help-28

[torn jolt]

Wait

Come to dm, please

Thanks!

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[dull seal]

What did you try?

Ok

Thats good

Ok and now what do u think

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[errant lichen]

what does that sign mean?

the U and upside down U

i know what they mean in the context of set theory but they're binary operators

and here there's only 1 argument

[kindred grove]

$\mathcal U$ contains multiple sets (namely subspaces of $V$) in it

and $\bigcap \mathcal U$ is the intersection of all the sets inside of it

@errant lichen

[glossy valve]

aPlatypus

[kindred grove]

so any intersection of subspaces of V is a subspace of V

that's what the theorem is saying

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@errant lichen Has your question been resolved?

[errant lichen]

ooooooh

makes sense

tysm

but how would the intersection be problematic?

the intersection

wouldn't it just be the null set?

or would it be problematic because

$\bigcap \mathcal u$

[glossy valve]

CrazyCuber217

[errant lichen]

belongs to u

and nothing can belong to the null set

?

but by that logic even the union of u would be problematic

[kindred grove]

well in a sense they're both problematic, as in they're weird edge cases

[errant lichen]

ahh fair

so it's not a sentence that's actually introducing any new info

thats specifivally related to linear alg?

[kindred grove]

no that's just set stuff

[errant lichen]

just a joke

oh cool im comfortable w set stuff for now

tysm

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[kindred grove]

.reopen

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✅

[kindred grove]

but yeah to answer the problematic aspect of the intersection

if you're taking the intersection of 0 sets

there's no constraint on the elements that can be inside

[errant lichen]

ahhh

and the union of 0 sets

is obviously 0

but intersection isn't as well defined?

[kindred grove]

well it would be an "everything" set essentially

[errant lichen]

is it actually defined that way?

or kinda like a dividing by 0 situation

[kindred grove]

yeah kinda like division by 0

that's why some ppl formalized set theory in the 20th century

[errant lichen]

oh just messy and doesn't make sense

[errant lichen]

to specifically state

that this isn't allowed?

and by formalize you mean like zfc and stuff right

[kindred grove]

yea

[errant lichen]

even more cut and dry than the set theory ik

[errant lichen]

crazy

sounds painful

thank god i don't have to deal w it for now 😭

[kindred grove]

let's all thank russell and others

in this confusing day

[errant lichen]

ong

[kindred grove]

alright I'm done here

you have more questions or no ?

@errant lichen

[errant lichen]

nope tysm

have a nice day!

.close

[kindred grove]

you too

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[pine trellis]

Hello, I need help

[pine trellis]

For the production cycle of a chemical, a factory bears a fixed cost of 1000 euro, a cost of 5 euro per kilogram produced and an additional cost equal (in euro) to 0.02% of the square of kilograms produced. The selling price per kilogram (in euro) is linked to the number x of kilograms produced (and sold) by the ratio x = 1000 - 20p. It determines, for a production cycle, the value of x for which the maximum profit, in the following two hypotheses: a) the maximum relative production capacity of a cycle is 500 kg; b) the maximum relative production capacity of a cycle is 400 kg

!status

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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

[pine trellis]

<@&286206848099549185>

I just need help with a simple thing

not the entire exercise

[wanton shore]

What do you need help with

[pine trellis]

Okay so

Im not sure how to word it since Im not english

but Im stuck in the part where I have to assign to every data a value

like "fixed costs = 1000 euro"

[wanton shore]

Okay

[pine trellis]

I struggle with this part

"and an additional cost equal (in euro) to 0.2% of the square of kilograms produced. The selling price per kilogram (in euro) is linked to the number x of kilograms produced (and sold) by the ratio x = 1000 - 20p. "

does the first count as 0.002x^2 ?

[wanton shore]

Wait

yes it is

[pine trellis]

am I supposed to "fuse" those values together?

im not sure how to process these values

[pine trellis]

you there?

[wanton shore]

yes

I'm there

[pine trellis]

do you know how to process these infos

[wanton shore]

Wait let me remember

Yes

[pine trellis]

what am I supposed to do then

[wanton shore]

You fuse them together

[pine trellis]

so like

if for example

I produce 2 kgs

[wanton shore]

yes

[pine trellis]

Price will be 2000 - 40p

[wanton shore]

yeah

[pine trellis]

-0.002 * (2000 - 40p) ^ 2 ?

