help-13

[strong pivot]

And C a weird C

[floral aurora]

but the first and third one im not sure

[strong pivot]

So whats the answer for 2

[floral aurora]

for all x in Q(R(x) or S(x)

[eager sparrow]

But x isn't really defined in the problem. It just says
"P(x): x is a farmer"

[strong pivot]

Oh youre right its true i cant read

[floral aurora]

xd

no worries

[eager sparrow]

That's why I was so confused

[floral aurora]

but that makes sense

[strong pivot]

No because Q is an assertion

You cant belong to an assertion

[strong pivot]

You have to tho

P(x) x is a farmer

[eager sparrow]

Yeah, I think only logical quantifiers can be put in the Q right?

[strong pivot]

However youre working in exampleville, (or else you cant say shit,but thats a problem in the way the question is asked)

[eager sparrow]

So in this case, it's ok to not define x since there is none stated?

But you should always define x right?

[strong pivot]

Yes

[eager sparrow]

Hey, is this correct?

[strong pivot]

P(x) is the assertion x is a farmer

[floral aurora]

How

Q is blonde farmers

The statement won't make sense then

If Q is not in it

[eager sparrow]

Ooof I asked the wrong question

[strong pivot]

An assertion would be A(x) or not A(x) with a a random property

Such as x is positive

So for all x in naturals, A(x)

[eager sparrow]

Yeah, wrong question

I mean, it should be logical quantifiers in the place of Q right?

[strong pivot]

Bit (for all x an integer,A(x)) is false

[strong pivot]

Where?

[eager sparrow]

Here

[strong pivot]

It could be for all x in U (R(x) or S(x))

That would be correct

[floral aurora]

i dont get this

All blonde farmers have blue eyes or are left-handed.

this is the second statement

your statement doesn't make sense

[strong pivot]

X is an element, so you have to say from where it comes

[floral aurora]

bcs for all x in A

where is Q

Q is blonde

its not answering the q

[strong pivot]

Otherwise it could be, for example,a number, a curve, any mathematical object

[floral aurora]

so how would u answer q2?

[strong pivot]

Its an example

[floral aurora]

?

[strong pivot]

For all x in A and B, (R(x) or S(x))

[floral aurora]

so its not the answer then

[strong pivot]

Or for all x in A and B, x is in C or D

That would be Q2

[floral aurora]

tesadxyeah but it says

it says

Q is blonde

so i need to use PQRS

i cant use A B

[strong pivot]

Or even for all x in U, (P(x) and Q(x)) implies (R(x) or S(x))

Q is an assertion

A is a set

An element x must belong to a set

And then there can be different relations between logical assertions

[floral aurora]

what would the first one be

is it not: exists(P and R)

[strong pivot]

Because in essence A is the set of all farmers and P(x) means x belongs to A
Its the same just shorter

[floral aurora]

oh

[strong pivot]

There exist x in U such that P(x) and R(x)

Or there exist x in A such that R(x)

Or there exist x in A such that x is in C

[floral aurora]

And what about 3?

Thanks

[strong pivot]

Try to find it

Youve already gotten 2 answers

[floral aurora]

The way to answer is so multiple choice

[strong pivot]

If its correct it is correct

Alwahs multiple ways to get an answer in math

[floral aurora]

idk how to do it

because statements starts with if

(R(x)or(R(x)and(S(x))implies(P(x)(S(x))

[floral aurora]

is that right

[strong pivot]

No the thing is if there are things that verify being farmers and ... then there are things that have blue eyes

With if there are meaning if there exist x such that

Try like that

[floral aurora]

there exists R(x)or(R(x))and(S(x) implies that (P(x)and(S(x))

is that right?

@strong pivot

@strong pivotwhen u get time pls respond ty

[strong pivot]

First of all if there exist R(x) means if there exist an element x such that x is left handed

So what is x

I didnt read thru all of it because giving you this many different set and properties is really annoying

A smarter way would have been to use A a szt and then A'(x) -> x is a part of A

It would be "there exists x in A and C" and "there exists x in C and D" implies "there exists x in A and D"

[cedar kiln]

@floral aurora Has your question been resolved?

[strong pivot]

That would be your way of saying it

Note that " mark the beginning znd end of an assertion

You can read it as "T" and "J" implies "K" : if T and J are true, K is true

@floral aurora

[floral aurora]

This is all q3?

Why is it so long?

