help-13

[fiery berry]

i got this result when i divided x^2 @gaunt hamlet

[gaunt hamlet]

So how'd you get -1/2?

[fiery berry]

what should i put for x

[gaunt hamlet]

It's the limit as x-> -∞

[fiery berry]

if i put inf to x numerator inf

-inf

denom is inf

so result should be negative ?

[gaunt hamlet]

The denominator isn't ∞

[fiery berry]

5/ inf - 2

how

[gaunt hamlet]

What's 5/∞ in limits?

[fiery berry]

0.000001

very very small number

oh okkkk

if you substract 2

it is negative

i understand it

[crimson sedge]

is the answer -inf or +inf

[fiery berry]

+inf

[gaunt hamlet]

It's 0, not just a small number

[fiery berry]

why we think infinites are zeros in limits

[gaunt hamlet]

They arent

Lim x->∞ 1/x = 0

[fiery berry]

what about inf-inf

[gaunt hamlet]

That's indeterminate

Depends on the function

[fiery berry]

ok thank you

.close

[cedar kiln]

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[hard wraith]

y^2 = x + 5, (x is equal to 4), this isnt a function since we get 2 outputs for it. what is this then?

[hard wraith]

this isnt a function so what is it

and is it not of any use?

[random shale]

i think by the definition as it's one to many it's not a function however don't think the curve is not useful

[hard wraith]

i do know that its a one to many but i keep getting confused as to what it is then

[random shale]

elliptic curves are also one to many but they can be used to encrypt information in one of the most secure ways known as of yet

[random shale]

it's just a curve

[hard wraith]

💀 wha...

[hard wraith]

is it important for calculus?

[random shale]

yeah it is

[hard wraith]

so what do we do with it?

[random shale]

modelling stuff

[hard wraith]

we assign an output for an input with a function right. so what does that do for us.

i donno how to frame the question honestly

its just bugging me

[random shale]

It's an example of an implicit curve, by definition it isn't a function

but some curves have really nice properties

even if they arent functions

[random shale]

.

one example

[hard wraith]

but they can have their own equations right

[random shale]

the circle equations is super useful and well that's not a function

[random shale]

yeah it has an equation it satisfies

[hard wraith]

how does it not being a function change how we look at it

we cant get one output so what does that do for us

[random shale]

ah ic

well it means it's not differentiable for one

[hard wraith]

OOOOH

cool thats something new

[random shale]

well

it's differentiable

but you need (x,y)

not just x

[hard wraith]

can you give an example

[random shale]

if a function is a bijection (one to one) then it's invertible

[random shale]

the circle $x^2+y^2=1 \Rightarrow 2x+2y\frac{dy}{dx}=0\Rightarrow \frac{dy}{dx}=-\frac{x}{y}$

[wraith dagger]

Max..

[hard wraith]

im sorry i dont get whats happening here

[random shale]

this is just the derivative of a circle

[hard wraith]

so... formula?

[random shale]

yeah (rate of change of the curve at any point)

[hard wraith]

ok

[random shale]

i mean the reason it's really good for encryption is the fact the majority of these curves dont have inverses

if a function is one to one then an inverse exists

[hard wraith]

is x^2 + y^2 = 1 a circles equation?

[random shale]

which means you can reverse the encryption

[random shale]

yes

[random shale]

but if it's many to many then it cant be reversed so it's basically impossible to "decrypt"

[hard wraith]

so just for a perfect circle or does it change for ellipses

[hard wraith]

hmm i get it

[random shale]

that's just for a circle

you can derive the formula I just shown

[hard wraith]

cus there would be 2 different outputs so its not possible to trace back to the og equation

[random shale]

imagine you have a circle of center (a,b)

now you want the circle to have a radius r

[hard wraith]

yeah

[random shale]

then you want all values x and y such that the distance from (a,b) is r

[hard wraith]

so like every coordinate surrounding the circumference?

[random shale]

yeah

[hard wraith]

ahh

[random shale]

so you want the distance from a,b to x,y to be r

by pythagoras that means you want $\sqrt{(x-a)^2+(y-b)^2}=r$

[hard wraith]

yes

[wraith dagger]

Max..

[hard wraith]

right

[random shale]

square both sides because sqrts are ugly

and you get $(x-a)^2+(y-b)^2=r^2$

[wraith dagger]

Max..

[hard wraith]

lol

[random shale]

this means that a circle with center (a,b) and radius r has equation $(x-a)^2+(y-b)^2=r^2$

[wraith dagger]

Max..

[random shale]

and the equation of a circle has endless uses

but it's not a function....

