help-23

[tall bough]

?

[buoyant shadow]

78.6

akchually

[tall bough]

what even does he need help with

[safe radish]

@pulsar kernel Has your question been resolved?

[safe radish]

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[light scroll]

im just wondering how did they get this here from the equation above

[plucky elk]

gonna need more context

[light scroll]

uhhh i mean i can send the whole question, not sure how its called in english but it should be cauchy's problem with particular differential equations

and then this is near the end of a question

should i send the pdf (its 3 pages) or send pictures, or is that too long

[safe radish]

@light scroll Has your question been resolved?

[plucky elk]

Equation (*) is probably enough

Send enough context where someone reading doesn't have to ask "what does that mean"

[light scroll]

part before this

[light scroll]

well yeah i get that but it was just this part specifically, i thought the rest of the question wasnt needed

.close

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[steel spruce]

i need help with a question, i got some ideas but i still dont know how to solve it at all

[steel spruce]

i deduced that since f(f(x)) = x and its the inverse of itself, it has to be a straight line, that to theres only two types of straight lines it can be, one perpendicular to a function f(x) = x, or one matching it

since there are two inputs which return themselves, it cant be the former or else we will have two outputs for one input, therefore it is a line the same as f(x) = x

i also made some equations, i found the inverse of the function to be (yd - b)/(a - yc) [f(x) = y], and equated it to our former function for values of 19 and 97, and obviously they will be the same for everything else

f(x) = x, and f(f(19)) = 19, f(f(19)) = f(19), f(f(x)) = x[given], f(f(97)) = 97, f(f(97)) = f(97)

i dont know what to do and im really stuck, their hint was just "f(f(x)) = x for all x use a convenient x"

i feel like i have a lot of info and enough to solve it, i think can bash to find a bunch of variables but the bash is ridiculously huge, but i am just left with my brain unable to connect the dots between this giant pile of discoveries

[woven kiln]

f(f(x)) means f(x) is self inverse

$f^{-1}(x)=\frac{ax + b}{cx+d}$

[flat frigate]

Rylo

[woven kiln]

$f(x)=\frac{ax + b}{cx+d}$

[flat frigate]

Rylo

[woven kiln]

$\frac{ax + b}{cx+d} =-\frac{dx-b}{cx -a}$

[flat frigate]

Rylo

[woven kiln]

If your inverse is right

[woven kiln]

this is true

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[gilded fable]

11)b)

[potent roost]

what have you tried?

@gilded fable ^

[gilded fable]

@potent roost i dunnot understand how to make the equation

[potent roost]

first, is that a graded test/homework?

[gilded fable]

i read the question for fifth time now

homework

[potent roost]

you get marks for it?

if yes we can't help you its against the rules

[gilded fable]

nahh this is for ,testing our level of knowledge

[potent roost]

alright then

what are the unknown values you can figure out from the question?

and what do you need to find out?

try assigning them to a variable

[gilded fable]

length

variable

[potent roost]

of?

there are 3 lengths you don't know

[gilded fable]

length of the stick?

[potent roost]

yes thats the first one

[gilded fable]

ehh

[potent roost]

what are the other two

[gilded fable]

2m and 4m?

[potent roost]

those values are known to you though

what is unknown

[gilded fable]

ehh

its

the

"x"

[potent roost]

well yes x is a variable name that you can assign to any unknown value

[gilded fable]

yeyeee

[potent roost]

and for this question you'll assign it to this

let x be the length of the stick

but there are still pieces of information you don't know in the question? What are they?

[gilded fable]

x= something something

hmmm

the

[potent roost]

hint: || related to the rectangle ||

[gilded fable]

sign?

[potent roost]

not sign

[gilded fable]

rectangle

is it the

formula?

[potent roost]

umm not really

do you know what size the rectangle is?

[gilded fable]

wait

idk how to explain

size of the rectangle in the question?

[potent roost]

yes is it given in the question? or is it not

[gilded fable]

yes it iss

uhh

[potent roost]

you sure?

[gilded fable]

the width is 4m

ehh

wait

[potent roost]

the width is not 4m

read again

[gilded fable]

eh??

[potent roost]

The length of the stick is longer than the length of the rectangle by 2m

[gilded fable]

and 4m

[potent roost]

2m is not the length of the rectangle

if the length of the stick was 10m then the length of rectangle would be 8m

you don't know the length and width of the rectangle

[gilded fable]

OHHH

[potent roost]

so what do you do

[gilded fable]

we

divide?

[potent roost]

hint ^

[potent roost]

what would you divide 💀

[gilded fable]

WAIT

it kinda hard cuz i learn it in my own lang so eng is kinda hard

am trying to

understand

[potent roost]

anyway, since you don't know the length and width you can assign it to a variable

[gilded fable]

so like 4x and 2x?

[potent roost]

therefore the 3 variables you have are
x,a,b where x is the length of the stick, a is the length of rect, b is width

[gilded fable]

x and a b

[potent roost]

not really

[potent roost]

lets translate this into math

can you try?

