help-10

[royal basin]

do you see the thin vertical line that extends AB?

[lavish nymph]

yea

[royal basin]

what is the angle made by it and AB at the point B?

in other words, what is the angle between two rays going in exactly opposite directions?

[lavish nymph]

180

[royal basin]

great

armed with that knowledge, are you able to find theta now?

[lavish nymph]

110?

[royal basin]

are you asking me or second guessing yourself

[lavish nymph]

asking

[royal basin]

well, i don't know, is it 110? why or why not?

[lavish nymph]

it is

so now would I just plug it in

to the equation

[royal basin]

yes sure you would "just plug it in"

[lavish nymph]

ok I get two decimal values 1.45 and -1.45

so wouldnt 1.45 be the answer

or is there more steps

[royal basin]

well, are there more steps?

[lavish nymph]

dont think so

[royal basin]

read the original problem and tell me what it asked you to find.

[royal basin]

you answered your own question. why ask me?

[lavish nymph]

so am I done

I think I am

but I am not sure

[royal basin]

read the original problem and tell me what it asked you to find.

[lavish nymph]

the distance from the door of her house to the door of her school

which is the question mark you had

so yes

can you help me with another

[royal basin]

probably

[lavish nymph]

im confused on 1 would I put 16 as the area or the s within the equation

[royal basin]

it looks like you are expected to know a particular formulation of heron's formula with a particular choice of symbols

so i don't think any of us can answer that for certain

[lavish nymph]

uh

so what do I do

[royal basin]

dunno. reread your notes i guess?

[lavish nymph]

what

@royal basin

would this equation be correct

I got 13 from this

nvm I finished

[obtuse pebble]

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[timid silo]

how come when u differentiate L is 0?

[obtuse pebble]

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[trail musk]

sum -(-n)^2, for 1<=n<=100

[velvet niche]

I do not understand whatt

[royal basin]

mr gamer is incorrect

there's a variety of ways to do this

[trail musk]

i don't see how i'm incorrect

[royal basin]

-(-n)^2 = -n^2

[trail musk]

oh my bad

it should be a factor of (-1)^(n+1)

[royal basin]

a sneaky way to do this is to apply the identity a^2 - b^2 = (a-b)(a+b) fifty times

@velvet niche do you see what i am talking about

[velvet niche]

yeah I get it

[velvet niche]

applying it 50 times is it really sneaky?

[royal basin]

well it's less brute force than the other method i have in mind

[velvet niche]

ik the answer

i just dont know how they got it

the answer is -5050

[obtuse pebble]

@velvet niche Has your question been resolved?

[velvet niche]

I got the answer yall nvm

1^2-2^2 is -3 which is term 1 and 3^2-4^2 is -7 which is term 2

[dreamy acorn]

wow

[velvet niche]

common difference is -4

and by plugging the values in the sum of n terms formula

n = 50

you get -5050

[dreamy acorn]

i got another method

[velvet niche]

what is it?

[velvet niche]

but you add all the numbers from 1 to 100?

wow thats a lot of time

[dreamy acorn]

that easy as pie

[velvet niche]

of you could add with sum of n terms nvm

wow thats a new method ill remember

[dreamy acorn]

By the way

1+100 is 101, 2+99=101

then you got 50*101

then 5050

[velvet niche]

yeaahh

what grade are you in?

[dreamy acorn]

Em

i dont study gcse

[velvet niche]

i dont either im in cbse

11th grade

[dreamy acorn]

ok

idk whats my grade but im 16

[velvet niche]

oh so 11th grade too ig

[timid silo]

If mocha will be 16 this year , he is of 11th grade for cbse.

[dreamy acorn]

in my place its called form 5

[velvet niche]

ohh

[timid silo]

Reminder: Dont dorget to close channel when u are done.

[timid silo]

Sounds more professional

[velvet niche]

oh how do i do it

i just leave?

[timid silo]

.close

[velvet niche]

ok

[timid silo]

No

[dreamy acorn]

k bye

[velvet niche]

.close

[obtuse pebble]

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[obtuse pebble]

Please don't occupy multiple help channels.

[restive jungle]

i dont know yet, but my guess would be

you multiplied x+3 on both sides, which has a value of 0

[half crown]

yeah, I know denominator will be 0 and it will be undefined but why does x = -3 comes thou

[restive jungle]

?

wdym

[half crown]

nvm want to try next question?

.close

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[next reef]

[obtuse pebble]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[half crown]

#help-8

[rich plume]

.close

[obtuse pebble]

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[solemn needle]

how do i find the fourier transform of this function

[obtuse pebble]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

@solemn needle Has your question been resolved?

[solemn needle]

1

[obtuse pebble]

@solemn needle Has your question been resolved?

[obtuse pebble]

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[thorny sky]

Hello, can you help me with this problem? I don't know how and where to start.

[thorny sky]

We need to find the proof of this property.

[trail musk]

Let there be an element e within H. Then for every such e:
f(e) = g
e = f^(-1)(g)
f(e) = f(f^(-1)(g))
g = f(f^(-1)(g))
Since this holds for all e, this holds for all g. Since g is the image of e under f, the set of all such g is equal to H

[thorny sky]

I don't follow. Huhu, im sorry.