[hard wraith]

hmm but does it not have a name?

or do we just call it not a function

[random shale]

It's just a curve

[hard wraith]

lol

[hard wraith]

ok

[random shale]

or equation

[hard wraith]

lemme look at it again

[random shale]

👍

just tag if u got any q

[hard wraith]

ok

thank you im much more clear now

[hard wraith]

ok so for the equation of circle x^2 + y^2 = 1, were assuming the the center is at origin right?

and the radius is 1?

@random shale

@random shale sorry to ping again

[cedar kiln]

@hard wraith Has your question been resolved?

[long arrow]

yes

[hard wraith]

thank you

i think ill keep it at that

wait no i still wanna know why it would take both x and y value to differentiate it

nvm

i get it

what is rate of change?

@long arrow if you could answer please?

<@&286206848099549185>

[long arrow]

rate of change tell you how quickly something changes in time

not only time, according to functions it is change in y to change in x

and generally the rate at which one quantity is changing with respect to another quantity

[hard wraith]

how does this definition apply to different objects

like lines and curves

[long arrow]

rate of change on [a,b]

basically change in y/change in x

[hard wraith]

isnt that the eqn for the a gradient

[long arrow]

yea slope is another version of finding average rate of change

[hard wraith]

ok

|x^2 - 4| = x + 2

could anyone explain to me what to do here

@long arrow

[hard wraith]

<@&286206848099549185>

[sterile ginkgo]

There are 2 cases

[hard wraith]

hmm

[sterile ginkgo]

Either the mod part will be negative

Or positive

It'll be positive or when x^2>4
So if x>2 or x<-2. x^2-4=x+2

Solve this, and check if the x value satisfies these conditions

Then try for negative

[hard wraith]

i dont understand

why are we solving for when x>2 and x<-2 again?

[sterile ginkgo]

There's a mod, right

[hard wraith]

yea

[sterile ginkgo]

So if the stuff inside the mod is positive

Just remove the mod

If it isn't

Then multiply the contents with -1 and remove the mod

So there are 2 cases and you need to solve them individually

[hard wraith]

right

honestly im lost...

[sterile ginkgo]

This function will basically follow 1 equation when the contents of the mod are positive

[hard wraith]

multiply the contents with -1?

[sterile ginkgo]

And it'll follow another equation when the contents are negative

[hard wraith]

all im doing is just taking off the modulus and making the number after the equal sign a positive for one eqn and a negative for the other

i donno im just following the books example

it doesnt give an explaination as to how were taking it off

[sterile ginkgo]

A negative sign means multiplying by -1

[sterile ginkgo]

Ok let's look at a simpler case

|x-5|=10

Now here there are 2 cases
1.If x-5 is positive, x>5
x-5=10, x=15
2.if x-5 is negative the mod will turn it positive so now
-(x-5) =10
5-x=10, x=-5

[hard wraith]

ooh

kk

[sterile ginkgo]

Now to try that for your q

[sterile ginkgo]

If x^2-4 is positive, |x^2 - 4| =x^2 - 4

If it is negative |x^2 - 4| =-(x^2 - 4)

Makes sense?

[hard wraith]

yea

thanks

[hard wraith]

im sorry to disturb again

i just cant do it

i got 2 values

but theres supposed to be another

one

i got 3 and 1

but donno how to get the other one

[hard wraith]

ok so i tried something

since when x>2 we multiply by 1 and when x<2 we multiply by -1

when x = 0 we multiply by 0?

i donno i just got the answer right no sure

[sterile ginkgo]

n=-2 will work too

[hard wraith]

how?

[sterile ginkgo]

If it's 0 you just keep it as it is

[hard wraith]

and do i need to do this for every other math

[sterile ginkgo]

If the mod is positive or 0 x>=2 or <=2

And if it's negative -2<x<2

The square means you can also have negative values

[hard wraith]

right

[cedar kiln]

@hard wraith Has your question been resolved?

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[undone star]

Hey, just have a quick question:
Prove that cos35 + cos45 + cos75 + cos85 = 2cos5cos20 (everything is in deg)

Im unsure how to do that

[undone star]

I got to the point where it simpliies to 2cos40cos5 + 2cos80cos5

[ancient lodge]

You can factor out cos 5, meaning you just need to prove cos 40 + cos 80 = cos 20

[undone star]

oh i see

ty

.close

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[hard wraith]

stuck again at |x² - 7x + 6| = 6 - x

[hard wraith]

i got the first 2 values

im struggling to understand how to get a third value

so i took off the modulus right
so for x>2, (x² - 7x +6 = 6 - x)
and for x<-2, (x² - 7x +6 = - 6 + x)
so x>2 right
x² - 6x = 0
x² = 6x
x = 6?
anyways
x<-2
x² - 8x + 12 = 0
x² - 2x - 6x + 12 = 0
x(x - 2) -6(x - 2) = 0
(x - 2) (x - 6) = 0
x = 2
x = 6

the last value is 0

checked with book

<@&286206848099549185>

[cedar kiln]

@hard wraith Has your question been resolved?

