help-38

[split chasm]

yes

and will that be greater or less than 1 at large negative values

[odd tapir]

less than

or wait

1+ 0 + 0

wouldn't it just be 1

[split chasm]

no

don't use the final value of the limit when you evaluate

[odd tapir]

so then 1 - (very small negative) - (very small negative)

so less than 1

[split chasm]

yes

[odd tapir]

what does that tell us?

[split chasm]

what'll be the square root of that

it'll be less than 1 as well right?

[odd tapir]

yeah

oh so you'll get a positive in the denominator

[split chasm]

yes

[odd tapir]

ah so 5/0+

which is why its +oo

[split chasm]

it's an indication that the denom approaches 0 from the positive side

yes

[odd tapir]

okok

thanks

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[trim jolt]

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

[real rose]

What do you know about reciprocal functions

[lapis quartz]

Asymptote

0 gives infinite

infinite gives 0

[real rose]

Ok

Can you model this function

Or at least understand how this might work

If $g(x)=\frac{1}{f(x)}$, then what happens to $f(x)$?

[solid kiln]

mathisfun

[lapis quartz]

f(x) = 1/g(x)

Starts of infinite at 0 and reaches 0 at infinity

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[turbid gazelle]

why does option d not work

[real rose]

Look at the difference between a and d

Also, why would d work?

[turbid gazelle]

LM = m - l and KN = n - k

l-k = m-n

KL = NM

LK = MN

@real rose

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[latent jay]

5 tons of potatoes were brought to the base, which is 20% of the base's needs. What is the need for the base (in tons)?

[chilly bobcat]

convert 20% to fractions first

[supple copper]

how much % would 10 tons of potatoes me?

[trim jolt]

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[south latch]

20%*what = 100%?

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[regal jetty]

coudl anyone pls help we with these two questions

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[north herald]

Hi, I am not sure how the correct answer is right - in fact I'm not sure if all the answers are right bc x should not be 4 or more due to the g(x) function having a square root. I probably don't know what a maximal domain is. I appreciate any help. Thanks

[limpid dawn]

this is bizarre

[north herald]

exactly what I'm thinking

[split chasm]

pretty much just domain

yeh, x cant be more than 4,
that only discounts option a)

why did you choose d specifically?
you are also given the domain of f and g

[north herald]

I misread the bracket as ) so I clicked on it -

and I also thought there was no way it can be infinity -

[split chasm]

d) seems right

who sets up these questions

[north herald]

but it can be 4] otherwise the sq root would be undefined.

can't

[limpid dawn]

this question is a set up

[split chasm]

why do you think there's an issue with x=4

what's sqrt(4-4)

[north herald]

oh wait sq root of 0 is 0

lmaoo

[split chasm]

but yeh, for the domain you want the intersection of the domains of f and g
i.e. intersection of (0,inf) and (-inf,4]
which is indeed option d)

[north herald]

I see, thanks for the clarification!

?close

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[trim jolt]

@dark ice Has your question been resolved?

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[lethal aurora]

Exercise 4. Given a right triangle ABC at A, with AB<AC. On the opposite ray of ray AB, take point D so that AD=AB.
a) Prove that CA is the bisector of angle BCD.
b) Draw BE perpendicular to CD at E (E∈CD). Let BE intersect CA at
I. Draw IF perpendicular to BC at F. Prove that triangle CEF is isosceles.
c) Compare the lengths of IE and IB.
d) Find the condition for triangle ABC so that triangle △BEF is isosceles at F.

[lethal aurora]

<@&286206848099549185>

Help me only the d one

...

<@&286206848099549185>

[split chasm]

Please be patient and follow the 15m rule.
In the meantime, its recommended that you show your work.

[lethal aurora]

ok

This one allowed to draw smth more

<@&286206848099549185> ? help me the d one

[umbral hazel]

!15m

[trim jolt]

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

[umbral hazel]

@lethal aurora If you cannot respect that rule, I will have to get a moderator involved

[trim lichen]

ramonov is already here isn't he

[lethal aurora]

kk

[split chasm]

I was expecting work to be coming

[umbral hazel]

Oops! I didn’t realize he was a mod 💀

My bad, Ramonov 😭

[split chasm]

ideally the diagram you've drawn as they all seem relevant

[lethal aurora]

.close

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[fiery hemlock]

Hello I’m trying to calculate the derivative of fx=ln(3x) by definition and although I got to the same result as the immediate derivative, I still got told that im not supposed to use l’h. And I don’t understand why. @real rose helped me and sent me all these formulas but im unable to apply them. Thanks.

[split chasm]

you're not supposed to use LH as if you're allowed to differentiate like that,
you could've just differentiated at the very start

[fiery hemlock]

Ok, and how do I do that?

[split chasm]

the process is actually quite length,
try looking up diffentiating ln(x) using first principles

[fiery hemlock]

Ok, I will. But technically (even tho I didn’t do it formally) I still got to the same result, that means I did it right. didn’t I?

[split chasm]

technically valid, but defeats the purpose

[fiery hemlock]

Ok thanks, I want to do it correctly but I don’t know how to. Should I look some videos on YouTube? Any recommendations to learn

[split chasm]

try looking up diffentiating ln(x) using first principles

[fiery hemlock]

Ok thx, I’ll probably be back

[mild oyster]

@lethal aurora
Still need help with the d?

[trim jolt]

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[mild oyster]

@lethal aurora
Anyway, i'll still give a hint.

1. This is VERY EASY to solve in 15 minutes, i haven't done this kind of math for a few years and i could still solve it under 14 minutes INCLUDING re-proving the theorems just for fun.
   You were not very patient OR
   your amount of knowledge is generally not good.

