help-13

[glad dust]

yes i agree, making it explicit will simplify the state diagram creation a fair amount

my professor mentions that "You must include an explanation of why the TM halts ". do you think my original write-up adequately addresses that?

[worldly chasm]

No

[glad dust]

why's that?

[worldly chasm]

well, it's either not correct or not complete, there is no reject state written there.

[glad dust]

unfortunately i do not know how to use it and would rather spend the time atm to working on the state diagram and manually checking

[glad dust]

ah

oh but

[worldly chasm]

Did I miss that?

It's not in the text I copy pasted.

oic.

my bad then

[glad dust]

nah its cool

thats on me for closing

[worldly chasm]

hmm... but it's wrong

it's strictly less than twice

not twice or less

if you run out of 2s then it doesn't matter if you're also out of 1s.

it's still a failure, right?

[glad dust]

yes

wait

sorry i do not think i follow

why isnt that addressed by the reject state i have already?

[worldly chasm]

Maybe I don't understand how you are imagining the turing machine to work.

we don't know that we have used up all of the 2s typically until we fall off the end of the string.

and once we do that, there's no ambiguity, it's a reject

At least, this is the way I designed it up there from your sketch from the last channel.

if this is not the same as you have in mind, then please explicitly explain how you're imagining it's going to work.

[glad dust]

ah i think i see, the issue is because in the way im building the machine, i dont keep track of the number of 2's correct? that means i never know when they complete processing, so i need to add reject states elsewhere within the machine?

[worldly chasm]

You cannot without an arbitrarily large number of states, (you'd have to separately code in "I've seen one 2" state and the "I've seen two 2s" state, and so on up to infinity in order to properly accept or reject all valid strings.)

[glad dust]

yeah so that means i have to properly include reject transitions within the varying states right

[worldly chasm]

yeah, there's only one state that can fall to a reject state, and that's the state B (looking for a 2 in the string)

if that state falls off of the end of the string, then it should transition to reject

[glad dust]

so there's that, falling off the tape in state A, and failing to locate any unmatched 1's correct ?

or am i misunderstanding

/missing one

[worldly chasm]

sorry, I misremembered my states.

State A is the "searching for a 2 state"

that's the one where falling off means reject

state B is "returning to the start"

state C is "searching for the first 1" and state D is "searching for the second 1"

if we fall off of the end of the string in states C or D then that's an accept

falling off the end in state B is impossible because we always move left until we fall off the front of the string.

[glad dust]

okay ive attempted to draw it out as best as i understand it. currently i only have 1 reject state and thats in A where it falls off

i am unsure if any others are needed, im currently testing it

ill send it in a moment so you can more clearly see my current understanding

it will be a little messy, i apologize for that

oh im stupid i dont account for only 0's on A even tho it should be possible

[glad dust]

okay im lowkey struggling to implement this ill come back to it later

[cedar kiln]

@glad dust Has your question been resolved?

[cedar kiln]

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[glad dust]

.

just gonna reclaim

[dull oxide]

@glad dust did you have a question?

[glad dust]

hello yes just some final clarification on this problem above:

this is the state diagram for it but

essentially

im working on creating a final description for the language that includes why the tm halts

i am now also realizing i do not reject a string that has exactly two times as many 1's as two's

[cedar kiln]

@glad dust Has your question been resolved?

[worldly chasm]

Sorry, I had to step away, I'm still afk, but I'll be back in a few hours

Minor personal emergency

[glad dust]

thats completely fine, ty for the help. i hope you sort out whatever came up without worry

[cedar kiln]

@glad dust Has your question been resolved?

[worldly chasm]

@glad dust state E should be more or less the same as state B, return to the start and then proceed to the next state (E -> A)

[glad dust]

what input would it transition on though?

[worldly chasm]

State E moves left and leaves the tape unchanged until it reads a _ then transitions to A and moves right

@glad dust

[glad dust]

like this then right

[worldly chasm]

Yup

Well, minus the bottom part

@glad dust

[glad dust]

oops i completely forgot to erase that thank you

i do have a question tho

[worldly chasm]

Hmm

[glad dust]

is it not necessary to account for potential inputs of solely 0's? shouldnt it be able to accept those? thats the last thing i wish to fix tho, id like the general meat of it sorted before doing that

[worldly chasm]

That would fail because it would fall off in state A

And that's correct behavior

[glad dust]

sorry, are you saying it woudl fail with the diagram as it is or it would fail the language in general? So am i mistaken in thinking it should pass? is it because no 1's and no 2's doesn't necessarily pass the requirement of " number of 1’s in w is less than twice the number of 2’s"? Then is my diagram complete?