[gilded fable]

X x 2m?

eh

hdjssjs

i feel so dumb

i understand ghe question but don't know how to put it

[potent roost]

the correct equation would be
x - a = 2

[potent roost]

if you subtract x - a you get 2 just like this example

[gilded fable]

ahhhh

cuz

the length different between this two is

2m

[potent roost]

yes

can you form 2 other equations?

[gilded fable]

x -b = 4

@vague gull

[vague gull]

henlo

[gilded fable]

.

[potent roost]

yes and the final one?

[gilded fable]

diagonal ?

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[gilded fable]

@potent roost thankss for da helpp

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[formal swan]

hi

[formal swan]

can someone help me understand this

  3 k + 12 k s - s^2 + 12 k s^2 + r s^2 + 3 s^4 - 
    3 r s^4 + (3 k - 2 s + 2 r s - s^2 - 12 k s^2 + r s^2 + 6 s^3 - 
       6 r s^3) #1 + (-1 - 3 k + r - 2 s - 12 k s + 2 r s + 2 s^2 - 
       2 r s^2) #1^2 + (-1 - 3 k + r - 2 s + 2 r s) #1^3 + (-1 + 
       r) #1^4 &, 1]```

how do i use this result

what is #1

[full zephyr]

Can you show it as it was given?

[lean otter]

what is this

[formal swan]

that is the result

as it isgiven

in mathematica

[full zephyr]

It’s just a mass of symbols you need to give us some actual context

[formal swan]

theres no content

its alebraic

so it is just symbols

[full zephyr]

What

[lean otter]

what did you ask for a example ?

[formal swan]

i have an algebraic equation that i solve for a and this is the result it spit out

and i have no idea how to work with this #1

[lean otter]

that's too vague tbh

[full zephyr]

Give us a screenshot or something

You already didn’t tell us you were solving an equation for a originally

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@formal swan Has your question been resolved?

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[rough nexus]

idk why but my answer in incorrect

[stoic dune]

Your sample size is 200,000?

[rough nexus]

yes?

[stoic dune]

Remember, sample size is "how many of the population did you record?"

If your population is made of people, your sample is as well

You have sampled 20 people

[rough nexus]

did I interchange sample mean and sample size?

[stoic dune]

Ye

[rough nexus]

how about this?

[stoic dune]

The boxes are interpreted correctly

[rough nexus]

wdym

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[ashen epoch]

how would you do this

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@ashen epoch Has your question been resolved?

[ashen epoch]

.close

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[lean otter]

Can anyone help with part b pls

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@lean otter Has your question been resolved?

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[polar laurel]

is it possible to reverse this integral or ?

[heady basin]

But what are u integrating

[polar laurel]

1

[heady basin]

Ah stupid me

[polar laurel]

the only thing i can think to do for dxdy is use to separate double integrals and add them together

[heady basin]

Is there a typo

Dydx instead of Dy dx

[polar laurel]

so i have to solve the problem as written and then change it from dydx to dxdy

[sharp crane]

can't you solve it just like this?

[polar laurel]

yes i can i have already its the easier way to solve it but im required to solve both ways

[heady basin]

So that would involve integrating X with respect to y

[polar laurel]

i think it'd be y with respect to x

[fresh dagger]

Do you have a function for y?

[polar laurel]

converting the 2 functions givin by the limits of the inside integral would give the functions arcsin(y) and arccos(y)

unless you mean the initial function thats being integrated than that would just be 1

[fresh dagger]

@polar laurel are you given a function for y?

[polar laurel]

the number 1

[fresh dagger]

As in y=f(x)

A function relating x and y

Is there one?

[polar laurel]

im looking for the area bounded by sin x and cosx between x= 0 and x= pi/4

[queen parcel]

Integrate!

I'd start with a diagram

[queen parcel]

Yup 🙂

[polar laurel]

that area is found using

[queen parcel]

Now you can get this area equal to an expression that involves two integrals

[polar laurel]

but i need to reverse that

[queen parcel]

I don't think you're trying to do a double integral

Although computing that may work

That does work lmao - haven't thought about these kinds of problems that way before

[polar laurel]

if it was up to me i wouldnt do double integrals but i gotta

[queen parcel]

That's weird

[polar laurel]

but i gotta reverse it and this is the best i got

im gonna go with adding two double integrals since i cant seem to find a better answer

[winter pivot]

we have:
sin(x) <= y <= cos(x)
0 <= x <= pi/4

[polar laurel]

ye

welllllll thanks for trying boy

.close

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[winter pivot]

0 <= x <= arccos(y)-arcsin(y)
0<= y <= sqrt(2-sqrt(2))/2

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[lean otter]

I'm confused on how to approach this. I'm thinking we should start by breaking down E[X] into a sum of E[X_i]'s, where i ranges from 1-10. Each individual in the group can spend either $4, $5, $9, or $0

[safe radish]

@lean otter Has your question been resolved?

[lean otter]

<@&286206848099549185>

[safe radish]

@lean otter Has your question been resolved?

[lean otter]

<@&286206848099549185>

[safe radish]

@lean otter Has your question been resolved?

