help-0

[spiral lily]

-2 is in the range

f(3)

[fringe rune]

sorry im just barely taking college algebra after years of not touching math so alot of this is new to me

wdym by f(3)

[spiral lily]

y=f(x) is the graph

for x=3 what is the y value

[fringe rune]

idk, sidenote- they do want interval notation for the answer though

[warm quarry]

okay so you agree -2 is in the range?

what bracket do you use if it is a closed or open interval?

[fringe rune]

id think -2 is open so therefore I use ( is that right?

[warm quarry]

so if it is open we can see this as:

(-2,0] <=> -2<y=<0

[warm quarry]

if it was open yes, but f(3)=-2 so -2 is also in the range

so (a,b] means a is not in the interval included but b is included

[fringe rune]

ohhhh okay

so for future circumstances, atleast at this basic level, if it ends in closed its all []?

im confused where or what the f(3) is

[warm quarry]

aaah okay let me help you with that first

do you know what f(x) means?

[fringe rune]

yeah i can plug anything into the x and it fills the x for the rest of the equation?

[warm quarry]

yes it gives us an function value at a certain x

now if we say f(3), this means we will use x=3 so it will fill in 3 for all x in the rest of the function

if you look at the graph, at x=3 we will some value y, which one do you think that is?

[fringe rune]

oh like the middle of the graph is x=3 so the bottom point from there is -2?

[warm quarry]

yes

so f(3)=-2

[fringe rune]

thank you so much

i understand that part now

[warm quarry]

okay

so since f(3) gives us -2

-2 is IN the range of the function

you understand that?

if it was like -1,99999999999 it wouldnt be in the range

[fringe rune]

okay

[warm quarry]

if it was in the range what bracket would u use?

and if it wasnt what then?

[fringe rune]

if in range [, if not ( ?

[warm quarry]

exactly

[fringe rune]

ohh so its [-2,0]

[warm quarry]

yup :)

[fringe rune]

thank you so much!

have a nice night

or day lol

[warm quarry]

thank you! you too

[fringe rune]

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[slow portal]

I need to write a lambda function that's bijective, from [0,1] U {2} to [0,1] and I have no idea how to

[little drum]

$x \mapsto \frac{x}{2} \forall x \in \left {\frac{1}{2^n}\right } \forall n = {-1, 0, 1, 2, \cdots}$

[little drum]

x -> x ow

@slow portal You were not able to write the function after the advice?

2 -> 1
1 -> 1/2
1/2 -> 1/4 , is x -> x/2 for all x in {2, 1, 1/2, ...}

you only had to change from roster form to set builder form

btw you'll still have to show why this is bijective ^^" Gl

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[alpine sable]

Let $\gamma: I \subseteq \mathbb{R} \to \mathbb{R}^n$ be continuous on the interval $I$ and let $t_0$ be an accumulation point of $I$. If the limit $\lim_{t \to t_0} \frac{\gamma(t) - \gamma(t_0)}{t - t_0} = \mathbf{L}$ exists, then are the following calculations correct?

$$
\begin{align*}

\lim_{t \to t_0} \frac{||\gamma(t) - \gamma(t_0) - (t - t_0)\mathbf{L}||}{|t- t_0|} &= \lim_{t \to t_0} \frac{ |t-t_0| \cdot \left|\left|\frac{\gamma(t) - \gamma(t_0)}{t-t_0} - \mathbf{L}\right|\right|}{|t- t_0|} \

&= \lim_{t \to t_0} \left|\left|\frac{\gamma(t) - \gamma(t_0)}{t-t_0} - \mathbf{L}\right|\right| \

&= \lim_{t \to t_0} \left|\left|\lim_{t \to t_0} \left( -\frac{\gamma(t) - \gamma(t_0)}{t - t_0} + \frac{\gamma(t) - \gamma(t_0)}{t-t_0}\right)\right|\right| \

&= \lim_{t \to t_0} ||\mathbf{0}|| = 0

\end{align*}
$$

[ocean seal]

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

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[noble oar]

I did part a here but I don't know how to do part b

[noble oar]

I did this but it doesn't look right

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@noble oar Has your question been resolved?

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[turbid field]

Given the graph of f(x)
How many vertical asymptotes does g(x) have?

[turbid field]

the lim of g(x) is too complex

is there another way?

[still prism]

what is f(x)?

[turbid field]

a 3rd degree function

[still prism]

did you just got the graph or can you give me the function itself?

[turbid field]

the problem statement just have a picture of it

i did try to solve the equations

but there are only 3 of them

and i got a = d/9 - 1/2, b = 7d/9 -3, c = 5d/3 - 9/2

i used geogebra to make a slider of d and found out that d = -5 is the best match of the picture

[still prism]

ok

so first we need to find any places that might have problematic behaviour

like dividing by 0

[turbid field]

you mean the roots of the denominator?

[still prism]

yes, but there are more, every point that is not defined

[turbid field]

wait

so g(x) equals to this

f(x) = 0 when x = -3 or x = x0 (x0 > -1)

but x = -3 is also a root of the numerator

so does it cancel out?

[fierce cipher]

Hint:

• Based on the graph:
  f(x) = a(x-b)(x+3)^2, for a<0 and -1<b<0
  f(x) - 2 = a(x+1)(x-c)(x-d) for c,d < -1
• Factorize both numerator and denominator, cancel out the similar terms and count how many terms left in the denominator. Also don't forget x^2+x≥0

[turbid field]

người VN ạ?