2. The hint (if you still haven't figured it out for some reason)
   is that the I is the orthocenter,
   prove that the shape is a trapezoid.
   I hope that you can do the rest.

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[scenic cloak]

Assume that the wavelengths of photosynthetically active radiations (PAR) are uniformly
distributed at integer nanometers in the red spectrum from 675 to 700 nm.
What are the mean and variance of the wavelength distribution for this radiation?
How do you solve this?

[trim lichen]

do you know in general how to find the mean and variance of a probability distribution?

[scenic cloak]

Yeah

[trim lichen]

ok so what's troubling you about this one in particular?

[scenic cloak]

Eh I don't know how to like find this... Cause I know what to do with regular numbers

[trim lichen]

that yours?

[scenic cloak]

Yes

[trim lichen]

or a friend's?

[scenic cloak]

Mine

[trim lichen]

then you... seem to have done it already?

like youve got your mean right there

[scenic cloak]

The question three is what I'm on

[trim lichen]

and the variance will take a bit of arithmetic to work out

[scenic cloak]

Where like I can get the mean cause I have a formula for that

[trim lichen]

but otherwise you seem to be using the readymade formula for the variance of a uniform

[scenic cloak]

Well no. I was trying to reverse engineer the variance formula

For a uniform bit like this

But I don't know how

[trim lichen]

you did it correctly, is what i'm saying...

[scenic cloak]

I'm saying I don't understand it

Why is it divided by twelve?

And added one and subtracted one

[trim lichen]

right

well ok so

i think it is best if you take the uniform distribution on {1, 2, ..., n} and find its variance the hard way

you will need, in one way or another, the formula $\sum_{k=1}^n k^2 = \frac{n(n+1)(2n+1)}{6}$

[solid kiln]

Ann

[scenic cloak]

Which is divided by six because?

[trim lichen]

mmm

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

there are a few different derivations of this on wikipedia i think

like my go-to is rawdogging it algebraically

[scenic cloak]

Ok ok thank you so much

I was looking for the reason so this is perfect

[trim jolt]

@scenic cloak Has your question been resolved?

[scenic cloak]

So is the general formula ((b-a+1)^2-1)/12?

[trim lichen]

yes

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[median iron]

$3x+8w^2\3w+8w^2\6+8w^2$

[solid kiln]

UCYT5040

[median iron]

x and w are odd, and odd*odd=odd

x is not a multiple of 3

obviously the bottom one is yes

but i cant think of any x or w values that have a gcd

so i think its 1/3 but the correct answer is 2/3

ohhh wait i see

because of w^2

3*3+8*9

9 and 72 are divisible by 9

and this doesnt work with x

so yeah 2/3

nvm then

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[wraith hinge]

is there any way to solve a question where the variable has a factorial in it

[wraith hinge]

or is that jot possiblw

just general question

[clear cloud]

You will have variable! = ... ?

[trim lichen]

there is no general technique

what equation are you facing right now?

[wraith hinge]

yes

[wraith hinge]

oh , no

[clear cloud]

Just look the rhs and see if its a factorial of smth

[wraith hinge]

it's just a general question because you can solve variables with logarithms , exponents, coefficients, so on and so forth and i was thinking if this could be applied to factorials

[wraith hinge]

aaaah okay

[clear cloud]

There is no inverse to factorial afaik

[wraith hinge]

yes , i can't think of one either

in that case thank u sm

variables with factorials would probably come out to something easily identifiable anyways like x! = 120

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[wraith hinge]

Ik the answer. But how do you show your reasoning and work in a question like this

[clear cloud]

Where a,b belong ?

[silver glade]

$\int\frac{1}{a^x b^x}dx=\int (ab)^{-x} dx=\int e^{-x \ln(ab)}dx$

[solid kiln]

Axe

[silver glade]

from here you can do a u-substitution

u = -x ln(ab)

[trim jolt]

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[real rose]

Work it out?

$\int a^xdx=\frac{a^x}{\ln(a)}+C$

[solid kiln]

mathisfun

[wraith hinge]

Got it!!!!

Thank you so much

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[wraith hinge]

Any way to do this without long division?

[trim lichen]

probably not tbh

can we at least assume b isnt 0 tho

[granite cove]

Can't you sub u = a + bx if b ≠ 0?

[trim lichen]

i guess you can

[real rose]

Yeah

Was about to say that

[trim lichen]

but op said no long division, and i feel like this bars us from splitting the fraction (...)/u^2 into A + B/u + C/u^2

[trim jolt]

@wraith hinge Has your question been resolved?

[wraith hinge]

Yes I think

[wraith hinge]

Okay yes that’s a lot neater than I was expecting

[wraith hinge]

No that is fine

Thank you guys

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[wraith hinge]

My textbook multiplied both the numerator and denominator by sin(3x).
How do I know it’s going to benefit me in this problem?

[trim lichen]

will it?

have you looked at what they do afterwards?

usually a weird step like this is setup for some manipulation in a subsequent step.

[wraith hinge]

Yes one sec

Let me send their solution

[night patio]

I thought it was just gonna be some sort of iteration of product to sums of the trig

[wraith hinge]

Please ping me

[real rose]

SO they did

Ok

[wraith hinge]

Yeah

[real rose]

$\sin(a)\cos(b)=\frac12(\sin(a+b)+\sin(a-b))$

[solid kiln]

mathisfun

[trim lichen]

oh they set up a double angle sine formula

2sin(3x)cos(3x) became sin(6x)

[real rose]

Nice solution I suppose

Very uh

Uncoventional

[wraith hinge]

But why? What’s the motivation?

