help-39

[quiet tendon]

which is what you want to be able to use rational root theorem

so now you want to list all possible rational roots of the polynomial 2x^3 + 15x^2 + 33x + 20

so you can consider all possible factors of 20, which are 1,2,4,5,10,20

[brisk steeple]

observe that the sum of pairs of coefficients is same

[quiet tendon]

^ this is a good observation that makes you want to immediately check +/- 1 as a candidate for a root

that would work here and reduce your cubic to a quadratic

[jolly nova]

guys many thanks for everything aight but
right now I am doubting if this is the intended solution; it really shouldn't involve any theorem that I haven't heard of

[quiet tendon]

practically speaking you'd just observe that -1 is a root

and then solve the remaining quadratic

i just thought it might be useful for future problems if you knew the theorem

[jolly nova]

yeah thanks

it sounds interesting

thanks a bunch for donating some of your knowledge and time

!!

I was thinking the same about donating knowledge, that's not really a thing
if anything, sharing knowledge only deepens your own understanding

oh meolve deleted their message

still goes

[brisk steeple]

in memories

🙂

[jolly nova]

:)

I vaguely remember an einstein quote about this general subject

that the ability to explain is the final test of proficiency

update:

I did do something wrong!
I put it into this form, which only makes it harder for myself. I thought it would be a good minimal reproducible example like in programming but in hindsight I should have provided you guys with the entire problem, my bad

[pearl pond]

@jolly nova Has your question been resolved?

[pearl pond]

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[spare comet]

would any one down to help me answer just a few question on this math study guide

[spare comet]

its algebra, more specifically simplfying exppressions, and polynomials

[muted shale]

!da2a

[pearl pond]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[spare comet]

How would I go about simplifying #7??

[brisk steeple]

simplify the numerator

first

then subtract the denominator's power

as they the same base

[fluid root]

(a^b)^c = a^bc

[brisk steeple]

eys

eye

aye

the expression will be
a^(bc-d) where d is the subtracting index, b and c being multiplied follow the laws of exponents.

in the denominator therefore.

+d -d if 1/d^n + d^-n d^n = 1/d^-n

[pearl pond]

@spare comet Has your question been resolved?

[spare comet]

hell osorry!

im reading now!

[pearl pond]

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[spare comet]

thanks!

[pearl pond]

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[flint halo]

is my answer considered incorrect?

[flint halo]

all i did was scale my gradient of f by 25 to make it a nicer vector to work with

<@&286206848099549185>

[midnight haven]

huh? I didn't understand the last step

[flint halo]

i scaled

the gradient vector

of f

by 25

[midnight haven]

why 1/6?

[flint halo]

??

what

oh idk why i wrote 1/6

ignore that

the only difference between my answer and the book answer is that my directional derivative is going faster

the answer is -11/25*sqrt(34)

[midnight haven]

correct then

[flint halo]

okay but why did i get points off ?

are you not supposed to scale gradient vectors ?

[midnight haven]

no, I don't think so

[flint halo]

.close

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[pearl pond]

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[echo reef]

guys i made a new acc in roblox because my old got hacked few weeks ago. can someone dono

[warm current]

<@&268886789983436800> spam/phishing

[echo reef]

i didnt spawn much

like 4 times in total

[last moth]

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[faint egret]

I don't understand the 2nd part of the question

Like 15% of what

I'll be back in 20 mins

[pearl pond]

@faint egret Has your question been resolved?

[faint egret]

No

[fluid root]

Of the total money he spends on it

In other words, insurance, repair and the diff between buying price and selling

[faint egret]

Ok

[pearl pond]

@faint egret Has your question been resolved?

[faint egret]

Yes

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[cinder ledge]

help

[pearl pond]

@cinder ledge Has your question been resolved?

[cinder ledge]

.close'

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[main oxide]

are you familiar with the extended euclidean algorithm for finding inverses?

basically 245x+748y=1 solving this will end up giving you x, the inverse you want

[vague fiber]

okay i will use this, thank you.

[main oxide]

yup you're welcome

[vague fiber]

why is it written with = 1? is the inverse like a gcd?

[main oxide]

in order for 245 to have an inverse, it must be relatively prime to 748

when you solve that equation and reduce it mod 748, it becomes 245x=1 mod 748 so you can see x really does get you the inverse

[vague fiber]

with the extended euclidean algorithm for this problem then, i would just start by performing the euclidean algorithm on 245 and 748 to find the gcd?

even though i already know that it is 1

[main oxide]

the extended euclidean algorithm gets you x and y

the euclidean algorithm alone just gets you the gcd, which is 1 so you're right that wouldn't get you new info alone

[vague fiber]

but to solve for x and y i use the original euclidean algorithm?

[main oxide]

no the extended

[pearl pond]

@vague fiber Has your question been resolved?

[vague fiber]

so once i find x and y, which is b?

nvm ridiculous question my bad

thank you for the help

.close

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[gentle stone]

how did they get 729

[acoustic path]

9 cubed is 729

[gentle stone]

oh

okay

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[gentle stone]

what part of my answer is wrong

[gentle stone]

maybe i went too far w/ 256

ooooooooooooooooooo

no it's not 108 either

[quiet tendon]

4³ is not 256, you went too far

where did h^12 come from? why did the k² not change?