[fierce cipher]

👍

[turbid field]

em mới học nên thắc mắc chỗ này xíu

x = -3 là nghiệm của cái mẫu nhưng cũng là nghiệm của tử
em vẽ lên geogebra thì thấy nó có tiệm cận là -3 :>

ảo quá nên em mới lên hỏi

[fierce cipher]

nếu rút gọn mà bên dưới vẫn còn x+3 thì x=-3 vẫn là tiệm cận đứng

[turbid field]

ủa

em bị mù

x = -3 là ko phải nghiệm đơn

:>

[fierce cipher]

quan trọng là bên trên chỉ có (x+3) còn bên dưới có tận (x+3)^2

[turbid field]

nãy em ko thấy

cảm ơn ạ

thank you @still prism

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[noble oar]

.reopen

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[neat raft]

hello, how do i find y without trigonometry?
x is easily 8 cm

[junior kraken]

!show

[lone heart]

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

[neat raft]

what do you mean show?

[junior kraken]

Is PT tangent to the circle ?

[neat raft]

i mean for x we can just use pythagoras

yes

it's tangent to the circle

[junior kraken]

,calc sqrt(16 + 16*3)

[final olive]

given that you say x=8 then using the common knowledge that the side opposite to 30 degree angle is half of the hypothenuse we get it

[junior kraken]

Without trig 😕

[final olive]

that's not trig

that's common sense

[neat raft]

yeah ive seen this one as well

but if there are no other explanations then that's okay

[final olive]

i learned it in like 5th grade or something

[junior kraken]

Trig is the tool to establish relation between sides and angles

[neat raft]

cause im teaching this kid and he's not learned trig yet lol

[final olive]

well i don't know what you want then

not possible to simplify further

[deep karma]

I need help on 12, and 15, I'm unsure of 12, in 12, the x = 1 but I don't know how to get the angle K and on 15 I'm completely stuck and don't know how to solve it pls help

[little drum]

without trig,
OP = 8. Draw center of OP call it M => OM = OT = TM [M is circumcenter] => TOP = 60° => y = 30°

[final olive]

open a new channel

[deep karma]

Teach me how,.,.,

[little drum]

!help

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To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[neat raft]

just use the help ABOVE without the name

[deep karma]

Ok thx

[neat raft]

ok let me see this but thank you

[little drum]

"but" ? did you not get it?

[neat raft]

no i mean like im a bit busy rn, i will check in a few minutes

so thank you

for the help

[little drum]

Alr sure

Also, be patient with the kid I like teaching kids math and ik how it feels lol

[neat raft]

yeah man hahaha

[neat raft]

but i never get mad when teaching, appreciate the advice

[little drum]

that looks complicated XOR

OP = 8. Draw center of OP call it M => OM = OT = TM [M is circumcenter] => TOP = 60° => y = 30°
should work

[junior kraken]

I also thought of extending OT to an external point K such that OT = TK

Congruency could be proved and then from height we could have said, that it's equilateral

[little drum]

that's actually better, no need to prove anything cause by Pythagoras you have PK = 8 = OK = OP

So, OKP is equilateral

[junior kraken]

This is really good!

I was too focused at angle P !

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[neat raft]

thank you for the help fellas

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[soft rapids]

I need some helppp

[soft rapids]

runn

I know my x = 2

I put 2 in place of x.

A(2) = 1/2 * (2-sin(2))

[soft rapids]

The area of ​​a circle segment in a unit circle is given by the formula.

Where A denotes area, and x denotes angle measured in radians
(a) Determine the area A for x = 2.

[little drum]

That looks right tho. What's wrong?

[soft rapids]

I get different values...when I try to solve the function.

I get 0.272

I suddenly get 0.491

Which of them are correct?

I'm getting confused.

What do you get?

[little drum]

,w 1 - 0.5 sin(2 rad)

[ocean seal]

Results provided by WolframAlpha

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

Requested by ansh_3502

[soft rapids]

Mhm

[soft rapids]

Why do you write 1 instead of 1/2?

[little drum]

2/2 = 1

[soft rapids]

I'm not quite there?

A(2) = 1/2 * (2-sin(2))

how do you get 2/2

in the equation there

1÷2×2 = 1?

You mean this?

@little drum

Ahh im understand

Thanks for help.

.close

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[deft plover]

oh wait i made a mistake

am I allwoed to just splits them all?

i dont think so right?

[fossil laurel]

no

would need to add ^3 to the n+1 as well

[zealous ingot]

it needs to be (n+1)^n

[little drum]

!original

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

[deft plover]

Well i have to proof that this an is convergent or divergent but i tried test for divergent first but i cant solve this

[little drum]

show question ?

[deft plover]

apperently we had to use ratio test idk why tho

but first i wanted to try divergent test cuz we are told to always do that first but i cant solve the limit

[little drum]

check |a_{n+1}/a_n|

Ratio Test

[deft plover]

yes

thats true

limit of that tho

but yes

[little drum]

did it perhaps not occur to you? :p

[deft plover]

oh thats the only test to check absolute convergent?

[little drum]

$L = \limsup_{n \to \infty} \left|\frac{a_{n+1}}{a_n}\right|$

[deft plover]

sup?

[little drum]

for absolute convergence L < 1 is required

[deft plover]

yes the answer is 3/4

and i worked it out correctly

i just dont know why they used this test

is it because this is the only test to proof a sum is absolute convergent or are there others also?

[little drum]

There are others also but depending on the series you have on hand, this is the most convenient to get it done with

[deft plover]

but why is this one the most convenient

[little drum]

because the ratio is simple to take limit of?

simple enough that you could get it done at least :p

[deft plover]

damnnnn

[little drum]

[deft plover]

valid tho

okay

now i have a hard question for you

ready?

[little drum]

Baii Brett

[deft plover]

find the sum

noooo dont leave

[little drum]

Lmao

that's telescopic tho?