[lean otter]

<@&286206848099549185> anyone? How do I approach this problem?

[charred flax]

Okay so my approach is to first plot out the probability table for a single person(so the probability that a person will buy the pencil or the wax figure) which is sort of given

||Then i will use that probability and generalize it to the ten people creating the expected number of people that will do each thing, so if there is a 0.5 chance of buying the pencil, i multiply by ten to find the apprx people who will do that||

||Then I will take that and multiply each expected number of people by the price||

||i.e. if I expect 2.9 people to buy the pencil then I do 2.9 * 4||

||I would then add up all of the expected money made and that should be it||

I spoilered the above so if u need a hint then move on to the next spoler

gl and if u need more help @ me

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[short rover]

$\int_{0}^{\pi/2} \int_{0}^{2\pi} a^2(1-\sin^2(u))(a^2\sin(u)) \dd{u} \dd{v}$

[flat frigate]

Sacha

[short rover]

hey, it's been a long time since i've done integrals and i'm kinda stuck, here a is a constant

should i just multiply everything out

[bright crow]

Since "a" is a constant, you can bring the a⁴ out of both integrals

[short rover]

$a^4 \int_{0}^{\pi/2} \int_{0}^{2\pi} \sin(u) - \sin^3(u) \dd{u} \dd{v}$

[flat frigate]

Sacha

[bright crow]

Then, observe that 1-sin²(u)=cos²(u)

[short rover]

ohhhhh

right that would be helpful

[bright crow]

It is convenient this way

[short rover]

yep that's what i was missing

lemme see if i can do it now

[bright crow]

Also, the whole of the inside integral doesn't have any "v" terms so, it's result would be a constant with respect to "v". Thus outside integral would be like definite integration of a constant.

[short rover]

got it, thank you!!

.close

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[gleaming rapids]

So I was on a role doing this practice test but then I hit this road block.. how is the answer 3? Why isn’t there 2 answers since it’s X and X^2?

[compact wraith]

Notice if you combine the 2 fractions you get the same denominator on both sides which means you can get rid of it

So your equation becomes $x(x+2) -2(x-1) =4x-1$

[gleaming rapids]

How do you combine the fractions if its subtraction?

[compact wraith]

Expanding and moving everything to the left gives us $x^2-4x+3=0$

[compact wraith]

Multiply the first fraction by x+2 top and bottom and the second fraction by x-1 top and bottom

[spice grove]

Same way you'd add normal fractions without variables.

By taking LCM and all.

[flat frigate]

Max..

Max..

[spice grove]

This gives two solutions and you're correct, but, x can't be equal to one of the solutions this gives.

[gleaming rapids]

But why? Can’t X be equal to one?

[spice grove]

It can't.

You have

[flat frigate]

What the hell am I doing here?

[gleaming rapids]

OOOH okay!

For your answer did you get 3?

[spice grove]

Sure.

[spice grove]

Solving this quadratic in x gives x=1,3.
We reject 1 from our answer.

[gleaming rapids]

Hmm on your previous comment, you say you got x^2-4x+3 however I got x^2+4x+1

Would they both give the same answer?

[spice grove]

They won't.

How'd you get x^2+4x+1?

[gleaming rapids]

Hmm from x^2+2=4x-1 from when you took out the denominator

I think I need more practice 🥲

[spice grove]

Well.

[gleaming rapids]

I’ll just hop on too khan academy thank you for your valuable time Max!

[spice grove]

$$x(x+2) - 2(x-1) = 4x-1$$

[flat frigate]

What the hell am I doing here?

[spice grove]

Is what you're solving.

Also, this is not max lol.

Anyway,

You should be able to solve it when you start over from here.

[gleaming rapids]

Ahh my bad I thought that was your name😔

How do I end this thread?

.end

[spice grove]

.close

[gleaming rapids]

Hm

.close

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[kind dove]

can somebody explain me why is there -2 (k-1)/n in summation ?

instead -2(k/n)

.close

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[dense compass]

I dont know how to solve this

[safe radish]

@dense compass Has your question been resolved?

[safe radish]

@dense compass Has your question been resolved?

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[lost bear]

can u conclude this?

[thin bridge]

what have you thought about?

[lost bear]

can conclude but

my friends told me cant

i was thinking bc f(a)=L

therefore lim-a = L

im not sure though

[thin bridge]

consider drawing some graphs and see if you can create some counterexamples

[lost bear]

ok hold on

[lost bear]

hmm this was my classmate's but i honestly dont get it

[thin bridge]

have you done stuff with piecewise defined functions before?

[lost bear]

yes but im still confused with the topic

[thin bridge]

does just knowing that f(2) = 3
give you any info about the limit as x→2?

i.e. does only knowing that point tell you anything about the rest of the function and what's happening around x=2?

[lost bear]

that it does not necessarily have to be equal to 4 it can be other points?

im confused huhu sorry

[lost bear]

idts?

[thin bridge]

idts?

[lost bear]

i dont think so

[thin bridge]

yeh, exactly.

just knowing f(2) tells you nothing else

[lost bear]

Ohh ok so there isn't sufficient information to conclude the rest of the function and what is happening around x=2

[thin bridge]

yes

[lost bear]

tysm!