[grave cloud]

this is the part where things go brrrr

you can not remove "x" unless x is not equal to zero

here, you wanna be like

x^2 = 6x

x^2 - 6x = 0

x(x-6) = 0

x = 0 or x = 6

[hard wraith]

Hence the question mark lol

[grave cloud]

lol

[hard wraith]

Sheeeeit

Should've thought about that

[grave cloud]

:))

yea be careful next time :))

[hard wraith]

Yeah

How do I train my intuition to pick these up

[grave cloud]

hmmm idk ? just practice :0

[hard wraith]

Do more maths?

[grave cloud]

thats what i did

[hard wraith]

Hmm k

Makes sense

Pretty straight forward

Ok

[grave cloud]

yep :))

alr if there are nothing left to question about, close this room by typing ".close"

[hard wraith]

Thank you that was disturbing

[hard wraith]

K

.close

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[cedar kiln]

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[midnight brook]

HI I dont understand if I am doing it right but to find h(1)
i do f'(x)*g(x) + f(x)*g'(x)
and it is
1x0.8 + 1x-1/4 right

[midnight brook]

I get 0.55 for the output and it seems to be wrong

[rain drift]

hi there, can you show you you got 0.55

[midnight brook]

1 * 0.8 + 1 * -1/4

0.8 is g(1)

-1/4 is the slope of g(x) aka the same as g'(x) right

[rain drift]

well for one we can represent g(x) as g(x) = -1/4x + 1 since we have a y-intercept and we can see that the slope is -1/4. So then g(1) would actually be 0.75. At least it looks like it goes through the point (0, 1)

[midnight brook]

oh that does make sense instead of using just eyes

[rain drift]

and since we have x < 2 for x = 1, then f(x) = x. so then f(x) * g(x) = h(x)= x(-1/4x + 1) = -1/4x^2 + x. So then h'(x) = -1/2x + 1 --> h'(1) = -1/2(1) + 1 = 1/2.

[cedar kiln]

@midnight brook Has your question been resolved?

[cedar kiln]

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[cedar kiln]

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[simple flare]

Hi, for this may I ask why isn’t let f=-1/x^2?

I remember we follow ILATE rule, isn’t -1/x^2 first?

[simple flare]

<@&286206848099549185>

[cedar kiln]

@simple flare Has your question been resolved?

[muted tendon]

Do you need help?

[simple flare]

Yea

I wonder why this doesn’t follow the rule

[muted tendon]

They followed

But the thing is they used the trick

They applied the ilate on just first part

[simple flare]

How? If follow the rules, should be this?

[simple flare]

Yea, I can’t see they follow the rule

Isn’t -1/x^2 comes before exponential ?

That part is for algebra

[muted tendon]

Check this

Break the integration

And keep the second part as it is

[simple flare]

I know this trick

I’m asking the first part which is using the ILATE rule

It doesn’t follow that rule

Isn’t -1/x^2 the algebra part?

[muted tendon]

Okk here firat part is algebraic which is 1/x now apply ilate

[simple flare]

It comes before exponential

[muted tendon]

Why -1/x^2

Its -1/x

[simple flare]

I’m not seeing this as integrand,

I’m using another part ask shown here

[simple flare]

This is another part

I’m asking about the ILATE rule

[simple flare]

I’m asking why for this question, we let u= exponential while v’=algebraic

If we follow the law, we should let u=algebraic while v’=exponential

[muted tendon]

There is no hard fast rule for ilate

That depends upon your ease

Of selection

They fins it is wothy to select -1/x^2 so they selected

[simple flare]

Oh, that means doesn’t really need depends on the rule?

[muted tendon]

Yess

[simple flare]

We can just switch?

[muted tendon]

Main thing is the integration

[simple flare]

Oh，I thought we need to follow because this is the first time I come across the questions which didn’t follow the rule

[simple flare]

Oh, btw, can I ask another question?

[muted tendon]

https://www.quora.com/Why-is-the-ILATE-rule-in-integration-necessary-Is-it-really-necessary-to-use-in-integration-by-parts

[muted tendon]

Sure

[simple flare]

For this question, I got the answer with #, however the correct answer is the top one

I try thrice and I’m still getting the same

[muted tendon]

Let me check

[muted tendon]

Should be ce^x

[simple flare]

May I know which part I’m wrong?

