help-39

[jolly parrot]

amy.ames.aims

[wheat trail]

i get up to here, and then become stuck

[hard tendon]

Try to use \ before arctan

I think this will work

[hot canyon]

hey, it'd first be nice to like, get rid of the (x - 9.5) term by a prior u-sub

I suppose the question is to integrate: $$\left[\int (\arctan^2 (x - 9.5) + 7.40) \dd x \right] \cdot \left[\int \arctan(x - 9.5) \right] + \int 3.70^2 \dd x$$

[jolly parrot]

Ansh

[hot canyon]

Right?

[wheat trail]

yup!

[wheat trail]

would u mind showing me how you'd do it?

[wheat trail]

wait actually it's $$ = \int arctan^2(x-9.5) + 7.40 + \int arctan(x-9.5) + \int 3.70^2 dx$$ my bad, I made a mistake when typing it out earlier

[jolly parrot]

amy.ames.aims

[hot canyon]

ohh

[wheat trail]

the original question was
$$ = \int \qty(\arctan(x-9.5) + 3.70)^2$$

[jolly parrot]

amy.ames.aims

[hot canyon]

Alrighty

I'll show you that then

First, let's get rid of that arctan argument, kay?

$I = \int (\arctan u + 3.70)^2 \dd u$

[jolly parrot]

Ansh

[wheat trail]

oo okay i see

so $$\int \arctan^2(u) + \int 7.4 \cdot arctan(u) + \int 3.7^2 du$$

[jolly parrot]

amy.ames.aims

[hot canyon]

Yes

or rather, let's only focus on

$$\int \arctan^2 u , , \dd u$$ and $$\int \arctan u , , \dd u$$

[jolly parrot]

Ansh

[wheat trail]

the integral of $\arctan(u) du$ is $$u \cdot \arctan(u) - \frac{ln |1+u^2|}{2} + c$$ right?

[jolly parrot]

amy.ames.aims

[hot canyon]

looks right, yes

yk 👀 you can actually just start with guessing an anti derivative lmao

[wheat trail]

skdjhkjhfg i don't think i can cause i have to show working

[hot canyon]

like, the integral has to have had a term like $$u(\arctan u)^2$$

[jolly parrot]

Ansh

[wheat trail]

wait ffor arctan or arctan^2?

[hot canyon]

for arctan^2

[wheat trail]

mmmmmmmmmmmmm is there a more accurate way to do it?

[hot canyon]

IBP of course, lemme see

You could potentially do this thing:

$\tan^{-1} u = \theta$

[jolly parrot]

Ansh

[hot canyon]

and integral equals: $$\int \theta^2 \sec^2 \theta \dd \theta$$

[jolly parrot]

Ansh

[hot canyon]

and apply IBP twice to get rid of the theta^2 term

$$= \theta^2 \tan \theta - 2\int \theta \tan \theta \dd \theta$$

[jolly parrot]

Ansh

[hot canyon]

again apply IBP to second integral, and you have your final integral lol

,w integrate x tan x dx

[jolly parrot]

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[hot canyon]

though you'll have an improper integral left out

but dw, if it was definite integral, you can deal with it somehow

[pearl pond]

@wheat trail Has your question been resolved?

[past oriole]

Lithium again

[pearl pond]

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[pearl pond]

Please don't occupy multiple help channels.

[earnest stratus]

Do not occupy multiple channels.

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.close

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[viscid pivot]

I need help I'm at variations

[viscid pivot]

Vk/n k is for classes n is for elements

This is after permutations

The problem is

Find x if:

V2/x=2x

well I solved it by factoring somehow and got 0, 3 the answer being 3

I don't understand this at all, but I want to understand this:

V2/x-5x=0

Vk/n is V=n(n-1)(n-2)...

the formula for variations

Or:

<@&286206848099549185>

I think the left part is x(x-1)(x-2)

[pearl pond]

@viscid pivot Has your question been resolved?

[viscid pivot]

<@&286206848099549185> 🥱 servers full of "mathematicians"

💀 dawg yall really cant solve 8-th grade problem? aren't PhD mfs in this server

[tulip mason]

Your problem is too hard 😪

[viscid pivot]

damn it man I've looked everywhere even in KA and still can't solve this

[sage solstice]

$$V^2_x = x(x-1)(x-2)$$

[jolly parrot]

NeoGeo

[sage solstice]

is this it?

and then you are solving

$$x(x-1)(x-2)=2x$$

[jolly parrot]

NeoGeo

[sage solstice]

?

you want to expand the left side and then move the term on the right over then solve

[viscid pivot]

channel is taken

oh wait

brain hurts im sorry let me have a look

[sage solstice]

oki

[viscid pivot]

ok so that's just it? I factor at the end

and x1=0 and x2=3

right?