[gentle stone]

now i have 108/(h^4^3) k^2^3 ........ and i have to multiply the exponents right?

i'm just confused

[quiet tendon]

4³ is not 108

and there is no h^4

[gentle stone]

fuck

okay lemme try again

[quiet tendon]

write this as (4/(hk²)) * (4/(hk²)) * (4:(hk²))

[gentle stone]

do the thing where it makes it a picture

[quiet tendon]

girl im on my phone, typing in latex is slow

ugh

[gloomy scroll]

Be brave neil. We believe in your mobile latexing skills

[quiet tendon]

$\frac{4}{hk^2} \cdot \frac{4}{hk^2} \cdot \frac{4}{hk^2}$

[jolly parrot]

neil

[quiet tendon]

hooray

[gentle stone]

so 64/hk^6?

[quiet tendon]

how many h’s are there

[gentle stone]

there's 3

[quiet tendon]

so the answer is

[gentle stone]

hk3^6?

wdym

[quiet tendon]

h³k^6

on the bottom

[gentle stone]

ahhhhhhhhhhhhh

[quiet tendon]

and just so you don’t have to write it out all the time, remember that (ab)^c = a^c * b^c and that (a/b)^c = a^c / b^c

so (4/(hk²))³ is (4)³ / (hk²)³

and 4³ is 64, (hk²)³ is h³ * (k²)³

and (k²)³ is k^(2*3) which is k^6

[gentle stone]

x^6 x^72?

[quiet tendon]

awesome

can you simplify that mire

more

[gentle stone]

ummmmmmmm

i would just divide ..........?

[quiet tendon]

no

where did division come from

[gentle stone]

idk i;m probably going to fail this exam bc it;s too much for my brain

but if i finish all the homework i have a chance of passing

• the makeup exam on module 1

[quiet tendon]

you have 6 x’s being multiplied by each other, and you’re multiplying that by 72 x’s being multiplied by each other

[gentle stone]

so 6 x 72?

x^432?? or 432x^6?

[quiet tendon]

no

no

simpler example

x³ * x²

is (xxx) * (x*x)

which is x^5

you add the exponents

[gentle stone]

oh so x^78?

[quiet tendon]

yes

[gentle stone]

= (-1)^9 (m^6)^9 (n^8)^9

= -m^54 n^72

[quiet tendon]

very good

that’s exactly the right approach

[gentle stone]

afk;asHTEsruktdyiutipgoydkutruehy

okay

so we have (5)⁷ (a)⁷ (b⁹)⁷ (c⁶)⁷ ???

did i do a right

did i do any of them right

[quiet tendon]

yes

continue simplifying

[gentle stone]

i got the answer for that one

it was right

is this like a reciprocal moment or is that only when the denom is bigger than the num???????????

@quiet tendon

[quiet tendon]

reciprocal moment

negative powers

mean reciprocal

x^(-a) = 1/(x^a)

[gentle stone]

latex pls

i can't see that

[meager trellis]

$x^{-a} = \frac1{x^a}$

[jolly parrot]

bee [it/its]

[gentle stone]

ahhhhhhh i got it

😵‍💫

[midnight haven]

the negative is just above the y so 4 will stay in the numerator

[gentle stone]

ok

and then

[midnight haven]

Well 4 will remain 4 in the numerator and y will go down into the denominator to become y^2

Hence 4/y^2

[gentle stone]

okay that makes sense

and it equalssssssss

32/y^2?

[midnight haven]

The answer will include 1/(y^2)

In the fraction side

[gentle stone]

:c

[midnight haven]

ender 1/y^2 in the fraction

You entered 4/y^2

4/y^2 will be the final answer yknow

[charred ocean]

4x4≠32

[midnight haven]

Since 4*(1/y^2)

=4/y^2

[gentle stone]

aaaaaaaaaaaaaaah

makes sense now

.close

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[pearl pond]

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[edgy otter]

Hi! What do I do from here?

[unborn abyss]

i think you're done

wait no

that's not how e^t gets differentiated, review your rules

[pearl pond]

@edgy otter Has your question been resolved?

[edgy otter]

is the -5 wrong?

[unborn abyss]

no, the -5 is right

[edgy otter]

So it's just -5e^t?

it still says im wrong though 😭

[muted shale]

$\frac{d}{dx}ae^{bx}=abe^{bx}$

[muted shale]

Why is there a - in front of the 1/5 all of a sudden

[edgy otter]

oh shoot

[jolly parrot]

Flappie

[edgy otter]

Yeah that was it

Thank you!!

.close

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[midnight haven]

Is there a pattern?

[pearl pond]

@midnight haven Has your question been resolved?

[pearl pond]

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[midnight haven]

.reopen

[pearl pond]

✅

@midnight haven Has your question been resolved?

[pearl pond]

@midnight haven Has your question been resolved?

[hybrid pelican]

This has to do with Interpolation. Do you know Lagrange Interpolation?

[midnight haven]

no i dont know

what is it ?

