help-49

[teal raptor]

and if you dare to study a step of logarithm.

you know that

(x-1)log16 = 4xlog6

which is followed by
(4x-4)log2 = 4x(log2 + log3)

[thorny oasis]

wtf does in terms of ln 2 and ln 3 mean

[teal raptor]

wait........

that doesn't matter

because ln x = $\log_e x$

[grand pond]

A_Note

[teal raptor]

it's another definition

related to e

so if you dare to study that, you'll instantly know that

(4x-4)ln2 = 4x(ln2 + ln3)

4xln2 - 4ln2 = 4xln2 + 4xln3

seperating x and number

and removing 4xln2 from both sides

4xln3 = -4ln2

xln3 = -ln2

x = -ln2/ln3

hehe i'm not helping more

[thorny oasis]

y this step

[midnight plank]

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[last slate]

Am i understanding the Jacobian the right way?

I'm really not sure about since my answer should include the basiss vectors.

[midnight plank]

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[low viper]

how x get rid of the negative

[obtuse basin]

-x = -1 * x,
d/dx (-1 * f(x)) = -1 * d/dx f(x)

[low viper]

still unclear

[low viper]

still unclear

[obtuse basin]

You are familiar with the property that d/dx (c * f(x)) = c * d/dx f(x), right?

[low viper]

no

[cedar mason]

actually do some studying before asking damn

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[light oak]

I have to estimate the area under f(x) with the given interval using 5 left rectangles

[light oak]

I have drawn the rectangles but I don’t get what to calculate for f(1/6) and so on

[visual tiger]

what's your formula for f(x)?

[light oak]

Square root of x

[visual tiger]

so f(1/6) is...

[light oak]

Square root of (1/6)?

[visual tiger]

yes

[light oak]

So you wouldn’t necessarily get an concrete value for the area because you using square roots?

[visual tiger]

why would square roots not be concrete?

[light oak]

Like an answer of 89 what I meant

[visual tiger]

well you won't get an integer answer, that's for sure

[light oak]

Because then it was be square root of 1/6 + square root of 1/3 + etc

[visual tiger]

the answer you will get is irrational, there's no doubt

if by "concrete" you mean "nice round answers" well this isn't one

[light oak]

So you wouldn’t be able to simplify into one number then

[visual tiger]

Also it's asking to estimate

[light oak]

Yeaaa sorry about that

[visual tiger]

so take an estimate of sqrt(1/6)

same for the others

Quick problem : this is actually 6 left rectangles

[light oak]

Why?

[visual tiger]

there's a hidden rectangle of f(0)*1/6

[light oak]

But how would you draw that ?

[visual tiger]

a line

like use a different color

So, your problem is that you're using 6 rectangles

we want 5

so what do we change?

[light oak]

Wait I thought I was using only 5 rectangles tho because I 5 separate values

[visual tiger]

as mentioned, it's 6 separate values

since you're tasked to use 5 left rectangles, one of the rectangles has to be f(0)*(b-a)/n

[light oak]

Okay so we get rid of f(5/6)*(1/6)

[visual tiger]

well there's more to it than this

how do you divide [0,1] equally into 5?

[light oak]

Ohhhhhhh my goodness

Bruh you right

I was looking at my teachers example and copied the n value and not the one from this problem

So it’s 1/5

[visual tiger]

yes

so the sum (area approximation) is actually?

[light oak]

Sum of what

[visual tiger]

You wrote $A\approx ...$

[grand pond]

rafilou2003

[visual tiger]

how does it change?

[light oak]

I don’t know how to estimate a square root of 1/5 though

[visual tiger]

it's ok

[visual tiger]

sqrt(1/5) = sqrt(5)/5

[light oak]

I thought it would be sqrt(1/4) which would be 1/2

[light oak]

3/5?

[visual tiger]

this isn't what I asked

you wrote before that $A\approx \frac{1}{6}f(\frac{1}{6}) + \frac{1}{6}f(\frac{2}{6})+...+ \frac{1}{6}f(\frac{5}{6})$

[grand pond]

rafilou2003

[visual tiger]

however, we saw that first of all that's not correct

because this is a division in 6 rectangles

So the correct formula should be $A \approx ...???$

[grand pond]

rafilou2003

[light oak]

1/5f(0) + 1/5f(1/5)… + 1/5 f(4/5)

[visual tiger]

yes

[light oak]

So that would be the sum/ area approximation then?

[visual tiger]

yes

[light oak]

Ok thanks

[visual tiger]

I'll write it now, using $\frac{1}{\sqrt{5}} = \frac{\sqrt{5}}{5}$, $A\approx \frac{\sqrt{5}}{25}(3 + \sqrt{2} + \sqrt{3})$, feel free to check

[grand pond]

rafilou2003

[light oak]

Ok

.close

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[gaunt ibex]

where do i start with this

i cant use u sub

[terse spear]

Didn't I help you with something similar?