[strong pivot]

Yes

Because the question is annoying

[floral aurora]

Holy

[strong pivot]

Some farmers are left handed means there exist x e U (a citizen of example ville) such that P(x) and R (x) (is left handed and a farmer)

Thats why its easier to use sets

Using elements is ok if the question is tricky or you arent too sure

But the better you are at that the less yiu use P(x) kind of stuff and the more you use sets

[floral aurora]

I see

Ok

Thanks

[floral aurora]

As for the statement, is it true or false

I don't get that either

Because for q2 I thought it was true since it intersects

But it was false

[cedar kiln]

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[floral aurora]

.reopen

[cedar kiln]

✅

[cedar kiln]

@floral aurora Has your question been resolved?

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[livid atlas]

I tried to get a pattern as the last two digits should be 36, but still wasnt able to find one to be able to solve this

[high spruce]

what's the pattern you got

[livid atlas]

I found that n=2 and then 7 gives 36 in the end and thus remainder is 36

[high spruce]

ok so you have trouble with formulating the general term?

[livid atlas]

Yes

also the answer is 33

[high spruce]

ok

what's the difference between consecutive terms

[livid atlas]

like here we are going with powers of 6

so like its 6,36,216....

[high spruce]

no I mean, between the values of n that leave remainder 36

[livid atlas]

so 6^2 is 36 and then 6^7 is 279936

I did not try to calculate after that as it was not making much sense

[high spruce]

you don't ne ed to calculate it like that

since weo nly need remainder

we only need to look at the last 2 digits

[livid atlas]

ok...

[high spruce]

so it'd go 06, 36, 16, 96, 76, 56, 36

it repeats after that

[livid atlas]

okk

[high spruce]

the values of n would be 2, 7, 12, 17 ...

because they repeat every 5

[livid atlas]

okk then as constraint is given as 165, we have to just go from there

[high spruce]

yes

you can think of it as , each value is 3 less than a multiple of 5

[livid atlas]

so 2+5n < 165

[high spruce]

yeah that works

[livid atlas]

cool i get 33

[high spruce]

👍

[livid atlas]

ahhhh finally

thanks a lot!

[high spruce]

no problem bro

[livid atlas]

discord is nice

how do i close this?

.close

[cedar kiln]

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[undone valve]

Hello

[undone valve]

I was wondering how you would do this question

[pastel fulcrum]

84/3 = 28 mi/h

$t = \frac{x}{v}$

[wraith dagger]

꧁╭⊱尺αιηωα𝗋𝖾⊱╮꧂

[pastel fulcrum]

So $t = \frac{35 mi}{28 mi/h} = 1.25h$, converting $1.25h \frac{60 min}{1 h} = 75 min$

[wraith dagger]

꧁╭⊱尺αιηωα𝗋𝖾⊱╮꧂

[pastel fulcrum]

@undone valve

[undone valve]

Thanks you

I don’t really know what to do in this question

[cedar kiln]

@undone valve Has your question been resolved?

[cedar kiln]

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[sullen gull]

$sec(x)=\frac{1}{cos(x)}$

[wraith dagger]

Tech support

[sullen gull]

$\frac{sin(x)}{cos^{2}(x)}$ this?

[wraith dagger]

Tech support

[sullen gull]

Is that the first derivative you got

I belive that can be represented how I have written things

Derive cos^2(x) using chain rule or cosx*cosx id say

Seems to work out when I do it

,w derive (cosx)^2

[wraith dagger]

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[sullen gull]

This is not the whole derivative, just the cos^2(x)

Division rule for derivatives needs the derivative of cos^2(x), but it isnt just this derivative

If you find it the rest is trivial

I can say this: derive the new function but with the known derivative of (cosx)^2

Id recommended not condensing expresions while you work with them, tanx and secx separate may result in you missing something

Tanx is just a fraction of sinx and cosx, same with sec
So you just write the fractions and multiply them together

Not good at taylor series or whatever b is

[cedar kiln]

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[jolly oak]

yo

[jolly oak]

oh

...

anyway

does anyone know how to figure out the density of a pumpkin given a bunch of measurements of it

i have radius, diameter, circumference, approx weight in lbs

i might be able to send a picture of the pumpkin

[cedar kiln]

@jolly oak Has your question been resolved?

[jolly oak]

<@&286206848099549185>

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@jolly oak Has your question been resolved?

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[abstract isle]

.reopen

[winter trench]

Is the domain the [T(v)] or the [v]

For 9

[cedar kiln]

@winter trench Has your question been resolved?

[winter trench]

<@&286206848099549185>

[cedar kiln]

@winter trench Has your question been resolved?

[modest lynx]

The domain is the values which are entered into the map, and the codomain or range is the set of values which are output.

The domain is the first R^2, the codomain is the second R^2

[placid seal]

.close

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[placid seal]

Due to inactiveness.

[cedar kiln]

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[ashen thicket]

I'm pretty stupid, why isn't the first equation valid

im just seperating the fraction and then factoring the e in

(x + y) / 2 = x/2 + y/2 or something like that

so e[(x+y)/2] = e[x/2 + y/2] = ex/2 + ey/2

[young pendant]

e is a variable, not exponential function in this case?