[patent badger]

What the fuck is this i stumbled upon those tags and i see this

[hybrid pelican]

Interpolation in general is a way to find a function that goes through specific points. In this case this points are given by the alphas

[hybrid pelican]

The whole equation can be written as $L(x)-x^3=0$ where $L(x):=\sum_{i=1}^n \alpha_i \ell_i(x)$

[jolly parrot]

226PHIL

[midnight haven]

oh i see

[hybrid pelican]

and $\ell_i(x)$ is the $i$th Lagrange polynomial of degree $n-1$:$\ell_i(x):= \prod_{1\leq m \leq n, m\neq i} \frac{x-\alpha_m}{\alpha_i-\alpha_m}$

[jolly parrot]

226PHIL

[hybrid pelican]

See also https://en.wikipedia.org/wiki/Lagrange_polynomial#Definition

[hybrid pelican]

Now to your question: what happens if you plug in the value $\alpha_i$ for $x$?

[jolly parrot]

226PHIL

[pearl pond]

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[pulsar stump]

how do i determine when this matrix of field $\mathbb{Z}_7$ has no solutions, one solution, more than one solution?

$A = \begin{pmatrix}
1 & 0 & 0 | b_1-b_2\
0 & 1 & 1 | 2b_2-b_1\
0 & 0 & 0 | b_3+b_2-2b_1\
\end{pmatrix}$

[unborn abyss]

gaussian elimination right?

[pulsar stump]

i dont know how to do it, i think i need for no solution to get the b's to equal anything but 0 for contradiction

[unborn abyss]

yeah

don't worry about the vertical bars

just write the full matrix

[jolly parrot]

Ayanokoji

[pulsar stump]

this is it

idk how to get 1 exact solution, or more than 1

[unborn abyss]

I don't think you can get 1 exact

[pulsar stump]

the question says you can but idk either

[unborn abyss]

well I guess if you count 0

[pulsar stump]

it is in Z_7

but how do i get more than 1, and exactly 1 solutions?

thats what idk how to do

[unborn abyss]

given any solution you can add 1 to a2 and subtract 1 from a3 and get another solution

[analog bronze]

i think if two rows are the same then you get more than one

[unborn abyss]

(or if one row is all 0s)

[pulsar stump]

the main issue im having is the exact solution, i feel like itll be clearer to eliminate cases after the exact 1 and no solutions conditions are found

[unborn abyss]

I'm fairly confident you can't get one exact solution for reasons I described earlier

[analog bronze]

right basically that

[pulsar stump]

btw we need to say what b's there's 1 solution for

[pulsar stump]

a2? a3?

[unborn abyss]

sorry I mean the second and third component of the solution

[pulsar stump]

yes, but there must be a 1 solution for some given b's

[unborn abyss]

like if you handed me some B's and said "this produces one unique solution (a1, a2, a3)" then I'd be able to hand you back a different solution for the same b's

which is (a1, a2+1, a3-1)

[halcyon plank]

@rigid grove

btw rafilou also explained it

but it still left me with shubuhat

[pearl pond]

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[gentle stone]

wtf is the algebraic equation\

[gentle stone]

i wanna say x-9 = 14

[kind rampart]

negative nine

[inland ivy]

Not quite

It should be x-(-9)=14

Actually, since it says difference you might need to add an absolute value as well

[gentle stone]

for the -9????

so x -|9| = 14?

[inland ivy]

No, around the whole difference

If you haven’t had to use absolute value for any previous questions where it says “difference” then ignore what I’m saying

It’s a bit of a weird way of wording it

[gentle stone]

which one is the difference, the 14?

[inland ivy]

No, the x-(-9)

[gentle stone]

oooh i got it

thank yyouoou

-11 + -x = -15?

[inland ivy]

Why the -x?

Why not just x?

[gentle stone]

oh thats right it's gonna be a -15

[inland ivy]

Yeah

[gentle stone]

yay i got it

okay so x

wait

wtf

is the same as ?

wdtm

[inland ivy]

Equals to

[gentle stone]

how would i write that

[cobalt monolith]

"Same as" here is the same as "is" in the previous question

Same means same

[gentle stone]

oh

so x * -6 = -54?

[cobalt monolith]

MULTIPLICATION

product = multiplication

as sum = addition

[gentle stone]

i like it when you yell at me in caps

[cobalt monolith]

I know

[gentle stone]

okay is that better math daddy

so x * -6 = -54?

[cobalt monolith]

why -6?

Where the minus came from?

[gentle stone]

it's a negative 54

so there jhas to be a negative somewhere

[cobalt monolith]

Product of a number and six

[gentle stone]

okay well then forget about the minus

[cobalt monolith]

is the same as negative 54

(negative 54)

six

The negative is not floating around in space

it is related to 54

and not to 6

[gentle stone]

so x is equal to nine

[cobalt monolith]

no, write the equation first

[gentle stone]

-9

i did it's x * 6 = -54

[cobalt monolith]

fine

[gentle stone]

so x is -9

yay

we finished the module!!!!!!!!!!!!!!!!!! yay

get hype w/ me

[cobalt monolith]

You finished the module

[gentle stone]

only 11 more to go

[brisk steeple]

😄

[gentle stone]

we

[cobalt monolith]

If it's we then it's bad

[gentle stone]

but you helped me figure stuff out

tysm ❤️

im gonna pass my exam bc of you

[cobalt monolith]

I hope you are, try to be more independent...