[worldly chasm]

It both fails given your language and and with your turing machine state transition diagram

And failing is correct behavior

Reject

As in a string with no 2s should always fail

Be rejected

Not part of the language

@glad dust

I hope it's not too confusing, I'm making a bit of a mess with the explanation

[glad dust]

ah i understand okay

[glad dust]

no im getting it

then theres nothing else to update the diagram with, correct? my only qualms prior involved a lack of 2's but that was just me misunderstanding the language

[worldly chasm]

It should be correct but I will admit I didn't double check to make sure all of the "i"s were dotted and "t"s crossed

[glad dust]

nah theres no need for that, thats something i should do by running a bunch of test strings

i deeply appreciate your help and your time, i feel like my understanding of the subject has improved significantly. thank you

[worldly chasm]

You're quite welcome

Sorry for being a bit flakey

[glad dust]

i dont mind that at all, especially since you helped

im not entitled to peoples time

.close

[cedar kiln]

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[earnest fog]

f(x) = 2x^2 - x for x ∈ R. g(x) = 1/x for x ∈ R, x ≠ 0. find the domain and range of fg(x).

[earnest fog]

im stuck on finding the range of fg(x)

this is what I hv so far

I know that from the answer that the range of fg(x) is the same as the range of f(x)

why is this the case?

im so confused

[cedar kiln]

@earnest fog Has your question been resolved?

[earnest fog]

<@&286206848099549185>

[humble marsh]

what's the range of f?

[earnest fog]

f(x) larger or equal to -1/8

[humble marsh]

sorry, typo; I meant the range of g

[earnest fog]

x cannot be 0

[humble marsh]

ok, and what's the range of f when we remove 0 from the domain?

[earnest fog]

I hv no idea

[humble marsh]

as a hint, here's what the graph looks like

(the open circle at 0 means that value is excluded from the function)

[earnest fog]

oh ok

[humble marsh]

does that make sense?

[earnest fog]

kinda

what next

how does that help with gf(x)

[humble marsh]

(fg)(x), right?

[earnest fog]

yes

that’s right

[humble marsh]

g(x) takes on all values except x = 0, so fg(x) takes on all values that f(x) does when x isn't 0

[earnest fog]

yes

[humble marsh]

so what are all the values f(x) takes on when x isn't 0?

[cedar kiln]

@earnest fog Has your question been resolved?

[cedar kiln]

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[upbeat tusk]

Can someone help me with number 3 and 4

I totally forgot about coordinates and stuff

I just know how to calculate 💀

<@&286206848099549185>

[cedar kiln]

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[azure oriole]

Do anyone have any idea how to solve this integral ?

[austere ember]

you can't

like the antiderivative is nonelementary

[azure oriole]

Well it seemed like it was impossible but i wanted to ask someone just to be sure, it came up in one exercise i was doing, what you think would be the most appropriate answer for that ? Proof or just how you written "Antideriative is non elementary, so it cannot be solved"

[neon prism]

You could do it numerically

Depends on what the problem is asking

Oh wait that’s an indefinite integral oops

[azure oriole]

I did it for differential equations, but yeah i got kinda dumb when i had seen this

So i guess the only thing you could do is to expand that to taylor's or smth like that

[neon prism]

yeah

are you sure you did the rest of the problem correctly?

or there's no derivative or anything to "cancel" it out?

[austere ember]

it's difficult to prove that an integral is nonelementary

what's the original

[azure oriole]

It was second order differential equation at the beginning i will send it in a moment

[neon prism]

isn't that seperable?

[austere ember]

no

[neon prism]

ok it's officially too late for me to be up

going to bed haha

[azure oriole]

Oke hehe

Thanks for your help

I noticed what i did wrong

.close

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[crimson sedge]

I forgot how to do these, i need help with both questions

[crimson sedge]

Isnt first one just in q3 where sin and cos are neg and tan is pos

[crimson sedge]

Yeah ik these but im just stuck on the reference angles, reference angles are always positive right?

[past wave]

can you send the question again?

[formal prism]

yes, unless the sign is mentioned

[crimson sedge]

Is b jsut tan 45

[formal prism]

cos 130 = cos ( 180 -50 )

[past wave]

that should be negative because of this ^

[formal prism]

so, -cos 50

it's in 2nd quadrant

[crimson sedge]

Alr, i fixed that one. Is B pos tan 45?

[past wave]

which quad is 215 in?

[crimson sedge]

3

[past wave]

is tan +ve or neg in that?

[crimson sedge]

Positive

[past wave]

there you go

[formal prism]

no

[crimson sedge]

…

[past wave]

hmmm

[crimson sedge]

Im confused

[formal prism]

tan (180+x) = tan 215

[crimson sedge]

Yeah

[past wave]

so third quad? therefore pos?

oh got it

[formal prism]

yea, cause tan, but the value is incorrect

[past wave]

yup

i guess you have this handled
ill leave

[crimson sedge]

I did 270-215

Instead of 180-x

I mean

215-180

So its tan 35

Then

[formal prism]

yes

[crimson sedge]

I also didnt know how to do this

Can we just assume that a/sin(a)= b/sin(b)

Cus of the sine rule

[formal prism]

let me tell you this

when you do these type of ques

use integral value of pi

what is sin (90+x)?

[crimson sedge]

1+x?

Pi/3 +x

[formal prism]

nothing to assume, that is the way to do it

[crimson sedge]

Idk what u mean by integral value

Exact value?