What is g there?

<@&286206848099549185>

[obtuse pebble]

@thorny sky Has your question been resolved?

[abstract ruin]

There are some serious errors in the above solution

(I'm assuming R(f) is the range of f, correct me if I'm wrong)

We can't assume that H is a subset of the domain of f

so f(e) might not exist

also, we can't assume f is invertible, so f^(-1)(e) might be a set containing more than one element

Still, the general idea is right, you're trying to show that two sets are equal, so the standard way to do that is to show that each is a subset of the other

[thorny sky]

Can you explain more? Huhu

[abstract ruin]

Sure

[thorny sky]

How should I start?

[abstract ruin]

$f(f^{-1}(H))$ is a set

[warm shale]

Lemma

[abstract ruin]

you want to show that it's the same set as H

So pick an arbitrary h in H and show that it's in f(f^{-1}(H))

and then vice versa

Here's how I'd start:

Let h be any element of H

Since H is a subset of R(f), there is an x such that f(x)=h

Hence x is an element of f^{-1}(H)

[thorny sky]

Okay, I'm writing it now. You're a great help!

[abstract ruin]

What kind of class is this for? Just curious

[thorny sky]

Set Theory

[abstract ruin]

Nice

yeah, you'll get lots of practice showing two sets are equal then!

[abstract ruin]

it follows that f(x) is an element of f(f^{-1}(H))

(this is just from the definition of f(S) where S is a set)

Since f(x)=h, we have

$h\in f(f^{-1}(H))$

[warm shale]

Lemma

[abstract ruin]

hence

$H\subseteq f(f^{-1}(H))$

[warm shale]

Lemma

[abstract ruin]

Then we have to show the other direction

[thorny sky]

How do we show the other direction? Im sorry, Im too dumb for this.

[abstract ruin]

it's alright

so you start now with an arbitrary element of f(f^{-1}(H))

so let's say

$a\in f(f^{-1}(H))$

[warm shale]

Lemma

[abstract ruin]

Then we ask, what does that mean?

Well, for any set S, if a is an element of f(S), that means there's an s in S such that f(s)=a

so we can say

there is an $s\in f^{-1}(H)$ such that $f(s)=a$

[warm shale]

Lemma

[abstract ruin]

but then what does that mean?

well,

$f^{-1}(H) = { x : f(x)\in H}$

[warm shale]

Lemma

[abstract ruin]

so if s is in f^{-1}(H)

that must mean f(s) is in H

but f(s)=a

so a is in H

and we've proved

$f(f^{-1}(H))\subseteq H$

[warm shale]

Lemma

[abstract ruin]

and so we're done

[thorny sky]

Woahhh!!! Wait wait wait, I'll absorb it all. I'll go back from the top. OMG! Thank you so much!

[abstract ruin]

yeah, you might want to read through it slower than I typed it, lol

but I hope it makes sense

[thorny sky]

Btw, im a 2nd yr univ student taking applied mathematics.

[abstract ruin]

ok, that makes sense

is this your school's "introduction to proof" course?

[thorny sky]

Yes. We're on the 2nd half of the sem. The first half was about logic and methods of proof. I barely passed the exam for that one and now, it's getting more complicated in set theory. If it can't be helped, I might retake this course. Im so afraid.

[abstract ruin]

well, I hope it goes well!

[thorny sky]

Is this part of the solution?

[abstract ruin]

not really - more of an explanation of the next step

[thorny sky]

Gosh! Im lost. Huhu

[abstract ruin]

wait, I misread - yes that step is important

[abstract ruin]

this one was the explanation of the definition

[thorny sky]

Can we go back? Im really sorry

[abstract ruin]

sorry, I'm multitasking - feel free to ping me

what do you need?

[thorny sky]

I cant get this part here

[abstract ruin]

this is the definition of f^{-1} of a set

you might have the word "preimage" in your notes

[thorny sky]

Thank so much! Got it already.

.close

[obtuse pebble]

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[spice storm]

consider a relation on A={a,b,c] defined by R={(a,a), (a,b), (b,a), (c,c)}

[spice storm]

This is not transitive, correct?

But it is reflexive bc a relates to itself directly, c relates to itself directly, and b relates to itself indirectly with (a,b) then (b,a)

[spice citrus]

Correct

*first message at least

It is reflexive as well

[spice storm]

good deal

thank you I appreciate it

.close

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[robust drum]

What is happened here?

[robust drum]

Where is the second pi?

the 3r?

1/3 * 3=1?

[timid silo]

Well yes

[robust drum]

Okey and where is the 3 r and pi?

[timid silo]

1/2 * 4/3 π r³
= 2/3 π r³

1/3 π r² * 3r
= 3/3 π r³

You can see that πr³ is present in both so either take that as common or imagine it as a single variable.
If you add both,
You get 5/3 * πr³

[robust drum]

Why as a single variable? Why its not 5/3 * 2 * (pi * r^3)?

