help-0

[gritty verge]

I’m not sure lol the person guided me to factor 0.5 out

Lemme send the question again

Part d

[iron mulch]

No you don’t do that. Factoring out a 1/2 would give you .5(4s/(s^2-1))

You would factor out a 2

[gritty verge]

Oh

But how do I do that ? O.0??

[iron mulch]

You factor out a 2…

Because 2 is a multiple of that fraction

Why wouldn’t you just use first principals on the original fraction?

[gritty verge]

That’s what i did lol

Then the person

Told me change the fractions

Ignore last line tho

It’s wrong i think haha

Basically i got until there

[iron mulch]

Also 1/(s^2-1) isn’t 1/s+1 + 1/s-1 ???

That’s completely wrong ??

Wait I’m having an aneurysm

[gritty verge]

Oml yes

Ur right

AHHAH omg dumb me

[iron mulch]

I fucking hate first principals

[gritty verge]

Same

[subtle mango]

what is first principal

[iron mulch]

I’m giving up its time for bed gn

[gritty verge]

Gun

[iron mulch]

Jelly why are you here asking that

[gritty verge]

Gn

First principle is like using the limits to diferenctiate

[iron mulch]

It’s the definition of a derivative

[gritty verge]

Ye

[subtle mango]

oh i got it

[gritty verge]

Haha help me OwO I’m dying

[subtle mango]

i think it's a bit messy to calculate the original fraction

[gritty verge]

As Long as i understand I’m fine with any method

🙂

[subtle mango]

so i wrote s/s^-1 to be 1/2( 1/s-1+1/s+1 )

[gritty verge]

Mhm

[subtle mango]

and the 2 fractions are easier to calculate, i can show you the first one

[gritty verge]

Okie sure

[lone heart]

@gritty verge Has your question been resolved?

[gritty verge]

Ooh

[lone heart]

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[covert gorge]

Hi, just a question. I can use the factoring by grouping method for a cubic polynomial only if the first two coefficients have the same ratio as the last 2 coefficients, right?

[lone heart]

@covert gorge Has your question been resolved?

[covert gorge]

<@&286206848099549185>

[lone heart]

@covert gorge Has your question been resolved?

[covert gorge]

no but i will close

.close

[lone heart]

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[tidal zealot]

how the heck am i susspoed to graph xe^-x

[oak perch]

Consider derivative and second derivative of xe^-x

[tidal zealot]

yeh

[oak perch]

So it increases on [0,1], decreases on [1,inf). Concave down on [0,2], concave up on [2,inf)

Those are enough to sketch

[tidal zealot]

how did u get those values

[oak perch]

This

[tidal zealot]

but when you derive its

,w -x^2*e^-x

[tidal zealot]

how do i get those point from it?

[tacit bobcat]

Are you just looking for a graphing calculator?

[oak perch]

I said derivative, not integral

[tidal zealot]

,w derive xe^-x

[ocean seal]

Results provided by WolframAlpha

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

Requested by jaxplaysgames#7117

[tidal zealot]

how do u tell it increases from 0,1

[oak perch]

Check your textbook

[tidal zealot]

the roots are only giving you the stantionary points

im confused on how u r getting these domains

[gritty compass]

I need help

[oak perch]

.

[gritty compass]

I’m a 13 year old and don’t quite u detestando a questsion

How does 8 square root turn into 2 in the power of

[vale junco]

ok

[gray isle]

8 = 2^3

[tidal zealot]

2^3

[vale junco]

what is square root?

[tidal zealot]

bro get the heck outta here!!!!

[vale junco]

u already wrote it

[tidal zealot]

my channel

[gritty compass]

I still don’t get it 💀

[vale junco]

open a new channel

its not urs

go to the availible channels

[gritty compass]

How do I open it

[vale junco]

just type ur question there

[tidal zealot]

,w derive -e^-x(x-1)

[ocean seal]

Results provided by WolframAlpha

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

Requested by jaxplaysgames#7117

[tidal zealot]

ok heres the second derivative

how did you know it concaves down from 0,2

ik what inflecction points are

but im unsure how you concluded on it to be concaved down from 0,2

@oak perch if ur not going to show me how to do it at least tell me, so i dont waste my time watining for an answer

telling me to review my textbook isnt helping

[oak perch]

Okay.I won’t, those are elementary facts, definitely in any textbook

[lone heart]

@tidal zealot Has your question been resolved?

[lone heart]

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[warm wedge]

In the second row in the table where, how is the probability for X=2 and Y= 1 1/18? What is the second case (2,1) is the first case. (1,2) comes to mind but it doesn't satisfy X>=Y.

[alpine sable]

it doesn't say that X refers to the same dice every time. Instead, I think it refers to the bigger number rolled

[warm wedge]

then how can we have all those zeros there then?

[alpine sable]

X is never less than Y ig

[rose sigil]

the probability that the bigger number is 2 and the smaller number is 5 is 0

[warm wedge]

guys I am really really slow when it comes to probability. but doesn't (1,2) mean exactly what layla said?