[ashen thicket]

nah its exponential function

but it shouldnt matter right

the original thing was

i implicity differentiated which worked fine, but then I re-arranged it and simplified it wrong

i just left out the exponent so i could write less

<@&286206848099549185>

[cedar kiln]

@ashen thicket Has your question been resolved?

[vestal sigil]

Why do you it isnt valid(looks fine to me)

[ashen thicket]

oh

i made a mistake somewhere

and got the wrong answer

done

.done

what was the command

.close

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[leaden gull]

Hi there. I need help on how to use a test to determine if the series converges or diverges. I'm pretty sure a Comparison Test needs to be applied but I'm not sure how to apply it for this problem.

[leaden gull]

I've tried comparing it to series such as the following but I don't believe it converges (p-series w/ p=1 is divergent ?)

[solid juniper]

isn't it a good thing that that doesn't converge?

[leaden gull]

wait

Oh okay because that bottom series is greater than the original problem it wouldn't converge by the direct comparison test, correct?

[leaden gull]

I got it now lol thanks

.close

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[solid juniper]

lol ok but umm

[solid juniper]

not sure that's right

[leaden gull]

I think

Oh

Maybe not then

Oh wait no that's the other way around

I see what you mean

.reopen

[cedar kiln]

✅

[leaden gull]

I just started working with series sorry lol

How else would I go about testing if it diverges or converges? I tried integral test (cannot integrate with elementary functions), root test (=1 so inconclusive), ratio test (=1 so inconclusive)

[solid juniper]

well comparison test is good

[leaden gull]

That's what I was thinking too, but I got stuck when trying to find out what to compare it to

[solid juniper]

this haha

[leaden gull]

wdym

[solid juniper]

ok actually I think you do need something a little different

[leaden gull]

Yea I think it doesn't work because this one (the one i replied to) is greater but divergent so no conclusion can be drawn I think ?

[solid juniper]

yea

[leaden gull]

idk what else to do tho

[solid juniper]

$\sum_{n=1}^\infty\frac{6n^{3}-2n^{2}}{\sqrt{n^{8}-4n^{2}+5}}\geq \sum_{n=1}^\infty\frac{6n^{3}-2n^{2}}{\sqrt{n^{8}}}=\sum_{n=1}^\infty\frac{6n^{3}-2n^{2}}{n^4}$ by comparison test

[wraith dagger]

layla💜

[wintry prism]

can't you just compare it to 1/n

with limit comparison

and ur done

div

[solid juniper]

I think it's simpler to compare with 1/n if you do this first

[leaden gull]

Ah ok

[solid juniper]

I mean like compare $\sum_{n=1}^\infty\frac{6n^{3}-2n^{2}}{n^4}$ to $\sum_{n=1}^\infty\frac{1}{n}$

[wraith dagger]

layla💜

[solid juniper]

you'll get that $\sum_{n=1}^\infty\frac{6n^{3}-2n^{2}}{n^4}$ diverges and so the original one diverges

[wraith dagger]

layla💜

[wintry prism]

yeah just this

and ur done

[leaden gull]

Gotcha.

Thanks guys

Much appreciated

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[solid juniper]

yep ^-^

[cedar kiln]

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[slate plinth]

quick question: if g(x)=f(x)-x, and f(x) is in [0, 1] and x is in [0, 1], does that mean g(x) is in [0, 1] too?

[slate plinth]

woohoo latex

if $g(x) = f(x)-x$ and $f(x) \in [0, 1]$ and $x \in [0, 1]$ does that mean $g(x) \in [0, 1]$ too?

[wraith dagger]

Noxta

[wintry prism]

what if f(x)=0 and x=1

then what's g(x)?

[slate plinth]

oh -1

so $g(x) \in [-1, 1]$ then

[wraith dagger]

Noxta

[wintry prism]

sounds correct

[slate plinth]

cool cool;

thanks

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[wild dune]

how do i find velocity upon impact?

[hoary notch]

conservation of energy

[cedar kiln]

@wild dune Has your question been resolved?

[wild dune]

yes

.closed

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@wild dune Has your question been resolved?

[wild dune]

sure

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[cedar kiln]

@latent wind Has your question been resolved?

[vestal sigil]

I think you can treat f(x) as another variable and find value of x and f(x)

[latent wind]

no it hasn't u can see that by ur self

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[errant pewter]

how do i calculate d^2f/dxdy?

thats the answer for it but i want to understand how it got to that answer

[cedar kiln]

@errant pewter Has your question been resolved?

[dire geode]

Differentiate your first equation with respect to y, treating x as a constant

[errant pewter]

could you walk me through it please

[dire geode]

No. What's stopping you?