[robust drum]

.

[timid silo]

For simplicity like

1/2 * 4/3 π r³
= 2/3 π r³
= 2/3 x

1/3 π r² * 3r
= 3/3 π r³
= 3/3 x

Instead of writing πr³ multiple times, let's just write it as x for now.

So

2/3 x + 3/3 x = 5/3 x

We have x = πr³ so

5/3 x = 5/3 πr³

[obtuse pebble]

@robust drum Has your question been resolved?

[obtuse pebble]

@robust drum Has your question been resolved?

[robust drum]

What if we not simply it?

[obtuse pebble]

@robust drum Has your question been resolved?

[robust drum]

<@&286206848099549185>

[tame narwhal]

what's your question?

[robust drum]

,rotate

[robust drum]

why is the solution 5/3 * pi * r^3 and not 5/3 * 2 *( pi * r^3)?

I didnt get it really

[tame narwhal]

It was answered above by someone else. 2/3 + 1 = 5/3

[robust drum]

Its not that

its about pi * r^3

[tame narwhal]

what about it? it's a common factor in both terms

[robust drum]

yes but how it can be 5/3 * pi * r^3 and not 5/3 * 2 *(pi * r^3)? Because you have two of this pi * r^3

[tame narwhal]

you don't add those

[robust drum]

Why?

[tame narwhal]

$\frac{2}{3} \pi r^3 + \pi r^3 = \left (\frac{2}{3} + 1 \right ) \pi r^3 = \frac{5}{3} \pi r^3$

[warm shale]

cwatson

[robust drum]

Hm. If you factorise pi * r^3, why it is equal to 1?

[tame narwhal]

what is $\frac{2}{3} x + x$?

[warm shale]

cwatson

[robust drum]

Hdym

ah

same terms

yes yes

[tame narwhal]

yes

[robust drum]

hm okey. I have to notice that if I factor out that its like here:
**(2/3 +1)**x

[hybrid gull]

Yes

[robust drum]

Hm okey. Thanks.

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[earnest orbit]

Imagine that you are going to travel to a place far away from the Earth. The gravitational force F that the Earth affects you with will decrease with the distance r to the center of the Earth. Calculate, using a generalized integral, the work required to take you infinitely far away from the Earth. How can I solve this question?

[forest sinew]

how can you get to work using force and distance

[ruby path]

$\dd W = \vec{F} \cdot \dd \vec{x}$

[warm shale]

NEONPerseus

[ruby path]

Are you aware of this relation

[ruby path]

I should apologise :/

[forest sinew]

nah ur good

urs is more mechanical anyways

[ruby path]

Lol

[earnest orbit]

I know that I solved the question 'Calculate the work required to travel from Earth to the moon', but not the other one.

https://gyazo.com/6e008c28193c3dae5fc6b8e8125cf755 like this but not the with using a generalized integral and infinitely

[obtuse pebble]

@earnest orbit Has your question been resolved?

[earnest orbit]

<@&286206848099549185>

.close

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[muted isle]

Just making sure but is BAC 29?

[lean dew]

no

[amber nest]

do you mean ABC

[lean dew]

well the question is asking for bac

[muted isle]

How do I solve it

[lean dew]

the angles correspond to each other

<B is congruent to <B'

they are the same measure

and interior angles of a triangle add to 180

with this information you can solve for <BAC

[muted isle]

You are a genius

It’s 27

Tysm @lean dew

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[spark rune]

just wondering, how did they get the y values?

[junior flame]

they just substituted it into y=sin x/cos x

they r using radians not degrees

[spark rune]

im just having a hard time visualizing that, could you elaborate please?

[junior flame]

so the x values are on the left side right

[spark rune]

yeah

[junior flame]

since sin 0 is 0

and cos 0 is 1

y = tan x where x is 0

gives 0/1 or 0

and they just do that for every value of x

[spark rune]

ohhhh i see

okok thank you

[junior flame]

also if ur unclear one pi radian is 180 degrees

[junior flame]

np

[spark rune]

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[thin meteor]

i got no clue how to do this anyone mind helping

[primal prawn]

Anyone know what this formula is?

[obtuse pebble]

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[timber pecan]

I am confused on what I should do on getting another dimension

[high wasp]

so

you are used to pyramid formulas?

[timber pecan]

not that I know of

i think I need pyth here

?

[high wasp]

yep

but first you need to find the area of the triangles at the pyramid

[timber pecan]

yeah?

[high wasp]

and you can find it with the surface area

[timber pecan]

ok? so should I do SA - the base?

[high wasp]

yep

and then divide it by 4

[timber pecan]

oh alright 👍

So I got 585 that would be for every lateral side

[high wasp]

yep

do you know what to do next?

[timber pecan]

nah I'm lost here

[high wasp]

ok

[timber pecan]

15 squared?

[high wasp]

noo

you have the area of the triangle rn

and the base

[timber pecan]

yea

[high wasp]

that is 30

[timber pecan]

yeah?