Also if there’s a more intuitive way to do this, can you please show me

[trim lichen]

not that i know of tbh

they seem to just do some wacky trig identity shit

[night patio]

The intuition is just to do these type of questions numerous times

And unfortunately that’s the only way

It’s a bit obtuse to see

But ig the “motivation” is just to use trig identity to turn the denominator into 1 so u can evaluate the trig terms separately

[wraith hinge]

Okay okay I’ll see if I see more problems like this one

Thank you so much

Appreciate it

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[bright seal]

$\int x^6\cdot e^x dx$

[solid kiln]

Task Bot

[real rose]

Integration by parts

[red mountain]

looks like IBP

[stoic oxide]

6 times

[real rose]

A really long one

[bright seal]

WHY

[real rose]

Because

Maybe I can write it up if I'm fast enough

Testing my typing skills

[red mountain]

you can figure out a general $\int x^ne^x\dd x$

[stoic oxide]

exercise: find a general form for int x^n e^x

[solid kiln]

Bonk

[real rose]

Yeah

[red mountain]

and then easily get an answer

[real rose]

Recursive formulae also exist

[lusty delta]

the terms follow a very predictable pattern so after doing 2 of the ibps you should be fine

[bright seal]

I don't understand why I have to do by parts

Nobody knows?

[red mountain]

,tex .int rules

[solid kiln]

Bonk

[bright seal]

,tex .int rules

[solid kiln]

Task Bot

[split chasm]

by parts can be useful when you are integrating a product of different types of functions and sub doesn't work

[bright seal]

I don't understand the command

[red mountain]

because you shouldnt use it

its my command

[bright seal]

Ah

[red mountain]

you need to look at the message below it

that got produced

[red mountain]

.

[bright seal]

How do I know that what is written is correct?

[red mountain]

???

[nimble stone]

(it is)

[red mountain]

why would it not be?

[bright seal]

Isn't it better to use public sources better?

[red mountain]

i just have it as a command so that i can easily reference it

[red mountain]

whats your point?

you can also look in your textbook

[bright seal]

Because it is a command that I cannot consult

[red mountain]

and youll see that its the exact same

[nimble stone]

google it then

[red mountain]

buty ou can just ask me?

[tacit loom]

you can also try the tabular method

[red mountain]

you asked, whats IBP

i tell you what IBP is

and then you dont trust it

then why bother?

[bright seal]

They are not official sources

Oh well now I read it

[red mountain]

this whole server is not an official source

yet you still come here and ask for help

[bright seal]

I fully concur with the sources provided, as their depth and validity render any disagreement unnecessary.

So we can proceed

[red mountain]

lol

anyway

let $I_n=\int x^ne^x\dd x$

[solid kiln]

Bonk

[red mountain]

and do IBP on that

then look for a recurrence relation

[bright seal]

But what does it mean to integrate by parts? What really happens?

The method of integration by parts was first systematically formulated by the French mathematician Brook Taylor in the early 18th century.

This ?

[red mountain]

do you know the product rule?

[bright seal]

I don't know the history of integration by parts

[red mountain]

why would you need that?

anyway, product rule is $[uv]'=udv+vdu$

[nimble stone]

go read a wikipedia entry if thats what you want

[solid kiln]

Bonk

[red mountain]

if you take the integral of this, you get $[uv]=\int u\dd v+\int v\dd u$

[solid kiln]

Bonk

[bright seal]

it provides deeper insight into the evolution of ideas and the thought processes of mathematicians.

[red mountain]

rearranging to give $\int u\dd v=uv-\int v\dd u$

[solid kiln]

Bonk

[supple copper]

It’s just the product rule backwards

That’s the thought process

And bonk just showed you exactly what I mean

[red mountain]

its like learning that 1+1=2 and then researching how mathematicians thousands of years ago figured it out

[bright seal]

Ah ok

[supple copper]

Being conscious of the thought process is important don’t stop thinking about that

But in math we use proofs to show this process

[red mountain]

sometimes it is useful to know why a result is reached, but this is not it

[supple copper]

Though sometimes the proofs pull shit out of their ass and it’s hard to tell why they would approach it that way

If the proof is good it’ll explain the why as well as the how

[bright seal]

double integrand(double x, void params) {
return xxxxxx * exp(x); // x^6 * e^x
}

Can I use this?

[red mountain]

no?

[bright seal]

Why

[red mountain]

why would you??

just solve it analytically

wtf

[bright seal]

Because it works I think

But I can use shortcuts

[supple copper]

The problem is teaching you integration by parts not integration by numerical method

[bright seal]

To solve the integral ( \int x^6 \cdot e^x , dx ), we can apply integration by parts multiple times. First, recall the integration by parts formula:

[
\int u , dv = uv - \int v , du
]

We'll choose:

• ( u = x^6 ) (since differentiating powers of ( x ) will simplify them),
• ( dv = e^x , dx ) (since the integral of ( e^x ) is straightforward).

Now, let's perform the integration by parts step-by-step.

First step:

• ( u = x^6 ), so ( du = 6x^5 , dx )
• ( dv = e^x , dx ), so ( v = e^x )

Using the integration by parts formula:

[
\int x^6 \cdot e^x , dx = x^6 \cdot e^x - \int e^x \cdot 6x^5 , dx
]

Second step:

Now, we need to integrate ( \int 6x^5 \cdot e^x , dx ). We apply integration by parts again:

• ( u = x^5 ), so ( du = 5x^4 , dx )
• ( dv = e^x , dx ), so ( v = e^x )

This gives:

[
\int 6x^5 \cdot e^x , dx = 6 \left( x^5 \cdot e^x - \int e^x \cdot 5x^4 , dx \right)
]

Third step:

Next, we repeat this process for ( \int 5x^4 \cdot e^x , dx ). This will require four more steps of applying integration by parts.