Or radians?

[formal prism]

integral value means integer values

[crimson sedge]

Oh

[formal prism]

like 1, 2,3, -1

[crimson sedge]

Is it 1+x

[formal prism]

no

[crimson sedge]

Idk what it is

[formal prism]

90+x is inside the bracket

sin ( 90+x) = cosx

[crimson sedge]

Ive never learnt this 😭

Either that or im losing my memory

[crimson sedge]

Why do it this way?

[formal prism]

caus the values are same

[crimson sedge]

Does that work for any degree or just 90

Also idk how to use that to solve this problem

[formal prism]

https://byjus.com/maths/trigonometry-angles/

might help

[crimson sedge]

I know how to do this on my hand like their exact values and stuff

[formal prism]

no no, scroll down

[crimson sedge]

I was just stuck on this question

[crimson sedge]

Oki

One sec

[formal prism]

check out the supplementary angle part

[formal prism]

.....

the formula is correct

use it

[crimson sedge]

I screenshotted those

Thank u

But i dont get

The part where it says b is obtuse or acute

[formal prism]

do more questions on that to get it

ahh, check some video out on yt

[crimson sedge]

Is it hard to explain?

[formal prism]

https://youtu.be/wT4xMAssvDk?si=LkXBWSLd56VUUNzt

[crimson sedge]

I got the acute value correct

[formal prism]

finally found a video for you

[crimson sedge]

Is the obtuse just 180-acute value?

[formal prism]

for me yes, it took me sometime to understand this topic myself

[crimson sedge]

Ah its ok ty

I will watch the video

I am just doing revision

Not the first time i learnt it i just forgot

[formal prism]

happens

[crimson sedge]

Thank u a lot

[formal prism]

anything greater than 90 is obtuse

less than that is acute

90 is right angle

[crimson sedge]

Yeah

Its ok i just have a few questions left ill see if i can figure them out, i appreciate the help a lot, ill close this now so others can use it

.close

[cedar kiln]

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[cedar kiln]

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[tawny cape]

Help please i need a guide to get started

[cedar kiln]

@tawny cape Has your question been resolved?

[tawny cape]

@help

@helper

<@&286206848099549185>

.close

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[storm fog]

I din't understand this, I mean, how did this solution come to the conclusion that x must be different from 1/2 and -1/2?

[hazy dawn]

Because you can't divide something by 0

[storm fog]

I understood the whole simplification, but not the conclusion

[storm fog]

Oh

So, after the simplification, the only way to solve this was changing the "x" with the alternatives values?

[hazy dawn]

If you notice -1/2 or 1/2 are both the value that make denominator 0

[hazy dawn]

And divide by 0 does not make sense

[storm fog]

Thank you, now I understand

[hazy dawn]

Welcome

[storm fog]

.close

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[gloomy spire]

How do you multiply radicals like 2√8•√2

[past wave]

root(a) * root(b) = root(ab)

if both a and b are pos

||or one of them is negative||

[gloomy spire]

Whats pos?

[past wave]

positive

[gloomy spire]

Imma try

[past wave]

to know why
$a^m * b^m = (ab)^m$

[wraith dagger]

George (Wumpus Man)

[gloomy spire]

So 2√16?

Can i still simplify?

[past wave]

yes you can

[gloomy spire]

So 2√4?

[past wave]

nope

[gloomy spire]

2√4²?

[past wave]

yes

what will that simplify to?

[gloomy spire]

Im done with math

Its so tiring

[past wave]

loll

what does root mean?

ping me when you reply

[gloomy spire]

Hm

Im now currently on no 2

√3•³√3

@past wave

[past wave]

hey

what does that mean?

[gloomy spire]

Wdum

[past wave]

root three * (root three)^3

or cube root three

[gloomy spire]

No

Cube root 3

And square root 3

[past wave]

express root and cube root in terms of exponent

[gloomy spire]

3¹/² and 3¹/³

There

[past wave]

yup

now what does a^m * a^n become?

[gloomy spire]

Now wut

[gloomy spire]

Whered you get m and n

I guess maybe a^m and a^n

Maybe exponent them then butterfly method?

[past wave]

i was just trying to generalise

[gloomy spire]

U mean?

Could that work?

[past wave]

i dont know what that is

[gloomy spire]

What part?

[past wave]

ok tell me this 3^4 * 3^5 = what?

tell me in terms of powers of three

[gloomy spire]

Huhhhh

Maybe 9^9?

@past wave

Yo

[past wave]

nope

3^(4+5)

the exponents add if base is same

[gloomy spire]

Whats the answer then?

3^9?

[gloomy spire]

Yoooo

[past wave]

hello

[past wave]

nope that was an example

[past wave]

use this

[past wave]

here

[gloomy spire]

So 3²/⁵?

Or 3¹/⁵

[past wave]

💀

[gloomy spire]

Wut

[past wave]

do you know how to add fractions?