[sage solstice]

i think so

you get a cubic tho

that may have 3 solutions

[viscid pivot]

my god why do they literally want to torture me

as if other problems weren't complicated enough

[sage solstice]

$$x^3 - 3x^2 + 2x = 2x$$

[jolly parrot]

NeoGeo

[sage solstice]

nah you're totally right

i appologise

0 is a repeated root

[viscid pivot]

so it's just factoring?

[sage solstice]

ye

[viscid pivot]

mind helping me with a few others of the same nature?

[sage solstice]

sure

[viscid pivot]

V2/x-3!*x=0

[sage solstice]

$$V^2_x - 3!*x$$

[jolly parrot]

NeoGeo

[sage solstice]

like this?

[viscid pivot]

yeah 3! factorial times x

[sage solstice]

yeah

so you just substitute in what V2_x is

[viscid pivot]

it's x(x-1)(x-2)

-6x

?

[sage solstice]

ye

just expand it

[viscid pivot]

and factoring again?

[sage solstice]

ye

[viscid pivot]

got cha

[viscid pivot]

huge thanks @sage solstice

.close

[pearl pond]

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[sharp basin]

i would like to understand why cos²x - cos²xsin²x = cos⁴x

[snow sail]

what did you try

[sharp basin]

im stuck here

[snow sail]

heres what i would suggest

do you agree this is just like

trivially true where cos(x) = 0?

[sharp basin]

yes

[snow sail]

okay

so assume cos(x) isnt 0

and divide by cos^2(x)

what do you get?

[sharp basin]

so if i divide cos^2x sin^2x by cos^2 x?

[snow sail]

divide everything by cos^2(x)

[sharp basin]

including the sin^4?

[snow sail]

👀

[snow sail]

start here

what is $\frac{ \cos^2 x - \cos ^2 x \sin ^2 x }{ \cos ^2 x } = \frac{ \cos ^4 x }{ \cos ^2 x}$

[jolly parrot]

jan Niku (join us for @pomo)

[snow sail]

simplify

[sharp basin]

$\cos^2x-cos^2xsin^2x=cos^4x$

[jolly parrot]

ApartGorgon9849

[sharp basin]

oh thanks

i got it

[snow sail]

do you see?

[sharp basin]

yes

[snow sail]

[sharp basin]

.close closes this right?

[pearl pond]

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[sweet fractal]

Anyone able to proof read this

"Crucial" was the wrong number, but that wouldn't change much

Just for safety I did the top half in two different cells

There was a little example would that was easily in the triple digits, so 13 feels a little small

[pearl pond]

@sweet fractal Has your question been resolved?

[pearl pond]

@sweet fractal Has your question been resolved?

[pearl pond]

@sweet fractal Has your question been resolved?

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[craggy cave]

Does anyone know how to prove this(epsilon being an arbitrary real number)? I know this must be trivial but I still don't know how to do it... The right side looks like Archimedean property but what about the left side? And is such an N unique?

[snow sail]

sure

well not immediately but we can probably figure it out right

[craggy cave]

any hints?

[snow sail]

so

lets try some

any restrictions on epsilon?

[craggy cave]

no, it's just a positivereal number

[snow sail]

not less than 1

[craggy cave]

I swear I've seen this somewhere but I forgot how to prove it

[snow sail]

can we reciprocate

$N \leq \frac{2}{\epsilon} \leq N+1$

[jolly parrot]

jan Niku (join us for @pomo)

[craggy cave]

and where does this lead us

hmmm

[snow sail]

epsilon is fixed, yea?

[craggy cave]

yes

[snow sail]

we get to pick N

so

$\lfloor \frac{2}{\epsilon} \rfloor \leq \frac{2}{\epsilon} \leq \lceil \frac{2}{\epsilon} \rceil$

[jolly parrot]

jan Niku (join us for @pomo)

[craggy cave]

Ohhhhhhhh

[snow sail]

[craggy cave]

I feel dumb

Thank uuuuuuu

.close

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[snow sail]

dont be sad

i was just guessing

im still doubting its right

but something like that

[pearl pond]

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[drifting quartz]

I am doing trigonometric equations at school and am very confused about how I would solve the following question. 'Solve for x in the domain [0,2pi]' 'cosx=(square root of three)/2' I'm sorry but I am unsure about how to add math symbols in.