Sorry I mean *

I mean -

[wanton shore]

0.002^2

[pine trellis]

not * sorry

[pine trellis]

is this correct

[wanton shore]

I made amistake

Yes it's correct

[pine trellis]

its okay

wait ill try to do it myself then will let you know

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[high bay]

does anything look wrong here besides probably the taylor polynomials?

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[high bay]

<@&286206848099549185>

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@high bay Has your question been resolved?

[kind blade]

Sorry I honestly can’t figure out which channel@I’m supposed to post my question in but please feel free to redirect me. This grade 11 course book someone made seems to have a lot mistakes in it so I was just wondering if someone could verify if this is correct? I don’t understand how the answer is 5b instead of 125b

[river wave]

Choose an open channel with no username

[river wave]

What’s 5^6

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[west quiver]

tan(x)' = 0

has no solution for reason: (cos(x))^2 cannot be zero

would that suffice/be correct as reasoning as well as the "proof" ive shown above

[astral steppe]

It’s not that (cos(x))^2 can’t be zero

It’s that 1/(cos(x))^2 can’t be zero

But yeah i would that’s rigorous enough

Maybe just say that since the numerator can never be zero it can never be zero

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[round rapids]

what kind of answer does it want

it looks like absolute value and linear action

[noble dew]

does it want a piecewise function?

[round rapids]

I dont think so

its all one function

[plain gate]

yes

so 3 equations

3 linear equations

with a domain

[static bramble]

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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

[noble dew]

Well it looks like there’s 3 lines on the graph, so just calculate the equations for each line along with their relevant domains

[plain gate]

1

[plain gate]

can you show me how to calculate the equation for the first line

and ill try to do the rest on my own

[noble dew]

It basically goes off of intuition

First line has a slope of 1, you can also see that if it kept going it’s y intercept would be 3, so the equation is y=x+3 on the interval [-3,-1]

Interval could also be [-3,-1), with the next one starting with [-1, it doesn’t really specify which one the graph though

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@plain gate Has your question been resolved?

[plain gate]

what about the domain for the first one

would it be

$-3 \leq x \leq -1$

[glossy valve]

pixel

[noble dew]

Yes, just make sure you aren’t double including endpoints for your functions

[plain gate]

wdym

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[lavish flame]

Hello, i may seem like an idiot

but some help with this question would be nice <:

specifically with d

[native stratus]

ok i might be wrong, but bear with me:
if the number of letters are n, there are total (n-1)! arrangements (not counting rotations)
then there are 2^(n-2) crossless arrangements since fixing the first letter, and inserting the others one by one in sequence, we have 2 options at each step except for the last where we only have 1

so it's just asking for the least n so that 2^{n-2}/(n-1)! < 0.01

[lavish flame]

Ohhh that makes sense

but to prove it, what kind of steps would you take in the mathematical process?

Because I'm quite new to this kind of math work, so i dont know how to prove theories really

[modest tinsel]

i thought it was n!

but im also unsure abt it

cause it gives 1/3 then (n-1)!

[native stratus]

there are n! if you are counting rotations, i am fixing the first letter

[modest tinsel]

okok

so then b) (5-1)! = 4!

8 / 4! = 1/3

[native stratus]

basically the only step that needs justification is that you have 2^(n-2) valid crossless arrangements (not counting rotation), you can probably argue by induction here

basically inserting an additional letter, you have two places to insert it

[lavish flame]

Oh okay thank you very much

[native stratus]

ye

i think they are counting arrangements with rotation, which is how they end up with 96

so its 2^{4} * 6

which 96

[modest tinsel]

ye

cause it wouldn't make sense otherwise

cause if it was without, then it'd be 96/120

so it must be with rotations

cause that gives 96/ 720

[lavish flame]

6!... i think i see another kind of pattern here

thank you so much for your help guys <:

[modest tinsel]

six letters

[lavish flame]

yeah

[modest tinsel]

so 6!

[lavish flame]

but, you can also inverse

by splitting terms

[modest tinsel]

ik how to get 36 out of the 96

[lavish flame]

very cool thing my teacher taught me

[modest tinsel]

idk about the other 60 tho

[lavish flame]

yeah

i think

my teacher is gonna whip me

for skill issue

anyway

thanks again

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[twin wolf]

how do i show this?

[nimble crane]

there's two things you need to check

a) that f(x) >= 0 for all x in R

b) that the integral of f(x) from -infinity to infinity is 1

[twin wolf]

how do i do this?

[nimble crane]

take a look at your function carefully

it's piecewise

so check that each section is >= 0

we can start with the easy case, which is when x is not in [a,b]

in that case, what is f(x)?