[deft plover]

what

telescopic?

[little drum]

arctan 2 - arctan 1 + arctan 3 - arctan 2 + arctan 4 - arctan 3 + ...

see terms cancelling?

[deft plover]

yes :-:

fuckkkkkkkkk

[little drum]

you'll be left with arctan (infty) - arctan 1

[deft plover]

so how would i write this down correctly

just what u did?

maybe this:
arctan(2) - arctan (1) + arctan (3) - arctan (2) + ........ + arctan (n) - arctan (n-1) + arctan (n+1) - arctan(n)

-arctan (1) + arctan (n+1) = arctan (n+1) - arctan (1) ?

but i must say n to infinity

somehow

[little drum]

Lol

:p you write the sum in terms of limit

[deft plover]

huh am i allowed to?

[little drum]

sum_1^inf = lim_{n to inf} sum_1^n ...

[deft plover]

i dont get that notation :-:

S_1^inf ?

so the Sn from like sumation n=1 to n? but now S to inf?

[little drum]

$\sum_{n = 1}^{\infty} f(n) = \lim_{n \to \infty} \sum_{i = 1}^{n} f(n)$

[deft plover]

ohh

and then

u allowed to move it in front of the sum i suppose?

[little drum]

hm

[deft plover]

this correct?

[little drum]

NO

WHAT

@deft plover somehow you always manage to add that one erroneous step

umm, this still has error

now ok

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[gloomy iris]

Hey i was wondering what you have to do, to say that you "took calc 1", while not being able to take the course

[gloomy iris]

Like is the course on khan enough?

[alpine sable]

https://youtu.be/MO-AExWdl4Q

this is equivalent to calc 1 i think, not 100% sure

[gloomy iris]

ye but after i have watched and understood, am i then qualified to say, on like a college application, that i took calc 1 as a 13-year-old

[narrow kelp]

some colleges will do online courses that will count

but then there are also ap exams, which are real college courses that colleges will sometimes not accept as taking the course 🤷‍♂️

[gloomy iris]

so do i have to pass an AP exam?

[narrow kelp]

that could be enough but its generally only for high school students

sometimes you can "test out" of a course by taking the final for it right away and if you get a very high score on it then they will exempt you from the class

[gloomy iris]

ok, but can i only take it once

[narrow kelp]

i dont know

ive never done it

[gloomy iris]

So basically, i watch the vid, understand it, and then go on some high schools website to take a practice exam

and does it have to be my local high school? Im not from the states, and i dont know if they do ap classes in my country

[narrow kelp]

they may not

if you have a college in mind then youll want to look into the specifics of what they require

[gloomy iris]

so if i want to get into MIT, then i take the practice exam on their website

also ive started calc 1 on khan academy, and wanted to know if finishing that would make me maybe pass

[narrow kelp]

itll take more than a practice exam

youll have to do something specific with MIT

like talk to them about taking a placement exam or something like that

[gloomy iris]

ok thanks bro

youre th goat

i wish for your pillow to bw cold on both sides tonight

[narrow kelp]

lol

[gloomy iris]

thanks

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[alpine sable]

can someone help me

[alpine sable]

helpp

[reef wren]

Be more specific

[reef wren]

But this seems wrong

[forest marsh]

You have to add or sub 32

[alpine sable]

The equation above shows how temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Celsius. Based on the equation, which of the following must be true?

A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of 59 degree Celsius.
A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.
A temperature increase of 59 degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.

A) I only
B) II only
C) III only
D) I and II only

[forest marsh]

I believe

[alpine sable]

ok A B C OR D tho

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[hollow vale]

Apologies if this is not strictly mathematical related, but someone may know the answer.

for Gradient Descent, how do we know what the gradient is if we only try one set of weights?

[hollow vale]

.close resolved

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[tight pier]

hi

[tight pier]

can somebody check my work

[ocean seal]

anti-algebraist 𝔸dωn𝓲²s

[tight pier]

ok thank

.solved

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[alpine sable]

The bit at the end there

where did the ln a come from?

please?

[fierce cipher]

Derivative of (ln a)x

It's chain rule

[alpine sable]

yeah I was trying to figure out the chain rule here, I get where this comes from as part of the chain rule

that part markes sense

but then the

the derivative of this part is just ln a?

[fierce cipher]

Yea

[alpine sable]

can't walk it through in my head

where did the x go

[fierce cipher]

Derivative of x is 1

[alpine sable]

oh of course.

thank you so much! been staring me in the face for an hour

studying after work is bad, falling asleep

ty ty ty

.close

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[royal saddle]

If i have a function say, a•(b)^x and another function say 45sin(x) were, a•(b)^x gives the population based on time, time=x and 45sin(x)= tempature and x is again time how would a formula for a graph the gives tempature, y based on population, x

[royal saddle]

I have to go just ping me with anything helpful if u can

<@&286206848099549185>

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[lavish sedge]

solve for t in the population equation and then put that in the temperature one

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[frozen narwhal]

Help with this trig homework please!! My teacher wasn’t here today so now I have to self teach new material ToT

[frozen narwhal]

The picture is loading…

I understand in order to get P. It’s
180 - 90 - 47•33’ but.. how do I subtract the 47•33’ ??

[vestal pine]

You can do it in a calculator, it equals to 47,55

[gray isle]

don't convert to decimal

there are 60' (60 minutes in a degree)

try applying that

[frozen narwhal]

I understand the 60 minutes= degree. But how would I subtract that?