[gaunt ibex]

this is different

[terse spear]

It's still similar

You can apply the same logic

[visual tiger]

have you seen complex numbers?

[gaunt ibex]

nope

[terse spear]

Manipulate it so it's all in terms of sine or cosine

[gaunt ibex]

i used the angle identites finally

bcz the answer in my book is like that

[terse spear]

You can use Pythagorean theorem and manipulate it

[gaunt ibex]

I need to use half-angle identities

ill get through it then

.close

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[wise cloak]

i need help

[wise cloak]

in phisycs

8th class

[wise cloak]

i need to figure out

why hookes law doesnt work on partial deformation

[tiny drum]

#old-network

[midnight plank]

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[timid tangle]

Hello

[timid tangle]

Does this mean p1 = x, p2 = y, p3 = z?

Does the vector matrice always follow the order: x, y, z?

[verbal rain]

xyz etc are just choices made for (1st dimension, 2nd dimension, 3rd dim..., n dim)

its arbitrary, all that matters is the order.

[timid tangle]

Oh okayyy

Thanks

.close

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[bitter tartan]

help

[bitter tartan]

is y1 angle c?

i dont get what triangle 2 is

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[potent veldt]

similar triangles

[brittle breach]

Lemme try one sec

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[still epoch]

I keep getting -root3/2

I don’t get it

[uncut cloud]

,rotate

[still epoch]

Because if you were to derive cos, it’ll be -sinx and evaluated at pi/3 is -root3/2

[nova yoke]

rate of change of g

[uncut cloud]

And g is itself the derivative of cos

[still epoch]

Oh then g(x) is -sin?

[nova yoke]

yea, that's what the limit evaluates to

basically the definition of the derivative of cos

[still epoch]

So it wants me to take another derivative

-cosx

[nova yoke]

yea

[still epoch]

Ah I see now

Thanks

[midnight plank]

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[gloomy fiber]

how do i prove a function is discontinuous everywhere?

[halcyon mulch]

more clear question please ?

maybe give us the fonction or what u tried/thought

[gloomy fiber]

dirichlet function

or a modification of dirichlet function

i.e f(x) = {x if x is rational; -x if x is irrational} (prove x is discontinuous everywhere except 0)

i already proved its continuous at 0

someone here suggested that i use the negation of the epsilon-delta definition for a everywhere continuous function

[halcyon mulch]

have you tried doing a typical proof like that ^

i can assure you it will work do a case for x is rational and x is irrational

and the espilon delta proof should follow

the only thing you will need is like density in the real number

your on the right track !@

[gloomy fiber]

i dont really know the epsilon definition for a continuous function

[halcyon mulch]

https://www.kent.ac.uk/smsas/personal/elm2/MA552/MA552Worksheet5.pdf

[gloomy fiber]

can x_0 = x?

[halcyon mulch]

well here that would be for a point

soryr

[gloomy fiber]

wait cant i use the same definition tho?

[halcyon mulch]

https://en.wikipedia.org/wiki/Nowhere_continuous_function

yeah pretty much just assume either case and keep going

you should be able to do it

[gloomy fiber]

can you show me the definition for all continuous too btw?

[halcyon mulch]

that is just

not discontinous (-infinity, infinity)

[gloomy fiber]

epsilon delta definition i meant

[halcyon mulch]

yeah its the smae thing u just gotta prove for other than 0

i found a similar proof that proves continuity everywhere

https://math.stackexchange.com/questions/3479360/proving-a-function-is-continuous-everywhere

https://en.wikipedia.org/wiki/Dirichlet_function#:~:text=The Dirichlet function is nowhere continuous.&text=If y is rational%2C then,f ( y ) %3D 1.

but here there is the short proof ur looking for

[gloomy fiber]

would anything greater than 1/2 not be suitable?

for epsilon

[midnight plank]

@gloomy fiber Has your question been resolved?

[gloomy fiber]

@halcyon mulch when writing a proof for continuity when writing the x^4-a can i assume x = a?

simply because it must if it is continuous

.close

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[last slate]

free

[last slate]

<@&286206848099549185>

i think i've got the answer just want to double check innit

Ello?

anyone there?

[oblique shell]

Should be $6^{\frac1{10}}$

[grand pond]

MTBO

[last slate]

yep that's what i'm thinkin

are ya sure?

[oblique shell]

Yes

[last slate]

what about

this one?

[oblique shell]

What do you think it is?

[last slate]

currently trying to make sense of it and solve it

2 mins

[spiral oyster]

isnt it 3/8-4/9

[last slate]

i can't seems to solve it

i'm confused on what to do with the 4/9

[spiral oyster]

arent you supposed to find comman denominator

[oblique shell]

Alrigjt so

[last slate]

i currently got (3 3/8) 4/9

[oblique shell]

4/9 you mesn

[last slate]

yes 4/9

[oblique shell]

not 3/9 rigjt?