[rose sigil]

P(X = 1 and Y = 2) looks like 0 by the table

[alpine sable]

you can roll either a 1 and 2, or a 2 and 1. Both rolls correspond to X=2, Y=1

[warm wedge]

ah now I see

thank you guys

[rose sigil]

np 💜

[warm wedge]

.close

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[jaunty socket]

does this make sense to you? im not 100% sure if i got this question right

[vale wigeon]

maybe you should specify that the marbles are distinct, and replace "3 or 4" with "at least 3" for elegance (though the latter is less obligatory)

[jaunty socket]

okay so I will word it like "James has 4 marbles. In how many ways can at least 3 marbles be picked. Assume each marble is distinct"

thanks for helpin' me :))

.close

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[alpine sable]

i have this

[alpine sable]

and i have to prove that this

have integers numbers and i really don't know how they got the answer

like they get 2^13*A(log base 2 of 16)

[mortal trellis]

it would probably be a good idea to multiply A(a)*A(b) and see if find a pattern

[alpine sable]

A(a)*A(b) = 2A(ab)

[mortal trellis]

good. so what happens if you repeat that?

[alpine sable]

4A(abc)

[mortal trellis]

and again?

[alpine sable]

8A(abcd) i think

[mortal trellis]

and again?

[alpine sable]

oh so 2^13 is the number of of how much it multiplies

[mortal trellis]

the exponent is the number, yeah

[alpine sable]

and the logarithm, how do they get log in base 2 of 16? do they transform each of them in base 2?

[mortal trellis]

yes

and then a bunch of stuff cancels

[alpine sable]

Ok, now i understand. Thank you.

.close

[lone heart]

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[solid island]

"If a population grows at a constant rate of 2.8% per year, then what percent will it grow over the next 10 years?"

[solid island]

How do I solve for that

[languid bolt]

ok so

lets start with an easy question

what will be the percentage of the population next year

[solid island]

5.6

[lone heart]

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[strong dome]

Hey,
Given G=(V,E) a directed Graph. Is there any way to calculate the maximum number of strongly connected components, only based on n nodes and e edges?

[rose sigil]

I probably won't be able to help but does that mean calculate the maximum number of strongly connected components among all directed graphs with n nodes and e edges?

[mortal trellis]

well if you want the max then I assume the best would be to pair up two vertices until you have no edges or vertices left

[lone heart]

@strong dome Has your question been resolved?

[strong dome]

yes, but as as in possible upper bound, assuming you are given n nodes and e edges

[strong dome]

yes that's good way to approach it if we build it through the process
I was thinking maybe there is some general proof or formula for it or like anything known that I don't know, which could help

[lone heart]

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[next flax]

Why is the coordinate C equal to 180

And not A

[vale wigeon]

neither the x coordinate nor the y coordinate of point C equals 180

[vale wigeon]

point C corresponds to an angle of 180°

[next flax]

what’s the difference

[vale wigeon]

well the correspondence between points and angles is specific to the unit circle as drawn here

while coordinates are by and large independent of what happens to be drawn on the plane

(aside from the axes which define them, of course)

[next flax]

How was I supposed to know C was the right answer

[lone heart]

@next flax Has your question been resolved?

[lone heart]

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[steep halo]

say A is a vector space and B is a subvector space of A, are the vectors of the base of B also part of the base of A? so can we add more "vectors" to the base of B to create a basis for A?

[steep halo]

i'm trying to understand the proof of the rank nullity theorem but i don't understand this piece here

[copper stone]

yeah

[worn fox]

You can always extend a basis of a subspace to a basis of the whole space

[copper stone]

you can complete the basis of B to create a basis of A

[steep halo]

1. We know that the kernel is a subspace of V, so we get it's base
2. We add vectors to this base so that it becomes a base of V
3. ?

it might be using some definition which i forgot

[worn fox]

3 is just definition of T(B)

The image of a map is just the space spanned by the image of the vectors in a basis

You take B, apply T to all the vectors and their span is the image of T

But then loads of those vectors are actually in the kernel of T so they're not contributing to the span at all bc they get sent to zero

[steep halo]

ok so the remaining vectors will be the ones that we added

[oak perch]

Yeah. Zorn’s lemma

[steep halo]

which being part of a basis are linearly independent so the dimension is the same as the one written there, aka n - k

[worn fox]

Yeah sure

Then the next trick is extending that to a basis of W iirc

[steep halo]

but why do we have to go though this intermediate step of proving that it's independent, we already knew it from it being part of a base

[worn fox]

We knew that the w_i were part of a base for V

[steep halo]

oh wait it's so that we can split it into different pieces that can be used to finish the proof

[worn fox]

It's not immediately obvious that this means the T(w_i) are linearly independent

They prove this

[steep halo]

ok got it, ty!

.close

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[urban flint]

Consider the random variable X with density f(x) = (1/6)x where 2 <= x <= 4.

Find Expected value E[X].

What i did: calculated the integral from 2 to 4 and got the answer 1.