[errant pewter]

so by that do you mean d/dy of the 33x^2y^4 - 10x^4y^6

@dire geode

[dire geode]

Yes

[errant pewter]

thanks kind sir

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[formal monolith]

hello can anyone help

[dire geode]

[formal monolith]

thanks man, how are you in terms of probability functions

how do i find the value of s?

[dire geode]

Integrate your density over the whole domain and set it equal to 1

[formal monolith]

yes i can understand that its a double integral and equal to 1 yep

but how do I do that without knowing the value of alpha and beta

[dire geode]

Your answer will be in terms of those

[formal monolith]

gotcha ok that makes sense, its not like a gamma distribution identity or anything

thankyou

how would i go about writing an expression for the bottom?

[dire geode]

Start with the definition of variance for each Qbar variables

[formal monolith]

sorry it might be a long one

yeah would that be Var(Q1+Q2+Q3+Q4)/4 etc.?

then utilise the variance equation for linear functions?

[dire geode]

Try it

[formal monolith]

yeah I have an answer but it seems wrong

is it V(Qbar)=variance/n

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[open thicket]

hey, im not sure i did this right

[open thicket]

Translation: a line goes through (1,3) and (-5,p) and has m=-3. What is p? And write the equation for the line.
p = y2 in my math

[rocky wave]

this is correct mate

well done

[open thicket]

ok ok

would it also be correct if the equation for the line is
y-3 = -3(x-1)

probably

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[heady sequoia]

how do they get the or part that I circled

[valid yacht]

substituted h=(w/4)+15?

oh the other way around actually

but why do that

just solve for w

,w factorize{x^2+240x-11200}

[wraith dagger]

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[valid yacht]

yeah why did they change it in h lol

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[tropic oxide]

is there something you are having trouble understanding in the problem?

...yes

as distraught as you might be right now, sobbing emoji will not really accelerate the process.

what will accelerate the process of you getting help is showing WHAT you need help with

so you understand how to calculate a_3 and a_4, but not a_5 and a_6?

well you have already calculated a_3 correctly as 2

now a_4 = a_3 + a_2

no

you did not actually put in the values of the terms...

you need to apply the formula, not merely state what value of n goes into it...

you already did that for a_3 and you calculated a_3 as 2

yes exactly

[stable patio]

google what an arithmetic sequence is

[fluid crescent]

yo

b is no

@crimson sedge

a5 is 5

oh ok

yes its arithematic

d - 8

d = 8

common difference is 8

[pale osprey]

8

[fluid crescent]

but i gotta explain how

so that you wont get confused

WAIT

FIRST ILL TEACH HOW TO GET COMMEND

SO

a = -3

b = 5

what you do it

b-a

so

5 - (-3)

is 8

and the check again

wait ill first tell you

this is a test isnt it

[pale osprey]

it is

it literally says

[fluid crescent]

no

[pale osprey]

lms graded

[fluid crescent]

oh really?

oh okk

ya boi

[vale kernel]

betbet

[fluid crescent]

no

its yes

the answer is yes

[pale osprey]

💀

chill

[fluid crescent]

😉

NOW WAIT @crimson sedge

[vale kernel]

i need help with this

[fluid crescent]

I AINT LETTING YOU GET AWAY

ILL TEACH YOU

SO YOU DONT HAVE TO ASK

WAIT ill look at this first

lemme give its defination

common difference is the difference between consecutive elements of a sequence

so lets say

a,b,c,d is a sequence

then

commen difference is

[vale kernel]

common difference is the second term - first term

[fluid crescent]

b-a

c-b

d-c

so all three have to be same

nice question

i like it

[vale kernel]

common difference is 1

for n

[fluid crescent]

8

common difference is 8

for here

[vale kernel]

f(n) is 8

n is 1

arithemtic

oaky @fluid crescent help me with this

pls

[fluid crescent]

@vale kernel oi so your question mind if i solve it?

[fluid crescent]

sure

[vale kernel]

yes i don't mind

look

common difrernece is

[fluid crescent]

5

[vale kernel]

8-3=??

11-8=??

[fluid crescent]

so you gotta make it fair righ>

?

[vale kernel]

ummm yes but no

[fluid crescent]

oh right

lol

[vale kernel]

i just need to know the probability

[fluid crescent]

but of wjat

i cant see what i need to find prob of

[vale kernel]

of black moving

[fluid crescent]

it doesnt whoe

ANSWER IS B

thats all

[fluid crescent]

where is it given tho

lol

B

[vale kernel]

if there no common difrence @crimson sedge its not arithemtic

ok

ok

ok

common differnece is found when second term - first term

[fluid crescent]

oi kelly

[vale kernel]

yo

[fluid crescent]

so

BRO pls im so confused

[undone halo]

first number, minus second number

[fluid crescent]

what probs

[crimson sedge]

other way around

U2-U1

[undone halo]

said it wrong

second number, minus first

[red orbit]

@crimson sedge you subtract second number by the first number and that is what is known as the common difference

[crimson sedge]

yes

its 9

[fluid crescent]

oh i dmed you sorry

how long do i have?