[gray isle]

90° = 89° + 1° = 89° + 60'

in a similar way to subtracting for
20 - 7

0 < 7, so you borrow 1 from the next digit

[vestal pine]

It should work like this: 60' = 1°, so 1/60 times 33 equals 0,55°

[gray isle]

don't convert to decimal

[frozen narwhal]

I know how to subtract and equate it when it’s asking me to convert to a decimal but it’s not here. so how would I subtract 90 - 47•55’ ?
Is there a formula?

[gray isle]

90° = 89° + 1° = 89° + 60'

that applies 1° = 60'

and where's 55' coming from

you have 33' in the question

[frozen narwhal]

Yes I understand this. How does it translate to the subtraction.

[vestal pine]

But why not use decimals? The number is not that large in decimals

[gray isle]

because they're not needed, and the question wants the answer in degs and minutes

[frozen narwhal]

Look at the picture again. It’s asking for degrees. Not decimals

[frozen narwhal]

That’s what I got originally but then it said I was wrong so I’m asking for help now 😭

[gray isle]

each unit in 89°60' is now greater
so you can subtract each one normally after the conversion

89° - 47° = ?
60' - 33' = ?

[frozen narwhal]

Why isn’t it 90- 47?

[gray isle]

borrow 1° from the 90

[frozen narwhal]

ohhhh

OH

[gray isle]

so you have 60' to subtract

[frozen narwhal]

= 42
= 27

So. 42• 27’ ?

[high niche]

It is not 90-47 because you have to take into account the 33’

You need to take 60’ (1 degree angle) out of the 90 degrees so that you can subtract the 33’

[gray isle]

yeh

[frozen narwhal]

YEAAAH

okay one sec

[vestal pine]

Is it like this? 89°60' - 47°33' = 42°27'

[gray isle]

yes...

[vestal pine]

my bad

[frozen narwhal]

So… in order to find out n. I know we have to use sin. But since the angle has the 33’ would you have to convert it to degrees or put it in a calculator like normal?

[gray isle]

calcs are capable of accepting minutes

use the $\boxed{\deg ' "}$ button

[ocean seal]

ℝαμOmeganato5
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[vestal pine]

y = n *sin (angle alpha). You can work with this

[frozen narwhal]

I GOT ITTTTTT

yay!!

[vestal pine]

gg

[frozen narwhal]

Are we allowed to do more than one question or do I have to open another channel after closing this one?

I still need a lot of help..

[vestal pine]

idk

[gray isle]

easier to make a new one to keep track of what question you need help on. make sure to close this one first though

[frozen narwhal]

Okay!! Thank you so much 🫶🏽🫶🏽

.close

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[wild ivy]

is their a resources channel?

[tacit arch]

#book-recommendations

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[unborn edge]

can someone help me understand vector standard form vs component form?

In physics were learning that the magnitude of a velocity vector is its speed, and i keep confusing a vector for velocity with speed. (like writing i+j+k vs sqrt(i^2+j^2+k^2))

[tacit arch]

what help do you need

do you have a problem you're working on

dm @fierce herald

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@unborn edge Has your question been resolved?

[unborn edge]

not really im lacking a conceptual undersatanding of the vectors. but i can post a problem for reference

[tacit arch]

what conceptual understanding exactly

[unborn edge]

74 is the question.

I guess it's more of a notation thing, but they gave us a scalar, so I thought they wanted a scalar, but my prof solution has it as a vector, which is like i+j notation.

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[tacit jewel]

A function relates each element of a set
with exactly one element of another set
(possibly the same set).

[tacit jewel]

this is the definition of a function

just wondering

we have $y=x^2$

[ocean seal]

pyrate

[tacit jewel]

what is this called then

just a nice way to format mappings?

[tribal geyser]

https://tenor.com/view/get-him-to-the-greek-p-diddy-deep-mind-fuck-gif-21406251

[tribal geyser]

A function

[hushed locust]

that's a formula

[tacit jewel]

right cause it doesnt specifiy any set or anything

what is x or y anyway

[hushed locust]

the usual convention would be to take x as an element in the domain and y to be the element in the codomain x is mapped to (i.e., the image of x under the function)

[north rover]

i feel like this would be a bijection, not 100% sure

[hushed locust]

no, because it quantifies over the elements of the domain, not of the codomain

so it does not guarantee that "each element of the other set" (codomain) is associated with an element of the original set (domain)

[tacit jewel]

smart person here

this is groundbreaking

anyway ty

just cause i have these hw problems to find all functions between these sets and im just thinking there's infinitely many until i came to this definition

.close

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[viral thunder]

unsure how to actually calculate this. i know i should just isolate the top right corner and then just multiply my answer by four but how do i find the equation of that lil quarter circle

[gray isle]

do you know the equation for a circle or semicircle

[viral thunder]

yeah circle is x^2 + y^2=1

[gray isle]

what about a semicircle? (the top half of that circle)

[viral thunder]

that i do not lnow

[gray isle]

solve that equation you gave for y

[north rover]

think about what would happen if you cut off the bottom portion of the circle

what sign of values would exist there?

[viral thunder]

pos

only positice

i need to restrict the circle to only positive y values

x^2 + rootY = 1?

[viral thunder]

ah okay i got that

i have a semi now

but i dont know how to take the integral of this

[gray isle]

to integrate, you can use trig sub

[viral thunder]

i have not learned trig sub

thats 4 units later in the class

so assume i can not use it

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[dusk umbra]

can someone explaint to me the difference between probability and probability density?

having a hard time intuiting why a small probability density wouldnt lead to a state being unlikely

i can understand it when i view it as making up a very small volume of a phase space, but not when i think about probability density

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[round obsidian]

Hello i would like to ask if anyone knows a good youtube channel with all the math of S1 and 2 and 3 ? going from the basic to triple intergers and fourier

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@round obsidian Has your question been resolved?