Answer says: 56/18

Is my answer wrong wrong or is the book wrong?

[lone heart]

@urban flint Has your question been resolved?

[heady pollen]

the integral just gives the area under the density curve

the area is always 1

ok after some google i found this:
expected value=integral of x*f(x) from 2 to 4

$\int_{2}^{4} x\cdot f(x) dx = \int_{2}^{4} \frac{1}{6}x^2 dx$

[ocean seal]

~Martin

[urban flint]

@heady pollen Thank you, i totally missed to multiply by x in the integral.

.close

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[dapper pawn]

is this correct?

<@&286206848099549185>

please

[lone heart]

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

[languid bolt]

Just find how many ways you can select the committee without restrictions

and then just subtract the number of ways you can choose 4 students or 4 teachers

[dapper pawn]

that is 10!

10!/4!4!

[languid bolt]

which one is 10!

[dapper pawn]

oops no

its a 4 member commitee so 4!

and one teacher one student

[languid bolt]

arrangement doesnt matter bro

[dapper pawn]

so 4!/1!1!

ok then without restriciton is 10C4

[languid bolt]

ok

how many ways you can choose the committee if you can only choose either 4 students or 4 teachers

[dapper pawn]

5C1 x 5C3 + 5C2 x 5C2 + 5C3 x 5C

[languid bolt]

what

can you explain what you just did?

[dapper pawn]

not gonna lie im confused

[dapper pawn]

this is like my last 2 braincells making an attempt

[languid bolt]

ok so first of all

you can try to find the number of ways you can pick 4 students

there is 5 students, pick 4

5C4

and then you can find the number of ways you can pick 4 teachers

there is 5 teachers, pick 4

5C4

do you understand this?

[dapper pawn]

5C4 x 5C4

[languid bolt]

no

[dapper pawn]

i understand thus far yes

[languid bolt]

5C4 is the number of ways you can pick 4 students/teachers

so.. without restriction you have 10C4 right?

you just subtract it

10C4 - 5C4 - 5C4

that is the number of cases where there is at least 1 student/teacher

because you removed the cases where there is no student/teacher (- 5C4 - 5C4)

[dapper pawn]

Uh

the answer to that is 0

[languid bolt]

bro

[dapper pawn]

10c4 - 5c4 - 5c4

[languid bolt]

no

it's not a variable

do you know N choose K

[dapper pawn]

oh lol

i gotchu

[languid bolt]

or N combinations of K

[dapper pawn]

10c4 is 210

[languid bolt]

ok ok

bro

texit

late af

[dapper pawn]

5c4 is 5

so its 210 - 5 - 5

[languid bolt]

yes

so you just put it over the number of cases without restiction

200/210 = 20/21

[languid bolt]

which is the answer here

[dapper pawn]

20/21

[languid bolt]

yeah

[dapper pawn]

my god

you're good lol

[languid bolt]

ty

[dapper pawn]

can you check this one for me

i dont think its correct since the number is so large

[languid bolt]

you dont multiply, you add for a

because it's number of cases

not probability (because you usually multiply in probability)

[dapper pawn]

so then i add 78 + 286 + 715 + 715 to get 1794

thats how many ways?

[languid bolt]

yes

[dapper pawn]

noice

b correct?

[languid bolt]

should be

[dapper pawn]

cool

[languid bolt]

idk for the calculations tho

too lazy to count

[dapper pawn]

nah i feel u dw

u r a g so imma get u to help me with my last question

[languid bolt]

so this is just like 5C4 but you also count the arrangemnts

it's called permutation

[dapper pawn]

yup

[languid bolt]

yeah, i think it's correct

[dapper pawn]

both a and b?

lets goo

[languid bolt]

for a

[dapper pawn]

oh lmao

okok

[languid bolt]

wait.. it might be multiply

my brain lagging

[dapper pawn]

lolz idk

number is so high i was skeptical abt it

[languid bolt]

me too

should be multiply tho

[dapper pawn]

ok imma change it back

[languid bolt]

yeah my bad

[dapper pawn]

you good dw cuh

[languid bolt]

b should be correct too

ok i gtg sleep

bye

[dapper pawn]

cya thanks for the help

.close

[lone heart]

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[slow wasp]

Help needed

[slow wasp]

<@&286206848099549185>

[lilac nest]

!15m

[lone heart]

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

[slow wasp]

sowy

[lilac nest]

What have you tried to do?

[slow wasp]

Umm Thinking that I tried to to 13(1-cos^2x)/2+cosx + cosx = 2

[alpine sable]

id suggest

multiplying 2+cosx

and change everything into cosine

[slow wasp]

Okay?

[alpine sable]

thats it

now solve the quad

[slow wasp]

didn't understood

[alpine sable]

multiply 2+cosx first

[slow wasp]

to which?

[alpine sable]

everything

[slow wasp]

okay?