[spiral oyster]

yea

[last slate]

yes

[oblique shell]

Alright, every time you got something of the form $(x^y)^z$ (notice the brackets, they are important), you can simply it to $x^{yz}$

[grand pond]

MTBO

[last slate]

hmm okay

[oblique shell]

So, you got $(3^{\frac38})^{\frac49}$, like you said

[grand pond]

MTBO

[last slate]

yep

[oblique shell]

So you just need to multiply the two rations

What is $\frac38\frac49$?

[grand pond]

MTBO

[last slate]

so it will be 3/12/72?

[oblique shell]

Why 3 over 12?

[last slate]

no no

uh

it's 3 and 12/72 sorry

[oblique shell]

Its $3^{\frac{12}{72}}$, correct

[grand pond]

MTBO

[last slate]

yes this

[oblique shell]

Thats $3^{\frac16}$

[grand pond]

MTBO

[last slate]

Yep

[last slate]

i understand that

So the final answer is 3 and 1/6

thanks!

i may have another question

what's this

i'm confuseda

<@&286206848099549185>

[gleaming arch]

@last slate working on it 🙂

we know definitely that 8^(1/3) = 2

my bad on not knowing fancy typing skills but yes 2^3 = 8

[last slate]

uhhh

/commands

/bot

[gleaming arch]

the cube root of 8 = 2

[last slate]

yes

[gleaming arch]

on top and bottom we know that 3 * 2 ^ something happens

[ (3 * 2) ^ (1/3) ] / [ 3 * 2 ^ (1/9) ]

[last slate]

uhm

[last slate]

wdym??

[gleaming arch]

haha I'm wondering the same thing

[last slate]

lmafooo

[gleaming arch]

Hold on, let me see if there's a fancy text markup on this server

[last slate]

Alr

[gleaming arch]

I'm new. Let me do some homework real quick 😛

[last slate]

oki

[gleaming arch]

do you have any idea how to make this: "8 ^ (1/3)" into fancy text?

/wolf

,wolf

[grand pond]

Please submit a valid query! For example, ,ask differentiate x+y^2 with respect to x.

Oct 9, 2023, 8:40 PM

[gleaming arch]

,wolf 8 ^ (1/3)

[grand pond]

Results provided by WolframAlpha

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

Requested by dustinwestglow

[gleaming arch]

@last slate how about that!

[last slate]

wooo u figured it out!

the fancy typing

[gleaming arch]

$(a^b)^c = a^{(b\times c)}$

[grand pond]

Cuantos_Hay_Tacos

[last slate]

5min gotta use the bathroom

[gleaming arch]

ok

this is rough ummm...

[last slate]

i'm back

[gleaming arch]

still working on it... jarvis skip the spinning rims

[last slate]

it's fine if you don't know i can get someone else

[gleaming arch]

thanks @last slate for letting me attempt it

[last slate]

thanks for trying to help

<@&286206848099549185> i request assistance!

let's see if I plug this into the graphing calc I get

0.654

wat

[last slate]

whAT

welpp

<@&286206848099549185>

shit well I didnt see the options

[last slate]

i see that

[last slate]

can u solve this one?

[meager path]

DO YOU KNOW YOUR INDICE LAWS

[last slate]

uhhh

what do you mean

i have no idea what INDICE LAWS are

[meager path]

INDEX IS ANOTHER WORD FOR EXPONENT/ORDER/POWER

[spiral oyster]

yeah we do

i*

[last slate]

uhh

not sure how that is relevant to me saying welp

uhhhh

[last slate]

WHY DO U WANT TO KILL ME

😭

[meager path]

DO YOU KNOW YOUR SURD LAWS

[last slate]

im just tryna do maths at 4 am

[last slate]

NO I DO NOT

[spiral oyster]

if you know tell him the steps

hes confused

so his little head could understand

[meager path]

YEAH MY WIFI SUCKS, I BELIEVE IN YOU THO

[spiral oyster]

WHY ARE WE SCREAMING LMAP

[last slate]

i loaveo you

will u marry me?

💍

[spiral oyster]

whtf

[meager path]

X =(

[spiral oyster]

isnt this 64/4?

[last slate]

is that a yes?

[spiral oyster]

6 4/4? or just 6? @meager path

[last slate]

im assuming it is

now we are married

ANYWAS

MOVING ON

I STILL NEED HELP DUDE

[spiral oyster]

<@&286206848099549185>

[meager path]

THE DOT THERE MEANS MULTIPLY,

SO 6³ × 6^¼

AND ONE OF THE EXPONENT LAWS SAY, WHEN MULTIPLYING 2 BASE NUMBERS , YOU ADD THEIR POWERS

SO 6³ × 6^¼
= 6^(3+ ¼)

[last slate]

wait it's a 7 then?