Eventually, after performing the integration by parts seven times, we end up with:

[
\int x^6 \cdot e^x , dx = x^6 \cdot e^x - 6x^5 \cdot e^x + 30x^4 \cdot e^x - 120x^3 \cdot e^x + 360x^2 \cdot e^x - 720x \cdot e^x + 720e^x + C
]

Where ( C ) is the constant of integration.

So, the final result is:

[
\int x^6 \cdot e^x , dx = e^x \left( x^6 - 6x^5 + 30x^4 - 120x^3 + 360x^2 - 720x + 720 \right) + C
]

[solid kiln]

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

[red mountain]

!nogpt

[trim jolt]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[red mountain]

<@&268886789983436800>

[bright seal]

How do you know that I use it?

[red mountain]

because you have no clue how IBP works and then wrote a whole answer in milliseconds

[bright seal]

What if it was prepared?

[red mountain]

dont try this bullshit with me

[bright seal]

.close

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[quartz cloud]

do i just graph this regularly or do i do something else since it says f(x) instead of y

[real rose]

Regular

y=f(x)

[quartz cloud]

alr thanks

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[still widget]

Calc 2, Surface Areas of Rotated Curves

I got the problem wrong and need help understanding what I did wrong.

[trim jolt]

@still widget Has your question been resolved?

[still widget]

Figured it out,

Derivative of x^3 is 3x^2 not 2x^2

.close

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[grand pivot]

CHILEE okay so this is my problem. i got down all the way to 1/x^2 -4/x+4-3/x+6+10 and i simplified to 1/x^2 -7/x+20 but its saying im wrong and that its +8 and not +20... how is it +8 if theyre all positive no?

[grand pivot]

muy importante

[split chasm]

should be +20 on the end yeh

[grand pivot]

ok so my professor is wrong?

[split chasm]

yes

[grand pivot]

PERIODDDDD

what would the domain be thpo

tho

cus its 0.25 plugged in right

hold lemme solve b4 u say

ok no

ngl idk what to do after

i have 1/x^2-7/x+20

if i plug in 1/(0.25)^2 and -7/(0.25) i get a weird numbe

im not allowwed to use calculayors

[vernal warren]

change 0.25 into 1/4 , for easier simplifcation

[grand pivot]

so it would be 1/1/4

^2

[tacit loom]

for f o g(x), you can also calculate g(x), then plug that value into f(x)

[vernal warren]

1/(1/4)^2 , yes

[grand pivot]

whats 1/4^2 😭

im like horrible in math i am sorry

[simple haven]

What is $\frac{1}{4} \cdot \frac{1}{4}$?

[solid kiln]

OmnipotentEntity

[grand pivot]

oh 1/16?

so

1/1/16

then

i have

-7/1/4

[vernal warren]

$$\frac{a}{\frac{b}{c}} = \frac{a}{1} \div \frac{b}{c}$$

[solid kiln]

JustToPro

[vernal warren]

in case u didnt know

[grand pivot]

im killingmyself

am i foinding

a common denom

[simple haven]

\begin{align*}
\frac{1}{\frac{a}{b}} &= \frac{1}{\frac{a}{b}} \cdot \frac{b}{b} \
&= \frac{b}{\frac{a}{b} \cdot b} \
&= \frac{b}{\frac{b}{b} \cdot a} \
&= \frac{b}{a}
\end{align*}

[grand pivot]

ok so

[solid kiln]

OmnipotentEntity

[grand pivot]

im literally so confused

[simple haven]

The above holds for any a,b ≠ 0

[grand pivot]

is there an easier way

[simple haven]

So if, for instance a = 1 and b = 16...

[simple haven]

There is an easier way, just read the first and last lines

The in-between is just a full justification

In case you find it confusing

[grand pivot]

wait so whyd u do 16/16

[simple haven]

You have 1/1/16

We want to find 1/a/b

And we proved that 1/a/b = b/a

[grand pivot]

oh we flippe

i thought if u flip it becomes -

[simple haven]

Yup

[grand pivot]

negatrive

[simple haven]

It doesn't become negative

[grand pivot]

WAITTTTTT😭

OK SO

i did

-8 over 1/16

vus i subrtacted

1 over 1/16 and 7/1/16

so i got -8 over 1/16

and then i did the reciprocal

16/1

and candcled out

and got -8

https://cdn.discordapp.com/attachments/1334379850689150987/1339747006087827456/trvlyrare-stan-twitter_1.gif

but how would that be in the domain tho

[grand pivot]

ayuda me

the domain'

ping me when yall answe

[trim jolt]

@grand pivot Has your question been resolved?

[grand pivot]

well no chile

[trim jolt]

@grand pivot Has your question been resolved?

[grand pivot]

I JUST WANNA KNOW HOW THE DOMAIN

😭

[forest phoenix]

Hello
Could you help me find the 3 partial derivatives shown in the image?
The equation deals with relative density.
TA= High temperature
TB= Low temperature.
The 3 equations to find are:

1. Partial derivative of density B/ Partial derivative of density A.
2. Partial derivative of density B/ Partial derivative of TB.
3. Partial derivative of density B/ Partial derivative of TA.
   I tried to do the first one, but I'm not sure if the procedure is correct. Could you help me, please.