.close

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[soft kestrel]

So I have to find out the weight of 3000 square metres of glass with a strength of 24mm.
My problem is that I cant figure out how to turn the square metres and mm into cubic metres so that I can calculate the weight using the density of glass.
I would appreciate some help.

[tall bough]

just google

[soft kestrel]

I did

[tall bough]

then u know

[soft kestrel]

No

[tall bough]

what did u google

[soft kestrel]

On how to get square metres and mm into cubic metres and when I try it I overshoot the mass of the glass by 80t

[tall bough]

how much cubicc metres is 3000 square metres

[soft kestrel]

The cubic metres is 3000^2 x 0.024 or am I wrong?

[tall bough]

idu what u mean with strenghth of 24mm

[soft kestrel]

So you have length width and the strength of glass

Or how is it called in english?

[tall bough]

strength is not a distance measure

24mm 'strength' sounds illogical

[soft kestrel]

But thats how you say it for glass

[tall bough]

huh

[soft kestrel]

depth?

[upper badge]

I think perhaps it refers to the thickness

[soft kestrel]

yes

[tall bough]

strength is measured in pascals

so u meant height?

[soft kestrel]

I guess so

[tall bough]

thats a very small height for a glass with a very very wide bottom

doesnt even look like a glass

[upper badge]

nah its 24 mm thick, which sounds about normal to me

[soft kestrel]

Its 5.10m x 1.70m x 24mm glass

[tall bough]

lol

a glass

that has

length and width in meters

wtf is this

ahhhhhh nvml

i thought it was a drinking glass

LOL

[upper badge]

where did 5.1 and 1.7 come from?

[soft kestrel]

But the two first measurements dont work for my calculation

So it is a real building with different types of glass. All of it covers 3000 square metres

And the one thats used the most has those measurements

[upper badge]

3000 m^2 × 0.024 m = x m^3
here x is the volume
using density = mass/volume, you can find the mass

[soft kestrel]

yes I tried that

[upper badge]

and?

[soft kestrel]

With the density of glass it never gets me to 240t which is the real weight of my glass

[upper badge]

whats the density?

[soft kestrel]

2.5 g per cubic cm

[upper badge]

and the value of volume that you got?

[soft kestrel]

216000 cubic metres

[upper badge]

3000 × 0.024 = 216000 ?

is what youre saying?

[soft kestrel]

well thats 72

[upper badge]

hmm so shouldnt the volume be 72 m^3?

[soft kestrel]

yes

but then what do I do with that

[upper badge]

density = mass/volume
mass = density × volume

and with mass (in kg) you can find your weight (in kg-f or N or whatever)

be sure to change the units tho

[soft kestrel]

Now I got 180kg?

[upper badge]

uhh not quite

you say density = 2.5 g/cm^3

if you wanna multiply by 72 m^3

express that 72 m^3 in terms of cm^3

[soft kestrel]

93312 kg now?

[upper badge]

ummm

[upper badge]

did you do this?

[soft kestrel]

yes

[upper badge]

what did you get?

[soft kestrel]

Well now it got me to 180t

[upper badge]

aight good

[soft kestrel]

Which means I am missing 60t

[upper badge]

oh damn -

[soft kestrel]

or atleast the 32t for the glass I already know

[upper badge]

are we talking about the math or?

[soft kestrel]

I really dont get it

[upper badge]

whats t btw

[soft kestrel]

tons

like 180t is 180.000 kg

[upper badge]

do you like know the answer?

[soft kestrel]

I mean I know that it should get me to around 240t

[upper badge]

around??

how do you know that?

answer key?

[soft kestrel]

No

As I said the building exists

And it says its 240t of glass

[upper badge]

wtf - we're doing actual math for actual stuff ??

[upper badge]

hmmmm

so umm the glass is basically a cuboid?

nvm thats irrelevant

[soft kestrel]

Well the pieces are

But all of it covers 3000 square metres

[upper badge]

hmm look 180t is correct

so your info is prolly wrong

[soft kestrel]

My info is by the government

[upper badge]

they're lying

[soft kestrel]

But then how come the glass I know weighs 212t

[upper badge]

who told you it weighs 212t?

your gov?

[soft kestrel]

Its 17 rows with 24 pieces of glass

[upper badge]

ummmmmmmmm

why the heck did you say 3000 sq m then??

where did that come from?

[soft kestrel]

Because I need it to calculate the rest of the glass

There is a little bit of glass in some areas that the big windows dont cover

[upper badge]

ok so you got 17 × 24 pieces of glasses each weighing 520.2 kg

and thats about 212 t

[upper badge]

and that extra bit has area 3000 sq m?

[soft kestrel]

No all of it has 3000 sq m

All of the glass combined

[upper badge]

then how much is it?

[soft kestrel]

how much is what?

[upper badge]

ohh i see so 35373600 cm^3 for the pieces

[soft kestrel]

what?

[upper badge]

510 × 170 × 17 × 24

[soft kestrel]

yea

so what now?