[gloomy spire]

I forgot

[past wave]

revise and come back

[gloomy spire]

Ohhh

Butterfly method

3⁵/6

3⁵/⁶*

@past wave

[past wave]

that is correct

nice

[gloomy spire]

Now?

Do i make it radical?

[past wave]

i think that is the answer

[gloomy spire]

I now have ⁶√3⁵

Now what

[past wave]

done

[gloomy spire]

I finished it

[past wave]

nice

[gloomy spire]

Now I'm in no 3

[past wave]

ohh

!1q

[cedar kiln]

It is suggested that you limit yourself to one question per help channel, opening a new one once your original question is answered and your original channel has been closed. This is to make your channel easier to follow for potential helpers and can bring attention to the fact that your question has changed.

[gloomy spire]

Can i close then just chat again?

[past wave]

if you close

then the channel will be hidden in a few mins

but yeah you can chat

its like a ticking time bomb
can close any time

[gloomy spire]

Alrighty

.close

[cedar kiln]

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[cedar kiln]

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[crimson sedge]

help

[cedar kiln]

@crimson sedge Has your question been resolved?

[crimson sedge]

<@&286206848099549185>

[nimble veldt]

!status

[cedar kiln]

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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[cedar kiln]

@crimson sedge Has your question been resolved?

[crimson sedge]

1

[pearl cipher]

whats the total number of people

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

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[midnight bramble]

Been trying to get my head round this but dont understand what im meant to do

[midnight bramble]

I think the weakest is C while strongest is B

Unsure if C can be the weakest as it would be a scatterplot with no correlation?

[cedar kiln]

@midnight bramble Has your question been resolved?

[midnight bramble]

<@&286206848099549185>

someone please help :)

[steel crest]

A has negative correlation since it is downwards

[midnight bramble]

but is it weak correlayion?

i got this

but am unsure about it

[steel crest]

Looks correct

[midnight bramble]

i kind of just eyeballed it for the values

would there be a better way to confirm?

[steel crest]

I mean you can put the data in excel, but I think they wanted you to eyeball

[midnight bramble]

could you teach me how to use excel for it please?

[steel crest]

U would need a scale and a lot of time, than you could technically measure all the data, to calculate the correlation,but I am pretty sure that is not what they want you to do

[midnight bramble]

Ok thanks!

@steel crest Is it something like this?

[steel crest]

Yes

[midnight bramble]

I know you said i shouldnt need to do it, but i like learning excel stuff

for some bizarre reason...

[steel crest]

I would just write the summation instead tho

[midnight bramble]

How would i go about doing that?

[steel crest]

First keep a cell for the x mean and y mean

Create rows which are x - x mean and y - y mean

Keep a cell for their variance

Keep rows multiplied by 1/variance

And then just take mean of product

[midnight bramble]

I shall try follow these steps as best i can

i remember doing something similar though

[midnight bramble]

i got up to this step and am unsure what to do

i may have made a mistake

[steel crest]

on sec

lemee show you

[midnight bramble]

:) thank you for taking the time to teach me

i appreciate it a lot

[steel crest]

so the values in E are the square of the values in C and the values in F are the square of the values in D

[midnight bramble]

for columns c and d

[steel crest]

the variance is the sqrt of the average of the values below it

yes?

[midnight bramble]

are you taking x value and subtracting the mean of all x values?

[steel crest]

yes

Ik this seems more complicated, but i like it more cause it gives me a feel of what is going on

[midnight bramble]

i too like excel as it makes things make more sense rather than learning formulas and stuff

i rummaged through some of my excel files and found this

[steel crest]

looks similar

[midnight bramble]

is it the same principple for column F and cell J8?

[steel crest]

Idk what cell J8 is in your sheet

[midnight bramble]

oh sorry i forgot to put that part in

[steel crest]

yeas, it is the same thing

[midnight bramble]

ah sweet

[midnight bramble]

i shall try learn this way of doing it as it seems clearer

[steel crest]

thanks

[midnight bramble]

:) thanks for sharing your knowledge

[midnight bramble]

for columns G, H and I, whats the reasoning behind doing it?

[steel crest]

those are normalised values

I is for their relation

so when are both are negative they are both below mean

and their product would tell me how related just those 2 values are

[midnight bramble]

what do you mean by "normalised values"

[steel crest]

i think it is called Z score

[midnight bramble]

oh not Z score

that scares me

When i do this part

I get this

is there something im missing?

this one shows the "formula" i entered

Using the excel feature (analysis toolpak, correlation, ...) i got this

Forgot that was a thing tbh

though not sure how to read it haha

[midnight bramble]

i tried to "reverse engineer" what you did in column G, but dont know how you got that value?

[steel crest]

vraince is the root of the average of the squares

maybe you just put average of the sqyares?

[midnight bramble]

hmm, ill double check what i did, thanks

[steel crest]

I have to go now

[midnight bramble]

:(

thanks for all the help mate

[steel crest]

Welcome

[midnight bramble]

just repasting it so i dont have to scroll up

Hey @steel crest , i know you have gone, but if possible could you give the formulatext for columns G, H, and I please so i can understand whats behind it?