I just got 2C

[muted tendon]

3rd line from bottom

[simple flare]

Oh, I just noticed🫠

Let me change first

[simple flare]

I got one last question, which I don’t know how to continue 🤡 or maybe I’m wrong at the middle

[muted tendon]

Dm me

[simple flare]

Okay

[simple flare]

I messaged already

.close

[cedar kiln]

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[modern wren]

how do you do this

[haughty wraith]

you just posted this

[modern wren]

i got how to do it

but like

and what it means but like

[haughty wraith]

why did u close the other thread then

[modern wren]

accident

I know what it means but I dont understand how to get to the final answer

anyone?

<@&286206848099549185>

[dire geode]

which problem

[modern wren]

12 and 14

[dire geode]

slope = rise divided by run

convert to a common unit before plugging in numbers

[modern wren]

like can you get the answer cuz i dont understand

like more detailed

ik how to do slope

but like with this quesiton no

[dire geode]

it's against the rules to give answers

[modern wren]

oh

ok

didnt know that

ok

[dire geode]

convert to a common unit first like i said

[dire geode]

what do you mean you "know how to do slope"

this is exactly a slope problem

[modern wren]

like i get it

now

thx

it was kinda confusing

cuz im canadian

and i hate american ft

and like that

so

like

yea

thx

.close

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[cedar kiln]

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[fast pilot]

Hi

[haughty wraith]

Hi

[fast pilot]

Need discrete math help

premises are

Not A -> I
A -> H
I -> K

conclusion is

Not K -> H

[short blade]

what’s giving you trouble?

they used contrapositives all the way through

[fast pilot]

Im having a hard time getting to the conclusion,

i dont know what laws to use

or what to do

[short blade]

start with I -> K

do you know what the contrapositive of this is?

[fast pilot]

not K -> not I?

[short blade]

yes

[fast pilot]

is that the contrapositive

okay okay

[short blade]

now take not A -> I

and find it’s contrapositive as well

[fast pilot]

not I -> A

[short blade]

yes

notice we have not K -> not I and not I -> A

and also A -> H

[fast pilot]

oh shit

so not k -> not H

YO

[short blade]

yes

[fast pilot]

i love you maximo

thank you so much

.close

[cedar kiln]

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[fast pilot]

.reopen

[cedar kiln]

✅

[fast pilot]

@short blade rq i made a mistake

its H implies A

not A implies H

This is correct

i had rewritten it wrong sorry

[short blade]

is this true tho

[fast pilot]

wdym?

[short blade]

like it looks like it doesn’t necessarily hold

[fast pilot]

can we use the converse on H -> A

[short blade]

converse isn’t necessarily true

[fast pilot]

and it is a possibility that its not valid

/true

[fast pilot]

are you sure we cant use it

[short blade]

it doesn't necessarily hold, the claim isn't equivalent

[fast pilot]

would inverse work?

<@&286206848099549185>

i think it may be invalid

/untrue

[short blade]

to show this is false it should suffice to say if K is false, H can still be false

so assume K is false, then I is false as well, so A is true. but there's no restriction on H so H can still be false without breaking the hypotheses

[fast pilot]

thank you, that makes complete sense, but how would we write that down?

[short blade]

suppose not K and not H
then not K -> not I -> A, and not H -> A still holds, so all hypotheses are still satisfied yet the conclusion does not follow

[fast pilot]

okay bet bet thank you!

so much

.close

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[merry tinsel]

if this was correct
$\frac{\frac{1}{:2}\left(x-1\right)^{-\frac{1}{2}}\cdot \left(2x+4\right)-\left(x-1\right)^{\frac{1}{2}}\cdot 2}{\left(2x+4\right)^2:} simplified \frac{\left(2x+4\right)-2\sqrt{x-1}}{\left(\sqrt{x-1}\right)\left(2x+4\right)^2}$

[cedar kiln]

Please don't occupy multiple help channels.

[wraith dagger]

Hoesmad

[merry tinsel]

Is this correct

[merry tinsel]

@dire geode

could u help?

[static edge]

u r missing a small mistake

should be like this

[merry tinsel]

oh i see

[static edge]

remember the 1/2 x (x-1)^(-1/2) on the front does not belong to the whole numerator

[merry tinsel]

are you able to simplify it further

[static edge]

yes

let me write it first

[static edge]

be careful, is 2x+4 = 2(x+4)?