[vale kernel]

oh tyty

all the time in the world

[red orbit]

YOU BROSKI

Define common for me

right now

Common difference

Ok

listen to me

listen to me

listen to me

listen to me

listen to me

You subtract the second term by the first time

that gets you common difference

BUT

yes

so clearly the answer is 9

but if you go on

and subtract the 3rd number by the 2nd

its 6

so 9,6

they are not common

Because they are the not the same number

subtract 3rd by 2nd to verify whether or not it is actualy a common difference

❤️

Yes

its -3

because its subtracting

instead of adding

mb

[red orbit]

decreasing**

[hushed spoke]

What have you tried till now?

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

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[split briar]

What do you call the points where $f'(x)=0$ in english?

[wraith dagger]

prop

[split briar]

I've googled and only found vertex is that the right term?

In my language we use "extremums"

[tropic oxide]

extremum (sg)/extrema (pl)
or extreme points
or sometimes stationary points

[pale osprey]

maxima

minima

point of inflection

it can be either of the three

[tropic oxide]

no, points of inflection are different

no

points of inflection are where f''(x) = 0

[pale osprey]

oh wait what

damn

my bad

[real heath]

no one can mess with ann kekw

literally the best mathematician ive seen in this server so far

[cedar kiln]

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[split briar]

thanks guys

[cedar kiln]

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[mighty drift]

k is ill defined

it's k(x) = f(x) / x

but then that's not k(n(x))

so it's actually product rule * chain rule on x -> 1/x

which is exactly how one usually proves the quotient rule

so just apply the quotient rule directly

but k o n != f / (f+g)

[mighty drift]

if this were to hold

but you're not even talking about the same function anymore

are you sure that (f / (f+g))(x) = k(n(x)) ?

see the problem ?

you get f(n(x)) rather than just f(x)

a mistake you made here by writing k(x) = f/x. If you wrote f(x) / x you would have noticed. This definition is not homogeneous as you define the value as a function. That was what led to your mistake

it may not. Stop hoping for coincidences that make mistakes work

it may not because you still introduce n' in there btw

so even if n(2) = 2, you'd also need n'(2) = 1

[cedar kiln]

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[crimson sedge]

An exam consists out of 20 questions, 3 possible answers each but only 1 is correct out of these 3.
How high is the probability to get all right by just ticking the answers randomly?
I used the binomial formula so basically
1×1/3²⁰×(1-1/3)²⁰-²⁰
Does that make sense? Because my calculator said its 2.86797...E-10
Its a really small number and im not sure if i did calculate it right

[tropic oxide]

it's 1/3^20

[gloomy lynx]

1/3^20 is indeed a small number

[tropic oxide]

so yeah, makes perfect sense it would be that small

,calc 3^-20

[wraith dagger]

Result:

2.8679719907924e-10

[tropic oxide]

yup

[crimson sedge]

Okay thanks for confirming!

.close

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[sonic bloom]

kinda stuck with |C*| im new to matrix dominantes

[tropic oxide]

@sonic bloom your first channel is here

[sonic bloom]

Thank u

[tropic oxide]

|C^T| = |C|

[sonic bloom]

I see but i don’t know how to do this task at |C^T| • B

[cedar kiln]

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[magic forge]

My question is how do you check the basis when the vectors are trig functions

[cedar kiln]

@magic forge Has your question been resolved?

[magic forge]

The homework is already due, it’s okay

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[manic verge]

I have a word problem.

[manic verge]

Arielle has a collection of grasshoppers and crickets, she has 561 insects in all. The number of grasshoppers is twice the number of cricket's. Find the number of *each* type of insect she has

I need help finding what the equation is

[weary bluff]

Let g be the number of grasshoppers and c be the number of crickets

c+g has to equal 561, correct?

[manic verge]

Yea

[weary bluff]

and g has to equal 2 times c

understand?

[manic verge]

Yea

[weary bluff]

Sorry, meant 2 times c

[past tree]

x+y=561-----1
x=2y given in question--------2
using 2
3y=561
you can find y and x then

[manic verge]

Ok

.close

Thanks

.close

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[hushed spoke]

Write it again

[cedar kiln]

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[cursive garden]

Can someone guide me on solving this question, wrote out a few lines and im stucked

[cursive garden]

i'm stuch here 😢

[cedar kiln]

@cursive garden Has your question been resolved?