[lilac nest]

You want to get rid of the denominator, so you multiply everything by 2+cos(x)

Then you want to change sin²(x) into an expression with cos instead, so you only remain with cosines and you basically have a quadratic equation to solve

[slow wasp]

okay so now

[ocean seal]

Akash Kumar

[slow wasp]

Like this?

[alpine sable]

no

[slow wasp]

okay so how?

$\frac{(13sin^2x)(2+cosx)}{(2+cosx)}+cosx(2+cosx)=2(2+cosx)$

Like this? or any changes?

[alpine sable]

u didnt multiply 2+cosx on the right side

[ocean seal]

Akash Kumar

[slow wasp]

any changes?

[alpine sable]

yes

ur good

[slow wasp]

okay now

[alpine sable]

clear everything up and you will get a quad

[slow wasp]

${(13sin^2x)+cosx(2+cosx)=2(2+cosx)$

[ocean seal]

Akash Kumar

[slow wasp]

Like this Hope so?

[alpine sable]

no

[slow wasp]

kay

so like should I keep cosx as A?

[slow wasp]

I did same

[alpine sable]

nah u didnt

u kept the 2+cosx

[slow wasp]

ah yes

$(13sin^2x)+cosx(2+cosx)=2(2+cosx)$

[alpine sable]

yes

now solve it

[ocean seal]

Akash Kumar

[slow wasp]

Okay

shall I use odd properties?

$sin^2x = 1-cos^2x?$

[ocean seal]

Akash Kumar

[alpine sable]

yes

[slender gull]

And for the sake of simplicity you can do u = cos(x) if that helps you solve it.

[slow wasp]

Okay Thanks for the Tip

wait I got as

$9-12cos^2x=0$

[ocean seal]

Akash Kumar

[slow wasp]

is it right Hope so?

@alpine sable sorry for Ping

okay I get it

wait I forgot F*ck

[slow wasp]

it's in a^2-b^2

I got x = ±0.866

[alpine sable]

how did you get 8.66

[slow wasp]

well 9-a^2+0

used quadratic equation

[alpine sable]

nah ur tryna get x

[slow wasp]

±sqt(3)/2

It's 30

[alpine sable]

yes cosx is +-sqrt3/2

so there should be 2 solutions

since 0<x<180

[slow wasp]

It's ±30

so It's 30

[alpine sable]

no

ill actually draw a graph

[slow wasp]

okay?

BTW help me to seperate

I didnot get you

[alpine sable]

now u can actually see that u will get 2 solutions

[slender gull]

This is more or less what I meant.

[slow wasp]

ah yes

pi/2 & pi

I see

[alpine sable]

wait no

[slow wasp]

bruh ~ _ ~

[alpine sable]

i shouldnt have added pi/2 and pi

its confusing

lemme delete

[slow wasp]

IK the values

Pi is 180

pi/2 is 90

[alpine sable]

i thought you were saying that the answer was pi/2 and pi

[slow wasp]

I'm saying in radians 😂

[alpine sable]

you have to get the answer now

[slow wasp]

It's pi/6

[alpine sable]

and?

[slow wasp]

-pi/6

[alpine sable]

look at the image

the red lines

[slow wasp]

It's -pi/3 or -pi/4 stmg

In negative

[slender gull]

@slow wasp -pi/6 would imply 11pi/6, which isn't what you want to have.

[slow wasp]

sorry to keep negavtive symbol

[slow wasp]

Yea

[slender gull]

Basically you're trying to solve the two cases separately.

First solve cos(x) = sqrt(3)/2

You get pi/6, yeah?

[slow wasp]

okay so for 12 should I divide by 3 & 4 or 6 & 2 or 1 & 12?

[slender gull]

Wdym

[slow wasp]

I'm making A^2-B^2 into (A+B) & (A-B)

[slender gull]

Yeah sure.

[slow wasp]

yup

[slow wasp]

umm which is suitable BTW?

[slender gull]

Doesn't change it at all. You can divide by anything you'd like. But I guess 12 should be good.

But I don't see the point, you already did that.

When you got +-sqrt(3)/2

[slow wasp]

wait It's in 9-12cos^2x form

[alpine sable]

hopefully this can help

[slow wasp]

achaa

alpha + beta = pi

[alpine sable]

u already got alpha

[slow wasp]

we need beta

[alpine sable]

alpha=pi/6

[slow wasp]

yes

[alpine sable]

now get beta

[slow wasp]

beta it will be -pi/4 or smtng?

[tacit arch]

Use this

[slow wasp]

how?

[tacit arch]

plug in alpha

[slow wasp]

okay

I get it

pi/6 + beta = pi

pi-pi/6

beta = 5pi/6

[slender gull]

That's right.

[slow wasp]

@alpine sable beta = 5pi/6

5*180/6

I got angle as 150

[alpine sable]

great

[slow wasp]

Okay so the angle are 150 & 30

@alpine sable BTW if u don't mind could you show me the working

[alpine sable]

i didnt do any working lmao

[slow wasp]

Thanks I get it now

.close

[lone heart]

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[leaden crescent]

I have no idea how to even start

[mortal trellis]

we know that the product of these matrices is the identity matrix

[marsh rapids]

That's enough equations

[leaden crescent]

ah okay

so do I just multiply and set equal to identity matrix?