[merry tinsel]

oh lol

mb

im trying to simplify it further so its easier when i need to set it to 0

to get the critical points

[static edge]

ahhh

i think this form will help you

[merry tinsel]

omg

iforgot about

conjugation

😂

[merry tinsel]

dont u have to multiply by the whole binomial?

[static edge]

for which part

[merry tinsel]

when ur conjugating

[static edge]

yep

[merry tinsel]

i meant dont u multiply by the whole numerator

when conjugating

[static edge]

yea, u multiply it with everything on the top

[merry tinsel]

ok so for my cp

i only get x =4

how would i use the numberline thing here

do i just calculate it at the point 4?

[static edge]

increasing function means that the derivative is positive right

u get -x + 4 > 0, so x < 4

[merry tinsel]

what

[static edge]

the question right?

ohh wait i think i get what u mean

[merry tinsel]

yeah

i need to test the sides

[static edge]

like this right?

[merry tinsel]

^ like this

ye same hting basically

[static edge]

well to show that x < 4 is increasing just plug in a random number less than 4 into the derivative function

[merry tinsel]

so there is no

interval?

[static edge]

there is

u just test it

[merry tinsel]

i did

its positive when its less than 4

[static edge]

yep

[merry tinsel]

so (-infi,4)

would be the interval?

oh wiat no

it DNE

at +-1 and -2, 0

so it would stop at 1

(1,4)

[static edge]

yes

[merry tinsel]

thanks 🙂

[static edge]

yw

[merry tinsel]

u know how to curve sketch right>

[static edge]

i think so

[merry tinsel]

why is tha useful 💀

takes 30mins

to sketch an estimate

[static edge]

that's a good point

[merry tinsel]

when i can just

pull out my phone

and do it under 10 secs

[static edge]

d e s m o s

[merry tinsel]

literally never finna use

that in my life 💀

[static edge]

i agree lol

[merry tinsel]

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[strange grove]

Really? The Leibniz formula? With 6! = 720 summands corresponding to all possible permutations?

Or do you mean Laplace expansion?

[solid juniper]

some row operations first might help a little

you can make some more 0s

but idk any good way lol

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[west stream]

ok

[west stream]

so i have a linear function called "0.133*x+25.6312"

when i put in the number 38,65 i get rougly 30. something which is correct

but when i put the function in geogebra and try to do it manually i get 32,85 to 30.

what is suspect is that there is something wrong with geogebra

[zenith sail]

That function has a very small rate of change, and both your inputs 32,85 and 38,65 are not very far apart

As a result, the function gives a number roughly equal to 30 for both inputs

[west stream]

the number is not 25k btw

[zenith sail]

Neither one is exactly 30, they're just both kinda close

[west stream]

im calculating bmi

the question is that i gotta show manually and mathematically what i get when y = 30

[zenith sail]

Oh

then say

30 = 0.133x + 25.6312

And solve the equation for x

[west stream]

this is what i did when i had to show it mathematically

[zenith sail]

Yeah

I mean I didn't check all those numbers but yeah that's what you should do

[west stream]

but it should be the same as geogebra

[zenith sail]

wait hang on

[west stream]

oki

[zenith sail]

Your 0,133 accidentally changed to 0,113

[west stream]

OHhhh

so it is geogebras fault?

[zenith sail]

No, what?

[west stream]

what do you mean?

[zenith sail]

wait, how did geogebra get it wrong?

[west stream]

ohhh i get what you mean

yea that worked

i put 0.113 in my calculations later on

instead of 133

[zenith sail]

yeah that's all

[west stream]

OMG

thank you so much

im so blind

[zenith sail]

Lol no problem 👍

Too many digits in this problem lol

[west stream]

truueee

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[earnest kettle]

how do I solve this?

[strange grove]

The average velocity is the ratio between the distance traveled and the time difference.

[earnest kettle]

?

ohhhh

okie

nvm

thank you

💖💖

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[crimson sedge]

can somebody teach me how to do algebra at a ninth grade level

[grand raft]

Just ask a question

Wdym teach💀

[crimson sedge]

I mean i need to learn how to do algebra

dude seriously came into the question room, roasted me, and then left ah no wonder i left this dumbass site for so long 🤣 🆗

[manic acorn]

Follow the book taught at your school, watch youtube videos etc.

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[prisma valve]

Hi I need help in part b and c

I dont understand what the question means

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@prisma valve Has your question been resolved?