[high wasp]

and you want to know the weight

yeah

because if you look at the picture

[timber pecan]

yeah

[high wasp]

it says that the base its 30

so you only need to put that info at the triangle area formula

[timber pecan]

wait so is it 585÷2 for a right triangle area?

[high wasp]

wait

[timber pecan]

idk man I'm struggling

[high wasp]

you can do that too

[timber pecan]

ok

[high wasp]

but

you need to see the base as 15

[timber pecan]

yeah

[high wasp]

so you can do that

and find the L

and after that you can do pyth to get the H

[timber pecan]

ok so 292.5÷15

[high wasp]

wait

yeah]

[timber pecan]

like this

[high wasp]

and then multiply by 2

ooo no

sorry

my bad

[timber pecan]

?

[high wasp]

you did it right

[timber pecan]

oh alright 👍

h is 19.5

[high wasp]

no

L is 19.5

but

rn im confused

[timber pecan]

oh

[high wasp]

did you use it A = (b.h)\2

?

[timber pecan]

yeah

should I times by 2 then?

[high wasp]

yeah

and then thats the correct L

[timber pecan]

oh ok

alright thank you I've got the rest now

.close

[obtuse pebble]

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[high wasp]

bye

[obtuse pebble]

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[obtuse pebble]

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[stark galleon]

why doesnt wolfram problem generator understand any answer form i put?

[stark galleon]

i have tried parens around the fractions

i have tried no parens

[static beacon]

use a diff calculator to see if your correct

https://www.integral-calculator.com/

[daring rock]

What's that keyboard icon? Maybe it will let you input actual fractions and exponents?

instead of using / and ^

[stark galleon]

No, it is just a few general things

e^x is just that

[civic zealot]

probably the spaces

it doesn't know what to do with 2/3 t^4

[timid silo]

use *

(I just tested it)

[stark galleon]

@timid silo can you show a full example?

-(3/4)t*4-(2/3)t*3-(3/2)t*2+C

this doesn't work for example

do i just do t*t?

[stark galleon]

ohhhh

• (3/4 * t^4) - (2/3 * t^3) - (3/2 * t^2) + C

still not working. wtf. you would think this would be trivial

[timid silo]

does it parse?

or is it still giving you the not understanding error

[stark galleon]

not understanding error

[dark vector]

try moving the t^4 outside of the brackets and the - into it

it might be interpreting that as (3/4t^4)

bc you definitely have the right answer

oh

[timid silo]

no it isn't read the text below

[dark vector]

i thought somebody else was answering

[timid silo]

this parses for me

might be a bug on your end

[stark galleon]

it might be..

[thick gyro]

imagine including +C

couldnt be me

[stark galleon]

@thick gyro are you saying it is incorrect?

[thick gyro]

that is correct

wolfram alpha is just being a bitch about it

[stark galleon]

why is it incorrect?

it doesn't work without the +C either, but in either case, +C is correct because it is an indefinite integral

also, it has an input for +C as well so it should understand that just fine, I have a feeling they are running some front-end code on my end that perhaps is borked out or else there is an issue with my session

[timid silo]

he was making a joke about our choice of variable naming

normal people use x for their constant of integration

[stark galleon]

I just passed Calc I and that is not what I was told to do

[timid silo]

tis a /j

[timid silo]

your answer is 100% correct

its just wolfie being high as usual

[stark galleon]

ah okay, so maybe i should pick a different practice space?

[timid silo]

yeah, probably

[stark galleon]

i'll just do that, this is completely gunking up my would-be productivity, lol

thanks @timid silo !

.close

[obtuse pebble]

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[silver plover]

Bit stuck

So a basis is a linearly independent spanning set

Do I just need to check whether these matrices are linearly independent, and if so then it is a basis?

[brave bramble]

Need to span the space as well

[tame narwhal]

if the dimension of the space is 3, then yes it'll be a basis if they're linearly independent

[silver plover]

Well it’s a 2x2 matrix

So does that mean it doesn’t span the set?

Since the basis set contains 3 matrices

Acc wait

I’m getting confused now

[brave bramble]

I don't personally know what the dimension of the skew-Hermitian 2×2 matrices is

[silver plover]

I think the matrices are linear independent

Just by looking at them

They seem so

Can’t think of any linear combinations

[tame narwhal]

it's possible the dimension is 3. the space of all real 2x2 symmetric matrices, for example, has dimension 3 (and not 4)

[silver plover]

why is this incorrect?

[tame narwhal]

sorry I don't know that one, but I think they preserve length

[strong pike]

Isn’t it?

[silver plover]

This is from my notes

So idk what I was incorrect

Are there 2 answers?

[strong pike]

Isometry implies isomorphism

Probably

I believe they preserve both length and angle, but I don’t think I can prove it

[tame narwhal]

yes I think you're right actually

[silver plover]

So would the answer be all of them ticked?

[tame narwhal]

seems so, yes

[silver plover]

ight kl

thx

[silver plover]

(ii)

preserves length

[obtuse pebble]

@silver plover Has your question been resolved?