There will be no one to help you in the exam

[gentle stone]

obvi but thats why i study w/ the homework, so i can pass the exam

and fyi ive done plenty modules on my own

i just get stuck on some things :c

[cobalt monolith]

🙂

What do you need this basic math for?

[gentle stone]

it's a prereq for business math

[cobalt monolith]

I see

[gentle stone]

what kind of math do u do

[cobalt monolith]

Things related to algorithms

Design and analysis of algorithms require all kinds of math

[gentle stone]

that makes sense

[cobalt monolith]

goodluck anyway

[gentle stone]

i have more but im doing a wee bit of work rn so i'll be back

thanks for the hel[

.close

[pearl pond]

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[agile ridge]

I deduced that (A-3E)a1+(A-3E)a2+(A-2E)a3
But then how to continue?

[little silo]

how this server works

where to ask questions

[gloomy scroll]

#❓how-to-get-help

[little silo]

doesnt work

bugged

doesnt click

[little silo]

r u pro math

[gloomy scroll]

I wouldn‘t call myself a pro of maths no

[little silo]

what they required me to do

[gloomy scroll]

What do you mean by it doesn‘t work? Because this is someone else‘s channel

[little silo]

do u know what have to do in this ss

[agile ridge]

read #❓how-to-get-help patiently

[gloomy scroll]

No. And you won‘t get any help by staying in this channel. It‘s someone else‘s

[little silo]

bro help nino is my little sister

[agile ridge]

?????

[little silo]

this our channel

family channel

[agile ridge]

wtf

[gloomy scroll]

I‘ll open one for you if you want. Look for the channel with my name ok?

[little silo]

ok

[pearl pond]

@agile ridge Has your question been resolved?

[agile ridge]

<@&286206848099549185>

[outer frigate]

I know that

what you need

[agile ridge]

。

[outer frigate]

give me a question

[agile ridge]

.

[pearl pond]

@agile ridge Has your question been resolved?

[agile ridge]

<@&286206848099549185> 😭

[outer frigate]

What you need

Give me a question

[cosmic raptor]

dawg they linked the question

[pearl pond]

@agile ridge Has your question been resolved?

[pearl pond]

Channel closed

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[pearl pond]

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[hallow condor]

whatd i mess up

[muted shale]

!original

[pearl pond]

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.

[muted shale]

whats the -169 for?

[hallow condor]

it was the 13 squared

[muted shale]

but why are you subtracting it?

keep that 169 term away and it should be correct

[hallow condor]

so just $\pi\left(\left(\frac{12}{x}-13\right)^2\right)$

[jolly parrot]

Big Yannis

[muted shale]

yeah

the radius is 12/x-13

and you square that

and multiply by pi

and you get the area of the circle at that x

[hallow condor]

I think i need height too

cuz its a shell

[muted shale]

wdym height?

[hallow condor]

cylindrical shell

[muted shale]

do you have an image with this?

[hallow condor]

closest example of my question

[muted shale]

,w graph y=12/x

[jolly parrot]

Results provided by WolframAlpha

Click here to refine your query online
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Requested by flappie.

[muted shale]

,w graph 12/x-13 from x=1 to x=6

[jolly parrot]

Results provided by WolframAlpha

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

Requested by flappie.

[muted shale]

here is we take these slices dx, the radius is (12/x-13), so the volume of this slice is pi r^2 dx = pi*(12/x-13)^2dx

then taking the integral of this from x=1 to 6

gives you your total volume

[hallow condor]

still aint working

[muted shale]

,w graph 12/x from x=1 to x=6

[jolly parrot]

Results provided by WolframAlpha

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

Requested by flappie.

[muted shale]

i genuine have no clue what theyre doing

it makes no sense

sorry

[hallow condor]

yeah its whack

thanks anyways

[pearl pond]

@hallow condor Has your question been resolved?

[hallow condor]

.close

[pearl pond]

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[fluid sphinx]

For a). can I just use geometry to find the area of the curve of the second graph?

[fluid sphinx]

rather than taking the integral?

[pine jay]

Well it seems you don’t have any other option

So yes

[fluid sphinx]

thanks!

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[foggy wagon]

Is it b or c

[burnt dust]

!status

[pearl pond]

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

[burnt dust]

@foggy wagon what part of it are you having trouble with?

the definitions?

[foggy wagon]

I am just confused

[foggy wagon]

I get the approach from the left side right side

But is it 3 for both the left and right

Or is it 8 when approaching from the right

[burnt dust]

where does 8 come from?

[foggy wagon]

Not 8 I meant + infinity

[burnt dust]

same question

where does infinite come from

[foggy wagon]

Idk it’s in the answer c

so answer b is correct ?

[quiet tendon]

yes

[foggy wagon]

Thank you

.close

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[scenic canyon]

I'm trying to find the estimate of the slope of the tnagent line to f(x) = x^4 at x = 4 by finding slopes of secant lines.

[rustic nacelle]

did you run into any problems/questions?

[scenic canyon]

I'm just confused is slope of tangent line is zero

That's what it seems like

[rustic nacelle]

Are you estimating the slope at x = 4 or x = -1?

This is what the graph of f(x)= x^4 looks like, as you correctly sketched. What do you think the tangent slope is at x = -1? Could it be 0, a negative number, a positive number? Is the magnitude less or more than 1 (if it's not 0)?