[steel crest]

I am still here for a bit, also
G3 = C3/E$2

[midnight bramble]

OHH

[steel crest]

I extend that till H

[midnight bramble]

You are taking the average of rows E and F, thats what cell E 2 was

[steel crest]

I3 = G3×H3

[midnight bramble]

i cant thank you enough! I thought i was stupid or going crazy

[steel crest]

E2 is root of average of row E

Welcome

[midnight bramble]

so E2 would be something like
=Sqrt( A)
A = SUM(E)/COUNT E?

or is there no need to do that second line and go straight to
=Sqrt(SumE/Count E)

After some time i finally got it

Thanks a lot @steel crest ! :)

[steel crest]

Welcome

Welcome

[midnight bramble]

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[pallid barn]

Can somebody explain why the answer to 2 is C(16,9) and not C(17,9)?

[pallid barn]

<@&286206848099549185>

[scenic stirrup]

its been 5 seconds chill with the ping

[pallid barn]

MB, I just figured that I ping when I have a question

[solid juniper]

why do you think it’s 17 choose 9?

[pallid barn]

I used the combination with repetition formula

Because there are 8 groups to choose from, I can format it as

x1+x2+...+x8 <= 9, as there are at least three already chosen

[pallid barn]

Then, because x1+x2+...+x8+x9 = 9 is equivalent to that inequality, I just found C(9 + 9 -1, 9)

17 choose 9

[solid juniper]

do you mean = 9?

[pallid barn]

No, because it says at least three

Wait...

I'm stupid

[solid juniper]

well there are different ways you could set it up but i think this is the easiest way to look at it

[pallid barn]

If 3 are already chosen... that just means there are 9 possible choices left.

[solid juniper]

yes

[pallid barn]

Okay, thank you

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[scenic stirrup]

why does it say C(17,9) in the problem text

[solid juniper]

i think that’s his answers

though it does look like a weird place

[scenic stirrup]

nvm my arithmetic needs work

[solid juniper]

[scenic stirrup]

im thinking of it as a stars and bars problem so $\binom{8+9-1}{9}$

[wraith dagger]

Vѳrtєx-

[solid juniper]

yes

[scenic stirrup]

yea i was tripping 8+9-1 is 16

oopsies

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[fickle viper]

Any optimization fans?

[graceful wyvern]

You need me to help?

[cedar kiln]

@fickle viper Has your question been resolved?

[fickle viper]

Yes please

if you know how to solve it

[ripe siren]

so do you know how the gradient works?

[fickle viper]

Yes, it is the derivative but a column vector

[ripe siren]

yea in optimisation its the opposite, but oh well

[fickle viper]

I think the gradient of y is grad F(x) + c(x-y) ? Not rly certain

because I have to expand it which makes it more complicated

[ripe siren]

yes

[fickle viper]

Oh rly? nice

[ripe siren]

oh wait actually no

[fickle viper]

I was nervous because chatgpt gave me different

[ripe siren]

its grad F(x) + c(y-x)

[fickle viper]

Why is it y-x?

[ripe siren]

because of chain rule the inside flips

[fickle viper]

????

(x1 - y1)^2 + ... + (xn - yn)^2

[ 2(x1 - y1) (-1)

OH

BECAUSE OF THE -1?

[ripe siren]

yea

[fickle viper]

Im so dumb

LOL

It all makes sense now

Hm but then after the gradient what do we get?

That is sad, I thought chat gpt should not be trusted haha

Psychological warfare

[ripe siren]

now set grad g(y) to zero,
grad F(x) = -c(y-x)
multiply by grad F(x) ^T both sides

ie take the norm both sides

then you get
|grad F(x)|^2=c^2 |y-x|^2

[fickle viper]

How is it grad F(x) = c(y-x) after setting grad q(y) to 0, because grad q(y) = grad F(x) + c(y-x)? so we are missing a negative?

grad F(x) = c(y-x)

you mean - grad F(x) = c(y-x)?

[ripe siren]

so the critical point obtained is when |y-x|^2=|grad F(x)|/c^2
plug that into the equation of q(y)

oh mb

but taking the norm, leads to the same place

[ripe siren]

yea I fixed it

[fickle viper]

How does multiply by grad F(x)^T both sides mean that we take the norm of both side

Because c(y-x) is not like grad F(x)^T at all

[ripe siren]

multiply by grad F(x)^T on the the right, is same as multiplying -c(y-x)^T to the right

[fickle viper]

Ohh because of the equality

[ripe siren]

ye

[fickle viper]

Oj yeah

so basically take the norm

wait not the norm but the norm squared*

.../

[ripe siren]

ye

[cedar kiln]

@fickle viper Has your question been resolved?

[fickle viper]

How do I plug that into the equation of q(y)?

it seems like chatgpt give a simpler solution, just solve for y?

reference

[fickle viper]

i think i understand, now i wonder how to do c and d?