[grand pivot]

Girl this AINT UR CHANNEL

There’s extra channels

[forest phoenix]

Sorry 😦

[trim jolt]

@grand pivot Has your question been resolved?

[grand pivot]

https://tenor.com/view/12-hours-after-my-shift-12-hours-work-tired-gif-7278434726926352333

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[fierce knoll]

why don't we continue with the final $1+\frac{1}{2\sqrt{x+1}}$?

[solid kiln]

sunsick

[fierce knoll]

what would be the difference between this and the previous ones

.close

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[cosmic gate]

hello

[cosmic gate]

For part a, since it was false, i was able to provide a counterexample

but because part b is true im guessing i need to construct a more rigoruous proof

i was thinking i could deal with in terms of cases but there were too many to deal witih

[trim lichen]

you don't need any casework here

[cosmic gate]

okay

[trim lichen]

element-chasing and unfolding all definitions is going to do you just fine

[cosmic gate]

uh so something like let x be the element of A intersection B

and then show that x also then must be an element of C

[trim lichen]

let x be an element of A ∩ B.

saying "the element" implies A ∩ B has only one element to begin with, which nobody said

[cosmic gate]

ah yeah my bad

[trim lichen]

but yes setup and goal are correct thus far

remember you will need to use $A \subseteq B^c \cup C$ at \textbf{some} point

[solid kiln]

Ann

[cosmic gate]

that is kinda where i had a problem

i have to use an arbitrary element in set A (lets say y for example) which causes me to not understand how we correlate this to x

[trim lichen]

you misunderstand

$A \subseteq B^c \cup C$ is not a goal, but an assertion. you'd only need to declare an arbitrary $y \in A$ if $A \subseteq B^c \cup C$ were a second goal.

[solid kiln]

Ann

[trim lichen]

here, however, you get from $x \in A \cap B$ that $x \in A$ and $x \in B$.

[solid kiln]

Ann

[trim lichen]

and then $x \in A$ together with $A \subseteq B^c \cup C$ implies $x \in B^c \cup C$

[solid kiln]

Ann

[cosmic gate]

oh

that makes so much sense

just a quick proof i wrote

[fresh mesa]

but what about $x \in B^c$

[solid kiln]

therealtdp

[fresh mesa]

its still an or

[cosmic gate]

i thought since it was an or statement, i could ignore it?

oh ig not then

well how about this

x being an element of b complement means that it must be either a element of the set C (meaning that we get our proof) or that it is part of the universal set - (B union C). If it is part of universal set - (B union C) then we know that there are no common elements between B and A meaning that their intersection is the empty set and since the empty set is a subset of everything, A union B must be a subset of C

[trim lichen]

i think this can be phrased simpler

x belongs to B, and besides this we know it belongs to B^c or to C. but it doesn't belong to B^c, therefore it must belong to C.

[cosmic gate]

yeah that is way more simpler lol

appreciate your help everyone

thank you

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[supple copper]

So the covariance between random variables can be an inner product, but the covariance between 2 vector random variables is a matrix, how does one turn that into an inner product?

[amber python]

take trace

[trim jolt]

@supple copper Has your question been resolved?

[supple copper]

Trace of the covariance becomes an inner product?

[amber python]

seems like it

[supple copper]

Huh ok

.close

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Please don't occupy multiple help channels.

[nimble stone]

.close

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[latent jay]

The difference of the squares of two consecutive natural numbers is 57. Determine the larger number

[fresh mesa]

let n be the natural number

then the next number is n+1

given, $(n+1)^2-n^2=57$

[solid kiln]

therealtdp

[fresh mesa]

you can solve

[latent jay]

i got it

[cosmic ferry]

29 ?

[latent jay]

but i dont understand

why $$-n^2$$

[fresh mesa]

which part you dont understand?

[solid kiln]

www.

[cosmic ferry]

consecutive means one and next

difference of SQUARES

[fresh mesa]

the difference of squares of two consecutive numbers

[latent jay]

i got it now

thank you guys

[fresh mesa]

[cosmic ferry]

😉

[latent jay]

thank you for help and good luck😘

[fresh mesa]

close it <3

[latent jay]

why you said 29

we got n=28

[cosmic ferry]

yeah but the greater natural number is asked

[latent jay]

i though just need find for n

[cosmic ferry]

haha thats where the question gets you

[latent jay]

yeah

😡

[cosmic ferry]

i was once asked the sum of digits of the answer
so my answer 33 was correct but soln had to be 3 + 3 thats 6

[latent jay]

damn

in this moments u need to be more careful

and read better what they want

but i didn’t

so yeah, thank you

gl

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[wraith hinge]

Hey guys I need a video on YouTube that explains Lagrange method on numerical analysis
I couldn’t find anything useful so can anyone provide me with something

[trim jolt]

@wraith hinge Has your question been resolved?

[trim jolt]

@wraith hinge Has your question been resolved?

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[fast compass]

Yo ts got me so mad I lost my voice where do I go from here

[trim musk]

what do you have to do lmao

[fast compass]

Find a polynomial that satisfies the given conditions.

[trim musk]

what conditions?

[regal gorge]

Expand it I guess

[fast compass]

I have to turn it into factors

[trim musk]

0 is also a root

multiply x

and remove the x+i

-i isnt a root

[regal gorge]

Do you need it fully expanded?