[scenic canyon]

My bad hold on let me send the question on the paper

[rustic nacelle]

On the left, how did you get positive slopes?

[scenic canyon]

That's how it came out when I plugged into the calculator

[rustic nacelle]

Suppose we're using x = -1 and x = -1.5 for our secant line. What is its tangent?

[scenic canyon]

I'm not following you at this point. Do you want me to plug those numbers into the slope I made?

[rustic nacelle]

Yes, how would you calculate the slope between these points?

And what does the $\frac{x^4 - 1}{-x + 1}$ formula refer to?

[jolly parrot]

fix error

[rustic nacelle]

I think I see where you went wrong

If you have two x values: l on the left and r on the right, then you'd compute the slope as "rise / run", in other words:

$\frac{r^4 - l^4}{r - l}$ (or $\frac{l^4 - r^4}{l - r}$ which is of course equal)

[jolly parrot]

fix error

[rustic nacelle]

x = -1.5 is on the left and x = -1 is on the right. So you should get:

$\frac{(-1)^4 - (-1.5)^4}{(-1) - (-1.5)}$

[jolly parrot]

fix error

[rustic nacelle]

@scenic canyon Does this make sense?

[scenic canyon]

No, cause I was using the two points (-1 , 1) and the point (-x, x^4) to find the slope which is rise over run.

[rustic nacelle]

Why is it -x and not x?

[scenic canyon]

I assumed it was -x cause I'm going to the left of the number line. Would it still just be x?

[rustic nacelle]

You are using x values that are already negative. e.g. when x = -4, -x will be 4

[scenic canyon]

It's a negative x value and I have the y which is x^4

[rustic nacelle]

Suppose that you have two points: (1, 1) and (2, 8). The slope of the line between them is 7, right?

[scenic canyon]

Yes

[rustic nacelle]

If one point is (-1, 1) and the other point is (-2, 8), what is the slope of the secant?

[scenic canyon]

I don't know

[rustic nacelle]

You did solve the first task of the quiz, right?

[scenic canyon]

Yes

[rustic nacelle]

Wait, it's not right

[rustic nacelle]

let's take (-1, 1) and (-2, 16). The "rise" is 16 - 1 = 15 and the "run" is (-2) - (-1) = -1. Do you agree?

That's the same as with the (1, 1) vs (2, 8) example. 8 - 1 and 2 - 1

[scenic canyon]

Yes

[rustic nacelle]

But you computed the "run" as -3

[scenic canyon]

Yes

[rustic nacelle]

Do you see where you went wrong in the first task now?

[scenic canyon]

Yes I should've got -15 correct

[rustic nacelle]

Yep

So the "run" is computer as "(the x value on the right) - (the x value on the left)", doesn't matter whether any of the values are negative

[scenic canyon]

Ok

[scenic canyon]

What should i do next?

[rustic nacelle]

Are you still not sure why the formula for the slope on the paper is not right?

[scenic canyon]

Are the numbers, right?

Imma look at it in a minute again

[rustic nacelle]

Can you answer this? #help-39 message

[pearl pond]

@scenic canyon Has your question been resolved?

[scenic canyon]

It's a negative number. It's less than 1?

[rustic nacelle]

You mean it's between 0 and -1? Or less than -1?

[scenic canyon]

Less than

[rustic nacelle]

Right. The tangent slope describes how quickly the function changes and in what direction. The blue graph shows what the slope of the tangent will be at each point in the function

So 0 means the function stays the same (at that point), a positive number means it's increasing and a negative number means it's decreasing

You can use secants to approximate these tangents, as shown in here (cyan line is the "ideal" tangent", lime lines are the approximations)

To compute the slope of a line, you divide how much the "y" increases/decreases by how the "x" changes. Then make a common sense check to see whether the answer makes sense: if the function is rapidly "falling" at this point, then -3.17 sounds reasonable. If instead you got +0.5, that would be a sign that you made a mistake.
You don't need to construct any formulas, just remember the general idea.

[scenic canyon]

Ok, so it just depends on the way ot is. And I gotta rewrite the formula? I know there's other ways to get it but I gotta do it like that cause he taught it like that

[rustic nacelle]

The general formula for the slope, if you have a function f and two points l and r is:

$\frac{f(r) - f(l)}{r - l}$

[jolly parrot]

fix error

[rustic nacelle]

In this case: $\frac{r^4 - l^4}{r - l}$

[jolly parrot]

fix error

[rustic nacelle]

For example if one point of the tangent is $l = -1$, then you get $\frac{r^4 - 1}{r + 1}$

[jolly parrot]

fix error

[scenic canyon]

Ok imma get home and rewrote it. Also sorry for all th trouble

[scenic canyon]

Ok so it's how I originally had it

[scenic canyon]

Ok so it's negative 4. Thank you so much. I'm also a little weak in eyesight so I may have misinputted in my calc causing some confusion

.close

[pearl pond]

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[pearl pond]

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[prime bane]

How In the world should I solve this

[prime bane]

It's related to pythogoras theorem cuz that's the chapter

[prime bane]

I tried something but I don't think it's right

<@&286206848099549185>

[brave mesa]

Lemme try

[prime bane]

Ok

[brave mesa]

I solved this

So

You know what system of equations is?