[mortal trellis]

yes

[leaden crescent]

okay that was easy what the

thank you guys very much

I was so confused

.close

[lone heart]

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[alpine sable]

are these 2 functions not the same?

i jsut rewrote it

[marsh rapids]

Not as many x^2

[alpine sable]

i combined 3x^2 with -x^2

[marsh rapids]

Should be +2x^2

[alpine sable]

ohhh mb

h should be the derived function of f

but it dosent seem to be correct

i used the partial rule thing

f'(t) X g(t) + f(t) X g'(t)

did i do something wrong

[marsh rapids]

Should be -2x

Also you can check that on desmos or Wolfram

[alpine sable]

ohh mb again ty

.close

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[harsh nimbus]

<@&286206848099549185>

[vale wigeon]

write down the parameterization.

then take its partial derivs wrt both parameters

[harsh nimbus]

what is r?

[slender marten]

It's the position vector for every point on the surface.

[lone heart]

@harsh nimbus Has your question been resolved?

[harsh nimbus]

ok

i am confused on how to parametrize this

is it 4sin(phi)cos(theta)i+4sin(phi)sin(theta)i+4cos(phi)k

[slender marten]

Yes.

$\vec{r} (\theta, \phi) = \langle 4\sin \phi \cos \theta, 4\sin \phi \sin \theta, 4\cos \phi \rangle$.

[ocean seal]

stabulo

[slender marten]

You can now calculate the cross product after computing the required partial derivatives.

[harsh nimbus]

yeah thanks it worked

very weird answer

but works

.close

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[wild dove]

hey guys i feel lost right now trying to figure out this problem

[wild dove]

i have no clue of what to do

i am thinking ouf using sigma but i have never learned it so i dont know what to do

plz help

[remote heron]

how many lionfish are there the first year?

[wild dove]

7000

[remote heron]

how about the second?

[wild dove]

7000 x 1.65

[remote heron]

and the third?

[wild dove]

7000 x 1.65 x 1.65

[remote heron]

how about the fourth

[wild dove]

Hmm

7000 x 1.65n

[remote heron]

youre on the right track but simplification error

[wild dove]

N-1

No but then 1 will be 0

Hb 7000 + 7000 x 1.65(n-1)

No

That doesn’t work

[remote heron]

$7000 \cdot (n-1)1.65 = 7000 \cdot \underbrace{1.65+\dots+1.65}_\text{n-1 many}$

[ocean seal]

jan Niku

[remote heron]

but you want $7000 \cdot \underbrace{1.65 \cdot \dots \cdot 1.65}_\text{n-1 many}$

[ocean seal]

jan Niku

[remote heron]

what can you use for repeated multiplication?

[wild dove]

Exponent?

[remote heron]

[wild dove]

So 7000 x 1.65^(n-1)

[remote heron]

is it true in the first year?

[wild dove]

I think so

Because anything yo the 0 power is 1

[remote heron]

so youre almost done with A

you should write a nicer definition IMO just to be sure its clear to yourself since u gotta use it a few more times

something like $f(n) = ...$ is the number of lionfish after $n$ years

or whatever

[ocean seal]

jan Niku

[wild dove]

Oh

f(n) = 7000 x (1.65^(n-1))

Is that part A?

[remote heron]

as long as you can show all the work

[wild dove]

ok perfect

part b is just plugging it in

f(6) = 7000 x (1.65^(6-1))

= 85609

and is part c just f(n)=7000(1.65^(n-1)) - 1300(n-1)

.close

[lone heart]

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[random mica]

Hello, how do you prove it for power 3 please ?

[random mica]

as far as i can go i just found f g f g = I

[heady pollen]

f^2=I
we call such f involutions

we have given:
$$f \circ g=g \circ f$$

[ocean seal]

~Martin

[heady pollen]

$$f^2=I$$
$$f \circ f=I$$
$$\implies f=f^-1$$

[ocean seal]

~Martin

[heady pollen]

so we know that f is it's own inverse

the same goes for g

$$(f \circ g)^{-1}=g^{-1} \circ f^{-1}=g \circ f=f \circ g$$

[ocean seal]

~Martin

[heady pollen]

so we have proven that f.g is also an involution

saying that
$$(f\circ g)^3=I$$
implies that
$$(f\circ g)^2(f\circ g)=I(f\circ g)=(f\circ g)=I$$

[ocean seal]

~Martin

[heady pollen]

this would imply that $$f \circ g^-1$$

[ocean seal]

~Martin

[heady pollen]

which is not always true

which contradicts the statement

so i must have made a mistake

but i cannot find it D;

[random mica]

thanks anyway, power 2 was easy but power 3 is a mountain

[heady pollen]

ok i am pretty sure the statement is false

[random mica]

f g power 3 is not equal to identity ?

[slow hound]

its difficult to prove something that isn't true

[random mica]

serge lang is a great mathematician, you think he did it on purpose to ask to prove something false and being stuck because is impossible

?