[drifting quartz]

.close

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[limpid roost]

If local linearity applies over an arbitrary small interval of a differentiable function then why doesn't convergence of a multivariate limit of all linear paths towards the origin imply convergence of all paths?

[pearl pond]

@limpid roost Has your question been resolved?

[toxic lichen]

"local linearity applies over an arbitrarily small interval of a differentiable function" is vague

but also, a non-linear path may well be shaped in such a way that it crosses many linear paths many times. and the pathwise limits may well be different for different linear paths.

[limpid roost]

Can you give me a function f(x,y) whose limit at the origin converges for all linear paths y=mx but diverges for some non-linear path?

I'm having a hard time seeing that

What I'm trying to say is that the tangent line becomes a better and better approximation to the path as the interval becomes smaller and smaller. So in some arbitrarily interval of x centered at 0: -ε<x<ε, the tangent line to the path at the origin should be arbitrarily close to the actual path. Hence local linearity. Why do you have to test non-linear paths at all?

[west sapphire]

For all $m\in [0,\infty)$, define $f(x,y) = m\sqrt{x^2 + y^2}$ for all $x,y$ on the line $y= mx$, which only leaves $f$ undefined on the $y$ axis, where we set $f(x,y) = 0$. Then, restricted to any line through the origin, the function is continuous and converges to zero as you approach the origin. But the unrestricted function is not continuous, because in any disk centered at the origin the function assumes arbitrarily large values.

[jolly parrot]

OurBelovedBungo

[toxic lichen]

sure, take f(x,y) = y/x for x not equal to 0 and 0 for x=0

and f(0,0) = whatever you want, it does not really matter

[limpid roost]

What if we also require that the function f(x,y) be differentiable

[toxic lichen]

well if your function of two variables is differentiable then it is also continuous and so its bivariate limit at the origin exists and is equal to f(0,0)

and that implies that all linear pathwise limits exist and are also equal to that

[limpid roost]

Right yeah

Differentiable except at the origin then

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@limpid roost Has your question been resolved?

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[tired jetty]

....

,,,,

[tired jetty]

I decided I wanted to start off by proving that if the curves have exactly one common tangent, then they touch each other

The discriminant of that long equation just above the red box must equal 0

From that, I arrived at $b_1=b_2$

[jolly parrot]

azeem321

[tired jetty]

But this result alone is not enough to conclude that the quadratic equations touch each other

So i am confused

oh shit

nvm

.close

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[rose fjord]

How can i slove this ? I had an idea of putting upper one to destry A. But i think thats wrong.

[pearl pond]

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[radiant socket]

part b pls

i got the angles

do i use sin rule?

[broken knot]

do you know how to find the area of a triangle while only knowing 1 angle and 2 side lengths

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[molten creek]

been working on this one for a while wondering why its not letting me go through is there something im missing algebra tiles

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[molten creek]

No

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[west osprey]

I am given the following ODE

$y'=\frac{(y-5)(y+5)}{10x},\qquad x>0$

now I am supposed to check for what $y(x_0)=y_0$ the function is falling or rising

[jolly parrot]

Luca

[west osprey]

is there an easy way to do this without solving the ODE and solving for $c(y_0)$?

[jolly parrot]

Luca

[west osprey]

I am pretty sure there is supposed to be

I can send the task as well

task c)

[pearl pond]

@west osprey Has your question been resolved?

[west osprey]

<@&286206848099549185>

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[pine shale]

$\sqrt{(a+2)^2}=a+2$

[jolly parrot]

Lyuka

[pine shale]

is only verified for $a \geq -2$ because the sqrt has to be $\geq 0$ right?

[jolly parrot]

Lyuka

[pine shale]

So the answer can't be a=every real numbers even if we could simplify the sqrt

is this right?

[midnight haven]

yes

[pine shale]

I see thank you

i have another question

how can i solve this expression

$\log _{:}\left(\frac{4\left(1-x\right)+x^2}{\left(x-2\right)^2}\right)$

[jolly parrot]

Lyuka

[inner matrix]

$\sqrt{(a+2)^2}=|a+2|$

[pine shale]

considering that $x\neq2$

[jolly parrot]

aol

Lyuka

[broken knot]

multiply out the top and try factor

[inner matrix]

Idk logariphms but i try help
$\frac{4(1-x)+x^2} {(x-2)^2}=\frac{4-4x+x^2} {(x-2)^2}=\frac{(2-x)^2} {(x-2)^2}$

[jolly parrot]

aol

[pine shale]

$\frac{\left(x-2\right)\left(x-2\right)}{\left(x-2\right)^2}$

[jolly parrot]

Lyuka

[broken knot]

cancel them out

[pine shale]

It's 1 but the correct answer was 0

[broken knot]

no

it's inside log

[pine shale]

oooh

[broken knot]

so it's log(1)

[pine shale]

you are right

Thank you both, guys

.close

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[inner matrix]

i heard about $log_ab=n$ but not $log (x)$
What it mean???