@prime bane

[prime bane]

No

I don't think so

[brave mesa]

Uhh

System of equations is literally system of equations

[prime bane]

Then yes

[brave mesa]

U have some equations that connected

[prime bane]

I know how to solve equations

[prime bane]

Ok

[brave mesa]

In system of equations you have 2+ unknown variables

[prime bane]

Ok

[brave mesa]

So here

[prime bane]

So this is a system of equations

[brave mesa]

U can make 2 equations

[prime bane]

Since it has 2 unknowns

[prime bane]

Yes I can

[brave mesa]

You can say that length of the wall is y

And we already know what x is

So

Using Pythagorean Theorem we can make 2 equations

[prime bane]

Ad² = y²+(X+16)²

And

[brave mesa]

I will help you with solving this system, but you need to make correct equations by yourself

[prime bane]

Ac² = y²+x²

[brave mesa]

So yes

Then replacr AD and AC with numbers to make this prettier

[prime bane]

Oh I get it now

I think I can solve it t

Thank you

[brave mesa]

How will you solve this?

[prime bane]

Simultaneous equations

[brave mesa]

Okay

Say me the answer that you got

I will say you what is a real answer

If you want

[prime bane]

X = 20

[brave mesa]

Correct

[prime bane]

Tysm

. close

.close

[pearl pond]

Channel closed

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[sharp smelt]

I'm confused as to what I have to do in problem 9

[sharp smelt]

so a triangular number is defined to be a number of the form $\frac{n(n+1}{2}$

[jolly parrot]

ƒ(Why am. I here)=I don't Know

[sharp smelt]

how do I use that here

I was thinking maybe

[cinder flower]

9a?

[sharp smelt]

yeah

one minute, typing out what I tried

[cinder flower]

kk

[sharp smelt]

$\frac{\left(\left(\frac{n\left(n+3\right)}{2}+1\right)\left(\frac{n\left(n+3\right)}{2}\right)+2\right)}{2}=t_x$

[jolly parrot]

ƒ(Why am. I here)=I don't Know

[sharp smelt]

is this right?

[cinder flower]

i think so

[sharp smelt]

cool thanks!

.close

[pearl pond]

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[wild fable]

how am i supposed to use g'(x) to find the mean?

[tulip ore]

do you know what integral would find the mean?

[wild fable]

i was gonna say cosx from 0 to pi/2 but thats not true because that equals 1 and i need to find when the integral = 1/2 right

[tulip ore]

thats not it

thats for median

[wild fable]

okk

ohh*

[tulip ore]

take a closer look at f

you know if you integrate anything thats just 0, you dont get any area

what remains is just that area from 0 to k

[tulip ore]

also, you can ignore the "equals 1" part for now, it doesnt matter in the question

[wild fable]

oh wait

$\int_{ }^{ }xf\left(x\right)dx$

[jolly parrot]

tox was here

[tulip ore]

thats the correct integral

[wild fable]

from 0 to pi/2

[tulip ore]

but not the right bounds

[wild fable]

its 0 to k isnt it

[tulip ore]

yep it is

[wild fable]

but k was found to be pi/2

[tulip ore]

thats not important

[wild fable]

alright

[tulip ore]

since k is pi/2 though you can leave that in

so the bounds are correct

[wild fable]

u just said it was wrong

😭

[tulip ore]

you didnt say you found out k from an earlier problem

[wild fable]

um

ok so whats my f(x) ?

[tulip ore]

since youre only integrating from 0 to k,

f(x) is just cos x

so you need to calculate $\int_0^kxf(x)\dd{x}$

[jolly parrot]

mtt

[wild fable]

what does the question want me to do with g(x)?

[tulip ore]

it wants you to find the derivative of g(x)

[tulip ore]

its relevant to how youll need to calculate this integral

because you need to integrate x cos(x)

and finding this derivative will give an easy way to integrate that

[wild fable]

oh

ok

i got g' = cosx(x+sinx+1)

[tulip ore]

thats not it, try that again

[wild fable]

oh oops

differentiated cosx wrong

its xcosx

[tulip ore]

since you know d/dx (x sin x + cos x) is x cos x,
what would the integral of x cos x dx be

[wild fable]

xsinx + cosx

[tulip ore]

so what would $\int_0^{\frac\pi2}x\cos x\dd{x}$ be

[jolly parrot]

mtt

[wild fable]

i got pi/2 - 1

but thats negative

[tulip ore]

pi/2 - 1 is not negative

[wild fable]

oh true

lol

for this

i just integrate cosx from 2 to pi/2?

[tulip ore]

not quite it

[wild fable]

or is it 0 to 2

i dont think its 0 to 2

[tulip ore]

it says "greater than or equal to 2"

what bounds would that suggest

[wild fable]

but the bound goes from 0 to k so i dont see how tis not 2 to pi/2

[tulip ore]

(d) is 0

[wild fable]

whats (d)?

oh

oops

nvm

why is it 0?

[tulip ore]

lets repeat

you said the bound goes from 0 to k

why is that?

[wild fable]

because its a PDF?