[twin wolf]

0

[nimble crane]

right, which is >= 0

now we check the other section

what do you think?

[twin wolf]

i think it is but how do we know what and b are

[nimble crane]

you don't need to

look at the condition, a <= x <= b

what does this tell you?

namely, what is the relationship between a and b?

[twin wolf]

x is between a and b?

[nimble crane]

sure, but how is a related to b?

if a <= x, and x <= b, then...?

a ? b

fill in the ?

[twin wolf]

a < b

[nimble crane]

yes...

yes.

okay

sorry, I was doubting myself for a second there lol

so a < b

[twin wolf]

lol

[nimble crane]

what does this mean about a - b?

err

b - a?

[twin wolf]

i mean b-a can still be negative if b and a are negative

[nimble crane]

can it?

[twin wolf]

yeah

[nimble crane]

try it yourself

[twin wolf]

like -8-9

-17

oh wwait

[nimble crane]

yeah

[twin wolf]

-17 - - 9

[nimble crane]

you have the two flipped

[twin wolf]

wait

[nimble crane]

b is always larger

[twin wolf]

im having a stroke

-8 + 9

wait

no

lol

8 - (-9)

[ionic pawn]

Hello

Anyo Anyone

[twin wolf]

-8 +9

[nimble crane]

mhm

[twin wolf]

ok so its positive

[nimble crane]

yeah

[ionic pawn]

Can help me please

[twin wolf]

so b-a must be greater than 0?

[nimble crane]

!help

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[nimble crane]

correct.

then 1/(b-a) > 0

[twin wolf]

okay cool

[nimble crane]

agree?

[twin wolf]

yes

[nimble crane]

okay, that's a) done

now you integrate from -inf to inf to show that the value you obtain when you do that is 1

that's b)

does that make sense?

[twin wolf]

ill try it now

[nimble crane]

okay

let me know how it goes

[twin wolf]

i can pull out 1/b-a out of the integral?

[nimble crane]

yeah

it's a constant

[twin wolf]

oops

didnt mean to add the left bracket

[glossy valve]

water beam

water beam

[twin wolf]

did i do osmething wrong here?

[nimble crane]

yeah, looks like it

[twin wolf]

whatd i do

[nimble crane]

a couple of things to note here

you're integrating from -infinity to infinity yes, but the integral of 0 is just 0, so you only need to actually integrate on the bounds for when the integral is nonzero

i.e. a and b

secondly, you have the wrong antiderivative for f(x) = 1

[twin wolf]

its not x?

[nimble crane]

it is x

maybe you did smth else wrong then

[twin wolf]

💀

uh

wat

[nimble crane]

you want to take the integral of f(x) from a to b

[twin wolf]

oh

lol

[nimble crane]

that's equivalent to doing it from -inf to inf, because the area under the curve of 0 is just 0

[twin wolf]

$\frac{1}{b-a}\int_{a}^{b}1dx=\left[\frac{x}{b-a}\right]_{a}^{b}$

[glossy valve]

water beam

[twin wolf]

$\frac{b}{b-a}-\frac{a}{b-a}=\frac{b-a}{b-a}=1$

[glossy valve]

water beam

[nimble crane]

mhm

there you go

[twin wolf]

https://tenor.com/view/cat-clapping-cat-silly-silly-cat-awkward-cat-gif-8634373961741432363

thanks

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[tropic yarrow]

can someone explain whats happening here

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[gray tiger]

Need some help. Is this right skewed?

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[gray tiger]

<@&286206848099549185>

How is this not right-skewed? Need help.

Is the answer bell shaped

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[tranquil belfry]

im doing b2=a2+c2-2accosB which gets me 168.68 what am I doing wrong

[tranquil belfry]

nvm. i forgot to take the square root

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[burnt socket]

my friend and i are stuck

we're tryna prove H contains its own inverses as part of the proving it's a subgroup

the definition for GL_2(Z_5) is that it's a set of invertible 2x2 matrices of mod 5 elements

so that means, we don't care what b is coz it's gonna go to 0 anyway

so that leaves a = {1,2,3,4}

[kindred grove]

ok

what makes you stuck ?

[burnt socket]

how to prove it has inverses in H

basically tryna augment this
a 0 | 1 0
b 1 | 0 1

[kindred grove]

I mean it's a 2x2 matrix

no need to complicate your life too much, just use the easy formula

[burnt socket]

?