[meager path]

ANY CONFUSION¿

[last slate]

6 4/4

or a 6 wait what

[meager path]

NO IDEA WHAT UR TALKING ABOUT QUEEN

[spiral oyster]

6 4/4 no?

[meager path]

WHEN I SAY 3^(2) I MEAN 3² BTW

YALL SHOULD SAY IT LIKE THAT TOO, UNLESS IDK WHAT UR SAYING/ASKING

[spiral oyster]

bro thia hwlpa alot

[spiral oyster]

whats the anwser pookie bear

[meager path]

I BELIEVE IN YOU

[spiral oyster]

I DONT

[last slate]

I'TS 6

IT'S 6

[spiral oyster]

IS IT?

[last slate]

MY BRAIN IS FRIED AT THIS TIME

[spiral oyster]

IS IT 6 11/4?

[meager path]

SADLY NOT

6³ • 6^¼
6³ × 6^¼
= 6^(3+ ¼)

[spiral oyster]

6 3/4??????????????????????????????//

[last slate]

6

i think

[meager path]

DO YALL KNOW HOW TO ADD FRACTIONS

[spiral oyster]

3 + 1 = 4/4

[spiral oyster]

YEA now ur making me think we cant

[last slate]

I DON'T KNOW ANYTHING

AT ALL

WHO AM I

MY BIRTHDAY

WHO'S MY MOTHER

WHY DID MY DAD LEAVE ME

I DON'T KNOW

AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA

[spiral oyster]

dude am acc being seriosu stop wasting my tie left2dye

time

[last slate]

ok i'm sowwy

I'TS 6 13/4

ISN'T IT????

omg

[meager path]

3 + ¼

3 IS A WHOLE NUMBER, AND IN ORDER TO ADD IT TO ¼, WE NEED TO TURN 3 INTO A FRACTION WITH DENOMINATOR 4

[last slate]

i realize how to add fractions

i forgot how to what

3 = 12/4

12 + 1

= 13/4

omg

omg

[meager path]

YES, BEAUTIFUL

GLORIOUS

[last slate]

THANK YOU SO MUCH

[meager path]

6³ • 6^¼
6³ × 6^¼
= 6^(3+ ¼)
= 6 ^(13/4)

[last slate]

❤️

[spiral oyster]

LMFAPPAPA

THANK U MAMI BAII

[last slate]

.close

[midnight plank]

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[honest frigate]

How do yoi simplify this

[uncut cloud]

What's 1/c^(-2)?

[honest frigate]

What

[unique cedar]

When dividing numbers with exponents of the same base, it’s just subtracting the exponent

[honest frigate]

Damn bro I really just didn't think

Alr thanks

.close

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[inland grove]

qucik question

at the bottom of the page

they are factoring the polynomial

how do i find out how to factor with a polynomial with the power of ^3

is it just guessing?

[fresh sparrow]

kinda

[midnight plank]

@inland grove Has your question been resolved?

[inland grove]

What do you mean by kinda

[fresh sparrow]

in this case, I don't think i would've derived it anyhow, it just looked like 1 could work and it miraculously does

[inland grove]

Oh alright

Thanks again

.close

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[torn path]

a band is planning a world tour with different cities in different countries, how many different concert schedules can be created ?

[torn path]

this is using permutations and conbinations

[midnight plank]

@torn path Has your question been resolved?

[torn path]

Travel arrangements and budgeting would make it easiest to play in all North American cities first, then 3 Asian cities and finally 4 European cities. How many different concert schedules can be created?

[torn path]

The band recently performed at the Prague and Tokyo venues, so they decided to leave them out on this tour. Family commitments may also mean that they would need to play at any 5 European or Asian venues first, followed by 2 North American venues. How many different concert schedules could be created in this case?

[sudden heart]

Looks like there are 15 cities total, so 15 options for the first city, 14 options for the second city, and so on. The answer for a should be 1514131211

Ah 15x14x13x12x11 idk why discord did that with the text

[torn path]

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[last slate]

If you can figure this out you are a genius

how do you find the values of a and k in the formula $f(x)=af(k(x-d))+c$

[grand pond]

RecRio

[royal portal]

So normally cuberoot x at 1 = 1

But here where one would be it’s at -5 from the central point

So a is -5

[last slate]

I was leaning more towards an algebraic way to solving it

[royal portal]

Ok ik

[royal portal]

Start with this formula

Plug in the x and y values

From the graph

And you get equations with unknowns

[last slate]

unknowns being a and k

[royal portal]

Yea

[last slate]

currently trying out where im finding what a is = to in terms of k

and subbing that back in

solving for k

and ultimately a

having a few hiccups though

[royal portal]

What do u have rn?