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[little obsidian]

I don’t understand how to make the substitution

[little obsidian]

For 1 a

<@&286206848099549185>

[timid silo]

How far have u gotten on this?

[little obsidian]

nowhere

i had to brush up on all of integration

i just dont get how to substitute it @timid silo

i guess i replace all the ys with the substitution but idk where to go from there

to get it in the form needed

[timid silo]

Have you input 1/u into all of the yʻs?

[little obsidian]

yes and that gets me x^2lnu+x/u=1/u^2

thats wrong actually the dy/dx should be lnulny

i still dont get where to go from that point

[dark stirrup]

You were already given advice

Use chain rule

[little obsidian]

where

[dark stirrup]

dy/dx

[little obsidian]

i got dy/dx i think

[dark stirrup]

You need du/dx

[little obsidian]

lnu * lny

du/dx is lny

at least if ive done everything correctly

@dark stirrup i dont get it man

what do i do with dy/dx and du/dx ive worked those out already

[dark stirrup]

Can you show what you've done so far

[little obsidian]

lol some random scribbles on the paper

i can take a picture

idk how useful itll be tho

[dark stirrup]

Better than nothing

[little obsidian]

ive worked out dy/dx and du/dx and dy/du

i think

@dark stirrup

[dark stirrup]

this is not correct

You integrated 1/u

[little obsidian]

oh

my brain is fried

time to rip this page out the notebook

is this more along the right lines @dark stirrup

[dark stirrup]

Remember what chain rule tells you: dy/dx=dy/du*du/dx

[little obsidian]

yeah i got dy/dx at the bottom there

[dark stirrup]

but where is your du/dx?

[little obsidian]

right above dy//dx

[dark stirrup]

How did you get this?

[little obsidian]

oh its not in terms of x

how do i get it in terms of x

u is equal to 1/y

[little obsidian]

yeah idk i understand it cant by du/dx cos its not in terms of x but u is defined in terms of y so not really sure what to do there

[dark stirrup]

you don't

[little obsidian]

uh

[dark stirrup]

dy/dx=dy/du*du/dx, you can find dy/du using y=1/u, you leave du/dx alone. The whole point is you're trying to get the expression shown in 1.a

[little obsidian]

ok let me try

@dark stirrup i think i got it

[dark stirrup]

Congrats

[little obsidian]

not sure how to do the rest of the homework tho lol

b for example

[dark stirrup]

Look up the term "integrating factor" for differential equations

I forget the exact definition

[little obsidian]

i know that we multiply through a differential equation by an integrating factor to get the equation into a certain form but i just dk how to do b

im gonna take a break from this

.close

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[spiral wraith]

how do I go about solving the rest

[spiral wraith]

also did I do the first part right

[fathom flicker]

write y(16)=25 as an ordered pair

dy/dx=f(x,y) so to evaluate it at a particular point you have to input both the x and y values for that point

[spiral wraith]

(16,25)

[native shale]

X is 16 when Y is 25

[spiral wraith]

do I input those into the sqrtx + sqrty = 9

[fathom flicker]

no

you don't want f(16)

[native shale]

Apparently not

[fathom flicker]

you want f'(16)

what's your formula for f' ?

[spiral wraith]

ohh i put that into -sqrty/sqrtx

[fathom flicker]

^

assuming that you differentiated correctly, yes

[spiral wraith]

-5/4

it says it's right so apparently I did

thank you!

[fathom flicker]

yeah, no problem

[spiral wraith]

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[sleek mural]

Could I plz get some help w/ #1 here?

[obtuse pebble]

@sleek mural Has your question been resolved?

[sleek mural]

Actually, #2, plz

[obtuse pebble]

@sleek mural Has your question been resolved?

[obtuse pebble]

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[stuck fog]

One spring, 20,000 cubic meters of sandblasting sand were collected from the streets of Helsinki. How thick would an even layer of sand be on the rectangular, 105-meter-long and 68-meter-wide grass field of the Olympic Stadium?
Hello, I need help in outlining the pattern and understanding what I am asked to solve in this question.

[stuck fog]

Is this how you would drawe the situation?

*write

<@&286206848099549185>

[obtuse pebble]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[sharp condor]

In the quesiton it's 105m long and 68m wide

So I'd argue that 105m would be on the bottom line of the cube

Rather than the height

And then, you will need the formula to find the volume of a cube

@stuck fog

[stuck fog]

Okay, thanks

How did you figure that volume is the thing that should be solved?

[sharp condor]

they ask how thick the even layer would be

And gave a volume

So basically they ask a height and they gave a volume, a length and a wideness

[stuck fog]

How can I get h to the left side of this formula: V=A*h

[sharp condor]

You don't need to use that formula directly

What is a square

[stuck fog]

What do you mean?

[sharp condor]

How do you know the A of a square

Well it's length*wideness of the square

And if you want a cube, a cube is a square*height

That gives you the volume of a cube

[stuck fog]

Oh, okay

If the volume of the cube is the square A times the height, what is the area of ​​a cube?