[slow hound]

$(f \circ g)^3 \iff f = g^-1$

[slow hound]

isn't he known for trolling

[heady pollen]

so we just found 2 mappings from S to S which commute such that the statement is false

im not sure what the standard notation is so i explained mine

[random mica]

oh

[heady pollen]

also since f.f=I and g.g=I but f!=I and g!=I in general
I would expect (f.f)^n=I for all even n

[random mica]

the statement is true for even integer and false for odd integer i guess then

[heady pollen]

🙂

[random mica]

thanks you !

[heady pollen]

you're welcome

[random mica]

maybe

@heady pollen what is the =:

[heady pollen]

a:=2
define a as 2

[random mica]

is not like a = 2 ?

[heady pollen]

yeah but i like to use := since that's what i have been taught
i guess you can use both

if we say f.g=2=a
then someone could see that as
f.g=2 what happens to equal to a

[random mica]

what is the motivation behind it

[heady pollen]

but if we say 2=:a we say we define a as the result of f.g

i guess it looks cool as well

also if we say f.g=u then someone might ask "what is u? where did that come from?"
if we say f.g=:u or u:=f.g then it is clear that we just defined u so others don't get the impression they forgot some u a few lines before

[random mica]

oh

i see the thing

thanksyou

is equivalent to "let X = f.g"

[lone heart]

@random mica Has your question been resolved?

[lone heart]

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[marble saffron]

d

[marble saffron]

@inland vessel

[inland vessel]

well... this is interesting

[marble saffron]

okay

so

whats your question again?

@inland vessel

[inland vessel]

.... yeah i dont have a question since im lost

[marble saffron]

okay

lets start from the beginning

with equivalence

and proposition

tell me

what is a proposition

[inland vessel]

A statement that can either be true or false

[marble saffron]

correct

[inland vessel]

An equvilence is "If Q is true then A is true"

for example

[marble saffron]

its more than that

[inland vessel]

well you or eric framed it that way so i gone with that

[marble saffron]

it also means that if Q is false then A is false

this is important

[inland vessel]

So: "If Q is true then A is true, but if Q is false then A is false"

[marble saffron]

yes

that is an equivalence

so now example

a+c=b is equivalent to b-c =a

does that make sense?

@inland vessel

[inland vessel]

in a way

[marble saffron]

is it confusing

[inland vessel]

in a way it is

[marble saffron]

why is it confusing

[inland vessel]

If a+c=b is true then b-c=a is true

well now its less confusing

[marble saffron]

okay

[inland vessel]

what else?

[marble saffron]

this is thr truth table for it

[inland vessel]

is this a formula?

[marble saffron]

p is the same as (a+c = b)

[inland vessel]

for all configurations that are if-then statements

?

[marble saffron]

q is the same as (b-c = a)

T means true

F means false

[inland vessel]

ik

but

is this a formula or a patterm for all configurations of statements that are if-then statements

[marble saffron]

this is the truth table for equivalence statments

[inland vessel]

ok now that's less confusing

[marble saffron]

equivalenve is the same as "if and only if"

[inland vessel]

but must i do "possible or true"?

or is it only true

and false

[marble saffron]

it doesnt matter, different books write it differently

just stay consistent

thats the most importent

[inland vessel]

that's the confusing part

[marble saffron]

remember

with equivalence statements

you are checking the proposition

so is it true that, Q is true if and only if A is true

[inland vessel]

and what do i do after?

is that a question?

oh

[marble saffron]

the proposition is kind of a question

that you answer

using

the truth table

[inland vessel]

So im going back

"If x,y are integers, then x+y produces an integer"

this is true

[marble saffron]

this is an if then statement

[inland vessel]

"If x,y are integers, then x+y does not produce an integer" is false

[marble saffron]

that is an impication

[inland vessel]

wot

[marble saffron]

not an equivalence

[inland vessel]

wait

[marble saffron]

implication is not the same thing as equivalence

[inland vessel]

this is only "if"

right?

no then

[marble saffron]

equivalence is if and only if

[inland vessel]

oh

[marble saffron]

implication is if, then

lets go back to equivalences

[inland vessel]

ok

[marble saffron]

look at the first row

how do you interpret it?

[inland vessel]

So for example:

"If x,y are integers, then x+y does not produce an integer" is an implication, because it has if-then.

oh

nvm that's a.... equivilence (the table)

[marble saffron]

so you are not completely correct with how you interpret it

[inland vessel]

"P is Q only if"

something like that

[marble saffron]

listen to me

in the first row it is true that x,y are integers

thats the first row and first column

in the second column

it is true that x+y is an integer

and in the last column

is it possible from this information that the first two columns are equivalent

the answer is true

[inland vessel]

yes

so

[marble saffron]

now try to interpret the second

row

[inland vessel]

Should I write

[marble saffron]

yes

do it

[inland vessel]

"x,y are not integers if x+y are integers"

maybe im doing this wrong

as usually

[marble saffron]

that is correct

but

youre not finished

[inland vessel]

"x,y are not integers if x+y are integers" impossible

[marble saffron]

what is impossible?