[jolly parrot]

aol

[broken knot]

either $\log_{10}$ or $\log_{2}$ or $\log_{e}$

[jolly parrot]

R31_

[rough stream]

Usually log10, but it depends on the class

[inner matrix]

a=10 or 2 or e?

[broken knot]

usually 10

[inner matrix]

Ok

[broken knot]

e in higher math, and 2 in computer science

[inner matrix]

Thanks

Byeer

.close

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[pine shale]

Having to pave a flat surface with tiles of regular geometric shape and equal side which of the following shapes can be combined? (without cutting the tiles)

[pine shale]

Square - hexagon

Octagon - square

Pentagon - equilateral triangle

Pentagon - Hexagon

I don't understand the logic behind the answer, which is B

[pine shale]

Is there any formula that i could have used

or was it pure logic?

[trim elk]

I got an idea

( n − 2 ) × 180 = sum of interior angles

[broken knot]

look at the interior angles

[trim elk]

((n − 2 ) × 180)/n = degrees of 1 interior angle

,w is ((4 − 2 ) × 180)/4= ((6 − 2 ) × 180)/6

[jolly parrot]

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[trim elk]

,w is ((8 − 2 ) × 180)/8= ((4 − 2 ) × 180)/4

😳

[broken knot]

you need to multiply it by a constant

like

if they tile the plane

there would exist an integer that you multiply and get 360

for an octagon and a square

you'd solve for integer solution to $m\times 135 + n\times 90 = 360$

[jolly parrot]

R31_

[trim elk]

,w solve m\times 135 + n\times 90 = 360

[broken knot]

since 1 interior angle of an octagon is 135

[jolly parrot]

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[broken knot]

,w solve m\times 135 + n\times 90 = 360 over integers

[jolly parrot]

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[trim elk]

[broken knot]

you don't need to know now to solve linear diophantine equations

you can just trial and error and see that a solution exists

[trim elk]

2 interior angles of shape a + 1 interior angle of shape b = 360

[broken knot]

for positive integer

[pine shale]

I understood the: get the value of one of the angle of a figure

in this case we get 135 and 90

then what exactly was i supposed to do?

[broken knot]

which, in other combination of shapes, is impossible

[broken knot]

basically

135m + 90n = 360

since you want them to tile the plane

[pine shale]

Okay, but like this i get 2 unknown values

m and n

or am i missing something obvious

[broken knot]

you need integer values

since you can't tile half an angle of a square

[pine shale]

ooh i see

so i go by trial and error

correct?

[broken knot]

which, by trial and error you can see that m=2 and n=1 works

in other shapes you can also use trial and error and see that no integer values work

[pine shale]

Thank you both :), everything is clear now

.close

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[scarlet spear]

Hi,

I have a little question:

I have the following word: WRASVERIE

9 letters in total. What's the formula to calculate how many unique combinations you can make?

All letters of the words must be used each time (the word also doesn't contain 9 unique letters😬).

[brisk hull]

you mean permutations right?

[scarlet spear]

Yes

[brisk hull]

alright

if you had the word
ABCDEFGHI

how many permutations would there be?

[scarlet spear]

362,880

[brisk hull]

yes, but use factorial notation from now alright?

9!

easier to work with

[scarlet spear]

oke

[brisk hull]

alright, now lets say you only had 4 letters

ABCD

that'd be 4! right?

[scarlet spear]

yes

[brisk hull]

actually lets take ABC

and list the permutations

3! = 6

[scarlet spear]

oke

but if you take ABCC for example

[brisk hull]

yes i'm getting to that wait

ABC
ACB
BAC
BCA
CAB
CBA

these are the permutations of ABC

now if I take ABB

ABB
ABB
BAB
BBA
BAB
BBA

all C's replaced by B

but here you'll see repetitions

so when we remove the repetitions
ABB
BAB
BBA

we get only 3

in other words, 3!/2!

so if you have things repeating and you need to permute them, you need to divide by the factorial of the number of times that one thing repeats

so in permutations of
ABCC

it'd be 4!/2!

or AABB

it'd be
$\frac{4!}{2! \times 2!}$

[jolly parrot]

Swas.py

[brisk hull]

so in your question you can divided 9! by the number of times E and R repeats

[scarlet spear]

I'll try to make that fancy command. sec

$\frac{9!}{2! \times 2!}$

[jolly parrot]

Bèta Wolf

[scarlet spear]

Can I take it a step further?