[prisma valve]

<@&286206848099549185>

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<@&286206848099549185>

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<@&286206848099549185>

[dapper raven]

at b

what they're asking is

think about the function f

it takes in a number and spits out a number

it is defined on (-0.1, 0.1)

meaning it can take in a number in that interval

and the function is such that if you fill in 0

you will be able to construct the point Q from part a

by taking (x = 0, y = f(0))

and also

for x in the same interval

f is such that (x, f(x)) gives coordinates that are on the original curve

i'm guessing the question for b is to find f

that would make the most sense

you're given some constraints as to what f can be

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[heady basalt]

Can someone check my work for this problem?

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@heady basalt Has your question been resolved?

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<@&286206848099549185>

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<@&286206848099549185>

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[faint snow]

That problem isn't for mortals like me

[vernal shell]

The triple integral is correct

I'll put it in wolfram alpha and see if you got the correct answer

Yup it's correct, great job 👍🏽

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[ember imp]

You can split the integral and then use the identity given

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[inland mist]

Can anyone help me with Parallel Lines and Transversals please?

[placid seal]

Hi!

My name is Eg Sheeran and I will be solving your problem!

[inland mist]

Oh, thank you Eg Sheeran!

[placid seal]

No problem.

Ok

Let's get started.

First of all...

[inland mist]

This is what it looks like

[placid seal]

Parallel lines are lines that never touch each other or meet

They stay the same distance and never meet

Transversal lines are lines that crosses two or more lines,

I hope this helped!

[inland mist]

It helped a little, thank you!

[placid seal]

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[subtle cosmos]

I need help understanding a proof

[subtle cosmos]

how do i make the jump from "phi is the root of f(x)" to "g_n = c phi^n + d phi conjugate^n"?

this is from a derivation of the binet's formula btw

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[fallow slate]

So, on the second to last equation at the last part, is it a text error that the R is not included at T(s)?

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[open wave]

how do i work this out

[hushed spoke]

What are you having trouble with in this?

[open wave]

not rly understanding it

like i can ik i gotta root it but its just confusing in this format lmao

[hushed spoke]

That is sqrt. 2nd root of n is n^(1/2)

[open wave]

0.5?

[hushed spoke]

And that as a fraction is?

[open wave]

1/2

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[high spruce]

I'm a little confused of what it means if a sequence generated by a recursion is constant

[cedar kiln]

@high spruce Has your question been resolved?

[sacred stone]

$a_{n+1}=a_n$ generates a constant sequence

[wraith dagger]

秋水

[high spruce]

oh that was my initial thought but I thought it was wrong for some reason

thanks, just wanted some clarification

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[crimson sedge]

$$\frac{\theta_m}{V_1 - V_{eq}} = \frac{K_t/R\cdot J_m}{s^2 + s(d_m + \frac{K_b}{R})\frac{1}{J_m}}$$

[wraith dagger]

broke

[crimson sedge]

How would i get the LHS to equal $\frac{\theta_m}{V_1}$

[wraith dagger]

broke

[crimson sedge]

my algebra is quite rusty

[floral forge]

Multiply both sides by (V_1-V_eq) and then divide both sides by V_1

[mental trail]

Multiply by $\frac{V_1-V_{eq}}{V_1}$

[wraith dagger]

rafilou2003

[crimson sedge]

great!! thank you

[floral forge]

Its .close

[crimson sedge]

.close

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[crimson sedge]

thanks!

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[wild sparrow]

Hello, so I have the following function:

Domain: R - {1}
lim x -> 1+ f(x) = ∞
lim x -> 1- f(x) = -∞

points of horizontal tangency = (0,0) and (2,5)

lim x -> ±∞ (f(x) - x) = 1
sign of (f(x) - (x+1)) -> positive or negative if x is plus or minus infinity

[wild sparrow]

i don't understand the last 2 statements

[wild sparrow]

Also vertical asymptote is at x = 1

i need to draw the function based off that data but i don't get the (f(x) - (x+1)) thing

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[keen bloom]

https://i.imgur.com/xhHvMdZ.png I am not sure how this is supposed to be pi/2 and not pi/4

[keen bloom]

i get everything else

[tropic oxide]

min to max is half a period

[keen bloom]

ohh i misunderstood it looking at another graph

i feel stupid now

i was looking at mid to max

this can be closed now ty

[tropic oxide]

type .close

[keen bloom]

o

.close

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[remote agate]

Hello. I have a task, which reads that 15 people are to beasted in a row of 15 seats. Bob, Kate and Don can't sit together as 3 ( but can as 2 ). In how many ways can all the people be seated?

[remote agate]

So I assume I need to find all of the possible variations and then substract the ones where the 3 are together

so all possible ones would be 15!

but from here onwards i dont know

the 3 can be arranged in 3! ways

[cedar kiln]

@remote agate Has your question been resolved?