[tulip ore]

thats not why

the bounds go from 0 to k because if they went anywhere bigger, you dont get a different result

f(x) is not cos(x)

f(x) is cos(x) when x is between 0 to k and 0 everywhere else

what this means is that if you want to find out the "probability that X is between 1 and 2", you can just do:

,,\int_1^2f(x)\dd{x}

[jolly parrot]

mtt

[wild fable]

ohh wait 2 is greater than pi/2 so it doesnt exist right

[tulip ore]

no

so its 0

not that it "doesnt exist"

"doesnt exist" is for limits

[wild fable]

ok yeah

cool cool

thanks

[tulip ore]

np

[wild fable]

.close

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[pure mirage]

hi, how would I go about parametrising a cylindrical surface?

[midnight haven]

wym by that

[pure mirage]

i want to parametrise it

for example the parametrisation of a circle in 3d space is
(ox + rcos theta, oy + rsin theta, z)

where o represents the center

[midnight haven]

oh ok yea this is way out of my knowledge

[pure mirage]

oh ok

[burnt dust]

Typically with polar angle and height

It gets a bit more complicated if it doesn’t line up with any axis

But if you are solving an actual problem, we usually can choose our own alignment

[burnt dust]

This is literally for a side of cylinder parallel to the z-axis

[pure mirage]

oh

[burnt dust]

You use z as the second parameter

[pure mirage]

my bad, z should be 0

[burnt dust]

If you don't fix z

And have it as a parameter

You are done

[pure mirage]

that's my cylindrical surface?

i'll have to bind z to constraints though then i guess

[burnt dust]

It should be constrained to the height you want your cylinder to start and end at

Otherwise it could be from -inf to inf if you want an infinite cylinder

[pure mirage]

I see

[burnt dust]

A cylinder is just a bunch of circles stacked on top of each other

[pure mirage]

true true

well thank you

[burnt dust]

Np

[pure mirage]

.close

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[chrome flame]

11 and 12 hints please

I guess power set and set of elements have no common thing

11 C?

[latent quail]

12. Hint: Mutuals

I have no idea about what’s going on at 11.

[chrome flame]

{(1,2) (1,1)(2,2)(3,3)(2,1)(1,3)(3,1)}

@latent quail

{(1,2) (1,1)(2,2)(3,3)(2,1)(1,3)(3,1)(3,2)(2,3)}

[cobalt monolith]

@chrome flame let's do 11 with a simple example

[chrome flame]

Yeah sure

[cobalt monolith]

Say A={1,2}

[chrome flame]

....

[cobalt monolith]

What is $A \cup P(A)$?

[jolly parrot]

Cain

[chrome flame]

Power set will be

{{},{1}{2,}{1,2}

[cobalt monolith]

OK, so A \cup P(A) != P(A)

so a isn't true right?

how about b?

you said it already (that there are no common elements),

So b isn't true either.

c?

Also follows from what you said, no common elements

@chrome flame so, what do you think about c?

So, because there are no common elements, (c) is true, and (d) isn't true because A \in P(A)

[chrome flame]

Hang on

[cobalt monolith]

And regarding 12, is this an equivalence relation?

[chrome flame]

A U p(a)=p(a)

A is true no?

[cobalt monolith]

no

In our example, $1 \in A \cup P(A)$ but $1 \notin P(A)$

[jolly parrot]

Cain

[pearl pond]

@chrome flame Has your question been resolved?

[pearl pond]

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[sharp smelt]

show that any integer of the form $6k+5$ is also of the form $3j+2$ but not conversely

[chrome flame]

.reopem

Ahhh

[sharp smelt]

oops

[chrome flame]

Sorry

[jolly parrot]

ƒ(Why am. I here)=I don't Know

[sharp smelt]

so$ 6k+5=3(2k)+5$

let $2k=i$

[jolly parrot]

ƒ(Why am. I here)=I don't Know

[sharp smelt]

so we have $3i+3+2$

[jolly parrot]

ƒ(Why am. I here)=I don't Know

[sharp smelt]

let (i+1)=j

so this is of the form 3j+2

[muted shale]

Given any k, show that there exists an i such that 6k+5=3i+2

Is what's being asked

[summer gorge]

its trivial\

[sharp smelt]

[muted shale]

And to show the converse, show that there exists an i, such that there exists no k so that 3i+2=6k+5

Does this help?

[sharp smelt]

I can just use a counter example

take j=1

[muted shale]

Exactly

[muted shale]

*i

[sharp smelt]

j=1

not i

[sharp smelt]

here

that will give you 5

[muted shale]

Ah wait

Yes mb

And no, j=1 does not work

Since then you can take k=0

[sharp smelt]

ah, right

[summer gorge]

but we can write $6k+5=3(2)k+3+2$

[jolly parrot]

convergence

[muted shale]

Take any even j

[sharp smelt]

ye, but not the other way round

[muted shale]

And it won't work

[sharp smelt]

right

thanks

let me note that down rq

[summer gorge]

proof by direct example works here

nvr mind you got that

[sharp smelt]

yeah, thanks both of you

.close

[pearl pond]

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[tulip tiger]

How would I show that any Galilean spacetimes are isomorphic (i.e. there is an affine isomorphism between them which preserves their time functionals t on the underlying vector space and distances between simultaneous events given by the inner product on ker t)

[tulip tiger]

The book I'm reading from doesn't give any useful definitions to this end

To be clear, my "working definition" is the following: A Galilean space-time A⁴ is a 4-dimensional affine space over R⁴, with
(1) a time functional t : R⁴ → R
(2) an inner product on ker t

[pearl pond]

@tulip tiger Has your question been resolved?