[upper badge]

all of what?

[soft kestrel]

all of the glass

[upper badge]

including the pieces + extra bits?

[soft kestrel]

yes

[upper badge]

you need to elect a new gov

[upper badge]

cuz thats less than this?

[upper badge]

jk lol

[soft kestrel]

Or we just go destroy the building

[upper badge]

ummm is there a problem with it?

seems like a waste -

[soft kestrel]

Well let me just add the other way we did it and then I'll just present both

[upper badge]

what other way?

[soft kestrel]

With the 3000 sq m

[upper badge]

the pieces account for about 35 million sq cm

[soft kestrel]

getting us to 180t

[upper badge]

you say total is 30 million sq cm

you see the problem?

[soft kestrel]

Yes

[upper badge]

so the 3000 sq m is wrong?

[soft kestrel]

Or what if

The government is werid

Take away 4 rows

[upper badge]

likely

[soft kestrel]

Is it below 35million?

[upper badge]

yep

so they lied about those 4 rows?

[soft kestrel]

then I see the problem

They say its 17 rows with 24 pieces of glass

and 4 more rows with no glass

[upper badge]

4 more??

[soft kestrel]

But they actually mean 4 of the 17 are without glass

[upper badge]

yeahhh

[soft kestrel]

So what am I calculating with now?

[upper badge]

whose calculation is this?

[soft kestrel]

Mine

[upper badge]

hmm ok

does that make sense?

[soft kestrel]

But how come the government calculated 240t?

[upper badge]

thats all ik

[upper badge]

I have 0 idea

[soft kestrel]

Wait now I have 162 for the pieces

[upper badge]

with 4 rows not made of glass?

[soft kestrel]

yes

13 x 24 x 520.2

[upper badge]

oh wait i made an error sorry -

[upper badge]

yeah thats right

so around 18 t for the extra bit?

[soft kestrel]

Wait

Can you explain that again

[upper badge]

total is 180t
pieces, as you said, is 162 t
so... umm extra is 18 t yeah?

[soft kestrel]

but how do we get 18t?

[upper badge]

180 - 162 = 18

[soft kestrel]

Think I can say that?

We talking about probably my most important math presentation ever

[upper badge]

ummm

I thought we were uncovering gov secrets but ok

what is your presentation on?

[soft kestrel]

I mean we are doing that too for some reason

Well there is this glass thing, probabilty and then I'll explain some stuff about however you translate this

[upper badge]

i didnt get it but thats ok

[soft kestrel]

So half of it is probability and the other half is the building

[upper badge]

I think we've lost track of what we needed to find?

maybe re-phrase the question in a better way in a new help channel?

[soft kestrel]

No

I only need to revisit the way we found out the

overall weight

[upper badge]

aight gl

[soft kestrel]

Thank you for the help

.close

[safe radish]

Channel closed

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[safe radish]

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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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[safe radish]

Please don't occupy multiple help channels.

[sick anchor]

can someone guide me on this? i cant understand the solutions

its very messy lol

ok so

[tall bough]

2AE=AC and 2DE=AC

so

both are equal

so equate them

and find x

[sick anchor]

ye

ok

wait

isnt it ae=ec

since they intersect at e?

[tall bough]

yes

[sick anchor]

so

do i still use the same solution

wait

i have a question

[tall bough]

?

[sick anchor]

why is ae times 2

[tall bough]

AE=EC, AE+EC=AC => AE+AE=AC => 2AE=AC

[sick anchor]

ohh

so ae=ec therefore ae+ae is possible

=ac

am i getting the pointt?

[tall bough]

ye

[sick anchor]

ight

wait so x = 0?

because thats what i got

3x - 28 = 3x - 28?

3x-3x->x, -28+28->0, x=0??

[tall bough]

equating same things make no sense

equate AE with DE

[sick anchor]

oh

ok

3x-28=1/2x+12->6x/6=40/6-> 6.6

i got an integer

[tall bough]

,w 3x-28=(1/2)x+12

[flat frigate]

Results provided by WolframAlpha

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

Requested by Grubert#2374

[sick anchor]

how

what did i do wrong?

[tall bough]

what did u do in steps

[sick anchor]

ok

so 3x

since the given was a fraction

i divided 3 by 1 which is 3

i mean

then multiplied it by 2

which got me 6

then i transposed -28=28+12

which resulted in 40

[tall bough]

no

[sick anchor]

ok

what do i do

[tall bough]

3x=(1/2)x+40 first

then 3x-(1/2)x=40

[sick anchor]

o

[sick anchor]

what happen to 40?

oh

[sick anchor]

negative 40?

o wait

nvm

how to simplify

this equation\

[tall bough]

what's 3 minus half

[sick anchor]

its a integer

[tall bough]

yeah

[sick anchor]

2.5

[tall bough]

yes

[sick anchor]

ok

it will be 2.5x?

2.5/2.5x=40/2.5 = 16

ooooooo

ok ok

whats the next step

[tall bough]

x is 16

[sick anchor]

yep so i already substituted got 20

for AE and DE

[tall bough]

then ac is 40

[sick anchor]

yup

thank you sir

or maam

[plucky elk]

.close

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[lean otter]

anyone help me i have 1 attempt and i cant seem to get the answer

[safe radish]

@lean otter Has your question been resolved?