[trim lichen]

step 0 would be to drink some water

[trim musk]

its a pretty weird polynomial though

[trim lichen]

and maybe use some kind of throat spray

[trim musk]

if i is a root -i should be a root

[trim lichen]

so that your throat and vocal cords can recover somehow

[trim musk]

my god im pretty sure hes joking

[fast compass]

these are the only instructions I got

[trim lichen]

oh, so they DIDN'T say for it to have real coefficients?

[fast compass]

no bitch I just said those were the only instructions

[bright quarry]

well then

[trim lichen]

...did you need to call me a bitch

[fast compass]

no comment

[trim lichen]

it's kinda rude to throw words like that around

yknow

anyway like ok it doesn't say that the polynomial has to have real coeffs

$z(z+i)(z-2-i)$ will do the job just fine

[solid kiln]

Ann

[trim lichen]

expand that thing and collect like terms or whatever

[regal gorge]

You missed a factor

[fast compass]

which one ?

[regal gorge]

I'm talking to Ann

I don't see the (z-2+i) factor

[trim lichen]

why would there need to be one like that?

remember there's no requirement for the coeffs to be real.

[regal gorge]

The factors are at the top I would assume

[trim lichen]

so roots don't need to come in conjugate pairs.

[regal gorge]

This isn't the correct way?

[trim lichen]

this one lacks -i as a root

it also has 2-i as a root, which wasn't required of it

[regal gorge]

The factors are 0, i, 2+i, 2-i

[trim lichen]

the roots as stated are 0, minus i, and 2+i.

no more, and no less.

2-i isn't required to be a root.

[regal gorge]

OH it says -i

[fast compass]

actually I added the 2-i

[regal gorge]

I was reading this lmao

[fast compass]

cause they said to do the opposite

[trim lichen]

who said to do what?

[regal gorge]

I read the original picture, Ann, that's where the confusion is

[fast compass]

they them

[trim lichen]

who are "they"?

[regal gorge]

Before they sent the actual canvas page

[fast compass]

brain mclogan video

[regal gorge]

Are you serious lmao

[fast compass]

yeah

https://youtu.be/COryZEJ9kT0?si=porkiltBvUDmGP01

[regal gorge]

He never mentioned that you can add your own factors

[trim lichen]

hold on lets give this a watch

[regal gorge]

Because that is not a thing

[fast compass]

he said to do the oppsite of 4+i so I just did the opposite of 2+i

[trim lichen]

conjugate, not opposite.

there's a specific word for it.

but also,

this guy leaves it unsaid that we want the polynomial to have real coefficients.

around 0:50 he said "we know that if 4+i is a zero then its conjugate must also be"

when in reality this hinges on the "real coefficients" thing

[fast compass]

ahhh ok

[fast compass]

What did i do wrong here?

[trim lichen]

a lot of things, apparently. did you try to do this in your head?

[fast compass]

damn dude no need to go hard on me no I didn't I am just not a wizard like you

[regal gorge]

Try factoring just (x-i)(x-2-i)

[fast compass]

thats what I did or so I thought

I haven't brought the outer x in yet

[trim lichen]

please don't call me "dude".

[regal gorge]

First you distribute the x to every term in (x-2-i) and then you distribute -i to (x-2-i)

[fast compass]

mb

[trim lichen]

then you should have had x(.....)

your work... didnt make that clear on a first reading

x(x+i)(x-2-i)
= x(x^2 - 2x - ix + ix - 2i - (-1))
= x(x^2 - 2x - 2i + 1)

you made a sign error when you put -i^2 as -1 when it should have been +1

and the whole "the leftmost x vanished into thin air" thing

"a lot" turned out to be just two

[fast compass]

my brain can't comprehend what the hell this means

[fast compass]

this

[trim lichen]

you tried to expand just the (x+i)(x-2-i) while leaving the lone x to their left as it is, correct?

[fast compass]

yes

[trim lichen]

yeah, what im saying is that you dropped that lone x.

and that's what confused me when i read your work.

[fast compass]

ahh ok sorry about that

[trim lichen]

also regarding the other half of this: i've seen quite a few instances when a helpee came in with their work, made a severe screwup partway through, and then it ended up being the case that they tried to skip some steps by doing it in their head.

so i was not trying to dispense some sort of value judgment at all there.

[fast compass]

oh ok thanks for clearing that up

thanks for helping everyone

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[storm plover]

heeeelp

[storm plover]

i need to find a vector v with module sqrt(5) and so he makes an agnle of 60degrees with vector u(2, -4)

pls i got an exam tommorrow

[pastel wren]

that handwriting is amazing

[storm plover]

thx

[pastel wren]

with modulus sqrt(5) or module sqrt(5) ?

[storm plover]

|v| is sqrt5

[pastel wren]

Okay, that's modulus

Let's see

[storm plover]

ok

will know

[storm plover]

ohh i see my fault

i multiplied

i shouldve divided

hold up

how to divide

if i divide -9.52 : u

i make

-9.52/u1 and same for the u2?

still wrong

whyyy

[pastel wren]

I think this approach might not be correct.

[storm plover]

why

no like i have a solution but i dont understand why is it wrong

?

anyone

<@&286206848099549185>

[pastel wren]

You might need to:

1. Find the unit vector of u
2. Add 60 to it's angle
3. Multiply it with sqrt(5)

[storm plover]

huh

no

[pastel wren]

He is

That thing is called dot product what you did right there

[storm plover]

ok

so what did i do wrong

yea thats what i did

[storm plover]

.

huh

wait

That what i have done so far

[pastel wren]

The problem here is you cannot just move u on the other side like that

[storm plover]

ohhh

cause its not two numbers

its one

its jusrt described as two

ye

hmmm

so if v*u = -9.52

(v1u1, v2u2) = -9,52

right

?

that doesnt help

i dont understand

ok

[pastel wren]

Yea well it's not possible to find it just using this formula

[storm plover]

what do i do

[pastel wren]

In your class / book, do you have any other formulas or methods mentioned? There are some complex methods to do this as well, but it might be out of the scope of your course.