[sharp condor]

Sry I left for a moment

the area of the cube doesn't really exists

But in this situation it's length*wideness

Basically, they gave you a square that you know the dimensions of

And you wanna fill it until there are 20k cubic meters

[stuck fog]

You have helped me a LOT, thank you so much!

[sharp condor]

Do you got the idea ?

[stuck fog]

Yes

[sharp condor]

Great

Don't forget to close the channel

[stuck fog]

.close

[obtuse pebble]

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[stuck fog]

Hi! I need help getting started with this problem: The pea soup can is a straight circular cylinder with a height of 103 mm and a bottom diameter of 72 mm.

a) What is the total surface area of ​​the bottoms and the shell of the can?

b) What is the volume of the can?

[timber island]

Well do you know the formulas for TSA and volume?

[stuck fog]

Oh sorry, I got them now😅 My roommate helped me. Have a great day!

[timber island]

Np

[stuck fog]

.close

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[timid silo]

Let f (x) be a differentiable function over [0, 1]. Suppose that f (0) =
f (1) = 0. Prove that f ′(x) − 2f (x) must have a zero inside (0, 1). Namely, there is a c ∈ (0, 1)
such that f ′(c) − 2f (c) = 0.

[timid silo]

I think you have to use Rolle's theorem, but I'm not sure how

[obtuse pebble]

@timid silo Has your question been resolved?

[wintry fable]

if f(x) increases, it has to decrease at some point
if f(x) decreases, it has to increase at some point

so set g(x) = f'(x) - 2f(x)

and check if theres a sign change

[timid silo]

I'm not sure how you'd do that without a function f(x)

[wintry fable]

and consider the fact that f(x) is differentiable

if f(x) is differentiable

and f(0) = f(1) = 0

f(x) always has a point where f'(x) = 0

no matter what f(x) is

[timid silo]

ic

[wintry fable]

so there is always a sign change

in g(x)

which proves the question

[timid silo]

I'm not sure how that proves it because it's f'(c) - 2f(c)

[steady python]

But how do you prove that f ′(c) = 2f (c) for {0 < c < 1} is true?

[wintry fable]

gimme a moment

[steady python]

I think its because f(x) is 0 for x = 0,1. So f(x)' - a*f(x) will equal zero between 0 and 1 for any value of a. F(x) will be entirely positive or negative if it has one local maxima, but the derivative will be positive and negative on either side.

[obtuse pebble]

@timid silo Has your question been resolved?

[timid silo]

.close

[obtuse pebble]

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[steady python]

Is there more to this question?

[obtuse pebble]

@bright plaza Has your question been resolved?

[obtuse pebble]

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[lean spear]

f'(x)= 12x^2 -6x

to find intervals for increasing and decreasing I make it look like 6x(2x - 1)

or no?

[restive jungle]

?

just find the zero points

forgot what those are called

[lean spear]

do I do this?

[restive jungle]

dont think so

[lean spear]

how do I find the zero points?

[restive jungle]

do you know what f'(x) means?

[royal basin]

@restive jungle ⚠️ the way you're wording this is potentially confusing.

[restive jungle]

wait i think theyre called critical points

[restive jungle]

yes

sor

[lost quartz]

If f'x>0 then increasing and <0 means decreasing

[royal basin]

yes, that'll help you

[restive jungle]

is it called a critical point or something

[restive jungle]

really

hm

[royal basin]

well she wants to know when f'(x) is positive and when it's negative

[restive jungle]

gotta brush up my skills

[royal basin]

so just finding the points at which f'(x) = 0 is necessary (ish) but not enough by itself

[restive jungle]

then just take a lil bit of points in the middle and

[lean spear]

so do I set 6x = 0 and 2x - 1 = 0

[lost quartz]

Yeah

And then try putting a value in between 0 an 1/2

[restive jungle]

see if its pos/neg

[lost quartz]

Then see if f'x is positive or negative

If + then in 0,1/2 f is increasing

[lean spear]

ok so its increasing on the intervals 0 and 1/2

how should I find decreasing?

[restive jungle]

anything that isnt increasing is decreasing

(well except for critical points)

[lean spear]

how do I find that?

I think I remember setting up a number line and picking a number on the sides of the intervals we got. 0 and 1/2

[restive jungle]

so you know 0 to 1/2 is increasing

[lost quartz]

Bruh if inc in 0,1/2 then dec in - inf,0U1/2,inf

[restive jungle]

so the others should be...?

[royal basin]

this feels like overthinknig

[royal basin]

bad notation

[lean spear]

oh

[lost quartz]

Inf= infinity

Inc and dec should be self explanatory

[lean spear]

I forgor that its positive between 0 and 1/2, not AT 0 and 1/2 meaning there could be decreasing inbetween

[lost quartz]

Yeah so double diff the func then see it's concavity change

[restive jungle]

isnt the orig function a cubic tho?

[lost quartz]

If you haven't studied this concept then skip this ques and do it again when tou are taught this

[lost quartz]

Yeah

[restive jungle]

and the derivative is a quadratic

so there shouldnt be a concavity right

[lost quartz]

Double diff has x in it so there should be a concavity change

[lean spear]

how do I find my min and max now? I feel like this is the part where I plug in numbers for x into the derivative function

[lost quartz]

And that change signifies the change in inc and dec function

[lost quartz]

Just put f'x = 0

And find values for x

[restive jungle]

?