[brisk hull]

yes

you can calculate that now

9!/4

[scarlet spear]

What if I want to know how many unique words there are with letter E as 6th letter.

From those 90720.

[brisk hull]

fix E as the the 6th letter, that means you're left with 8 letters to arrange

[scarlet spear]

Cause that's kinda my real issue. 😳

[brisk hull]

and only R repeats in that

and you know how to do that

[scarlet spear]

Oh right

it's been so long 🙈

Easier than I thought

And muCh easier when someone helps you 🙂

Thanks a lot! ❤️

[brisk hull]

[scarlet spear]

$\frac{8!}{2!}$

[jolly parrot]

Bèta Wolf

[scarlet spear]

That is a neat bot.

20,160

.Close

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[pearl pond]

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[jolly parrot]

Cringelord

[midnight anchor]

what do you need to do

okay so start by taking the first derivative

this will give you the equation for the slope, so plug in x=1 and you have the slope at x=1

[jolly parrot]

Cringelord

[midnight anchor]

yeah plug it in to get the slope

ok so thats the slope at this point, now to form an equation for the tangent you are going to want to use point slope form

right

and x1 is just 1, bc thats given

so put it all together

i just graphed it on desmos and it looks fine to me

i think your derivative is wrong

this is the derivative calculator

oh shoot i put a wrong number whole up

still different

chain rule 1/inside * derivative of inside

[pearl pond]

@green yoke Has your question been resolved?

[pearl pond]

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[slim kestrel]

the five thousand billion billion freely moving electrons in a penny repel each other

[slim kestrel]

why don’t they fly out the penny

[midnight anchor]

Probably bc the protons, idk im not a chemist this is a math server lol

[midnight haven]

They are held by the nuclear force of attraction

[slim kestrel]

is there a server for that

[carmine spade]

https://discord.gg/eexdsFw

[grave thistle]

Electrons are attached to their close nuclei while electrons of different atoms are at relatively large distances so they see atoms as neutral objects from outside. Interactions between individual atoms can be considered as the residual Coulomb forces of the individual charges which are anyway compensated by the molecular attractive interactions of the quantum type (Van der Waals). Hope this suffies.

[pearl pond]

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[midnight haven]

.open

dude

[midnight haven]

finally

[nocturne galleon]

#help-6

[midnight haven]

what

[white kiln]

@nocturne galleon please patiently wait for help

[nocturne galleon]

ok

[midnight haven]

can u help me brother

[midnight anchor]

Post the question

[midnight haven]

ight

A circle has a diameter of 10cm find how long is it

[sharp quest]

how long is what?

[midnight haven]

how long is the cirlce

[midnight anchor]

Assuming you mean circumference C=pi(D)

[midnight haven]

height

yeah

my english is not very good im not a native speaker i live in greece so i had to translate it

so can you help me?

when i say height i mean lenght

A circle has a diameter of 10cm find its lenght

[white kiln]

do you know how to find circumference using diameter?

[midnight haven]

idk what r u saying

even if tolf me that in greek i wouldnt understand it

im shitty at math

[sharp quest]

the length around a circle (circumference) is the diameter times pi

[midnight haven]

thanks

so its 31.4

?

[sharp quest]

roughly, yes

[midnight haven]

thanks bro

then it say that i have to find

the Circumference of a bikes will whichs is 30cm radius

i do the same thing

?

C=2πr=2·π·30≈188.49556

is it right?

[white kiln]

yes

[midnight haven]

a Circumference of two circles have a difference of 30cm.Find how much their radius differ(of the 2 circles)

[white kiln]

let radius of smaller circle = $r_1$, bigger circle = $r_2$
$$2\pi r_2 - 2\pi r_1 = 30$$
continue to solve the equation to find out difference

[jolly parrot]

exploseph

[midnight haven]

so its C=2p x r = 2 x p =6,28 x 30 =188,4

@white kiln

no u cant

here

[white kiln]

no

[midnight haven]

delete it

[white kiln]

you can use another unoccupied channel

[midnight haven]

or banned

no

delete it

[white kiln]

in #help-13

[midnight haven]

so is it right @white kiln

[white kiln]

$2\pi r_2 - 2\pi r_1 = 30$
$(r_2 - r_1) \cdot 2\pi = 30$
$(r_2 - r_1) = \frac{30}{2\pi}$

[jolly parrot]

exploseph

[midnight haven]

so my guess was wrong?