[real gazelle]

For basic integrals, I can recommend Khan Academy. Organic Chemistry Tutor and Paul's Online Notes also have very good content.

[round obsidian]

thx u r saving me mate

[real gazelle]

you're welcome

type .close if that's all for now

[round obsidian]

.close

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[weak breach]

Hello, does anyone know how to multiply?

[weak breach]

I dont

can someone teach me

[prime badge]

can you add?

because they are similar and you maybe don't know how to add, and that seems more important

[raw jetty]

what is your bio

[north rover]

kids...do that sometimes.

[broken pivot]

Its very unlikely that a 13+ person doesnt know how to multiply

Just saying...

[north rover]

there are exceptions for GEDs, etc. but considering his bio he is probably not of that age, so i agree here

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[broken pivot]

What does GED mean

Special education?

[tardy stag]

.close

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[north rover]

basically, adults redoing elementary, middle, and high school math (this is united states specific, i believe)

[broken pivot]

I see, thanks!

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[uncut hollow]

suppose I throw an object at a height of h meters, at an angle theta (between 0 and 180) and at an initial velocity v
now suppose the parabola of that object, where the thrower is at f(0) = h
taking a second degree parabola ax² + bx + h, what would be the appropriate values for a and b to graph the curve of the object being thrown?

[remote heron]

how much math do you know?

do you just want the answer?

[uncut hollow]

yessir

i have never done any physics so I was just learning about hte concept

[remote heron]

https://www.desmos.com/calculator/xheeipyjqj

[uncut hollow]

heres some traces of stuff I wrote

oh thats nice

[remote heron]

although, maybe you want some different form

you can search "projectile motion desmos" in google to see many other choices

[remote heron]

they make it look more complicated than it is

[uncut hollow]

this was my attempt at finding it a bit

also that lmfao

[remote heron]

oh, you know calculus

[uncut hollow]

i'll go check it out

appreciate the source :)

[uncut hollow]

a tiny bit

i'm not very good at it

[remote heron]

so yea, you can use that

[uncut hollow]

appreciate the help fam

[remote heron]

you start with newtons 2

y'' = -g

[uncut hollow]

i'll search that up :)

[remote heron]

np

[uncut hollow]

.close

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[wanton wigeon]

Hey there I am given an optimisation project in which i need some help
The project gives me three data sets about frequency Real part of impedance and complex part of impedance
As they are dataset they are in the form of arrays having 50 values each
Impedance is the net resisting property or the net resistance offered to the current in an AC circuit
Now what I need to do is that i am given 8 circuit elements out of which i have to build generic combinations of circuit elements and an error function that returns the error in
chosen model and optimizes (minimizes) the error by changing the combinations such that my circuit fits accurately according to the dataset
I need help in the optimisation or mathematical part i will deeply explain all the things to anyone who would like to help me in the mathematical part

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@wanton wigeon Has your question been resolved?

[wanton wigeon]

no

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@wanton wigeon Has your question been resolved?

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@wanton wigeon Has your question been resolved?

[dire plover]

so you have an AC source?

[hazy trench]

https://youtu.be/hMuoeP-lbS4?si=Mp1DitERKMFdYarj

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[craggy grail]

can somebody learn me how to simplify a fraction

please

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[undone maple]

Hi, i'm doing normalization for some variables which would be used to multiply with some other variables. In this case should I use min-max or min to get the normalized values?

[solid anvil]

Hi, can you give more context about what will you use variables for? i would be glad to help

[undone maple]

Thanks, sure. I'm making an estimation expression for bill cost which consists of several major components like rent, electricity, maintenance, etc.

It looks like this: ```
C = w1 * rent + w2 * electricity + w3 * maintenance

where w1/2/3 are weights i might need to adjust.

[solid anvil]

are you training a neural network model or something similar ?

[undone maple]

I hope i can make a simple linear model since it's not like very polynomial

But i need to first get the rent/electricity/etc values normalized

[solid anvil]

alright you have few options

[undone maple]

btw the maintenance cost is bit complicated like this ```
maintence = electricity * MaintPriceQuote

[solid anvil]

you can use either one of these:
Sigmoid Activation Function
Hyperbolic Tangent Function
Rectified Linear Unit Function (ReLU)
and many more ones

these are used in neural networks to normalise the given data but in your situation i would suggest you to use a ReLU

simply because of its simplicity and relatively easy to implement and compute properties and it would serve more than enough precision for your problem

[undone maple]

Since the variables I have are non-negative, that means ReLU is giving same output as this function right? output = input / max_variable

[solid anvil]

pretty much yeah

oh my bad, i didn't even think about the price not being negative 🤦‍♂️

[undone maple]

oh no problem,

your answer is very helpful

[undone maple]

And since I need electricity to multiply with other variables, that means I'd better not get the normalized electricity values equal to zero, is that right?

[solid anvil]

sorry i didn't get that completely, can you clarify which one of these are you trying to implement?
maintence = electricity * MaintPriceQuote
maintence = w2 * electricity * MaintPriceQuote

like the electricity that is used to maintain?

unless you get a separate bill for "maintenance electricity" i believe you can't do that

or perhaps you can measure the amount of how much electricity is used for maintenance

[undone maple]

like me see, the whole expression like this:

cost = w1 * rent + w2 * electricity + w3 * electricity * MaintPriceQuote

the electricity in the two components are exactly same one

[solid anvil]

what is MaintPriceQuote referring to ?