[lost quartz]

Nvm on phone so couldn't write in detail

[restive jungle]

i dont get it, if the derivative is positive, then the slope is positive, so it has to be increasing

and the derivative is a quadratic, so it only makes 1 turn

[lost quartz]

Hmm

[restive jungle]

if there were parts in it where the derivative dipped under 0, there would be more critical points right

quadratics only have 2 roots

[lean spear]

so 12x^2 - 6x = 0 gives me 12x^2 = 6x

[restive jungle]

mhm

[lean spear]

and then divide both sides by 6x?

that doesnt feel right

[restive jungle]

you assumed x isnt 0

[lean spear]

oh ok

[restive jungle]

you can only divide both sides by 6x when x isnt 0

[lean spear]

so we have a min at x = 0

[restive jungle]

min of which function?

[lean spear]

derivative

[lean spear]

how did they find this?

.close

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[rancid cape]

Years of course

What's your question?

Sir

[timid silo]

use the definitions. it might help with intuition if you plot f

[obtuse pebble]

@thorny sky Has your question been resolved?

[rancid cape]

Then you are stupid

Just accept it

Even my 11 years old son knows how to start it

[obtuse pebble]

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[timid silo]

<@&268886789983436800>
msg id: 1105822435468660808

user id: 1050802255642771509

[obtuse pebble]

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[half crown]

if the square is inside circle where all the square vertex touches the circumference of circle. Does the diagonal of square passes through center?

[gilded drift]

yes, proof:
Focus on BAC
We know that since it's a square, it's a right angle
Points that form a right angle in a circle(when the points are touching it's circumference) produce a triangle that's hypotenuse always touches the center

[half crown]

yes

[half crown]

oh yeah from the semi-circular theorm

I get it now

.close

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[gritty path]

is this right?

[wanton hull]

no

irrational plus irrational can never be rational

[gritty path]

how to

[eternal thistle]

Sqrt 2 + (-sqrt(2))

[eternal thistle]

How did you transform sqrt(3) into sqrt(9)

Clarify your steps

[wanton hull]

$\sqrt{3} + \frac{\sqrt{3}}{2} \implies \frac{2\sqrt{3}}{2} + \frac{\sqrt{3}}{2}$

[warm shale]

bettim

[wanton hull]

lol okay u win

unique irrationals*

[royal basin]

=, not =>

[royal basin]

define "unique"?

[wanton hull]

ah yes wait

[wanton hull]

a,b , a\neq b

[gritty path]

so answer is

[wanton hull]

yes

[royal basin]

sqrt(2) and -sqrt(2) are unequal.

[eternal thistle]

(Sqrt(2) +2) + (- sqrt(2))

Wrong person

[wanton hull]

😦

why yall booing me

[eternal thistle]

In fact. We don't know if e+ pi is rational or not

Could be rational

[eternal thistle]

Yes

[gritty path]

?

[eternal thistle]

No

[gritty path]

is the 5, 3?

[royal basin]

no, switching the five out for a three doesn't make it correct either.

show work for how you got this and we will tell you exactly where you went wrong

[gritty path]

wait how do i do it

[royal basin]

3/2 + sqrt(3) is honestly already simplified enough imo

if you were asked to write it as a single fraction you could do (3 + 2sqrt(3))/2 maybe

but you havent given us any problem statement

[gritty path]

this is the original equation

[royal basin]

that's not a question either.

what are you asked to do with this?

find the 10th decimal digit?

also http://xyproblem.info/ -- (2 + 1/2) + 1/2 is not equal to 3/2 ...

[gritty path]

how do i type ut

[topaz walrus]

use LaTex

[royal basin]

how do you type what?

[topaz walrus]

stuff in Latex

using Texit

[royal basin]

question was not addressed to you @topaz walrus

[topaz walrus]

just telling jeez

[topaz walrus]

umm no

[royal basin]

$2 \frac{1}{2} + \frac{1}{2} \neq \frac{3}{2}$

[warm shale]

Ann

[royal basin]

and $3 + 2\sqrt{3} \neq 5 \sqrt{3}$

[warm shale]

Ann

[topaz walrus]

u dont add integers to irrational numbers

i mean

[topaz walrus]

not like this

[wanton hull]

what?

really?

[gritty path]

then how to

[robust sleet]

,w 3 + 2sqrt(3)

[warm shale]

Results provided by WolframAlpha

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

Requested by Gooaaa#5829

[robust sleet]

,w 5sqrt(3)

[royal basin]

two-and-a-half plus a half is not equal to three halves @wanton hull

[warm shale]

Results provided by WolframAlpha

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

Requested by Gooaaa#5829

[royal basin]

2 1/2 means 2+1/2 and not 2*1/2 yes i know this is stupid but this is how it is with mixed numbers @wanton hull

[wanton hull]

ahhhhhhhhhhhhh okok i thought that 2 was 1/2 times 2

[wanton hull]

lol

[royal basin]

what's $2 + \frac{1}{2} + \frac{1}{2}$?