[white kiln]

unfortunately yes

[midnight haven]

οκ

btw thanks for helping me

.close

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[white kiln]

glad that i helped

[pearl pond]

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[drowsy trench]

what sort of distribution is this

[sharp quest]

standard normal

[drowsy trench]

oh lol

wasnt used the squiggly n
thanks

.close

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[languid quest]

Does this mean logarithms are inverses of exponential forms?

I'm confused

[tired jetty]

yh

[languid quest]

Oh

I don't quite get it, so when you write it as a logarithm are you taking the inverse of it?

And what's the point?

[timber mountain]

part of it is just to have a solution to equations like 10^x = 2

[languid quest]

Mhm

[timber mountain]

=> x = log(2)

there’s also other uses like natural logarithm

[languid quest]

But how is that an inverse? Aren't you just rewriting it?

[timber mountain]

that’s what an inverse is

f(inverse(x)) = x

10^log(x) = x

log(10^x) = x

[languid quest]

I thought this was an inverse

[timber mountain]

it is

[languid quest]

Like flipping the x and y

[timber mountain]

x = 2^y means y = log₂(x)

but 2^y = x doesn’t isolate y

[languid quest]

What is this doing?

I graphed it and it became a straight line huuuh?

[languid quest]

Mhm

[timber mountain]

the line is x = log(2)

if you have like x^2 = 1 you’ll get lines x = -1 and x = 1

[languid quest]

But how is it an inverse if they're the same graph?

[timber mountain]

what

[languid quest]

When you graph it they're the same, right?

[timber mountain]

ok the inverse is 2^y = x right

[languid quest]

Yeah

[timber mountain]

and y = log_2(x) is the same equation

as the inverse

[languid quest]

Mhm

[timber mountain]

so it’s the inverse

[languid quest]

So how is it the inverse though

Aren't they the same

[timber mountain]

it is the same equation as the inverse

rewritten differently

[languid quest]

Wait an inverse is switching x and y

So how is that an inverse?

[timber mountain]

bruh

2^y = x becomes y = log_2(x) when you isolate y

y = 2^x is the original

[languid quest]

Mhm

Oh

[timber mountain]

so the inverse of y = 2^x is y = log_2(x)

[languid quest]

Oh i see

But the inverse is also x = 2^y, right?

[white kiln]

yes, but jnmwn's formula is a better way to express the relation

[languid quest]

Oh ok

Thanks

[pearl pond]

@languid quest Has your question been resolved?

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[languid charm]

Looking for help with a limacron problem. Finding the area of the inner circle r = 1-6cosTheta

[pearl pond]

@languid charm Has your question been resolved?

[languid charm]

I ended up with this equation. If someone could @ me or dm verifying I'd appreciate it 🙂

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[midnight haven]

yes

because they both equal zero?

[amber rivet]

Two variables are a bit complexer

Also there is no real solution to this since when you say 3x+2y=0 you look for specific x and y

Which isnt equal to the x and y from the second equation

Except 0 of course

2x+5y=-11 ≠ 6x+4y

You trying to solve this with gauß?

With gauß you get x=2 and y=-3

The equation you mentioned couldnt

3x+2y=6x+4y

[amber rivet]

This has infinite solutions

[pearl pond]

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[wheat siren]

Hey

[wheat siren]

How do I do this?

It takes 6 hours for 20 workers to seed 40 acres

How long does it take for 10 workers to seed 90?

Is it 6/2 for 10 workers to seed 40

For 3 hours = 40 acres

¾ hours = 10 acres with 10 workers

×9

?

Nvm

6x2 is 40 acres with 10 workers

10 acres 10 workers is 3 hours

3 hours x 9 = 27 hrs

[pearl pond]

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[midnight haven]

I need help

[pearl pond]

@midnight haven Has your question been resolved?

[midnight haven]

What is the probability that on two successive morning there will be no cancellation

A 64% B 16% C 10.2% D 9.1%

I said c

[pearl pond]

@midnight haven Has your question been resolved?

[plush bramble]

without more information, it's impossible to tell

[candid spire]

@midnight haven can you explain a little more

[pearl pond]

@midnight haven Has your question been resolved?