[inland vessel]

"x,y are not integers if x+y are integers"

[marble saffron]

no

[inland vessel]

... ok then

🤷

then its a flop

[marble saffron]

ill tell you

listen

are you here?

[inland vessel]

yes you told me to stop

lol

[marble saffron]

okay listen

what is impossible is that(if x,y are integers then x+y is an integer)

[inland vessel]

that's not impossible

2+3 , 2+5 , 2+6

they all become integers

[marble saffron]

yes but that statement is impossible if x,y are not integers and x+y is an integer

[inland vessel]

but you didn't say that in your previous statement

so thats why i objected

[marble saffron]

(if and x,y are integers only if x+y is an integer) is impossible if (x,y are not integers and x+y is an integer)

does that make sense?

[inland vessel]

in... a way???

now we're back to using if statements

[marble saffron]

that was a mistake

sry

[inland vessel]

So

(x,y are not integers if x+y is an integer)

This is your proposition? or just the equvilence

[marble saffron]

no

[inland vessel]

uhm

then idk then

[marble saffron]

you can write the proposition in two ways

[inland vessel]

(if and x,y are integers only if x+y is an integer) is your proposition?

or is that rather, your statement

itself

[marble saffron]

( x+y is an integer if and only if x,y are integers?) or (is x,y are integers equivalent to that x+y is an integer)

ye

ye its the statement

[inland vessel]

(if and x,y are integers only if x+y is an integer) Is your statement, ok.

So

[marble saffron]

oh yea cause were talking about equivalences

im mixing them up

[inland vessel]

sm

h

im

säs

[marble saffron]

there i fixed it

[inland vessel]

(x+y is an integer if and only x,y are integers)

(x+y is an integer if and only x,y are integers) is impossible.

[marble saffron]

do i need to explain it better?

listen

[inland vessel]

well this is more and more confusing

[marble saffron]

when we are doing truth tables

we are acting as if

[inland vessel]

my god

[marble saffron]

we dont know whether the proposition is impossible or possible

(x+y is an integer if and only x,y are integers)

and we find out

by doing the truth table

[inland vessel]

ok

[marble saffron]

so you should think of that statement as neither true nor false

yet

[inland vessel]

so what's after

[marble saffron]

okay

you take every possiblitity

that x,y are integers or not

ect

and see if it corresponds to an equivalence

does that make sense?

[inland vessel]

(x+y is an integer if and only x,y are integers) -- statement

(x,y are integers and x+y is integer) -- Possible?

in this case ^

[marble saffron]

first is correct

wait

[inland vessel]

lol

[marble saffron]

second is wrong

[inland vessel]

wat

[marble saffron]

there should not be "then"

just "x,y are integers and x+y is an integer"

not "then"

yes now, what is possible?

[inland vessel]

oh...

(x,y are integers and x+y is integer) -- These conditions are possible if (x+y is an integer if and only x,y are integers).?

[marble saffron]

which one is it?

just answer the question

what is possible?

[inland vessel]

idk

[marble saffron]

in that case

[inland vessel]

(x,y are integers and x+y is integer) <-- this is possible

[marble saffron]

no

[inland vessel]

well then idk then

[marble saffron]

in that case the proposition is possible

so (x+y is an integer if and only if x,y are integers)

this is possible then

[inland vessel]

Proposition: (x+y is an integer if and only x,y are integers)

The proposition is possible if (x+y is an integer if and only if x,y are integers)
The proposition is not possible if (x+y is an integer if and only x,y are not integers)

[marble saffron]

no if (x,y are integers and x+y is an integer) then the proposition is possible, the proposition is "(x+y is an integer if and only if x,y are integers)"

[inland vessel]

then idk

idk what to do

[marble saffron]

lets make it more abstract

A is equivalent to B

this is the proposition

okay?

[inland vessel]

So:

(x+y is an integer if x,y are integers) is our proposition

[marble saffron]

no

forget

that

just think of A and B

okay?

[inland vessel]

ok?

[marble saffron]

so again A is equivalent to B (this is the proposition)

okay?

[inland vessel]

yes

[marble saffron]

now if A is true and B is true, is it then possible for the proposition to be true?

[inland vessel]

sure? but im not sure if i do particularly understand the example

[marble saffron]

A is just something that can either be true or false, B is also something that can be true or false

and the equivalence says that if A is true then B must also be true and if A is false then B must also be false

[inland vessel]

A is true if and only B is true is our proposition??? im so confused

rn

[marble saffron]

yes

[inland vessel]

woah woah woah

then

If A is true then B is also true. Is a statement.

Is our equvilence

[marble saffron]

no the proposition is the equivalence

[inland vessel]

....

dude

[marble saffron]

if and only if

is the same

as equivalence

[inland vessel]

now im extreamly confused

[marble saffron]

why

[inland vessel]

"and the equivalence says that if A is true then B must also be true and if A is false then B must also be false"

you're saying "if" now

[marble saffron]

thats correct

[inland vessel]

If A is true then B is also true. Is a statement.