[last slate]

figured out that $a = {5}/{-k^3}$

[grand pond]

RecRio

[last slate]

using my points (-5 and 3)

trying to sub in to the equation

I'm getting $5=({5}/{k^3})(-k^3)$

[royal portal]

Also btw k doesn’t rlly matter

[grand pond]

RecRio

[last slate]

ik it's 1 but I'm just trying to figure this out for when it isn't

because if I can't figure out it's 1 when it is 1 I won't have much luck when it isn't

I heard about a guess and check method for this question but that doesn't feel right to me 😂

[royal portal]

Don’t worry about k

Only a matters

[last slate]

here or..

[royal portal]

In general you can factor out k^3

For cubics

And you agree a times k^3 is just some other scalar

[royal portal]

In this formula

[last slate]

yeah sure, but I'd like to be able to solve something like this if I wanted to

[last slate]

yeah this is impossible

to solve

im telling you, this has to be some kind of wrong question or something

or maybe just impossibly hard lol

[midnight plank]

@last slate Has your question been resolved?

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[jovial river]

Hey, can I assume, in questions like those, that AD is a vertical line segment?

[soft token]

Is it explicitly given?

[jovial river]

No, the only things mentioned are in the picture I sent

but because the angle of x is equal to y I think I can assume that

but i am unsure

[soft token]

If i rotate the whole figure by let's say 45°, everything posited in the question still works.

So, would AD be still vertical then?

Btw, i don't see why you even need it?

Vertical doesn't give you anything meaningful. Does it?

[jovial river]

I solved it under the assumption that $m(\angle ABQ) + m(\angle QBC) = m(\angle DCQ) + m(\angle BCQ)$

[grand pond]

Monkagoras

[jovial river]

if m(ABQ) + m(QBC) = 180 and m(DCQ) + m(BCQ) = 180 that would ne true

[soft token]

Well, that holds always since AD is a line.

It doesn't need to be vertical.

[jovial river]

Oh, I see

didn't really think of that, thank you

.close

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[graceful frost]

how do I do this question

<@&286206848099549185>

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[graceful frost]

.clos3

.close

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[graceful frost]

does anyone know how to do this question?

<@&286206848099549185>

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@graceful frost Has your question been resolved?

[graceful frost]

<@&286206848099549185>

@graceful frost

@uncut drift

[uncut drift]

!15m

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[graceful frost]

.close

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[heady latch]

What is the derivative of x* sqrt (x^2 -4x+4)

[nova yoke]

did you try and get stuck somewhere?

if so, please show how far you got

[heady latch]

I just don’t know if I’m correct

[nova yoke]

no that's not quite right

using the product rule is correct

but in the second term where you have to differentiate sqrt (x^2 -4x+4), that part is wrong

you want to use the chain rule for that

[heady latch]

Didn’t I use that?

1/2 * (x^2-4x+4)^ -1/2 * D(x^2-4x+4)

@nova yoke ?

[nova yoke]

I would expect to see a square root in the denominator of the second term

[heady latch]

yea but on the right side my outcome is 1

[nova yoke]

since the derivative of sqrt(x) is 1/(2sqrt(x))

why is it 1

that would imply that you differentiated x

but you differentiated sqrt(x^2 - 4x + 4)

[heady latch]

Should I write 1* (2x-4)/ 2* sqrt ( x^2-4x+4)

But its still gonna have the same outcome no?

its still gonna be 2x-2?

<@&286206848099549185>

[nova yoke]

oh i didn't notice that you're taking the square root of a perfect square

why not just simplify it before even doing the differentiation?

sqrt(x^2 - 4x + 4) = sqrt((x-2)^2) = |x-2|

(note the absolute value which you'll still have to contend with)

[heady latch]

yea

what is the outcome?

[nova yoke]

not differentiable at all at x=2, otherwise break it into two cases, x<2 and x>2

[heady latch]

im so confused

[nova yoke]

if x<2 then |x-2| = -(x-2), and if x>2 then |x-2| = x-2

[heady latch]

oh so its -(x-2)?

I gtg eat brb

but what is the answer now?

[midnight plank]

@heady latch Has your question been resolved?

[heady latch]

nah but im done

.close

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[median cipher]

am using cosin law but am just not getting it right

[lyric charm]

!show

[midnight plank]

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

[median cipher]

i did cos=11^2+15^2-20^2/2(11)(15)

[lyric charm]

missing parentheses

[median cipher]

where?

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[placid vessel]

This is 1

right?

[midnight plank]

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[vestal pewter]

I need help understanding fourier transform, specifcally why a finite sine wave is seen as many waves

[rain isle]

i am unsure exactly what this question is asking for

i assume it means "length it streches to" but how do i calculate that from whats givin?

[midnight plank]

@rain isle Has your question been resolved?