[cedar kiln]

@remote agate Has your question been resolved?

[lament sedge]

So the problem comes down to finding how can those 3 people be organized

@remote agate

and as a first step you can always simplify the problem

lets say there are only 5 people

The three people are bob kate don(b,k,d)

and call the other two people a and b

try to find how many ways you can arrange this

where b,k,d sit next to each other

@remote agate you there?

[lament sedge]

also try finding this out

if the order of how those people sit has to be b,k,d

[remote agate]

it doesnt matter i think. its just that these 3 cant sit together

[lament sedge]

I know

sorry

one min

[remote agate]

i feel like its 15! - ( x * 3! ( how we can sit the 3 ) )

[lament sedge]

ya

[remote agate]

since whenever we have those 3, we have 12! remaining for other people

[lament sedge]

thats correct

[remote agate]

but idk how to get x

unless i write down all variations

like xxx............, .xxx...........

[lament sedge]

you dont need to

if you have 15 people

[remote agate]

i can visualise it, but idk how to put it to paper

[lament sedge]

3 of them

will be the pople

so call them s

so s is just

the number of ways you can arrange the 3 people

so with that you get 12 people plus s

sorry if this does not make sense

[remote agate]

tbh not much since idk how to put it in a formula

[lament sedge]

basically

think of how you can arrange it if the three people sat in the order b,k,d

and then multipky by 3!

for the 3! different ways you can arrange the 3 people

[remote agate]

yes

but is there a quick way to count it

[lament sedge]

hear

[remote agate]

unless i write down all varians of bkd............, .bkd..........., ..bkd..........

[lament sedge]

you 12 people plus bkd

so there are 13!

different ways to arrange that

[remote agate]

hmm

[lament sedge]

*3!

[remote agate]

15! - ( 13! * 3!)

[lament sedge]

yup

[remote agate]

seems to make sense

[lament sedge]

I was just not wanting to say the ansswer

[remote agate]

ye, cuz i want to understand it 🙂

[lament sedge]

sorry

does it make sense

[remote agate]

and i think i get it now

[lament sedge]

sorry

for the confusion

was trying hard not to say the answer lol

[remote agate]

thx. ill write it down but ye it makes sense.

!complete

!close

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[inner quest]

it seems like constant hazard and exponential but not sure

[cedar kiln]

@inner quest Has your question been resolved?

[inner quest]

<@&286206848099549185>

[modest lynx]

What does s(t) represent?

[inner quest]

survival function*

[modest lynx]

Is that the fraction of the initial population that is alive at that time? I asked because it isn't explained in the question what quantity it represents.

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[thorn kelp]

i want to learn the method for finding a cube root via long division method

[thorn kelp]

umm

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[final coral]

how do i deal with this?

[quartz frost]

$\bar{z+i}=\bar{z}-i$

i think

[wraith dagger]

~Martin

[quartz frost]

think of the left bar to be over z+i haha

[wraith dagger]

Basudev

[final coral]

so it is just -2bi?

[gleaming cloud]

Yes

[final coral]

ok thx

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Please don't occupy multiple help channels.

[floral aurora]

i am not sure how to make the formula for each question

[strong pivot]

Try having it in natural language

@floral aurora

[floral aurora]

i tried researching everywhere

@eager sparrow tried to help, but he doesn't understand notation

[strong pivot]

I do

[eager sparrow]

∃(P(x)∧R(x)) = Some farmers are left handed

Yeah I kinda do now

[strong pivot]

Just put the conditions in usual language

[eager sparrow]

While you were gone, I watched youtube tutorials, and kinda understood it now

[floral aurora]

i dont get that

[floral aurora]

i watched vids but didnt xd

[strong pivot]

Like blue eyed left handers are borh in c and d

Try that

[eager sparrow]

Nah he already knows that

[strong pivot]

So x is an element

[eager sparrow]

The problem is that he needs to translate it to predicate notations

[strong pivot]

P(x) is an assertion of which the value true/false depends on x

Then "and" "or" are pretty straight forward

[strong pivot]

Then he has to give it a try ?

I guess

[floral aurora]

would the second one be

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

[eager sparrow]

∀(Q(x)∧P(x)) Ʌ (S(x)∨R(x))

[floral aurora]

for this one

would it be

forall (Q(x))orS(x))

[strong pivot]

(Technically doesnt mean anything if u dont define x)

So x e u

[floral aurora]

is that the second one?

but how would that make sense bcs

its only asking for blonde farmers

[strong pivot]

Otherwise it means nothinf

[floral aurora]

oh

blue eyes too

[eager sparrow]

The x I think is already defined in the picture

[floral aurora]

oh

left handed*

[strong pivot]

Logically isnt

[floral aurora]

so R too

[strong pivot]

X is a mute variable

You can put anything instead

[floral aurora]

what would be the second one?

