the same ans

[elder canopy]

rlly?

bruh is she just trolling me?!!?!

[fallen hound]

maybe she said it cause u didnt put cm

some teacher can get like that

[long tinsel]

Maybe they're being petty because your integration variable is r and not x

[fallen hound]

or maybe I am wrong too

[elder canopy]

ok, but that wouldn't make sense for c and d.....

[fallen hound]

let me check c and d

[long tinsel]

tbf you very clearly have x there and r as the integration variable

That is fair ground for docking

[elder canopy]

you mean b? but isn't that the variable they gave for length?

[long tinsel]

yes, but you need to integrate wrt to x too

not r

or replace the x with r

as it stands e^(-x/10) is a constant wrt the integration

But that's just a theory

[elder canopy]

wait wait huh? where is this r coming from?

[long tinsel]

what's this

[elder canopy]

x

shoot mb did it look like an r?

[long tinsel]

then what's this

[long tinsel]

I'd read it as an r

[elder canopy]

x

[long tinsel]

you have two scripts for x?

[quiet berry]

For A, you put x instead of b after integrating and plugging in the bounds, that might’ve been the problem

[elder canopy]

accident mb

[long tinsel]

pfft I'm grasping at straws

go tell your teacher if there's no problem

if they're being cryptic on purpose then they don't like you

[fallen hound]

isnt c wrong?

shouldnt the integral be of xe^-x/10

nvm I am blind

[elder canopy]

really? that's so fucked up if that's the case, but I doubt she would take off the entire problem over that....

[quiet berry]

¯_(ツ)_/¯

[fallen hound]

you never know

my chem teacher docked 50% marks because I didnt write specific words in the textbook

[elder canopy]

wait bruh wtf... I replugged part c into the calculator and got 1.68 instead of 2.5 cm.....

wait @fallen hound can I see how you did it? I'm starting to doubt my own work...

[fallen hound]

in A I did the same thing you did

[elder canopy]

hmm ok

ughh I hate the way some teachers grade

bc if part A is wrong, then the numbers I used for part C and D is also wrong

so now we can't understand what's wrong w/ A, then the rest of the problem remains a mystery.......

[quiet berry]

also you didn't add the units in part A

[odd edge]

@elder canopy Has your question been resolved?

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[boreal musk]

I have watched videos where they say “suppose there is a polynomial P(x) = some kind of equation” what does P(x) mean ?? Explain it in simple terms as if you are explaining someone with no proper knowledge as I don’t.

[glad shell]

its just a name

like when we write random function we say let f(x) = some random function

[long tinsel]

this sounds like a chatgpt prompt

But yeah

what he said

[boreal musk]

Ooh ..

[clever fjord]

argon

[long tinsel]

It's convenient shorthand to show values of a polynomial

Assuming you don't know what a function is yet, there's a few conditions you need to know before using this notation in general

But for all polynomials it's fine

[boreal musk]

If we had 2 variables x and y then would we write it as P(x,y)=…?

[long tinsel]

sure

[boreal musk]

Thanks!

[boreal musk]

Is there any resource you know from where I can self study about functions?

[long tinsel]

Just look up an organic chemistry tutor video

It's a very simple concept to get behind

[boreal musk]

I will !! Thanks for your help.

.close

[odd edge]

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[odd edge]

Available help channel!

Send your question here to claim the channel.

Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[lavish jackal]

what about it

[stiff hazel]

um.

[mystic saffron]

He wants to change it to slope form

[lavish jackal]

what have you tried?

do you know y=mx+b?

[mystic saffron]

He does, i don't think he understands how to solve

[lavish jackal]

!noans

[odd edge]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[stiff hazel]

.

okay

hold on

what do you know so far about slope form?

[lavish jackal]

,tex .point slope

here's a hint

[clever fjord]

enzi²

[stiff hazel]

yep!

just consider f(x) to be y for now

for example

[lavish jackal]

f(x) is same as y

[stiff hazel]

f(x) = 5x+3

[lavish jackal]

but different notation

[lavish jackal]

google it

[stiff hazel]

f(x) = y, 5 = m (like a multiplier) x = x, + 3 = b

[stiff hazel]

@mystic saffron

a way of writing something

basically

okay

[mystic saffron]

I don't think so he knows what functions are as well

[stiff hazel]

so, remember how we said you can think of f(x) as y?