[west iron]

F = -kx

F = force applied
x = spring stretch distance
k = spring constant (spring rate here ig)

[midnight plank]

@rain isle Has your question been resolved?

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[spiral oyster]

Can someone explain what to do after having 16/3

I don’t understand

<@&286206848099549185>

[last slate]

same

[fallow scarab]

!15m

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[spiral oyster]

?

[last slate]

i don't understand how to do it

[fallow scarab]

@spiral oyster

[spiral oyster]

Ok?

[last slate]

omg thank you so much

[spiral oyster]

THANK YOU SO MICH

[last slate]

me being an idiot forgot how to divide fractions 🤦‍♂️

[spiral oyster]

😭 we were stuck on that for 30 mins

45**

[last slate]

yes we are idiots 😭

[spiral oyster]

.close

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[glacial quail]

i keep getting 3.6 but it's 2.38

[slender walrus]

show work

[glacial quail]

heres a better image

[glacial quail]

ok

sooo [-7/x+3 + 2 ln |x-1|] where b = 10 and a = 3

[slender walrus]

you didn't integrate that first term properly

[glacial quail]

probably how so tho

im guessing it's the sign

[slender walrus]

assuming you meant
-7/(x+3)
how are you getting that?

[brittle charm]

isn’t the x+3 squared

[glacial quail]

yep

[brittle charm]

so the primitive of 1/u^2 is -1/u + C

[glacial quail]

hang on

This is what I did

Where did I go wrong

[slender walrus]

exactly where mentioned

[brittle charm]

after the first equal sign

[slender walrus]

$\int \frac{-7}{(x+3)^2} \dd{x} \redneq \frac{-7}{x+3} \ \gray{+C}$

[grand pond]

ℝam()n()v

[glacial quail]

ok

how so tho

genuinely

[slender walrus]

show the work/rules you're aplpying here

[glacial quail]

bc im using the integration rule

[brittle charm]

the primitive function of 1/u^2 is -1/u + C

see there is a - sign

[glacial quail]

omd

nm

[glacial quail]

thanks i just realised just before u said that

i cant believe i did that all this time

i was so confused i thought i was following the steps exactly

[brittle charm]

np

that’s a common mistake

[glacial quail]

it's literally bc it was very small on the document i was viewing it on

regardless thanks for the explanation

[midnight plank]

@glacial quail Has your question been resolved?

[midnight plank]

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[jovial river]

Hey, how can I find x here?

[jovial river]

if it is too blurred the angles are 100, 95 and 60 degrees

[slender walrus]

do you know the interior angle sum of a polygon with 4 sides?

[jovial river]

not really, the book has not yet mentioned that

[ember sinew]

The interior angle sum of a polygon with 4 sides always stays constant as long as the shape has 4 sides and 4 angles.

[slender walrus]

i'd recommended looking up interior angle sum of a polygon

[ember sinew]

Consider a square. Or a rectangle. You have four 90 degree angles. If you add them all up, you get 90*4 = 360

[jovial river]

oh, now I see, I can transform that polygon into two triangles which the sum is of angles is 360^o

Thank you, didn't think of that

[ember sinew]

You don't have to think about two triangles. Once you know that the sum of all angles is 360, you can just do 360 - (angles) = x.

But yeah, there are many ways of solving it

[jovial river]

Understood, ty for the help

.close

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[misty void]

What happens when you get an undefined limit when doing improper integrals?

[misty void]

is this correct?

<@&286206848099549185>

original integral

im fairly sure i integrated correctly

just not sure whether having an undefined limit is normal and what that means

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[midnight plank]

@misty void Has your question been resolved?

[midnight plank]

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[knotty depot]

How do I solve this is I don’t know the total production

[knotty depot]

Suppose a company manufactures two types of electronic devices, A and B. The quality control process classifies each device as either "defective" (D) or "non-defective "(ND). It is known that:
• 10% of all devices produced are type A.
• 30% of Type A devices are "defective"
• 20% of all devices produced are Type B.
• 15% of Type B devices are "defective".
A) Calculate the probability that a randomly selected device is Type A and "defective".
B) Calculate the probability that a randomly selected evice is "defective".
C) Given that a device is "defective", what is the probability that the device is of Type A.
D) Returning to part A), if it is known that 5% of all devices are defective, are the events "Type A" and "Defective" independent? Explain why or why not?