[eager sparrow]

Is there any way for it to make sense @strong pivot ?

[strong pivot]

So it would be there exist an element x in u such that x P(x) is true

For example

[floral aurora]

but

question says all blonde farmers

wouldn't you use

for all

[strong pivot]

So it would for all x in A (R(x) or S(x) )

For 2)

[floral aurora]

but P(x)

is x is a farmer

so wb that one

[strong pivot]

No

X doesnt mean anything

It could be y instead

You need to define it

So if you say x in Y you say it is x, an element of the set Y

[floral aurora]

ah i see

[strong pivot]

If you want to you could wwrite there exist ♤ in U such that P(♤)

Its just annoying for the reader (and you)

[floral aurora]

is the first one right: exist(P(x)andR(x))?

[strong pivot]

Well you dont define x

So its weird

Caps

[floral aurora]

this question is weird

because it does not tell us x

so im so confused

[strong pivot]

Math is weird

[strong pivot]

Where is it a problem?

[eager sparrow]

∀(Q(x)∧P(x)) →(S(x)∨R(x))
This is for the 2nd question
@strong pivot Is this correct now?

[strong pivot]

No define x

[floral aurora]

what is the first question?

[eager sparrow]

Is this what you're talking about

[strong pivot]

Write there are left handed farmers as a logical assertion ?

[strong pivot]

I have no idea what that means

[floral aurora]

how would you do that

[strong pivot]

But you say for all( x is verifying q and p )then either s is true for x ir r is true for x

[floral aurora]

so the thing galm did

[strong pivot]

But you dont define x

[floral aurora]

exists(P(x) and R(x)

[strong pivot]

Doesnt mean anything

[floral aurora]

which translates: there are left handed farmers?

oh

[strong pivot]

.

For two

[floral aurora]

thats for two right

[eager sparrow]

Is this it?

[floral aurora]

yeah

[floral aurora]

yeah

[strong pivot]

So i say for all x in A

[eager sparrow]

Like what @strong pivot talking about

[strong pivot]

So x is defined as an element of the set A

[eager sparrow]

Like the definition or is it something else?

[strong pivot]

Yes

I believe this aims to make you distinguish logical assertions and sets

[eager sparrow]

Ah I see, that's why I was confused

[strong pivot]

Basically x in U verifies Q ~ (is the same as) x is in B

[floral aurora]

so wait

@strong pivot

taking your 2nd one into account

[strong pivot]

~ basically means is the same as, both are always true when either is true

[floral aurora]

that means the statement is true right? because D intersects in both B and C

[strong pivot]

Sure

What is true sorry

[floral aurora]

you have to write statements

and then write if its true or false

[strong pivot]

Yes

[floral aurora]

so for number 2, we wrote statement

the statement is true or false?

im thinking its true

[eager sparrow]

E( (P(x) ∧ R(x)) ∧ (R(x)ɅS(x)) ) → E(P(X)∧S(X))
Don't mind me, just putting my answer
BTW this is mine for number 3

[strong pivot]

1 is rrue 2 is false

[strong pivot]

Define x

[floral aurora]

doesnt C and B

[floral aurora]

intersect in D

tho

[eager sparrow]

AAAAH I GET It

[strong pivot]

Yes but not ALL farmers are left handed or whatever

Sime are just farmers

[eager sparrow]

Is X a set of all people in Exampleville? @strong pivot ?

[strong pivot]

U

U is the set of all ppl

[floral aurora]

wait im sorry

we skipped the first one

how would u do the first one?

[strong pivot]

So that means there are left handed farmers

So there are ppl who are both left handed and farmers right?

[eager sparrow]

∃(P(x)∧R(x)) here is the first 1

I'm just gonna resend it

[eager sparrow]

Yes

[strong pivot]

No there exists x in u

Then the rest i perfect

Just define what x is

[eager sparrow]

I mean, at the problem, x is already defined
Do I have to redefine it again? or not?

[floral aurora]

i think you got the second one wrong btw

[strong pivot]

No it isnt

[floral aurora]

second one mentions all blonde farmers

Q is not in the statement

did you mena

for all x in Q

[eager sparrow]

So just replace x with U right?

[strong pivot]

Na because x is an element and Ua set

So you get x € some set

And U C a bigger set

[floral aurora]

ok

the second one i fixed

[strong pivot]

€ being the weird e

[floral aurora]

im confident in the second answer