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[toxic cliff]

3x=5 is parallel with y-axis, and y=3 is parallel with x-axis.
x-axis and y-axis are perpendicular.

[safe radish]

@delicate ridge Has your question been resolved?

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[wraith root]

Pls pls pls pls anyone know mathematics discrete need help 1 hour left for homwork😭😭😭

True or false with justification

<@&286206848099549185>

<@&286206848099549185>

[ancient escarp]

wait 15 minutes to ping helpers, do not ping them more than once

[ancient escarp]

read this

and apparently read #rules too

[wraith root]

It’s emergency 🚨 so

[ancient escarp]

nobody cares

[compact wraith]

I care

[wraith root]

Less goo

[stoic dune]

I'll use + for XOR.
Try adding A to both sides.

[wraith root]

I sid ven diagram

Did

[stoic dune]

Oh, I guess I'm using that + is associative

[wraith root]

Its true

[compact wraith]

You need to show that all elements $x\in B$ then $x\in C$ that shows $B \subset C$ then show the same for $x \in C$

[flat frigate]

Max..

[wraith root]

Iam tryna do somthing nothing work

[stoic dune]

.

[wraith root]

What the $

€you mean?

[stoic dune]

Assume x is in A+B. Show x is in A+C.
And vice versa.

[compact wraith]

Try describing it in words

[wraith root]

thats xor but not +

[compact wraith]

We're told this is true

[stoic dune]

Oh kekw

I forgot the statement for a second there

[wraith root]

😣

[compact wraith]

$x\in B not A\Rightarrow x\in A+B \Rightarrow x\in A+C$ But as x is not in A but in A+C it therefore is in C

[flat frigate]

Max..

[compact wraith]

That proves $B\subset C$

[flat frigate]

Max..

[compact wraith]

You can do an identical proof for the inverse

And hence B=C

[wraith root]

From where you got x€ b\a

And thats mean x€ A+B

[compact wraith]

I've assumed it

Also remember that A n B isn't in A XOR B

Proof isn't finish so assume $x \in A n B \Rightarrow x\notin A + B \Rightarrow x\notin A + C \Rightarrow x \in A n C$ So $B \subset C $ by the first proof and this one. And this proof is identical for the other direction so we proved B=C

[flat frigate]

Max..

[safe radish]

@wraith root Has your question been resolved?

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[next sun]

so i was practicing for the AB calc ap exam and got this answer which i think is correct but apparently isnt
but the correct answer was this which i dont understand how you're supposed to see
why is my answer wrong and how was i supposed to tell that i should've taken out the 1/4?
(please ping on reply)
ty in advance

[cosmic grove]

if you want to apply that antiderivative formula with ln, you need to have this form : u'/u

let u = x²+4, x² = u-4, x = sqrt(u-4) or -sqrt(u-4)
du = 2x dx
du/2x = dx = du/(2sqrt(u-4))
1/(x²+4) dx = du/(2usqrt(u-4))
we can't integrate this

[next sun]

.close

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[lean otter]

I am studying 2nd degree equation, and I wanted to know why this guy put b squared (he is solving question b)

[worthy hemlock]

Because it's part of the equation

That's part of the discriminant

[lean otter]

where? 3x?

[worthy hemlock]

No

The discriminant

[lean otter]

what is discriminant
god im brazillian 😭

[worthy hemlock]

The equation that's given

[full zephyr]

Discriminante lmao

It’s basically the same in Portuguese

[lean otter]

let me think

[worthy hemlock]

The discriminant is b^2 - 4ac, that is the equation

[lean otter]

how do I find out the discriminant

[worthy hemlock]

Part of the quadratic equation

The stuff under the square root

[full zephyr]

Is that from your class

[lean otter]

no

[full zephyr]

Probably why

We can’t solve all quadratic equations over the real numbers

[lean otter]

where you see the square root

[full zephyr]

You need to go and learn about the quadratic formula and discriminant

[worthy hemlock]

[lean otter]

no im gonna kill myself bye

.close

[safe radish]

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[worthy hemlock]

Interesting reaction

[full zephyr]

Not quite sure what to think about that

[safe radish]

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[fiery gyro]

need help trying to find weight using height and volume to find weight/mass

[fiery gyro]

14ft and 5864ft3

[full zephyr]

…Volume of?

[fiery gyro]

of a pile / cone

<@&286206848099549185>

<@&286206848099549185>

[safe radish]

@fiery gyro Has your question been resolved?

[fiery gyro]

<@&286206848099549185>

.close

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[north acorn]

Can someone help witht his?

[safe radish]

@north acorn Has your question been resolved?

[safe radish]

@north acorn Has your question been resolved?

[safe radish]

@north acorn Has your question been resolved?

[north acorn]

<@&286206848099549185>

@meager igloo

[noble condor]

oWo

[north acorn]

Hello blaze

I need a genius to help me solve this problem

[north acorn]

@median finch

A swift bite to the neck is all that it takes to quickly kill a dying, previously majestic fox on the ground.