[kindred grove]

if $A = \begin{bmatrix}e & f \ g & h\end{bmatrix}$, then $$A^{-1} = \frac{1}{\det(A)}\begin{bmatrix}h & -f \ -g & e\end{bmatrix}$$

[burnt socket]

1/det(A) is just a. how do i figure out what goes where b is

wait

det(A) = a

so 1/a not a

what's the ... ?

[kindred grove]

if $A = \begin{bmatrix}e & f \ g & h\end{bmatrix}$, then $$A^{-1} = \frac{1}{\det(A)}\begin{bmatrix}h & -f \ -g & e\end{bmatrix}$$

[glossy valve]

aPlatypus

[kindred grove]

@burnt socket

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[gloomy briar]

I need help

[burnt socket]

oh thanks. figured it!

[gloomy briar]

I need to find interval of x

[burnt socket]

|x-3|-4 >= 0 * |x| -2

|x-3|-4 >= 0

|x-3| >= 4

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@gloomy briar Has your question been resolved?

[wide sundial]

What about x = 1

[burnt socket]

what about it?

[wide sundial]

Plug x = 1 into the question what do you get

[burnt socket]

2>=0 which is true

[wide sundial]

And is this true for x = 1

[burnt socket]

ah, nope

so how d'you do it

[sharp fable]

you guys overided this poor mans channel 🤣

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[mild umbra]

Is the theta for 11 the right angle?

10*

Because if it is

Which ones the opposite and which is the hyp

Plz help

[lilac flume]

thee hyp is side c

the side opp to the right angle is the hypotenuse

[mild umbra]

Yh

But both angle a and b are 45

Cant seem to solve this one

Cos 45=8/c

I got 6

But that doesn't seem right

O nvm

It isnt 45

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[storm tusk]

is this E.?

[nova basin]

yes

[storm tusk]

Ok so basically when I have this O with a "-" then I choose the value for it regarding the highest O value in the given term?

So √x is smaller than x and x³ is the biggest, so O with - is O(x³)

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[dense plank]

Hello! I need help on this question. I am confused on how the capsule is made up of two half cylinders. Do I combine them into one full cylinder or do I need to cut them up into two? I am still confused on this question. <@&286206848099549185>

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[unreal sierra]

Its not made of 2 half cylinders consider it one cylinder with height 0.8cm and radius 0.2cm. The other components are 2 equal hemispheres of radius 0.2 m which you can consider as one full sphere either way the answer you get stays the same

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[river lynx]

I am having trouble with this exercise I used the example to do it but im off and I think its because there are 3 dice so I dont know how it will affect the probabilities

[river lynx]

I did the exercise based on the example as it is kinda similar

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<@&286206848099549185>

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[dense plank]

ok! i think i got it now! thanks! 😄

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[thick hamlet]

<@&286206848099549185> anyone specializzed in sets?

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[proper island]

why is it the antideravitive of the 4th degree?

[umbral dome]

presumably they added up the terms up to the third degree for the estimate, so that the fourth degree term is the first term not added

[proper island]

wdym

ohh

wait i think ur cooking

lemme think for a sec

okay i get it now

thx @umbral dome

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[radiant mica]

wow

[winter latch]

Wdym

[noble dew]

wait what

lmao

[winged marsh]

yea you gotta assume the values inside the root to be a variable

and then equate it to K

as its an infinite series

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[winged marsh]

is it 2

should be something like this

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[cunning bane]

How do i do this

[proper island]

set them both equal

[cunning bane]

so x + b = ax^2

but ik x = 1

so 1 + b = a

[proper island]

take 1st derivitabe

[cunning bane]

how ?

[proper island]

uhh

what lvl of math u in

[cunning bane]

calc

[proper island]

ye so take deriavite

you get x = 2ax

[cunning bane]

but how do i know what a and b i

[proper island]

a=1/2

or smht

idk

im dumb

b is only the shift

a affect the slope

1=a2x

a = 1/2x

and at x=1

a=1/2

[proper island]

so plug a=1/2 in at x=1

you get b

or smth

idk im dumb

[cunning bane]

wait that makes sense

thanks

[proper island]

👍

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[upbeat jay]

im working on this trig sub question,
and that is what i have, im not sure if im ont the right track

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[umbral dome]

looks good so far

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[lusty sorrel]

Hi

[lusty sorrel]

$\text{ Given } A = { x \in \mathbb{R} \lvert \exists a \in \matbb{R} \text { so that } x = \frac{a^2+a+m}{a+1} } \text{ Prove that } A_m=\mathbb{R} \text{, } \forall m < 0 \text{ , } m \in \mathbb{R}$

[glossy valve]

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

[lusty sorrel]

What i did is to write the fraction as $a+\frac{m}{a+1}$. So basically I need to prove that the set defined by this expression is equivalent to $\matbb{R}$.