[fickle viper]

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[agile bear]

https://gyazo.com/f6683ec3a4bbf7070865bfab8161dcff I subtracted used the formula for the area of a circle and divided it by 2

[agile bear]

why is it wrong?

8pi - .5pi = 7.5pi?

[untold blade]

the first semicircle area is pi/2 then u subtract the quarter of a circle which would be -pi(2)^2/4 which is just pi

so pi/2-pi

oh shoot

other way around -pi/2 + pi

😭😭

[sweet knoll]

isn’t it 1.5pi or am I tripping

wait..

0.5pi

[agile bear]

but the integrals from 4 to 1

so

wouldnt i

ohhhhhhh it would be a quarter of the circle

shit ur right

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[agile bear]

bro isnt that just pi/2

.reopen

[cedar kiln]

✅

[agile bear]

https://gyazo.com/2c165ea28168768294e292c79f8ecba2

it is still incorrect for whatever reason unless im tripping

@uncut veldt

[ancient lodge]

?

Area of the quarter circle from 1 to 2 is pi/4, area of the quarter circle from 2 to 4 is pi

pi - pi/4 = 3pi/4

[agile bear]

wait so

we wont take a quarter of the area for the second circle?

[ancient lodge]

you do

but idk why you subtracted pi/2

that's the semicircle, not the quarter circle

[agile bear]

ohhh

wait

i got the scaling of the graph wrong

thanks

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[mental storm]

Could someone explain how I can determine concavity (part c)? Would I need to find f double prime or is there some easier way

[mental storm]

NVM

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[heavy ferry]

I don't quite understand this question. I have already determined the two functions to be 1+5^x and 4x+2, but I do not understand how the sum of these functions has a maximum of any kind.

[heavy ferry]

hold on im dumb i thought that was a plus

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[fossil coral]

What did I do wrong?

[drifting marlin]

a_3 = 3(3!)

what is 3!?

[fossil coral]

ohhh

3! = 321

3x2x1

ok

a_4 = 3 x 4 x 3 x 2 x 1 = 72

[fossil coral]

thank you.

[fossil coral]

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[daring rain]

When deriving implicit function systems like this, does one need to take the absolute value of the jacobians' determinants, or just the determinants?

[hollow trail]

it should just be the determinants, no absolute value

[pearl cipher]

yes use the determinant directly

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[daring rain]

thank you!!

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[fickle viper]

Is log(1+e^x) strongly convex?

[pearl cipher]

define strongly convex

[fickle viper]

@pearl cipher whats up brother

LOL

second derivative > 0

But idk, becuase I have the second derivative, and not sure

It gets close to 0 but like

does it get to 0.

im gonna copy it to the other one

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[livid hound]

Could someone please give me a visual representation (like a desmos graph or drawing) of each choice 🙏🏻. I’m confused on what they mean

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[olive briar]

E[XAdele​]=n×pAdele​?

is this the answer

since the random variable XAdele represents the number of votes Adele receives out of naudience members. Each audience member independently votes for Adele with probability pAdele

so it follows bionomial ?

[long swan]

yes, by linearity of expectation

[olive briar]

and this is Multinomial distribution?

so it wouldbe

n!/(i! * j! * k!) * P^i * P^j * P^k ?

[olive briar]

for C) is just using the pdf func
and get 0.0945
d) is Binomial distribution with n=8 and pAdele=0.5 right? 0.21875
e) Given XAdele=3 , the remaining n′=5 votes are distributed between Lizzo and Taylor. The conditional probs are

p lizza = 0.3/0.5 = 0.6
p taylor = 0.2/0.5 = 0.4

then P(XLizzo​=3,XTaylor​=2∣XAdele​=3)=5!/(3!2!)​×(0.6)^3×(0.4)^2 = 0.3456

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[short spade]

What is the word used to describe both the bottom and top of a an object f.e a cube? Like how all sides can just be called "sides"

[vivid wadi]

for a prism those are called the bases

but depends on what you mean by top and bottom

you can make any side in any position by rotating the object

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[idle tusk]

faces?

[fair geyser]

faces includes sides

there's no word

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[lucid pendant]

Is the degree of an expression given by the EXPONENT?

[teal wraith]

yes

but if there are more than 1 terms u add

like 7z^2+ 5z^3 is 5

[lucid pendant]

thx

[coral jewel]

polynomial?

yes, the degree of polynomial is the exponent of the term with highest power

[lucid pendant]

If two lines are perpendicular is the product of the gradient then -1?

[vivid wadi]

what do you think?

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[lucid pendant]

I do think this is correct, the part PRODUCT OF THE GRADIENT THEN -1 I filled in myself

.reopen

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[hearty sluice]

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[ocean thicket]

If I know an object is X distance away from me, and I can count the pixels it moves in a photo horizontal from where it was to it’s new end point, how do I calculate it’s speed

[vivid wadi]

do you know the time difference between the photos?

[ocean thicket]

Yes.

5.03 seconds

[vivid wadi]

You can directly find the velocity in pixel/second

then convert pixel to the measure youre using

[ocean thicket]

Distance to the thing is about let’s say 5 km, pixel movement is about… just gonna estimate 250 pixels or so?