[cursive garden]

<@&286206848099549185>

[keen elbow]

this looks like test

[cedar kiln]

@cursive garden Has your question been resolved?

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[median raptor]

This function is onto but not one- to-one. How can I prove it ?

[cedar kiln]

@median raptor Has your question been resolved?

[modest lynx]

find two values of x that give the same output

[cedar kiln]

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[earnest kettle]

Why is it positive and not negative 10?

[tropic oxide]

-(-2)*5 = 10

[earnest kettle]

oh

I’m dumb

nvm 💀

thank you

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[crimson sedge]

I thought i had this figured out but I still need help can anyone help me with simplifying radicals

[leaden snow]

post your problem

[crimson sedge]

i need to simplify the 5th root of 160 @leaden snow

[muted bear]

Prome factorize 160

[leaden snow]

didn't you ask this already?

you figured out that $160 = 2^5 \cdot 5$ right?

[wraith dagger]

nvx

[crimson sedge]

ya i did but thought i understood it

i realized i didn't though

[crimson sedge]

i got the prime factorization

[crimson sedge]

I haven't learned how to do that yet.

[leaden snow]

that's the prime factorization which you claimed to have

[crimson sedge]

nvm i think i figured it out

i mean i haven't learned the symbols and stuff yet

i just haven't been taught how to do it with the symbols

[leaden snow]

how did you write it?

[crimson sedge]

Usually my teacher just writes it as 5th root of 2^5 x 5th root of 5

Just a question if the thing im trying to simplify is 5th root does that mean that i get the 5th root of all of the factors?

nvm my math teacher sent me a message about it I figured it out.

.close

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[civic stirrup]

I don’t really see why you can conclude x3= lambda, x2 = lambda and x1 = 1/2(3lambda +4 lambda)

[cedar kiln]

@civic stirrup Has your question been resolved?

[civic stirrup]

<@&286206848099549185>

[dire geode]

x3 is a free variable meaning it can be anything and the linear system will still hold true

so the free variable is denoted lambda

https://adamdhalla.medium.com/linear-algebra-3-solving-ax-0-free-variables-and-pivot-variables-and-echelon-form-ce8cca411e60

[civic stirrup]

Alright

But what about x1

[civic stirrup]

Why is x1 written down that way?

[dire geode]

do you mean x3?

[civic stirrup]

No, x3 is lambda, but I don’t see how you can conclude that x1 is 1/2(3lambda + 4lambda)

[dire geode]

did you follow why x2=lambda?

[dire geode]

once you do that^, multiply the matrix by the x vector (x1, lambda, lambda) and use your equation.

[civic stirrup]

I’m not sure no

[dire geode]

write out the multiplication of the matrix by the x vector

this gives you 3 equations

[civic stirrup]

-2x1 + 3x2 + 4x3

Is that the first equation?

[dire geode]

you need an equal sign for an equation

[civic stirrup]

Oh obviously

Damn I find this so hard

[civic stirrup]

I am really not sure what to do.

Thanks a lot for your patience though

I am somewhat new to this

Is it just

-2x1 + 3x2 + 4x3 = 0

[dire geode]

https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:matrices

[dire geode]

yes

that's one equation. find the other 2

[civic stirrup]

So what do I do with all the equations?

[civic stirrup]

Substitute them into each other or smth?

[dire geode]

https://www.khanacademy.org/math/algebra-home/alg-system-of-equations/alg-equivalent-systems-of-equations/v/solving-systems-of-equations-by-elimination

[civic stirrup]

Thanks!

[cedar kiln]

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[cedar kiln]

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[delicate dagger]

How do I solve this?

[crimson sedge]

@crimson sedge

[crimson sedge]

go to one of the help channels in the available categories

this is already claimed

send your question in one of those

oh okie

Sorry @delicate dagger

[delicate dagger]

Can someone help with this?

.close

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[solid anchor]

So i'm doing my hw rn and this problem comes up and it says that a worker is mixing two colors red and yellow to make orange. The issue is that when it says that it mixes 8 gallons of red paint and 10 gallons of yellow paint it makes 18 gallons of orange paint but then it says the worker mixed it wrong. Plus the graph is kinda wonky

[cedar kiln]

@solid anchor Has your question been resolved?

[solid anchor]

<@&286206848099549185>

[cedar kiln]

@solid anchor Has your question been resolved?

[dire geode]

how are people supposed to help you?

[solid anchor]

tbh idk

.close

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[mossy mango]

im quite unsure whats the connection between

vector space and fields

in the picture, there are 8 axioms given to vector spaces

9 to fields

they are quite similiar, but what's the connection?