[tulip tiger]

<@&286206848099549185>

[pearl pond]

@tulip tiger Has your question been resolved?

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@tulip tiger Has your question been resolved?

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[severe quarry]

\begin{problem} Perform SVD on $A = \mrm{1 & 0 & 1 \ 1 & 0 & 1 \ 0 & 0 & 0 \ 1 & 1 & 0}$, i.e. find $U, V, S$ with $A = U \cdot S \cdot V^{\tr}$. \end{problem}

[severe quarry]

So, I got the eigenvalues and eigenvectors

[pearl pond]

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[severe quarry]

.close

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[final locust]

hello! I just wanna ask u guys if anyone here knows what does the formula 2n+1 represents? I know that 2n-1 represents first n odd numbers. But does 2n+1 represent anything?

[inland ivy]

it's the same thing, just reindexed

2n-1 gives the n'th odd number, where the 1st odd number is considered to be 1

2n+1 gives the (n+1)'th odd number

[final locust]

so the formula for its sum is also the same? (being n^2?)

[inland ivy]

no, not quite

I think it'll be (n+1)^2

[final locust]

hmmm. Let me dwell on this longer. I'll be back here in a few hours. Thanks for guiding me!

.close

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[muted shale]

!da2a

[pearl pond]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[inland ivy]

<@&268886789983436800>

[muted shale]

<@&268886789983436800>

[tepid kindle]

banned

[inland ivy]

what the hell is goin on

[unborn abyss]

children

[fallow cosmos]

NSFW spammer, move along.

[inland ivy]

how are discord's NSFW filters THIS bad

[pearl pond]

@warm junco Has your question been resolved?

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[meager totem]

i need help with this math question
id say i know 0% of what they wanted could someone please help me
i just need help with assignment 2

[pearl pond]

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[pearl pond]

@meager totem Has your question been resolved?

[meager totem]

<@&286206848099549185>

[rancid summit]

compound principal is a strange term to me, but i'm assuming it means future value or amount since the principal is already given. do you remember that $A = P (1+r)^n$ where $A$ is the compound principal (Amount)? for items a, b and c just replace the values in the previous formula, in particular changing $n$ to the amount of years given by each item. for item d you have to subtract the $A$ you found in item c by $P$. for item e you have to calculate the simple interest/profit (do you remember the formula?) for 3 years and subtract it from the $A$ from item c. remember that $9%=0.09$ in the formula.

[jolly parrot]

ruruchan_2001

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[brittle onyx]

,rccw

[brittle onyx]

Is this right

[rough forge]

yes

[brittle onyx]

How did u get the answer

[rough forge]

wdym

[brittle onyx]

Because my teacher is thinking that the ans is B

[rough forge]

,w arcsin(1/2)-arccos(-sqrt(3)/2)+arctan(sqrt(3))

[jolly parrot]

Results provided by WolframAlpha

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

Requested by adoniszgks

[brittle onyx]

Ohk

Thx

.close

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[distant pendant]

<@&286206848099549185>

With venn diagramm

[fossil herald]

lvl Asian HAHAHAHAHAHA

[distant pendant]

Hhhhhhh

?

[distant pendant]

.

[latent quail]

!15m

[pearl pond]

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.

[pearl pond]

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

[distant pendant]

2

[latent quail]

Show your work

[distant pendant]

It’s in germany tho

Well hhh

Ik but then u have a lot of unknows

[atomic jasper]

Find the number of people like sprite and coke but excluding the one who like 3 of them. And find the number of people who like sprite and Fanta but excluding the one who like 3 of them. Both in terms of x.

And you can solve for x

[distant pendant]

Ig i tried it but lemme check again

[distant pendant]

I am lost idk how

[atomic jasper]

Ok so there are 12 people like coke and sprite

And 10 people like Fanta and sprite

if x is the number of people who like coke, sprite, and Fanta.

[atomic jasper]

What would the answer be for these questions

[distant pendant]

😵‍💫

[atomic jasper]

Umm so if you subtract the number of people who like these 3 brands (coke, Fanta, and sprite), then it would be people who don’t like these 3 brands together.

so for people who like sprite and coke but not Fanta, it would be 12-x

And 10-x for people who like sprite and Fanta but not coke.

[distant pendant]

Then

[atomic jasper]

Then you know that people who only like sprite is 9 people.

And the total number of people who like sprite is 24

[distant pendant]

Like this

But then it’s 3,5

[atomic jasper]

Add them together, you get x+9+(10-x)+(12-x)=24

[atomic jasper]

And you solve for x

[atomic jasper]

You forgot to add x

[distant pendant]

Ok i forgot the x

Then X=7

[atomic jasper]

Yes

[distant pendant]

Ok i can handle the rest

I actually did that already and y=22 people who like only cola was 15 and who like only fanta was 13 but i was not sure

I found this on internet so inthought my answer was wrong

[atomic jasper]

You are right

[light helm]

that image seems to be for a different problem

[atomic jasper]

This is a different question cuz coke only has 30 but the question is 34

[distant pendant]

Right I didn’t even notice tho