Like starts 5 km away, moves to the right 250 pixels in 5.03 seconds

Not sure how to calculate that speed

[ocean thicket]

No idea how to do that

It’s for a dumb project

[vivid wadi]

so you're saying
5km = 250 pixels
and it moves 250 pixels in 5.03 seconds right?

[ocean thicket]

No.

Like I know an object is 5km away from where I am standing

Got a camera with it

It moves 250 pixels straight to the right in 5.03 seconds

[vivid wadi]

does the object start centralized in the middle?

[ocean thicket]

Not sure what you mean

[vivid wadi]

like in the middle of the screen

[ocean thicket]

Yes

Straight on from me

Like it’s basically a floating ball - not a ufo before thinking I’m crazy - that I know from where I am standing is 5 Km from me, then it moves straight to the right 250 pixels

It doesn’t really appear to change size either

[vivid wadi]

so like this yeah?

250px*

you have that the velocity is (150/5.03)pixels/second, but i dont think there is enough info to find out much how a pixel is

[ocean thicket]

If I knew the diameter of the ball could you know?

Like if the ball took up say 2-5 pixels and I knew it to be a foot wide?

[vivid wadi]

yeah you could

[crimson sedge]

Do you like goyda?

[vivid wadi]

5px = 1 foot then 1px = 0.2 foot

(250/5.03) px/s = (250/5.03)*0.2 foot/s

[crimson sedge]

I like Breaking Bad

[vivid wadi]

who dis

[crimson sedge]

we can say that this is a Russian division

I from Russia

[vivid wadi]

um

maybe try #discussion or #chill

[crimson sedge]

Да без б

[vivid wadi]

não falo russo meu parceiro

[vivid wadi]

and the other bound if you assume 2px = 1 foot is (250/5.03)*0.5 foot/s

so from 9.94foot/s to 24.85foot/s, using those assumptions

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[crimson sedge]

hey guys whats wrong with this basic algebra??

[crimson delta]

when you "move" the 50 like that, what you actually are doing is dividing both sides of the equality by 50

but you didnt divide the 200 by 50

[crimson sedge]

Ohhhhh

I see that makes a lot of sense

thanks dena!

[crimson delta]

in general I would recommend to always think of it as adding/subtracting/multiplying/dividing both sides by the same number

instead of "moving" some number

[crimson sedge]

yeah i just realised that

i been doing it wrong my whole life

xD

you need to understand what you're doing

[crimson sedge]

thats true

thank you guys btw

take care

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[crimson sedge]

I plan on getting deeper into maths soon so I will understand better eventually

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[azure swift]

This channel will lock, open a new channel

[inner ingot]

sure

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[peak spruce]

hey, i couldnt figure out what should I do here

[dreamy void]

substitution x = sin(theta), apply long division to get the quadratic

[peak spruce]

thank you

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[cedar kiln]

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[lavish isle]

How can i shorten case 1 and 2?

[cedar kiln]

@lavish isle Has your question been resolved?

[lavish isle]

<@&286206848099549185> sorry to bother?

[cedar kiln]

@lavish isle Has your question been resolved?

[cedar kiln]

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[crimson sedge]

Solve for x

Idk where to start

[dusk finch]

this looks pretty tough

[crimson sedge]

yes it's weird af

[dusk finch]

is this a regular question?

Or some kind of bonus / challenge question

[crimson sedge]

Regular

[dusk finch]

,w solve sqrt(x-1)+sqrt(3-x)=x^2-4x+5

[wraith dagger]

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Requested by methisalwaysright

[dusk finch]

okay, there is probably not a nice way to get the sols algebraically

so I will go with my way

[dusk finch]

Try looking at the domain of the LHS

[crimson sedge]

x is greater or equal than 3

[dusk finch]

if x is greater than 3, then 3-x is gonna be negative

and you cant have a negative number in the root

[crimson sedge]

oops yes

x is lower or equal than 3

[dusk finch]

there is one more condition

[crimson sedge]

and greater or equal than 1

[dusk finch]

Yeah

so 1 <= x <= 3

that's a pretty small domain

if there is a solution, it's somewhere within this domain

now it would be pretty useful to get the range

[dusk finch]

Btw what's your mathematical background? Do you know some calculus or precalculus? Would you be able to sketch both functions (The RHS and the LHS)?

[crimson sedge]

like draw the graphs?