[storm plover]

idk all i have is basic apuntation of everything

teacher didnt teach anything

ok i should jsut try to understand an answer

could you help?

@pastel wren

says

if v(x, y)

[pastel wren]

Yea that's right

[storm plover]

ok

you see that cos60 = to

where did they got 1/2

[pastel wren]

cos60 is equal to 1/2

[storm plover]

why does my calculator says 0.952

[pastel wren]

because its probably accepting radians

[storm plover]

and it should accept? degrees?

[pastel wren]

radian is another unit of rotation

[pastel wren]

yes

[storm plover]

held on let me check

ok it gives 0.5

[pastel wren]

Yea

[storm plover]

why does

2x-4y/ sqrt5*sqrt20 = 2x-4y

[pastel wren]

Look at this , a.b = a1.b1 + a2.b2

similarly

u.v = u1.v1 + u2.v2

[storm plover]

huh

oh oh yea

ok

[pastel wren]

We know u1 and u2, it's 2 and -4

We don't know v1 and v2, so we just write x and y for it,

[storm plover]

no yea

and v1 and v2 is x and y

[pastel wren]

Yea

[storm plover]

why is it divided by sqrt5 *sqrt20 = the same

[pastel wren]

You can also write v1 and v2, it's just a variable but x and y is more easier to read.

[pastel wren]

We rearranged the formula

So

[storm plover]

OHHH

SO TEN * 0.5

[pastel wren]

u.v = |u||v| cos(O) 

becomes

u.v / |u||v| = cos(O)

[storm plover]

OHHHHHH

OHHHH

ok bet

bet

[pastel wren]

So you get 2 equations, you solve for x and y , and you get 2 pairs of x and y, becuse there are 2 possible vectors (60 degrees in 2 directions)

[storm plover]

so thats the only possible way to solve that

ok

ok

idk how will i remember it

ill probably do the second

one same

i should try to understand it

[pastel wren]

It's not too hard just divide it into smaller steps. Write the solution twice , once while looking at it, once on your own.

1. You know that |v| = 5, so expand it, you get the first equation.
2. You know that the angles make 60 degrees. So cos(60) = u.v/|u||v|, and expand it.
3. You get two equations from steps 1 and 2, just solve for x and y, and it's done.

[storm plover]

thx

will try

[pastel wren]

np 🫡

[storm plover]

.close

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[storm plover]

.reopen

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✅

[storm plover]

where did they get 40y

got it

.

.close

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[storm plover]

why do they have one there

[mystic veldt]

absolute value of -1 is 1

[storm plover]

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[storm plover]

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[storm plover]

thx

i forgot abt that, thought it was parentesis

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[marsh coral]

What is the next number in this integer sequence? 1, 4, 8, 12, 16, 22, 30, 37, 47, 56, 65, 74, 85, 93/

[marsh coral]

The sequence of differences I can see is 3,4,4,4,6,8,7,10,9,9,9,11,8.. Some regularity with the fours and the nines but idk

I could not find this in the database for integer sequences on oeis org.. so its not a super known one

[trim lichen]

is there a construction given for this sequence or did they just give it to you with zero context

[wraith hinge]

well the issue with that type of problem is you could always find a polynomial function with a domain of n where n are integers that gives you each of those terms for each n

[marsh coral]

zero context. I dont need to find a formula, but the next number only

[trim lichen]

if zero context then all the terms after the last one shown are equal to 19 bc i said so

[wraith hinge]

exactly

[marsh coral]

so you say the next number is 19?

[jaunty scarab]

no

[wraith hinge]

no

[jaunty scarab]

she's saying that if you have no context, the next number can be whatever, for any reason

[wraith hinge]

the point is the question is nonsense

[marsh coral]

well the sick part is, its part of an code challenge for a job

[wraith hinge]

oh dang

[trim lichen]

who?

[trim lichen]

im a she...

[jaunty scarab]

sorry, i default to he pretty much all the time

[trim lichen]

bruh

[wraith hinge]

😂

[marsh coral]

i'm just glad it wasnt an obvious answer to the question then 😄

[trim lichen]

i have a feminine name, a girl on my pfp, a pink role diamond and you still misgender me

that takes balls

☠️ 💀 ☠️ 💀 ☠️ 💀 ☠️ 💀 ☠️ 💀 ☠️

[jaunty scarab]

that's all i see

[trim lichen]

ok but Ann is a girl name at least

[jaunty scarab]

eeeeeeeeeeeeeeh

[trim lichen]

anyway let's take this to #「helpers-lounge」 at least

cause this is getting off topic

[wraith hinge]

what channel is no access

[trim lichen]

a cool kids club that only green names can see

[wraith hinge]

:(

[jaunty scarab]

back to the question at hand. You do have additional context

you said it was a part of a code challenge for a job

[cunning cliff]

just get used to defaulting to 'they'

[jaunty scarab]

which means at some point, you'd have additional information

[jaunty scarab]

100% more letters per pronoun? heresy.

[cunning cliff]

100% less people you mistakenly offend

[jaunty scarab]

if only that were true...