[modern compass]

fields are vector spaces over themselves

[mossy mango]

???huh

so any fields fit the axioms of vectors spaces too?

[modern compass]

Take a field, consider it as both the set of 'vectors' and the set of 'scalars'
Then it will satisfy the axioms of a vector space.

For example: the reals R
if a,b,c,d are in R
Then a+b is in R
1a = a is in R
0 + a = a is in R
c(a+b) = ca+cb is in R
(c+b)a = ca+ba is in R
etc

[mossy mango]

ah ook

thxx

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[frail lark]

what does this sign mean?

[frail lark]

it looks like the integral summation sign

with a circle

[modern compass]

without context it's hard to say.
usually it means a contour integral in complex analysis

[frail lark]

contour integral?

isnt complex analysis just seeing how complex numbers work

[modern compass]

Sure. in the same way real analysis is seeing how real numbers work.

[frail lark]

i havent studied either, should i?

[modern compass]

it also includes calculus of complex valued functions.

[frail lark]

complex valued functions?

what field of math teaches you this

[modern compass]

complex analysis

[frail lark]

i saw this sign in a thermodynamics proof which i want to learn

ok, khan academy good for thisd?

[modern compass]

no idea

[frail lark]

where did you learn it

[modern compass]

I took a complex analysis course in college.

you can usually get it after calculus 2 or 3.

[frail lark]

COLLEGE???

i dont have time for that im only in 7th :(

is there any other reliable source you would personally recommend

[modern compass]

find a complex analysis book.

schaum's is good, with lots of examples and worked solutions.

[frail lark]

ok, what is the price of it

could you give a website which has it for pretty cheap price

if possible

[modern compass]

i'm not google.

[frail lark]

whats the title though

sorry

[modern compass]

something like schaum's complex analysis
I don't remember exactly.

that should be enough to find you a copy or a pdf

[frail lark]

OH PDF even better

[cedar kiln]

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[mental lotus]

i need help

[mental lotus]

for gadient question

gradien??

???

how do i solve it

i don't know the formula on how to do it

.close

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[kindred hornet]

Basketball Teams A and B are engaged in a best-of-7 playoff series: the series will end as soon as one of the teams has collected four wins. The teams are evenly matched: in a single game, each team has a 1/2 probability of winning. But it happens that Team A has won 2 of the first 3 games in the series. What is the probability that Team A will go on to win the series?

i got 3*(½)^3+3*(½)^2=3/4 is that correct?

[cedar kiln]

@kindred hornet Has your question been resolved?

[kindred hornet]

anyone?

[kindred hornet]

<@&286206848099549185>

[cedar kiln]

@kindred hornet Has your question been resolved?

[kindred hornet]

pls someone

for gods sak

[cedar kiln]

@kindred hornet Has your question been resolved?

[kindred hornet]

bruh

.close

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[cedar kiln]

✅

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[hushed bough]

not sure how to use homogenous or any other method for this?

[cedar kiln]

Please don't occupy multiple help channels.

[hushed bough]

<@&286206848099549185>

@tropic oxide sorry for the ping just moved the chat to here if you can help feel free

[tropic oxide]

ok let me be more blunt

DEs are not exactly my strong suit, and i don't want to be pinged for DE problems even more than i don't want to be pinged out of the blue in general.

also close your fucking channels

unless you like receiving the warning box about not using multiple

[hushed bough]

sorry ann

[hushed bough]

got it

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[cedar kiln]

@ripe jacinth Has your question been resolved?

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[oblique lynx]

Hey, I have this function and I have to (a) find the derivative f'(x) and then find on which intervals is this function decreasing/increasing. (b) find extremas of this function.

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<@&286206848099549185>

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@oblique lynx Has your question been resolved?

[pale osprey]

homogenous should work fine

im getting something here

pretty compact answer

[cedar kiln]

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[oblique lynx]

yo, this channel is already occupied

[maiden shadow]

have you tried finding first derivative with quotient rule

f' > 0, increasing
f' = 0 critical point, such as maximum minimum)
f' < 0 decreasing

[pale osprey]

My bad

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[wheat vector]

I have no clue how to do this question

[wheat vector]

direct substitution gives you 0/0

and using lhopitals doesn't work because the denominator will always be 0 when you plug in 0 for x

like d/dx [e^x^2] = (2x)(e^x^2)

[hollow minnow]

$\frac{e^{-x^2}}{2f(x)}$

[wraith dagger]

Pure

[hollow minnow]

the x cancel

[wheat vector]

what'd you do there

[hollow minnow]

Differentiating the top and bottom

The numerator becomes x/f(x)

Denom is 2xe^x^2

Simplify it

[wheat vector]

wouldn't it be f'(x)/2xe^x^2 tho

[hollow minnow]

we’re given f’(x) is x/f(x)

[wheat vector]

so there's no need to plug in 0 and 3 for f(x) and x

[hollow minnow]

?