[unique forge]

you don’t need to know the total production. if you feel like you have to, just make some number up

[knotty depot]

Then how can I know if they are independent or not

[unique forge]

by checking if they satisfy the condition of being independent events

[knotty depot]

Well I think they are but idk what the question asks

Like we have a stochastic definition

And a normal one

[chrome depot]

use the AND rule for A

I'm not sure how I can explain the res

t

[knotty depot]

No

[chrome depot]

welp, bye I suppose

[knotty depot]

We have to know they are independent before we use that

I think that by nature they are

But idk how to show that

Like being from type A doesn’t have an effect on if an item is defective

It’s just correlation not causation

[unique forge]

yes, but does correlation suggest dependence

[knotty depot]

That’s what I don’t know

I mean I can use bayes theorem to find the chances of each event given another but idk what the total defective products are

[unique forge]

also you’re overthinking this by a lot
all you need is some probabilities and show whether or not they satisfy the definition of probability for independent events

[knotty depot]

I don’t get it dude I’m sorry I am such a loser who can’t learn shit

[unique forge]

that being said i think the question is slightly flawed

[knotty depot]

I could answer it if I know what the 100% of all production was

[unique forge]

you sure do, it’s given in the question

[knotty depot]

I can’t answer any of those questions if they are dependent ie not independent

No it says 10% is type A 20% is type b

Where does the other 70% come from and what is its error / defect rate

[fast estuary]

It is irrelevant what the other devices are

[knotty depot]

I am literally reading a definition of independence and still don’t get it

[fast estuary]

You can use that second condition here im p.sure

[knotty depot]

Then no they are not

Or they are

[fast estuary]

If probability of being defective = P(defective | type A)

[knotty depot]

Stochasgixallh

Stochastically yes

[fast estuary]

Then they are independent

[knotty depot]

P( type A given that it’s defective ) = p(type A?)

[fast estuary]

Should be both ways im pretty sure

Either direction

[knotty depot]

Not all unions are independent

[fast estuary]

P(A) = P(A given defective)

And

P(Defective) = P(Defective given A)

[knotty depot]

How do you know that applies@

It’s not about blindly using formulae

[fast estuary]

Because theyre asking me to check independence

That is how you check

By determining if those quantities are equal

If they arent, then theyre not independent

Its by definition that you check this way

I have no choice but to abide by the definition of independent event

Youre not blindly invoking formulae, you are appealing to the actual definition you're tasked with checking

[knotty depot]

So they are not independent

I still don’t see how you can know this without knowing the defect rate of the other 70% of profit

Product

Am I wrong here ?

Bc idk how to answer the other ones if they are not independent

[midnight plank]

@knotty depot Has your question been resolved?

[knotty depot]

.close

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[viscid quartz]

why is the answer for this 0 ;-;

[blissful pier]

Simplify $\frac{1}{x-2}+\frac{1}{2}$

[viscid quartz]

i plugged in 2 and got 4

[grand pond]

PajamaMamaLlama

[viscid quartz]

2+(x-2)/2(x-2)

...?

[blissful pier]

[midnight snow]

cancel

[blissful pier]

Now we have: $\frac{x}{\frac{2+x-2}{2(x-2)}}$

[grand pond]

PajamaMamaLlama

[viscid quartz]

yez

[blissful pier]

just cancel stuff

[viscid quartz]

can we cancel the x-2's here

[midnight snow]

no

[viscid quartz]

and the 2

[blissful pier]

nope, not quite

[midnight snow]

CRIMe

[viscid quartz]

sORRY

[blissful pier]

what's 2-2?

[viscid quartz]

0

OH

[blissful pier]

$\frac{x}{\frac{x}{2(x-2)}}$

[grand pond]

PajamaMamaLlama

[viscid quartz]

yez

adn then multiply...?

[blissful pier]

Rewrite this, and see if you see anything

$\frac{x}{\frac{x}{2(x-2)}}=x\div\frac{x}{2(x-2)}$

[grand pond]

PajamaMamaLlama

[viscid quartz]

x times 2(x-2) / x

which is 0!!!

wait but why cant we plug in 2 at the way begenning

[midnight snow]

division by 0

it is not allowed

[viscid quartz]

so that we get 2/(1/-2 + 2) + 1/2

o bc 1/-2+2 cant jus dissapear

[midnight snow]

ya

[viscid quartz]

thankx :))

[blissful pier]

[viscid quartz]

i shoulve paid attention in math last year 😔

[blissful pier]

we all learn at our own pace, even it if you fall behind no reason you can't catch up!

[viscid quartz]

thankss smm :))))

.close

[midnight plank]

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[blissful pier]

[midnight plank]

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[queen thistle]

Can someone explain how this simplification worked

For some reason its not clicking

[midnight snow]

taking e^x^2 common

[queen thistle]

oh my

that

oh

yeah

that makes sense now

okay thank you

.close

[midnight plank]

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[near sun]

https://gyazo.com/dff0df8120cb99e7f689322cdc4df0ee

[near sun]

i was wondering if i was doing this correct

i just solved for the top to be zero but im not sure if thats right

[midnight plank]

@near sun Has your question been resolved?