[undone maple]

i think that's the pricing from maintenance company who gonna work on the refitting

their price are measured by how much electricity used, hence need to multiply with electricity price here

[solid anvil]

sorry to ask this much but what exactly does the company have to do with electricity that you use in your home?

and generally speaking it would not yield correct results if you multiply a single variable by two different weights

so with my understanding i would suggest you to do this:

[undone maple]

Oops I think i messed with the components a bit, and you are right this is not adding up. The company rents the place to us and also takes care of refitting to some extent.

They have a unique pricing strategy for refitting which relates to how much they tools wear out and they decided to measure it by how much electricity used in refitting.

[solid anvil]

C = R + E + M
R = (Rent x Wr)
E = (Electricity x We)
M = (Maintenance x Wm)

[solid anvil]

Oh Ok

i goet it now

So the thing is do you know how much electricity they use in refitting ? like do they report it or something

?

[undone maple]

we are with them in refitting so we can see the usage

and they will confirm the final cost with us with the reports too

[solid anvil]

ok so you know how much they use and what that costs

[undone maple]

yes I believe so 🙂

[solid anvil]

alright then

[undone maple]

so the whole expression can be revised to this if am right C = w1 * rent + w2 * electricity_reported * electricityPricingQuote + w3 * eletricity_reported * maintenancePriceQuote

[solid anvil]

C = R + E + M
R = (Rent x Wr)
E = (Electricity x We)
M = ((Electricity Used in Maintenance)x Wm)

[solid anvil]

seems about right

[solid anvil]

what i was going for was to set the weight for maintenance (Wm) to match the pricing strategy of the maintenance company

So M would yield the total cost of maintenance depending on the Electricity Used in Maintenance

if there is anything else that i can help with, feel free to ask

[undone maple]

Thanks for this. So if I get the chance to train the simple model for better weights I should eventually get a decent model for future use right?🙂

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[viral crane]

best website for a level math questions?

[crystal leaf]

huh

what do you actually mean?

[viral crane]

For A level maths what are some good website for questions

[dim oasis]

Khan academy has problem sets along with lessons

I used WolframAlpha's problem generator and Paul's Online Math Notes a lot when taking calculus/related courses

[crystal leaf]

https://alevelmathsrevision.com/

you can use free resources from here

[dim oasis]

Of course a site dedicated to A levels would be best, like

Wolfram and Khan are generally in the format of U.S. curriculum

[crystal leaf]

yep

close the channel

[dim oasis]

OP can close when they are satisfied; they could have followup questions

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[soft wasp]

What is the largest area that a quadrilateral inscribed in a circle of radius R can have if one of its angles is alpha?

[soft wasp]

So I found a formuła for the field of wuadrilateral in a circle

But I don't know how to use the fact that I am given about the R and alpha

[icy sedge]

4.10

[soft wasp]

?

[icy sedge]

4.10 can anyone solve

[soft wasp]

this channel is occupied

.close

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[uneven crystal]

Need to calculate Sabd, are the triangles atleast similiar?

[elder umbra]

I need assistance with a math equation

[topaz path]

choose one of the available math channels and post your question there

[topaz path]

DBC looks like a 90deg angle

find all angles in that triangle, which should be easy since you know all sides

and check if ABD+DBC is 90deg

[uneven crystal]

.closed

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[alpine sable]

Trying to determine difference of multi sets

[alpine sable]

Let's say A=[1] and B=[1,1]

What is A-B? Is it an empty multi set?

Can you somehow have a negative amount of 1s? Is this undefined?

[tough relic]

You can't have repeating elements in a set.

A set is a list of distinct elements.

[carmine reef]

multiset

[alpine sable]

This is a multi set or a baga

Bah

Bag

[tough relic]

Oh

My bad 🙇‍♂️

[severe portal]

This definition from wikipedia(https://en.wikipedia.org/wiki/Multiset basically says it will be an empty multi set

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@alpine sable Has your question been resolved?

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[raw quartz]

Hey is it possible to determine the sign of the roots of a quadratic equation without solving it?

[tough relic]

Let's say we have a quadratic equation $ax^2+bx+c=0$ and $x_1$ and $x_2$ are the roots of the equation.$\$
Then you can use the fact that $x_1 x_2=\frac{c}{a}$. So if this result is negative, then the roots have opposite signs, and if the result is positive, both roots have the same sign.

[ocean seal]

GoldBarley

[raw quartz]

thx for the help 👍

.close

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[sick tangle]

i need help with a

[waxen flame]

An initial condition is given by the problem which you can use. Lynn sold 80 cushions for £15 each. You can substitute those values into the provided equation to solve for H.

[sick tangle]

10?

[waxen flame]

correct.

[sick tangle]

ty!

[sick tangle]

I need help with d

i did b

[waxen flame]

I don't see a d on your image.

[sick tangle]

i mean

c

oops

heres the markscheme

[waxen flame]

That all looks correct. What's your quesiton?

[sick tangle]

i need help with understanding c

i dont get it

all i understand is the first 2 lines

[waxen flame]

The original revenue should be apparent. Just plug the price of 15 pounds into the revenue function.

[sick tangle]

yes

[waxen flame]

You've determined the optimal price, p, so substitute that into the revenue function, r, to determine what revenue you can expect with the optimal price.

[sick tangle]

got it ty

.solved

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[amber knot]

Hi

[amber knot]

Does anyone know how to solve this

<@&286206848099549185>

[forest marsh]

Tu auras plus de chance en filant une traduction

[amber knot]

Here is the English translation

<@&286206848099549185>

[lone heart]

@amber knot Has your question been resolved?

[loud warren]

je regarde tout de suite l'exo

@amber knot peut tu me dire ou tu as des difficultés?