[marsh coral]

well the numbers actually as presented are in three columns

anyways I give up

thx guys n gals

[jaunty scarab]

then you should present them in three columns

[cunning cliff]

yeah so this is pretty random

[marsh coral]

yes, random af imo

[jaunty scarab]

!original

[trim jolt]

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.

[marsh coral]

i wont get the job

i mean idk how to make a table here

[cunning cliff]

so is this a math question, or a non-verbal reasoning question?

[jaunty scarab]

take a screenshot?

[cunning cliff]

oh its a job interview

[marsh coral]

sec

[jaunty scarab]

or use spaces and shift+enter for new lines?

[marsh coral]

its not a job interview. its a code challenge, to get a chnce at even interview

sec

1,4,8
12,16
22,30
37,47
56,65
74,85
93, ?

the first row has 3 numbers but maybe one can disregard the 8

the differences row-wise, as I calculated, then become
11,12
10,14
15,17
19,18
18,20
19, ?

that seems manageable

to find a pattern

woops i wrote one row wrong, its 12,16 not 12,6

fml

[jaunty scarab]

this looks familiar...

[cunning cliff]

1 4 8
12 16
22 30
37 47
56 65
74 85
93 ?

you're given this?

[marsh coral]

pretty much yes

But wait.. Can there be a pattern of patterns? It feels like when we hit "37" things change. The first 7 numbers maintain a pattern, then the remaining 7 maintain some other pattern? Notice that the first 7 numbers are all even. In the next 7, the first number is 3, then 4, then 5, .. 6, 7, 8 ,9..

[cunning cliff]

looks like id fail this challenge too

is there no more context you can give

its not related to coding in any way?

[marsh coral]

No. its a engineering company in Sweden, doing a coding challenge with 5 questions. For example on question was about Turing machines, another about those typical inductive reasoning stuff you do at tests

one was about circles and distances etc

[cunning cliff]

[jaunty scarab]

we kinda need all the context, man

[marsh coral]

each question is in a vacuum

there is no context

[jaunty scarab]

but there IS a question, that you have yet to provide

which company is this? do we have access to the challenge?

[marsh coral]

Sure, thechallenge.scania.com/home/play

its the 5th question but you may have to solve the simple innitial riddle

so, I just tested 102, and it was the correct answer. But sad to not find a true formula for it

[marsh coral]

ahh it was column on my phone lol

[jaunty scarab]

there's a reason why we ask for the originals -.-

[marsh coral]

sure but the image to the right is the fibonacci sequence, has nothing to do with the problem

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[rare wraith]

uhm I need help with a problem
It says solve for y
5y + 8 = 2y - 3x + 5

[rare wraith]

i looked on youtube and everything bro noone says how to solve this

i got a test on friday

and honestly the only part i know is that you need to minus the 5y on the left

[wraith hinge]

What do you think solve for y means

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@rare wraith Has your question been resolved?

[pastel wren]

You need to move all the y terms on one side, and everything else on the other side. Then simplify if possible.

[austere cedar]

This is "solving a linear equation" if you did want to use Youtube

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[eager ocean]

hi guys can someone help me out with construction of right-angled triangle
Im struggling to construct it when its given only the sides a+b and c

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[wraith hinge]

just wondering do u guys help with math psmts like e.g if im done my psmt can u guys double check and stuff

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[wraith hinge]

$$\int_{55}^{60}\left(10.9\cdot\sin\left(0.099034x+1.86684\right)-5.5\right)dx$$

[solid kiln]

Goat(Ninja)

[wraith hinge]

$$\int_{60}^{88.9}\left(0.00000136229x^{4}-0.000370009x^{3}+0.0306637x^{2}-0.853778x+7.27995+1.2\right)\ dx$$

[solid kiln]

Goat(Ninja)

[zinc ginkgo]

,w \int_{55}^{60}\left(10.9\cdot\sin\left(0.099034x+1.86684\right)-5.5\right)dx

[solid kiln]

Results provided by WolframAlpha

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Requested by rie.mann

[zinc ginkgo]

if you got ~24.15 then you're good

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[sleek quail]

Twelve points are given in the plane, so that no three points lie on the same line.

Five distinct segments joining pairs of these points are chosen at random, with all 12choose2 = 66 such segments equally likely to be chosen. What is the probability that at least one triangle is formed by the chosen segments? (The triangle's three vertices must all come from the original set of 12 points.)

[shrewd ridge]

5 segments make 1 triangle or 2, it's about subtracting 2-cases

counting 2-triangle is the hard part

so like

here's 9 points with one triangle drawn

we can choose a side and a point, and that makes 2 triangles

like this or this

[trim jolt]

@sleek quail Has your question been resolved?

[shrewd ridge]

or we can choose a side and 2 points, that's even smarter

[sleek quail]

hm im a little confused

can u explain the process a little more

idrk that many concepts but the lesson for this week is using the PIE counting process

so it suppsoedly is mainly that

[shrewd ridge]

there are 220 potential triangles: 12c3
if you do 220(9c2) you make all ways that have a triangle

both 1 and 2, except the 2-ways are repeated, they appear twice

[sleek quail]

whered the 9c2 come from..?

[shrewd ridge]

my bad

[sleek quail]

choosing a segment from the remaining points..?

idk my brain cannot think at 9pm

[shrewd ridge]

63c2 i guess?

choosing two segments from remaining 63

[sleek quail]

ermmm

huh

[shrewd ridge]

this will result in every "1-triangle way" once and every "2-triangle" way twice

i actually don't get it fully, it's some weird geometry mixed in

like you need to somehow know that 5 segments can;t make 3 triangles

so from 220(63c2) we subtract 2-triangle