[fallen vigil]

You also need to make sure the 2nd derivative changes signs on opposite sides of the points

By the points I mean 0 and 6

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[sharp dawn]

anybody know why this would be wrong

[olive matrix]

the only issues i see are that maybe it wants a different symbol than U?
and that mayyyyyyyybe it thinks it should be increasing at -2 (like it should be closed there) but that would be a bit odd imo

[sharp dawn]

yeah it says to use U so idk what im doing /:

[olive matrix]

try the closed thing then

[sharp dawn]

yeah ive tried that also 😂

i think its just broke i hate this software

[eager cargo]

it should be [-2,-1]u[2,inf) i think

[fallow scarab]

What definition of increasing do you use

[olive matrix]

some definitions include "constant" in increasing

which i think is very silly

[eager cargo]

ah

ye thats weird then

[sharp dawn]

yeah ive tried that and the way we learned it we only use the closed signs for increasing decreasing

[sharp dawn]

wdym?

[eager cargo]

do they want you to specify where it increases constantly,(5,inf) or where it also increases only to a certain point?

[fallow scarab]

Math definition

[sharp dawn]

heres what it gives as an example explanation

[sharp dawn]

"as x-values increase, y values increase" or something like that

[slender walrus]

union wasn't appropriate imo

[sharp dawn]

wdym

[slender walrus]

you should be providing a list

[fallow scarab]

Try (-2,-1), (2, inf)

[eager cargo]

yeah in the examples they dont use unions

[slender walrus]

there's a glaring issue when you have something like
#help-18 message

[sharp dawn]

damn i think i ran out of attempts

[sharp dawn]

thats the way my teacher taught me to answer it 🤷‍♂️

unfortunate

[eager cargo]

thats how my teacher is teaching it right now as well, idk tbh

it looked right to me

[midnight plank]

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[warm reef]

confused with part ii - is there some formula i have forgotten

im aware that the distance will be perpendicular to the line

but im not sure how to actually set it up

[potent veldt]

Similar triangles

[velvet pagoda]

I think you need close brackets at -2 and 2

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[brittle breach]

hi

this is from an answer key

and i find this graph inaccurate

because

this part of the graph is depicted as if it never crosses 1

but it actually does go below 1

and then it goes back up

infinitely towards 1

but never actually reaches 1

so that graph should show that it goes down and then goes back up increasing infinitely towards 1 on both left and right sides of the graph, correct?

can someone confirm my correction?

i think the answer key is wrong

and here's some evidence i can also show

desmos agrees with me

[brittle breach]

but this does not follow desmos's

i mean that might be enough just for rough scratch

but i still think that's wrong

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[elder ivy]

Ok I just wanna make sure that the answer is 50.93 meters in the y axis when the is parallel to the goal post

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[midnight plank]

@elder ivy Has your question been resolved?

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[glacial fossil]

Hi i had a question

[vale zephyr]

ask

[glacial fossil]

I was trying to do question 2 and could not grasp it with proofs so is it possible to get it

I tried y=mx+b form

ended up a answer that was not good

[vale zephyr]

show your diagram

whatever you have made

[glacial fossil]

ok

one sec

sec

[vale zephyr]

what about line 3?

[glacial fossil]

line 3 is an unknown so i imagined it as a line intersecting point 2,-3 so point a was the poi of the intersection between 4x-3y-1=0 and point b is line intersection between 2x-3y-13=0 and point 2,3

so update diagram will be

and poi of lines 1 and 2 is 2,3

but got stuck over here

on this step

But not sure

?

@vale zephyr ?

.close

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[half sun]

chat are they the same

(i dont see where i made a whoopsy daisy)

[midnight plank]

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[midnight plank]

@half sun Has your question been resolved?

[still rose]

You wrote 0.5y^-2/3

No part of your answers match

Consider showing your work

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[dull yoke]

show work

use fbd

[old sapphire]

(W_net = F * D =(1150-625)*40 = 35000 )

[grand pond]

hamr

[old sapphire]

And then i can find acceleration

F = m * a

(\frac{W_{net}}{m} = a)

[grand pond]

hamr

[old sapphire]

then use the formila

(v_f^{2} = v_i^{2}+2ad)

[grand pond]

hamr

[old sapphire]

(v_i=0)

[grand pond]

hamr

[old sapphire]

right

is this right proces?

answer is

(\sqrt{2ad})

[dull yoke]

its been a minute since ive done this stuff, but why use work? u have F_net = ma, so (1150-625) = 90 * a, then use v_f ^ 2 = v_i^2 + 2ad formula

[grand pond]

hamr

[old sapphire]

oh

good point

[old sapphire]

so then u can solve for a as

875/90

a = 875/90

d = 40

and then this sqrt thing is dervied from the (v_f^{2} = v_i^{2}+2ad)

[grand pond]

hamr

[dull yoke]

im not understanding why youre trying to involve work when it doesnt need to be used

[old sapphire]

yeah

idk

we are learning work rn