So this is our statement

[marble saffron]

no

[inland vessel]

ok, so then i dont know

[marble saffron]

A is true if and only if B is true

[inland vessel]

A is true and only if B is true

Ok so that's our fuckin proposition

[marble saffron]

yes

only if

[inland vessel]

so now.

[marble saffron]

now

we want to know if the proposition is correct

so

[inland vessel]

A is true and only if B is true

1. If A is true and B is true, then our proposition is possible.
2. If A is true and B is not true, then our proposition is not possible.
   3.If A is false and B is true, then our proposition is not possible.
   4.If A is false and B is false, then our proposition is possible.

[marble saffron]

we look at all possibilities

[marble saffron]

correct

good job

[inland vessel]

where

[marble saffron]

number them

3 is not possible

the rest is correct

good job

[inland vessel]

A is true and only if B is true -- proposition

1. If A is true and B is true, then our proposition is possible.
2. If A is true and B is not true, then our proposition is not possible.
   3.If A is false and B is true, then our proposition is not possible.
   4.If A is false and B is false, then our proposition is possible

so there is a pattern

yes?

[marble saffron]

yes

[inland vessel]

ok

[marble saffron]

this is the pattern of an equivalence

for an implication its different

[inland vessel]

but its the same concept

proposition and then condition

but this time our proposition must be an implication? @marble saffron

[marble saffron]

this is the pattern for implication

[inland vessel]

Proposition: If A is true then B is true is an implication

right?

[marble saffron]

yes

correct

[inland vessel]

So therefore:

[marble saffron]

also

[inland vessel]

?

[marble saffron]

just to add

if A is true then B is true, and if B is true then A is true, then A and B are equivalent

so an equivalence is an implication in both directions

[inland vessel]

Proposition: If A is true then B is true

A is true and B is true, then our proposition is possible
A is true and B is false, then our proposition is impossible
A is false and B is true then our proposition is possible.
A is false and B is false then our proposition is possible.

for implication

[marble saffron]

yes

[inland vessel]

Applying patterns:

If x,y are integers then x+y become integers

Conditions:

1. x,y are integers and x+y are integers , then our proposition is possible.
   2.x,y are integers and x+y are not integers, then our proposition is impossible.
2. x,y are not integers and x+y are integers, then our proposition is possible
3. x,y are not integers and x+y are not integers, then our proposition is possible

[marble saffron]

correct

good job

[inland vessel]

this is what happens when the book assumes things you don't know

💀

[marble saffron]

als

also

[inland vessel]

?

[marble saffron]

lets go back to A and B for a second

[inland vessel]

?

[marble saffron]

lets imagine there are 2 propositions

if A then B, and also if B then A

if both of these are true

then that is the same as saying

A if and only if B

2 implications in both directions is the same as an equivalence

[inland vessel]

oki

[marble saffron]

alright

[inland vessel]

do i need to understand the pattern

or do i follow the pattern

[marble saffron]

which one?

[marble saffron]

you should understand them

[inland vessel]

because so far i can only follow them

with minimal understanding

[marble saffron]

just continue reading the book i guess

[inland vessel]

like do i need to

memorise it

that's the thing

[marble saffron]

.close

[lone heart]

Channel closed

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[carmine sonnet]

Anne plans to retire at 65, and wants a perpetual monthly income of $4000 from then on. Knowing that market fluctuations happen, she invested in a fund that pays the Inflation Index + 6% per year to guarantee she won’t lose money with the devaluation of the currency in relation to inflation.

Anne calculates how much the 6% coupon is equivalent to monthly and applies the perpetuity formula, thus obtaining an estimate for the amount she needs to have saved to reach her goal. This amount will be approximately:

a) 1 million
b) 900 thousand
c) 820 thousand
d) 740 thousand

[carmine sonnet]

Ok so basically I’m having a tough time figuring out how I should approach this question even though it literally explains to me how lol. Can someone please enlighten me? I guess I should figure out which one of those amounts Anne should have in order to have a perpetual income of $4000/mo? But how?

[lone heart]

@carmine sonnet Has your question been resolved?

[lone heart]

@carmine sonnet Has your question been resolved?

[lone heart]

@carmine sonnet Has your question been resolved?

[carmine sonnet]

<@&286206848099549185>

[remote heron]

sounds like she needs the interest to be 4000 /mo

[carmine sonnet]

Basically I am supposed to make "4K" into the annual amount

so 48k

and make the 6% into the decimals

So
PV = C / R
48,000 / 0.06 = 800,000

I was doing it wrong because I was doing 4000/6

omg

.close

[lone heart]

Channel closed

Closed by @carmine sonnet

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[alpine sable]

random question, but is there any way to calculate the tangents lines of a circle or ellipse without using calc? i know you can calculate the tangent line of a circle without calc but only if you are given a point on the circle and not anywhere else.