[glossy valve]

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

[lusty sorrel]

Intuitevely it is. But is there a way to come-up with a rigourous proof?

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[lusty sorrel]

<@&286206848099549185>

[low echo]

Hi

[lusty sorrel]

Hello

Sorry, i think i've just found the solution

I should write this: $\frac{a^2+a+m}{a+1}=x$ to this: $a^2+a(1-x)+m-x=0$

[glossy valve]

nomemory

[lusty sorrel]

Then I should put the condition delta > 0

But delta is $x^2+2x+1-4m$ so if m < 0 we know the discriminant is greater than 0 $\forall x$

[glossy valve]

nomemory

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[fleet pewter]

can someone explain how to do this?

[torn jolt]

Alr, I can try.

But pls go easy on me, trigonometry isn’t my best topic.

I’m gonna help you the way my teacher would explain it.

[fleet pewter]

sure 👍

[torn jolt]

First, we must convert cot to 1/tan because the stupid calculator cannot do co-tangent.

secx becomes 1/cosx

[fleet pewter]

This is my working so far

[torn jolt]

Yeah same

[fleet pewter]

after that idk alr xD

[torn jolt]

But just shift sec over 😭

[fleet pewter]

o

if shift over then is divide?

[torn jolt]

Ya

Wait

Let me think

Wait what, I think i messed up

[fleet pewter]

its ok take ur time xD

[torn jolt]

Idk, I think someone else has to help you. Trigonometry is my kryptonite.

[fleet pewter]

o its ok no worries
ty for ur time

[torn jolt]

Yw 😭

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[fleet pewter]

^

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[arctic nacelle]

so trace = 6 hence third eigenvalue is 2

but how do i get k and m

the determinant is 10+3k-m

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[hoary surge]

1.f

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[hoary surge]

.repoen

damn

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[viscid token]

can i get some help on how to start this pls

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@viscid token Has your question been resolved?

[oblique yoke]

Hey! I can try to help!

[toxic vector]

Y=c2 from 5/(c2 from 13)

Idk what's totally Z idk that much math terms on English

[viscid token]

hello

[toxic vector]

U know combinatorics?

[viscid token]

so i actually did the first bit where it asked to find the distribution of Y, but im a bit stuck on the 2nd part where it asks to find Z and stuff

[viscid token]

yo

[viscid token]

nah, maybe i have another term but i can show u my working rq

[toxic vector]

Aight

Wait Lemmy translate whole problem

[viscid token]

I think that’s part A

Ignore the stuff on the right, I’m just tryna figure out part B which is finding Z

[oblique yoke]

Uhmm

[toxic vector]

So

% of Y

Is probability of getting red(at least one) ones divided by all probabilities

As I get the problem idk

[oblique yoke]

To find the distribution of ( Y ), let's first consider the possible values that ( Y ) can take. Since Bob selects two balls at random without replacement, ( Y ) can take values from 0 to 2.

When ( Y = 0 ), it means Bob drew 0 red balls, which can happen in only one way: drawing both blue balls.
When ( Y = 1 ), Bob could have drawn one red ball and one blue ball. There are ( \binom{5}{1} \times \binom{7}{1} ) ways to choose one red ball and one blue ball.
When ( Y = 2 ), Bob drew both red balls. This can happen in only one way: drawing both red balls.

[glossy valve]

evil murkius

[viscid token]

Bob can only select 2 balls, so the possible values Y can be is 0,1,2 is what I got from the question

Then I just did some probability calculations from there

That’s how I got 7/22 for 0 red, 35/132 for 1 red and 5/33 for 2 red

I just don’t get how to do part B

[oblique yoke]

So, the probability mass function (PMF) of ( Y ) is:

[
P(Y = 0) = \frac{\binom{7}{2}}{\binom{12}{2}}, \quad P(Y = 1) = \frac{\binom{5}{1} \times \binom{7}{1}}{\binom{12}{2}}, \quad P(Y = 2) = \frac{\binom{5}{2}}{\binom{12}{2}}
]

To find the distribution of ( Z ), the total of two independent random variables ( Y_1 ) and ( Y_2 ), we can use the convolution of their probability mass functions.

[
P(Z = z) = \sum_{k=0}^{z} P(Y_1 = k) \times P(Y_2 = z-k)
]

[glossy valve]

evil murkius

[oblique yoke]

Dw, evil murkius is here!