[dusk finch]

Yep

[crimson sedge]

maybe for the right side only

and i dont know calculus

[dusk finch]

okay

for the LHS, what's the value for x = 1? And for x = 2? And for x = 3?

you could get at least an approximate sketch

just by somehow joining these 3 points

[crimson sedge]

for x=1 it's sqrt of 2

for x=2 it's 2

for x=3 it's sqrt of 2

[dusk finch]

okay, cool

this is how an approximate sketch would look like

Few key things to note:
The graph of LHS has to be symmetrical around x = 2. To see it, You already saw that f(1) = sqrt(2) = f(3). You could also try to see if f(1.5) = f(2.5) to verify it

The most important thing is perhaps that those 2 graphs touch at (2, 2)

which means that at x = 2, they're gonna be equal

and thus x = 2 is a solution

[crimson sedge]

thank you very much

[dusk finch]

showing that there is no other solution would be probably pretty tough without calculus, but I think it makes some sense intuitively

[dusk finch]

It's a really hard problem btw, dont worry too much about it

[crimson sedge]

hopefully i won't get one like this on the test

[dusk finch]

if you wanted to solve it in the normal way, you would get an 8th degree polynomial

which is basically unsolvable by hand

so the only way here was guessing the root

[crimson sedge]

thanks again

.close

[cedar kiln]

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[cedar kiln]

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[sinful harbor]

Im so confused on every step of this please help me

[boreal light]

well you are integrating from f(x)=0 to a

[sinful harbor]

I factorised it first

[native heath]

!status

[cedar kiln]

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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[native heath]

also 'entirely on graphical or numerical methods'? what do they want from you

[boreal light]

ig everyone is here, i will take my leave xD

[sinful harbor]

Like I can’t use a calculator only

[runic garnet]

they want integration utilized

[mellow isle]

integration yay

[sinful harbor]

2

[runic garnet]

@sinful harbor what have you tried

[native heath]

...isn't integration 'numerical' lmao what

[native heath]

show work

[boreal light]

no

[native heath]

oh

okay ig

lmao

[sinful harbor]

And I know that I need to set that to equal 10

[native heath]

uhh what's this

[sinful harbor]

But idk the limits

[native heath]

it's a to 0

[runic garnet]

ok good

[sinful harbor]

Why 0

[runic garnet]

now what do u think

[sinful harbor]

I know the upper limit is a

[native heath]

oh hm it's not 0

[sinful harbor]

Idk the lower limit

[runic garnet]

u just solved for the lower limit

[native heath]

just put from wherever it's positive

yeah she solved for that

[sinful harbor]

What 8?

[native heath]

oh that's what she did

[runic garnet]

try it

find f(8)

see what u get

(if u want to double check)

[sinful harbor]

With the lower limit as 8 and the upper limit as a?

[runic garnet]

yea

[sinful harbor]

Ok I’ll try that ty brb

[native heath]

yeah

[runic garnet]

$\int_8^a x^{\frac 13} - 4x^{-\frac 13} , dx$

[native heath]

that integral looks wrong

[native heath]

!occupied

[cedar kiln]

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).

[native heath]

oh ok

[native heath]

that integral cant be right

[runic garnet]

how so

[sinful harbor]

Now if I made that equal 10 how tf do I solve that

Im so confused im only 16 why so hard

[native heath]

i meant for her image

[native heath]

you didn't integrate it... at all

[runic garnet]

yea whats wrong about that

[sinful harbor]

Ohhh

Im an idiot

I forgot to integrate

One second

[native heath]

...did she integrate it-

lmao yeah

[runic garnet]

no im saying whats wrong with the integral

[native heath]

i meant her integral solution ;-;

it's fine

[runic garnet]

ohh ok i see

[sinful harbor]

Does that look ok

[runic garnet]

u shouldnt put the integral symbol again after you integrate

its not correct when you do that

[sinful harbor]

Oh ok mb but if I got rid of that

Then where do I go after that

[runic garnet]

simplify

[sinful harbor]

Ok

[native heath]

uh

yeah apart from the integral sign

put limits

[sinful harbor]

I did below

[runic garnet]

also drop the dx after u do the integral

[sinful harbor]

Ok ty

[runic garnet]

doesnt make sense to keep it after you integrate

[sinful harbor]

Im stuck in how to simplify

Cuz I have a

[native heath]

you should have a single term in a no

i cant read it though

too small

[runic garnet]

simplify the numbers in the right parentheses

[sinful harbor]

Oh ok I’ll make bigger

[runic garnet]

whats 8^(4/3)

[sinful harbor]

16

[runic garnet]

times 3/4 ?

[sinful harbor]

12

[runic garnet]

ok so

(0.75 a^(4/3) - 6a^(2/3)) - (12 - something)

what does something equal

[sinful harbor]

I think it’s -12+24

[runic garnet]

• 24 ?

oh after u distributed the -

[sinful harbor]

Mhm I’ll show u what I did?

[runic garnet]

good

(0.75 a^(4/3) - 6a^(2/3)) - 12 + 24

[sinful harbor]

Idk what to do with the a’s

[runic garnet]

what is that whole thing equal to

[sinful harbor]

10

[runic garnet]

good

(0.75 a^(4/3) - 6a^(2/3)) - 12 + 24 = 10

now what

[sinful harbor]

Make the bits with a’s equal -2

[runic garnet]

yes

(0.75 a^(4/3) - 6a^(2/3)) = -2

now what

[sinful harbor]

Factorise maybe idk

[runic garnet]

no

[sinful harbor]

I need to get the as by themselves I think l