This sentence contains all letters a-z. Prove me wrong.

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@north acorn Has your question been resolved?

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[wispy rain]

What are the use of Lp spaces? What is the criterion for a function being Lebesgue integrable? If a function is Lebesgue integrable, is its L1 norm finite?

[safe radish]

@wispy rain Has your question been resolved?

[grizzled fossil]

L^2 is a hilbert space, L^p plenty of use in prob for example, it induces a norm… so many uses

For 2) and 3) its just checking definition

[wispy rain]

Ok so both f+ and f- being integrable implies f+ + f- will be integrable and hence the L1 norm is finite

How do I prove that $fg$ is measurable where $fg$ is the convolution of two integrable functions?

[flat frigate]

allmight

[grizzled fossil]

Huh? I can integrate x just fine

And make it equal to inf or whatever

[wispy rain]

I don't get it

[grizzled fossil]

You said integrabel implied positive and negative finite

[wispy rain]

This is the definition I could find
A nonnegative measurable function f is called Lebesgue integrable if its Lebesgue integral intfdmu is finite. An arbitrary measurable function is integrable if f^+ and f^- are each Lebesgue integrable, where f^+ and f^- denote the positive and negative parts of f, respectively.

[grizzled fossil]

That is just to define it as int f^+ -int f^-

No reason why an integral can’t be inf

[wispy rain]

But if the integral is infinity then by definition it is not Lebesgue Integrable?

I'm sorry I'm slow to understand. But this definition is really confusing me

[grizzled fossil]

That is not a thing

No reason to have that as a restriction in def

For a non negative simple function $s$ with standard representation we define $$I_\mu(s)=\sum_{j=1}^{n} a_j , \mu(A_j) \in [0,\infty]$$

The mu integral of f is then defined as sup over I_\mu(s) where s<=f

Which then also takes values in [0,\infty]

[flat frigate]

ScapeProf

[wispy rain]

Ok. So Lebesgue Integrability is just the ability to find a simple fnction that is equal to it almost everywhere

But if we know that the integral is finite and the function is measurable -> the function is Lebesgue Integrable

[grizzled fossil]

No reason for finite

[wispy rain]

Are all measurable functions Lebesgue Integrable?

[grizzled fossil]

No

[wispy rain]

Can you share the exact definition of Lebesgue Integrable?

[grizzled fossil]

For a function $f$ in $\mathcal{L}(\mu)$ we define the integral $\int f , d\mu$ of $f$ with respect to $\mu$ with [\int f, d\mu=E_\mu(f^+)-E_\mu(f^-)]

[flat frigate]

ScapeProf

[grizzled fossil]

Since in L(\mu) either positive or negative finite

E_mu is just int f du

[wispy rain]

Ok thanks

Just one more thing. Can there be a function that is not measurable but having finite integral?

[grizzled fossil]

How are you gonna integrate something not measureable

[wispy rain]

Like I have a function, and by some inequality I get an integrable function greater than it and this function has a finite integral

What can be said about the measurability of the original function

[grizzled fossil]

Nothing

[wispy rain]

Ok So I'll share the original question that I was trying to prove

Given $f, g \in L^1(\mathbb{R})$ prove that $f*g$ is measurable

[flat frigate]

allmight

[grizzled fossil]

I can just send you how my book did it if you want

[wispy rain]

Yes please do. I have been trying to prove this for three days now

[grizzled fossil]

Not English but they just define smth then use Tonelli

[wispy rain]

Where does it prove f*g is measurable?

[grizzled fossil]

Last line it has in $\mathcal{M}_\bC(\mathcal{B}(\bR))$

[wispy rain]

Ok got it thanks

[flat frigate]

ScapeProf

[wispy rain]

How did it follow that $f*g \in \mathcal{M}_\bC(\mathcal{B}(\bR))$?

[flat frigate]

allmight

[wispy rain]

Positive part and the negative part both had finite integral. Does this imply the result?

[grizzled fossil]

You show \phi and \psi measureable

Closed under addition

[wispy rain]

Okk

Can you also please share the part of Tonelli theorem used?

[wispy rain]

.close

[safe radish]

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[stable cave]

Hello, I'm working in the textbook and Im having problems with 12/13, mostly because Im not sure which star is m1/m2

[stable cave]

For 12, When I have m2 as sirius I get

-1.5-0.12=log(b1/b2)
-1.62=log(b1/b2)
10^-1.62=(b1/b2)
0.02=(b1/b2)

When I have m1 as sirius I get

0.12-(-1.5)=log(b1/b2)
1.62=log(b1/b2)
10^1.62=(b1/b2)
41.7=(b1/b2)

is the smaller number always m1?

[grizzled fossil]

It just says the function we have is positiv and measureable

[x\mapsto \int_Y f(x,y) , \nu (dy), \quad (x \in X)] is positiv and measureable.

[flat frigate]

ScapeProf

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[terse lotus]

how do I find domain? (R= range, A= asymptote, y-int= y-intercept)

[ancient escarp]

what numbers are you able to plug into that function?