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[turbid moss]

Ok

[turbid moss]

Let V be a 2 dimensional vector space over some field. Suppose (T-3I)(T-2I)v = 0 for some nonzero v. 3 is not an eigenvalue. Show that T is diagonlizable.

[timid spindle]

can you send a picture of the question? its changed since you last wrote it

[turbid moss]

I cannot

[short salmon]

which came first? (T-2I) or (T-3I)?

unfortunately it matters

[turbid moss]

oh my mistake

[timid spindle]

you also said 3 was not an eigenvalue, which is also very important

[turbid moss]

yeah damn

[timid spindle]

$(T-3I)(T-2I)v = 0$

[jolly parrot]

iCaird

[timid spindle]

because 3 is not an eigenvalue, T-3I is invertible

so we cant times both sides by its inverse and get $(T-2I)v = 0 \implies Tv = 2v$

[jolly parrot]

iCaird

[timid spindle]

this is what you had

so v is an evector with evalue 2

[turbid moss]

yeah I got this far

[timid spindle]

but i am not sure if we are able to find another eigenvector with the information given

[short salmon]

its also a 2 dimensional space

so brute force is an option

[timid spindle]

how would you brute force it? you know nothing about T

[short salmon]

we know its a 2x2 matrix

and can do algebra with its entries

iirc, that is

[turbid moss]

what is iirc

[short salmon]

if i remember correctly

[remote roost]

is 3 an eigenvalue?

[turbid moss]

no

[short salmon]

we are given that its a 2x2 matrix, right?

[turbid moss]

we can assume yes

its given as an operator though

[short salmon]

right

i think there isnt enough info

because the eigenvalue 2 could easily have multiplicity 2

[remote roost]

tbh i'm not sure if it's even true

consider $T = \begin{pmatrix} 2 & 1 \ 0 & 2 \end{pmatrix}$

[timid spindle]

i think theres more to the question you're not remembering

[jolly parrot]

giannis_money

[turbid moss]

Ok I thought so

I'll close and come back after finding it

.close

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[turbid moss]

.reopen

[pearl pond]

✅

[turbid moss]

.close

[pearl pond]

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[short salmon]

link is broken

[brittle junco]

hows this? @short salmon

<@&286206848099549185>

[pearl pond]

@brittle junco Has your question been resolved?

[brittle junco]

uh

[pearl pond]

@brittle junco Has your question been resolved?

[pearl pond]

@brittle junco Has your question been resolved?

[pearl pond]

@brittle junco Has your question been resolved?

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[midnight haven]

is there any ""ACTUAL"" function like integration which calculate the length of the line of the curve between 2 given points..

eg: Lets say a function f(x) = x²; is there any way I can calculate the length of the curve from like 0 to 1?

[need to calculate the length of black line]

[toxic lichen]

yes

look up arc length formula

it does involve an integral

[midnight haven]

where?

[toxic lichen]

paul's online math notes has it i think

[midnight haven]

1 min

can you give me a link?

[toxic lichen]

http://tutorial.math.lamar.edu

[midnight haven]

thanks I'll check out

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[inland lark]

someone help

[inland lark]

<@&286206848099549185>

[pearl pond]

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@inland lark Has your question been resolved?

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[tulip phoenix]

since ABC and PQR are congruent, BC and QR should be the same

since BC is 2AB

3x+3 = 9x-6

from there its simple algebra for x and then substitutuin for the rest of the side lengths

[pearl pond]

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[delicate bluff]

can anyone prove how this is the same. This is a probability rule

[delicate bluff]

for stats

[rugged saffron]

P(A|B) = P(A n B)/P(B) yea

and P(B|A) = P(B n A)/P(A)

B n A is the same as A n B

so it should follow on from there pre easily

[pearl sluice]

Yes, this is pretty much a defintion.

I'll elaborate a bit on @rugged saffron's answer so that you have some more intuition. Let's put names to these events.

Let's say A is "Vetnus has a cold", B is "Vetnus stays home from school".

P(A|B) means in words: "if Vetnus stays home from school, what is the probability that they have a cold?"

P(B|A) answers the question, "if Vetnus has a cold, what is the probability that they stay home from school?"

In this light, let's look at the LHS and RHS again.

P(B) is the probability that you have a cold.

If you have a cold, what's your probability of staying home from school? That's P(A|B).

The LHS is the probability that you have a cold and are staying home from school.

Similarly, the RHS is the probability that... you are staying home from school and have a cold.

[pearl pond]

@delicate bluff Has your question been resolved?