[amber knot]

J’ai pas compris quoi faire

[loud warren]

donc faut que tu regardes quelle config de la fusée est meilleur considérant les données que tu as

tu as une liste avec plusieurs contraintes

par exemple l'angle doit être entre 30 et 45°

[amber knot]

Mais comment est-ce que je commence par résoudre le problème

Est ce que je fait une démarche pour chaque fuser ?

[loud warren]

oui

ce que je te conseille c'est de verifier si chaque contrainte est respecté.

Tu as:

• la navette doit etre a une vitesse inferieure a 10 km/s
• l'angle doit être entre 30 et 45°
• la projection orthogonale de le force de friction doit être inferieur a 40 000 GN
• la projection orthogonale de la force de friction sur la droite perpendiculaire à l'axe de la navette doit être inferieur a 120000 GN

Je dirais que tu devrais commencer par calculer l'angle, puis la vitesse puis les forces et après tu compare

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[lone heart]

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[snow berry]

Hi

[snow berry]

I know what a scalar and vector projection is, but what is orthogonal?

well, perpendicular

[fathom yacht]

its 90 degres on the line ig

[snow berry]

but is there a projection

[hushed locust]

it's just a vector orthogonal to a which together with the vector projection adds up to b

[snow berry]

so it should be 0

orth b to a = 0?

[vale crag]

no

[hushed locust]

edited, orthogonal to a*

[snow berry]

I know what proj and comp is

wtf is orth

okay

[vale crag]

well orth is comp if we have the same understanding of comp

[snow berry]

comp is a scalar

[vale crag]

ah oops yeah

[snow berry]

bruh I hate this

[vale crag]

I mean they define orth for you really, the difference between the projection and the original vector

you just gotta roll with it

[snow berry]

so

wait

[hushed locust]

and it is called that because it's orthogonal (a1 = proj_b a, a2 = orth_b a)

[snow berry]

so orthogonal means it shoud b 0 right?

No no no

sorry

[vale crag]

what is 0 ?

[snow berry]

if it is orthogonal, the matrix(the vectors) get unchanged

[hushed locust]

proj_a (b) produces a vector which is parallel to a
orth_a (b) produces a vector which is orthogonal to a, defined in such a way that
proj_a (b) + orth_a (b) = b

[snow berry]

man this shit so fucked

an orth should mean the comp is = 0 right?

because the vectors are at 90 degrees and no length of b is pointing towards direction of A

[vale crag]

no

b can be anything

[snow berry]

with comp = 0

[vale crag]

doesn't have to be orthogonal to a

[snow berry]

proj should also be 0

therefore we are subtracting b vector with the resultant proj(orthogonal values will equal to 0)

[hushed locust]

,tikz[scale=3] \begin{scope}[thick, ->, blue!40!white] \draw (0,0) -- (1,0) node[midway, below]{$\mathcolor{black}{\operatorname{proj}}{\mathcolor{red!40!white}{\vb a}}\mathcolor{blue!40!white}{\vb b}$};
\draw (0,0) -- (0,1) node[midway, left]{$\mathcolor{black}{\operatorname{orth}}{\mathcolor{red!40!white}{\vb a}} \mathcolor{blue!40!white}{\vb b}$};
\draw (0,0) -- (1,1) node[midway, below]{$\mathcolor{blue!40!white}{\vb b}$};
\draw[red!40!white] (1,0) -- (2,0) node[midway, below]{$\mathcolor{red!40!white}{\vb a}$}; \end{scope}

[ocean seal]

cloud

[fossil laurel]

wow

[lone heart]

@snow berry Has your question been resolved?

[snow berry]

i llbrb

[lone heart]

@snow berry Has your question been resolved?

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[amber saddle]

Hi, stuck on optimization questions again

I don’t know where to begin looking when constructing an equation for this question

[mellow viper]

This is optimization?

[amber saddle]

it was in the practice problems for optimizations and related rates

I think the diagram is something like this?

[mellow viper]

Ohhh I see

[gleaming lagoon]

hi it’s my alt account

[amber saddle]

hi

[gleaming lagoon]

So I think you should first differentiate the pythagorean theorem

[amber saddle]

I found an equation relating M and N

[gleaming lagoon]

How I see it

[amber saddle]

In respects to which variable?

[gleaming lagoon]

Just use plain a^2 + b^2 = c^2

then you should get

aa' + bb' = c*c'

idk why it did that

[amber saddle]

discord shenanigans

[gleaming lagoon]

I view this more of a related rates rather than optimization cause you’re not really optimizing anything

[amber saddle]

makes sense yeah

alright, let me fiddle with it and i'll report back

[gleaming lagoon]

kk

And this AB is constant, rate of A to midpoint of AB plus rate of B to midpoint AB should equal 0

[amber saddle]

i'm sort of lost as to what this accomplishes

[gleaming lagoon]

Lemme send a photo rq

sorry if sloppy

[gleaming lagoon]

Since the rate of CD in both triangles are related, we can treat as a systems of equations

[amber saddle]

ooh

hang on let me parse this

ohh that is incredibly neat

[gleaming lagoon]

thanks

Now you can use that rate to find the rate between AD and BD and then you can break them up into components to find the true direction and speed

[amber saddle]

makes sense!

i'll go work on it a bit

[gleaming lagoon]

yay good luck

did you get a rate for AC?

AD i mean

[amber saddle]

i was thinking we could set one side of the triangle as X and the other as 6-X

if that would work

[lone heart]

@amber saddle Has your question been resolved?

[amber saddle]

No but I did get this

(?)

[amber saddle]

I think I got something

Am I on the right track

[amber saddle]

hey, i did a little more work but i cant seem to get past this point^

did i calculate the respective dx's correctly?