[viscid token]

Lol

[oblique yoke]

Did i help u in any way??

[viscid token]

Uhm

I don’t really get what u typed out tbh

[oblique yoke]

My abd

My bad

U need help rn

Wirh

Wirh

With

?

B?

[viscid token]

it's alright boss

ty for ur time

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[heady widget]

i got 6x^2 as area

NB^2 = 4x^2 + 3x^2

[graceful loom]

Use pythagoras twice

[heady widget]

NB^2 = 7x^2

[heady widget]

yeah i want to check whether

is correct

[graceful loom]

split it into three triangles

The white region

Only two matters

[heady widget]

how about i write my working you correct it out?

[buoyant wadi]

Another approach is find the area of ABCD, then remove the areas of ABN, BCM, and DMN

[heady widget]

NB^2 = 7x^2
NB = 7x
NM^2 = x^2+ 2x^2
NM=3x^2
BM= 7x-3x= 4x
area 4x*3x/2= 6x^2 @graceful loom

[heady widget]

that would take way longer tho

[buoyant wadi]

Not necessarily

Like, finding the area of a square and right angle triangles is a pretty straightforward calculation

Less back and forth than finding the lengths of BM and NM imo

And also, doing two methods is a good way to error check
(Noting that I did make an error with one method that I found after using the other)

[heady widget]

i find it easier to find sides you know like doing a puzzle

is my answer correct tho

[buoyant wadi]

Sorry but I don't think so

For one thing, NB^2 = (4x)^2 + (3x)^2 = 16x^2 + 9x^2 = 25x^2

Making NB = 5x

[buoyant wadi]

This is fair though, do whatever method calls to you

[heady widget]

i got everything wrong??

[buoyant wadi]

Yeah unfortunately, you didn't carry through the exponents properly in a few places

[heady widget]

sorry for wasting your time

[buoyant wadi]

Dude you're fine, I'm literally here to help out!

[heady widget]

i am just gonna do it again since you didnt write out the entire answer

[buoyant wadi]

Yeah that's a good plan!

Just remember that (ax)^2 = (a^2)(x^2)

[heady widget]

thank you

[buoyant wadi]

No prob

I'll hang out here if you wanna run your thinking past me or anything

[heady widget]

nm2 = (x)^2 + (2x)^2 - x^2 + 4x^2= 5x^2
since NM^2 = 5x^2
so should i keep it as sqrt 5x^2??

then use it later

[buoyant wadi]

You can yeah

You could simplify a little by pulling out the x,
sqrt(5x^2) = sqrt(5)x

But it doesn't make much of a difference

[heady widget]

5x^2 - sqrt 5x^2

=bm^2 = 20

or bm =20 ?

[heady widget]

is the area 5 sqrt 5x

[buoyant wadi]

You're on the right track, it's correct that BM^2 = 20x^2

[heady widget]

ok so i put sqrt 20 * 5/ 2 @buoyant wadi

i get this

[buoyant wadi]

That's very close, can you simplify for me?

Be careful of where the brackets for sqrt are, and try not to drop the x terms

[heady widget]

5* sqrt 5 x

[heady widget]

is the fraction wrong tho

[buoyant wadi]

Well it depends on where the brackets for the sqrt are

1. sqrt(20)*5/2
2. sqrt(20*5)/2
3. sqrt(20*5/2)

Can you tell me which one you mean? Only one will get you the right answer

[heady widget]

1st one

[buoyant wadi]

Okay, I think you might've made an error somewhere then

What you're trying to do is BM*NM/2 right?

[heady widget]

yeah

[buoyant wadi]

Can you tell me what the lengths of BM and NM are again?

[heady widget]

sqrt 20x =BM nm = 5x

[buoyant wadi]

You might have BN and NM confused, you got sqrt(5)x here

[heady widget]

bro my ass is failing

holy shit i am making so many mistakes

[buoyant wadi]

Lmao it's fine, it's easy to get symbols mixed up

This is actually a good example of why doing it in two ways can be helpful

Since if you got a different answer doing it a different way, you would know at least one of them was a mistake

[heady widget]

sqrt 20 * sqrt 5

divided by 2

????

corret???

[buoyant wadi]

Yeah, and that will simplify very nicely actually

sqrt(a)*sqrt(b) = sqrt(ab)

[heady widget]

5x ??

area

[buoyant wadi]

5x^2, but yeah!