[delicate bluff]

Omg thank you so much, I really appreciate it <3

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[coral tinsel]

hello

[coral tinsel]

.close

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[vocal lark]

🤦‍♂️

I understand why you are confused with this

[midnight haven]

😅😅

[vocal lark]

I think the author intended to say that he measured elevation angles to Juliet's balcony from two points

[midnight haven]

ohh so its mistyped

?

[timid spindle]

Where is the confusion here? There are two people 100m apart, each measuring the angle of elevation of the balcony

[midnight haven]

I don't know where to start with this

[vocal lark]

says only one person is measuring

doesn't say where the measuring is happening, specifically (south of Juliet's balcony, and from a point east in Paris)

you have to read between the lines

[timid spindle]

The second measurement is implied to be taken by Paris, bc the sentence before was talking about him

[foggy carbon]

set up variables + equations

[vocal lark]

3-dimensional.

you need to find y.

(the height)

hrm, hang on

the hypotenuse in the ground plane is 100

[midnight haven]

yea

[midnight haven]

so i would have to find the hypothenuse for one of the tringle right?

[vocal lark]

,rotate

[vocal lark]

you need 3 variables and 3 equations

let the other unknown side in the ground plane be z

I think we can solve this using a couple of trig identities and Pythagorus

[midnight haven]

Should we find the angle first for the bottom tringle?

[vocal lark]

no

find ways to relate x, y, and z

look at each triangle individually

[midnight haven]

oh ok

[vocal lark]

I have no idea why I solved for x first

ok, I have it. What did you put down for your equations?

[midnight haven]

one minute

[midnight haven]

oh that helps 😅

[vocal lark]

^✅

3 equations.

what did you get

[midnight haven]

I don't i have learnt trig identites

[vocal lark]

also, I messed up a little. That 100 should be 100^2

in equation 3

so everywhere you see 100...one sec

[vocal lark]

this is a trig problem, isn't it?

I can't imagine solving without

[midnight haven]

Yea our teacher gave us this question before learning it

[vocal lark]

are you studying sine, cosine and tangent now?

[midnight haven]

We have finished that

[vocal lark]

then you know trig identities.

soh cah toa

are 3 identities

[midnight haven]

ohh i thought u meant proving them

[vocal lark]

these identities I'm thinking of are definitions, they don't get proved

are you able to follow this solution?

or do you need an explanation

[midnight haven]

can you give a bit of an explanation

[vocal lark]

ok.

the problem implies we don't know how far south Romeo is from Juliet's balcony.
We are told that from this point, Paris 100m away. But we don't know how far east it is from Juliet's balcony.
Obviously, we don't know how high her balcony is.
These are 3 unknown distances

I set up the two triangles where the angles to the balcony are measured

then I connected the points the angles were measured from with another line segment. This is the 100m distance to Paris

that's the figure

[midnight haven]

yea

[vocal lark]

I knew we could relate some variables for each of the 3 triangles

High school math teaches us that we can solve systems of N linear equations if we have N unknowns

we can usually get away with one quadratic equation but I don't want to hurt my head trying to be precise about those conditions

I just didn't want to introduce more than 3 variables

We needed to relate x, y, and z

easy way to do that with the triangles above-ground is tangent.

ground plane is obviously (?) Pythagorean Theorem.

.

We focus on filling in the variables in equation 3 (Pythagorean Theorem) with expressions only in terms of y, the unknown we actually care about

so I rewrote (1) and (2) in terms of y.

and plugged them into (3)

questions?

[midnight haven]

No that's good thanks

[vocal lark]

ok

[pearl pond]

@midnight haven Has your question been resolved?

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[pearl pond]

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[steady steppe]

I have 50 students (distinguishable). I have 3 grades A,C and FX. In how many ways can they get grades, 20 students get A, 25 students get C and 5 students FX ?

[pearl pond]

@steady steppe Has your question been resolved?

[raven girder]

${50\choose 20}{30 \choose 25}{5 \choose 5} = {50\choose 20}{30\choose 25}$

[jolly parrot]

jnkena

[pearl pond]

@steady steppe Has your question been resolved?

[steady steppe]

thx

[pearl pond]

@steady steppe Has your question been resolved?

[pearl pond]

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[gusty saddle]

Do you not understand the solution provided here ?

[pearl pond]

@supple bolt Has your question been resolved?

[pearl pond]

@supple bolt Has your question been resolved?

[pearl pond]

@supple bolt Has your question been resolved?

[pearl pond]

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