.close

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[sage moss]

.reopen

.open

.claim

Ugh

[sage moss]

Ok so

I need help with isosceles trapezoid

Idk how to answer this

[raw jetty]

,rccw

[raw jetty]

"given an icoseles trapezoid on the right, solve for the unknown angles x and y"?

[lone heart]

@sage moss Has your question been resolved?

[paper mango]

@sage moss ?

[sage moss]

Ty I understnd it now

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[vague chasm]

not sure how to solve this, i see two ways. one is that u only look at the second card because the first doesent matter or i can look at the chance of picking 2 out of the 4 that are the same pair.

[oak chasm]

Well, you get three cards.

You choose 2 of them to be the pair.

The other one is a different rank.

[vague chasm]

so i start with 13.(4 2) i imagine

[oak chasm]

Do you mean 4C2 by that?

[vague chasm]

yes

[oak chasm]

OK, you have three cards, and you're choosing two to be the pair, so that would be 3C2.

So, it would be 13 3C2, then what?

[vague chasm]

i mean the 4 as the 4 equal cards, is this not right?

[oak chasm]

Ahh, I see.

Let's see.

OK, so 13 4C2 tells you which two cards out of the deck you have.

Then how many ways are there to choose the third card?

[vague chasm]

12. 1C48?

[lethal fox]

i think it would be easier to take the inverse of getting three different cards + three of the same

[oak chasm]

What is the 1 2 for?

[vague chasm]

12 because there are 12 ranks left

[oak chasm]

Well, the 48 handles that.

There are 48 cards of a different rank.

So, you choose a rank. You choose 2 cards from the 4 in that rank. Then you choose 1 card from the 48 that are left.

Which is 13 4C2 48C1.

[vague chasm]

ah yes , so is that it?

[oak chasm]

It depends on if the order of the three cards in your hand matters.

If so, you multiply by 3!. Otherwise, you're done.

[vague chasm]

i see thx alot

.close

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[oak chasm]

No problem.

[lone heart]

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[vapid steppe]

how to derive that $F_{net}=\dv{p}{t}$

[ocean seal]

Jash

[hushed locust]

that's just newton's second law

usually newton's laws are taken as axioms in newtonian mechanics

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[tepid ravine]

Confused on how would i prove this?

[tepid ravine]

might seem like an easy question but unsure how would i prove this

i'm just confused about what is the difference for this and the real-varialbe case

like wouldn't i just simply replace h->0 to be z_0 -> 0

and then use the same argument

[paper mango]

yes, formally you'd use a sequence that converges to 0

since they wrote analogous maybe they mean that it shall be more primitive and just use z_0 -> 0 yeah

[tardy stag]

i think it's basically recapitulate the proof you did in real analysis but this time with complex numbers

[lone heart]

@tepid ravine Has your question been resolved?

[tepid ravine]

@paper mango @tardy stag this is what i had

is this right?

[paper mango]

yes but three things

why is the proof twice there

why does it start with

and the only step that should be more explicit is when splitting lim[a+b] into lim[a]+lim[b]

which only holds if lim[a] and lim[b] exist

[lone heart]

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[tepid ravine]

How would you mention this?

[tacit arch]

Basically just say this

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[outer steppe]

Can someone help me with solving circuits using matrices?

[outer steppe]

Im having trouble with the circuits, loops...

these are some qn's off yt and we can start with the easiest

[paper mango]

oyoyo not circuits

[paper mango]

on which one are you currently stuck

[outer steppe]

can we try the 2nd pic with 2 loops?

[paper mango]

ok I'll say in advance I'm not familiar with the topic :D

[outer steppe]

oh

[paper mango]

just thought I'd let the conversation start

[outer steppe]

okay

[paper mango]

for any closed loop U = R * I must hold right

and I1 = I2 + I3 I'd assume

Don't you then set up a linear system of equations for each inner loop

that is, setting up U = R * I for each loop

and if there are e.g. two resistors R1 and R2, then R = R1 + R2

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[paper mango]

nubudi with physics knowledge currently available it seems :[

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@carmine topaz Has your question been resolved?

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[ember isle]

i am confused on how c_n is defined here:

[ember isle]

i don't really understand what that means

the subscript R on the integral

[kind sparrow]

That just means from -inf to inf

[ember isle]

o

big ty

that'll be all for now

.close

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[molten plover]

The number of 4 digit numbers formed with the digits 1, 1, 2, 2, 3, 4 is

[molten plover]

6P4 / (2! * 2! )
?

pls ping if answered

[abstract brook]

hello

[molten plover]

hi

@abstract brook @alpine sable

Please ping me @molten plover if you answer the question

[abstract brook]

ok

what question?

[lone heart]

@molten plover Has your question been resolved?

[paper cipher]

no

U gotta make cases

do yk bucket method

@molten plover ?

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[bold wind]

Hey, for a course System Dynamics I need to Make a choice of Td (i'm using a PID controller) now to choose the propper Td I have made some Root Locus plots in Matlab for diffrent Td's. Now my question is which Td do I choose and why?

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@bold wind Has your question been resolved?

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@bold wind Has your question been resolved?

[molten plover]

nope, tell me cases

[lone heart]

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[twilit meadow]

https://www.desmos.com/calculator/yvywtsn2s3
so basically i need help calculating the suitable parameter b ensuring that it intersects with the points and has 2 troughs and 1 crests. note: the midpoint of the sinusoid is not the same as the point's y=10.035. it is shifted by 10.035-0.4904
from trial and error the b value is about 0.9278 but i am interested in how to find the algebraic route to the solution

[twilit meadow]

thanks 🙏

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@twilit meadow Has your question been resolved?

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@twilit meadow Has your question been resolved?

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@twilit meadow Has your question been resolved?