[wheat vector]

they define f(0) as 3

(0/3)/(2xe^x^2)

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[latent mulch]

you see the first line in the solution, the effectively factored that term..

can we do algebra with leibneiz notation

[sullen saffron]

This line?

[latent mulch]

yea

like what does d/dx even mean

what are you deriving yk

[sullen saffron]

d^2y/dx^2 means the derivative with respect to x of dy/dx.

[latent mulch]

yea

[sullen saffron]

That's what the RHS says.

[latent mulch]

ok

so you can kinda do like algebra with these

like you see how they did dy/dx = dy/du * du/dx

[sullen saffron]

There's no algebra here.

[latent mulch]

thats like expanding

[sullen saffron]

No. This is a result of the chain rule.

[latent mulch]

ok

thanks

[sullen saffron]

A memory technique is that you can imagine them as fractions in this case.

[latent mulch]

yea that kinda helps

cuz they are kinda cancelling ig

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[stark jasper]

With a gantt chart (A Level Decision Edexcel), are you allowed to "split" activities?

[midnight oxide]

oh

[stark jasper]

(Total workers required, Activity ID)

So if there's only 2 workers available, you can complete the activity in the minimum amount of time

I will assume that it's allowed

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[opal ravine]

But what if its imaginary?

Is it just 2 Im<u,v> in place of 2Re

or?

[crimson delta]

<u,v> is some complex number z

then <v,u> is conj(z)

[neon moon]

It doesn’t matter. You can convert one of them as conjugate by inner product symmtry property, and then you will see that they add up to two times the real part.

[crimson delta]

and for any complex number z you have z+conj(z)=2 Re(z)

[opal ravine]

I got this question where I have to find the scalar product of <u,v> when both vectors are imaginary (C^n)

And apparently the answer is (|u+v|² - |u+iv|²)/2

but I got no clue how the result is that

[crimson delta]

essentially just multiply out (|u+v|² - |u+iv|²)/2

[opal ravine]

what do you mean?

[crimson delta]

|u+v|^2=<u+v, u+v>, yes?

[opal ravine]

yeah

[crimson delta]

and this you can "multiply out"

i.e. use linearity

same for the other term

then everything cancels and you are just left with <u,v>

[opal ravine]

What about if we do it using norms?

[crimson delta]

well without a scalar product there is no scalar product

[opal ravine]

wait is scalar product and dot product the same thing?

[crimson delta]

in a general normed space there is no scalar product

yes

or maybe depending on the author one of them might only be on R or something

[opal ravine]

but its saying it can be proved via norms

[crimson delta]

can you state the full problem exactly as given?

[opal ravine]

Thats the question translated without edits

But I think this is closer to what it is?

[crimson delta]

yes so we are given that the norm is given by a scalar product

which means we can easily calculate any scalar products of the form <u,u> by just computing the norm of u

but what if we want to calculate an arbitrary scalar product <u,v>

[crimson delta]

turns out we can still calculate that by calculating the norms of u+v and u+iv and then using this

so "being able to calculate all norms" <=> "being able to calculate all scalar products"

[opal ravine]

my brain hurts

so we have to compute norm of the vector u

actually wait

or what

[crimson delta]

imagine we had two machines.
one can calculate <u,v> for any vectors u and v we give it
the other one can calculate |x| for any vector x we give it

turns out that both machines can do the same things then.
the first can also calculate any norm |x| (by just calculating <x,x>)
the second can also calculate any scalar product <u,v> (by calculating (|u+v|² - |u+iv|²)/2 )

[opal ravine]

but why (|u+v|² - |u+iv|²)/2 )

that was the main question

[crimson delta]

because (|u+v|² - |u+iv|²)/2 = <u,v>

[opal ravine]

but is there any proof of that

[crimson delta]

.

[opal ravine]

dont get it

what does using linearity mean

is there some video explaining it or something along those lines?

[crimson delta]

here from the first to the second line they "multiplied out" the scalar produt

<u+v,u+v> = <u,u>+<u,v>+<v,u>+<v,v>

compared to "(u+v)(u+v)=uu+uv+vu+vv"

[opal ravine]

you said that "<u,v> is some complex number z
then <v,u> is conj(z)"

but what about <u,u>

and <v,v>

is it just | |v| |^2

and | |u| |^2

[crimson delta]

yes

[opal ravine]

aight

gimme a sec

so doesnt it become this?

which is

but thats not correct is it?

[crimson delta]

not sure where you got that from

<u,v>+<v,u> = 2Re(<u,v>)

[opal ravine]

so | |u+v| |^2 =

or?

[crimson delta]

yes