[heady widget]

holy shit thank you so much, you are such a patient person,

[buoyant wadi]

It's no problem, I was done with everything I needed to do today anyway 🙂

[heady widget]

thank you so much,bye bye!

[buoyant wadi]

Good luck with everything else!

[heady widget]

👍

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[steady flicker]

Hello! Studying for a math test, I’m doing some review questions. Not sure what went wrong, answer should be 1/6 but I got 1/24 😻💀

[torn jolt]

ok

sso

actually

i'm probably not the best person for this

[steady flicker]

no worries! any help accepted

i love your username btw

[quartz gale]

The problem is that you didn’t calculate the right probability

Do you know about Probability with assumption ?

[steady flicker]

lemme check my notes

i don't think we covered that

[ember shadow]

Looks like conditional probability?

[quartz gale]

That’s unlikely

[steady flicker]

i can check again

[quartz gale]

Ah yes right that’s what it’s called

[ember shadow]

OP had the right first step though

She wants p(M | P)

[quartz gale]

Yeah that’s why I asked for definition

[steady flicker]

yep def covered that

[steady flicker]

ohhhh

[ember shadow]

You know the formula for it?

[steady flicker]

sometimes the line blurs for me, what would be the diff between p(M|P) and p(M∩P)?

[steady flicker]

yes

but contextually, what's the difference?

i don't know how to put it

[ember shadow]

The union is what you're given in the problem statement.. It's the prob of picking a random person from the whole sample who is male, or wears pink, or both

[steady flicker]

but i know that P(M|P) would be like "what's the chance you select a male assuming that he wears pink?" so what would p(M∩P) be

[ember shadow]

Conditional probability is the probability of picking a random person who is male, given that it's someone who wears pink

[steady flicker]

ohhh got it

[steady flicker]

okay i just finally understood what this meant 💀

[ember shadow]

The intersection is probability of picking a person from the whole sample, who is male and wears pink

[steady flicker]

got itttt

i understand the key words in the problem now, thanks!

[ember shadow]

Yw

[steady flicker]

have a good night or rest of your day :)

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[nova ice]

finding s_n for arithmetic equations

i was wondering if i did this correctly

and also: what the hell is going on here

why are there dots??

[graceful loom]

Um so that it doesn't get printed off the page

[nova ice]

oh

[graceful loom]

To save paper

[nova ice]

its spacers

[graceful loom]

Ye

[nova ice]

wait actually

[graceful loom]

Or else we would write all the elements in between

which is a waste of ink

and paper

[nova ice]

its just an insert answer here thing??

oh

wait no

its

ok

good god

i get it

[graceful loom]

Right what are you confused about?

[nova ice]

ok sorry

the question is Find Sn for the following arithmetic sequences described.

its just a sequence/ series?? ill figure that out

wait

no its a series

how does one find s_n for a series

im aware i have some pretty hefty knowledge gaps so pls bear with me if this is stupid obvious to anyone who knows anything

[graceful loom]

Do you know the general formula of an arithmetic sequence?

[graceful loom]

series is a summation

In this case it is a sequence

There is no sum here

[nova ice]

i was also wondering if i did problem b at the top correctly, since im not too familiar w this concept

[nova ice]

they are all being added though?

[graceful loom]

Oh right

Well technically its more like a sum

Than a series

But for this case it is not really the matter

[nova ice]

mhm

so its still technically a series

[graceful loom]

*technically

We are taking a summation over a formula from i=1 to i=something

Ok back to the problem

Do you know the general formula for S_n of an arithmetic sequence?

[nova ice]

mmmm

S_n = n * (a_1+ a_n)/2

?

[graceful loom]

Yes

So we need to find n

How do we find such n?

Any thoughts?

@nova ice

[nova ice]

yeah sorry im trying to supplement with khan academy lol

in a normal problem theyd give me a1 d and a_n

and you have to solve for n with that and then plug it in to S_n = n * (a_1+ a_n)/2

but with this its just a string of numbers

[nova ice]

i feel at a loose end they havent given much info

<@&286206848099549185>

[graceful loom]

Hi I'm back lol

I just finished dinner

sry for the delay

@nova ice

Right, consider the sequence 4,10,16...106

Note that this one is a SEQUENCE

Not a sum

Do you agree?

[nova ice]

oh lmao no worries dude

yep

not stuff being added

[graceful loom]

Yes. How many terms are in the sequence?