[terse lotus]

-1?

[ancient escarp]

just -1?

[terse lotus]

-16, -4, -1, -1/4, and -1/16

[ancient escarp]

you’re just telling me values you get when you plug integers into that function

that’s not what im asking

what numbers can you plug in for x and get an answer?

[terse lotus]

ohh

-2, -1, 0, 1, and 2?

[ancient escarp]

just those numbers?

why can’t you plug in 3?

or -3?

(or is your domain restricted?)

[terse lotus]

i can plug in those numbers but my teacher suggested those so that it’s easier

[potent roost]

that was for plotting

[ancient escarp]

well if you can plug in those numbers, it doesn’t matter if you did or not

what matters is if you can

so which numbers are you able to plug into that function?

[terse lotus]

all numbers on the x-axis?

[ancient escarp]

exactly, you can plug in any number

[terse lotus]

Oh so is it all real numbers?

[ancient escarp]

yep

[terse lotus]

ok thank you!

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[oblique jay]

Need some guidance for this question

[shy temple]

Don't know about martingales, but the first 2 parts can be done without them. If you know $X_t$, then $X_{t+1}$ can be $X_{t}$, with probability $X_t/100$ (drawing from one of the $X_t$ empty bins) or $X_{t}-1$ with probability $\dfrac{100-X_t}{100}$. Now you can find the conditional expectation. Tower law should give second one

[flat frigate]

1345631

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[oblique jay]

Ok. How exactly do I combine knowing the probabilities to get the conditional expectation?

[shy temple]

Use the usual formula for expectation

[oblique jay]

I see. So for the second part, using Tower Law I should be finding $E(X_{t+1}) = E(E(X_{t+1} \mid X_{t}))$

[flat frigate]

robie

[shy temple]

yes

[oblique jay]

I see ok thanks. I will try it out

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[clever sorrel]

I'm unsure of how the author got to the last line

this is my attempt

please ping me if you answer

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[sonic plinth]

Can someone push me in the right direction to do these practice questions? I'm very lost for all 3 of them because I dont know where/how to start

[sonic plinth]

I think for number 9, I'm just very confused on how to rearrange it so that it can be factored by decomp

for the other two I'm just very very lost

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<@&286206848099549185>

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[silver zodiac]

For Q10 you need to expand it out first

For the triangle use pythagoras

And for Q9 just use the quadratic formula

[plucky elk]

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[cinder viper]

@pine magnet You should try #geometry-and-trigonometry

I'm weak in geometry sorry

[pine magnet]

they dont respond

[cinder viper]

I see

[pine magnet]

all g

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[scenic mist]

how did you try to solve the question?

you can start by finding out the total length of the cirumference, and then finding the fraction of the circumference that is arc ab

@pine magnet

[pine magnet]

idk what to do @scenic mist

[pine berry]

are you allowed to use calculators

[pine magnet]

yes

[pine berry]

well do you see 2 angles are 43

in q11

those 2

since x is radius

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[pine magnet]

ya thats how I got 4.1

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[candid atlas]

Hi can someone give me a practice problem on Area and Length scale factor on a world problem, I need to review for my exam again

[worthy hemlock]

You can Google problems. It's nobody job here to give you problems. We're here to help you out if you get stuck on concepts and need some assistance or guidance

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[candid atlas]

Can you tell me what to search up because I cant find any problems related to my subjecy

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[potent bay]

what does world problem mean?

if you multiply the sides by 2 how much does the volume grow?

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[marble fern]

i need to differentiate this equation using logarithmic differentiation

[marble fern]

it's very complicated i can't figure it out

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[bronze prism]

Well, take the log first

Since products, ratios and powers turn into sums, differences and factors respectively, you'll get an equation that's easier to differentiate

But when you differentiate ln(f), you get f'/f

Since you know f and (ln(f))', you can deduce f'

[marble fern]

i finished it now

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[crude geyser]

how do you find y here? is it:

12/y = 15/30?

[drowsy moss]

close the hypotenuse of the large triangle is not 30

[crude geyser]

oh wait so its 15/45

[drowsy moss]

yep

[crude geyser]

12/y = 15/45 then solve for y right

[drowsy moss]

assuming that's a typo, yes

[crude geyser]

oh yeah

thank you

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[trim swan]

Quick question about notation:

[trim swan]

Suppose I have a set A which is a subset of B. If I want to define an element r in A, and concisely say that it is also in B by the subset relation, is the following notation readable/appropriate?

Let $r \in A \subseteq B$ such that...

[flat frigate]

tatpoj

[drowsy moss]

that seems fine

[trim swan]

I thought so, but sometimes it's hard to tell if it's easier for me to decipher my writing because I'm the one who wrote it lol

Thank you

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[coral mantle]

Can someone help me ?

[coral mantle]

My answer is

[crisp portal]

Any know to solve cube ols create a off topic channel for cube like chess go

[coral mantle]

Why would you write here bro

[crisp portal]

Ok soory bro

[coral mantle]

.close

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