[warm shale]

Ann

[royal basin]

no!!!!

[topaz walrus]

hooly crap

[royal basin]

maskman, tell me
do you know how fraction arithmetic works?

yes or no

i dont want to see any more bs computations

just tell me

[topaz walrus]

jesus

[royal basin]

"yes, i know how fraction arithmetic works"
or
"no, i do not know how fraction arithmetic works"

[gritty path]

can i get an, i forgot option lol

[topaz walrus]

Maskman convert the mixed fraction to an improper fraction

[royal basin]

no, you cannot.

[gritty path]

no i do not know

[topaz walrus]

then add the common fractions

[royal basin]

then review fraction arithmetic

without roots

[topaz walrus]

2 1/2 is 5/2

[royal basin]

because you've forgotten it all

[topaz walrus]

how did u get to irrationals without learning this stuff properly

[robust sleet]

he forgor

[gritty path]

that was 6 or 7 years ago sorry if i have a forgetful memory😭

[topaz walrus]

yea but isnt fractions a common part of almost every question

how

[robust sleet]

6, 7 years ago what

[royal basin]

... how old are you?

[gritty path]

15

[topaz walrus]

DAMN

OLDER THAN ME

[gritty path]

sorry 😔

[topaz walrus]

just practise

[royal basin]

so you learned fractions at age 8 and you have not had any practice with them between then and now

is that what you are saying

[gritty path]

yeh lol

[royal basin]

i find that hard to believe

[gritty path]

my mind skipped basic math

[royal basin]

still, you're in need of a review either way

[gritty path]

i only followed the solution of my friends, do i add the fractionf first? 1/2 + 1/2?

[topaz walrus]

no

21/2 is not 1/2

[gritty path]

oh ok I'm still wrong

lol

[topaz walrus]

2 1/2 is 5/2

[gritty path]

ehhh

whut😭😭 i really did forget

[topaz walrus]

now did u get it

[gritty path]

i still don't

that's why i came here to get it lol

[topaz walrus]

$2 \frac{1}/{2}$

[gritty path]

that 2years quarantine prob brainwashed me lol jk

[warm shale]

Elix!r

[topaz walrus]

oh god

i need to learn

latex

[gritty path]

😭

[topaz walrus]

look

u know 2 1/2

[gritty path]

yeh?

[topaz walrus]

multiply the whole number part to the denominator and add the numerator

thats the numerator of the fraction

then by the original denominator

[gritty path]

so 2/2?

[topaz walrus]

no

[gritty path]

my brain is not braining, I don't even know what the denominator anymore☠️

[topaz walrus]

2*2 + 1

5

5/2 is ur fraction

[gritty path]

wait show it step by step I don't get it

[topaz walrus]

😭

wish i knew latex

i could teach u

[gritty path]

do it like this

[topaz walrus]

not for every fraction

[gritty path]

2 1/2, now what

[topaz walrus]

do this

[gritty path]

what's the denominator again, sorry for me being clueless

[topaz walrus]

the bottom number of the fraction

[gritty path]

ok 1/2*2 now what

[topaz walrus]

umm no

@royal basin

help me

rip

[topaz walrus]

go to khanacademy and watch videos of converting mixed fraction to improper fraction

https://khanacademy.org/

ok wait

i understood

[gritty path]

but in elementary school they teached 2 1/2 is 2/2 because 2 times 1/2 is 2/2

whut

[topaz walrus]

??????????

helllo

2 + 1/2 is not 1

its 2.5

[gritty path]

no it's times

multiply*

[topaz walrus]

ummmmmmm

2/2 is 1

[gritty path]

yeh so 1

huh

[topaz walrus]

look

$2\frac{1}{2}$

[warm shale]

Elix!r

[topaz walrus]

@gritty path

[gritty path]

yeh?

[topaz walrus]

u see the bottom part of the fraction

[gritty path]

ye?

[topaz walrus]

multiply the bottom part(denominator) into the whole number part and whatever u got add the numerator to it

after that u will get a number

that number will the numerator of the improper fraction or the converted fraction

the denominator will be the same as before

[gritty path]

OHHHHHHH omg it's all coming back

flashbacks

[topaz walrus]

so $2\frac{1}{2}$ becomes $\frac{5}{2}

[warm shale]

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

[gritty path]

ohh tnxxx

[topaz walrus]

did u get it now?

i will give another mixed fraction

[gritty path]

wait so answer is 4√3?

[gritty path]

sure

[topaz walrus]

convert $7\frac{5}{9}$

[warm shale]

Elix!r

[topaz walrus]

heres the problem

[gritty path]

68/9? wait am i wrong

[topaz walrus]

u are the opposite of inncorrect

aka

CORRECT

[gritty path]

Ohhhhhhh yeyyyy

so 2 + √3 is 3√3 right?

[topaz walrus]

u cant add integers to irrationals directly into one irrational