We are trying to solve for "n" btw

[nova ice]

ah so sorry! my discord isnt pinging for some reason

106 terms

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[nova ice]

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[primal haven]

Good morning, Got some help earlier but got busy and coming back to working out these series/parallel worksheets. Not needing answers but it get very overwhelming in my head

Would appreciate helping me putting this in order

[lime ether]

you might want to go to a physics discord

[primal haven]

I tried but this is all math

As well as eletrical engineering lol

[lime ether]

looks like a circuit to me

[primal haven]

It is, its all calculating based on given information

[lime ether]

use loop rule and junction rule👍🏻

[primal haven]

lol thank you

Gonna have a strongly written email to all of those old mathematician after all of this though.

[lime ether]

yea lol electrical engineering seems rough i never liked circuits

[primal haven]

All for AMT certification. Honestly doubt I personally will ever need any of this, at the very least not in this fashion

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[torn jolt]

How would you do that

[graceful loom]

!status

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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

@torn jolt Has your question been resolved?

[graceful loom]

@torn jolt

Which part are you confused about?

[torn jolt]

My friend taught me

Value of v

You gotta differentiate

But I got a question

Why do you initially differentiate

To find v

@graceful loom

[graceful loom]

Since we want to find the minimum value

[torn jolt]

You mean the value of v?

[graceful loom]

Yes

[torn jolt]

I mean a) i)

[graceful loom]

Yeah

We take its differential

[torn jolt]

Wouldn’t the first f(x) give the Gradient

[graceful loom]

C is a function

To find the minimum cost we need to find dC/dv=0

[torn jolt]

Oh

Differentiating makes it = to 0

?

@graceful loom right?

[graceful loom]

No

It is the gradient function of C

[torn jolt]

But in this instance

When it’s a function

And you differentiate it

It makes it equal to 0

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[lofty wigeon]

c) 3, 6, 11, 18, 27, 38, 51, 66, 83, 102, . ..

an = an-1 + (2n+1)
a0 = 3
n >= 1

[lofty wigeon]

Can I solve it like this?

The question was find the formula of the sequence

[rare dock]

lots of ways. one is to notice the sequence grows quadratically

that nails it down pretty quickly

[lofty wigeon]

First time hearing about increasing quadratically. interesting

Thank you

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[quaint prawn]

🦦

[rare dock]

🦫

[quaint prawn]

🫡

[quaint prawn]

🌎

[rare dock]

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[slate night]

Prove that this function with x different to 1 and -1 has no extremities

So I calculated its derivative

Heh?

Wdym 6?

That doesn't answer the question

What is?

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[viral ore]

i need to represent this as sigma notation, so far i have (next picture to the problem). i was thinking it would (n+1)! at the bottom but i get stumped at the third given term, 12 isn't a factorial of any whole number

[fathom saddle]

10! does happen to be that last number

Indeed I think it's supposed to be (n+1)! but they typo'd that third term

[viral ore]

probably is

thanks

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[ionic zinc]

is it safe to assume, that the max min points you derive from the derivative of a cubic function are its global max and min

[velvet sedge]

no

[graceful loom]

N

No

[velvet sedge]

if you are including entire real line its 100% not global min/max

[ionic zinc]

what about local max or min

[velvet sedge]

yes

so long as they

[ionic zinc]

wait so whats the difference

[graceful loom]

Look you are considering a delta neighberbood when it is a local max or min

[ionic zinc]

huh

what

[graceful loom]

You are considering it over the entire domain if it is global

[velvet sedge]

local min max occur at x-values where f'(x)=0 and f''(x) not equal to 0

[ionic zinc]

okay

so in terms of problem solving

like

[graceful loom]

@velvet sedge shouldn’t it be better to use the delta neighberbood definition though

[ionic zinc]

when im asked to find a maximum price, quantity or whatever

of a cubic function

[velvet sedge]

depends on how rigorous they wish to be

[graceful loom]

Yeah

I mean for intuition that works the best

@rough tide plz open a new channel

[torn jolt]

this wrong

x⁶ has a local min

[ionic zinc]

im sorry my

[velvet sedge]

yea

[ionic zinc]

internet fucked

[ionic zinc]

Is it safe to assume thay

Theyre asking for

Local max or min

?

[graceful loom]

Well safe to say yeah

But it’s not too rigorous

[ionic zinc]

Okay

Can u give me an example of a application based q

Where they may ask for global max or min

Finding global max or min is so confusing

[graceful loom]

The difference is considering a delta neighberbood of the point vs the whole domain

[ionic zinc]

Okay whats a delta

Neighbourhood

😭

[graceful loom]

It’s more like analysis level

But for intuition it works the best