help-0

[woeful pulsar]

maybe try it out with various a and b

b= 1, 2, 3, 4 for example

and a=3.14156

[jade peak]

b=1 --> 3.10

b=2 --> 3.14

u were right

3 is also 3.14

that is due to limit of display

3

it does just round based on decimal

thanks...

[sour kelp]

someone told me a graph that is symmetric with the x axis can not be a function. So what about f(x)=0?

[vale wigeon]

that's the one exception

unless it's the graph of the zero function, it's going to fail the vertical line test

[sour kelp]

ok, thank you

[alpine sable]

Hey, I have a question, what is x=log 0 , base e?

[rigid smelt]

undefined

[alpine sable]

why

[rigid smelt]

because there is no x such that e^x = 0

[alpine sable]

cant we even use*i , for a complex solution or is there not even a complex solution

[rigid smelt]

again, it is undefined

[alpine sable]

oh,

[rigid smelt]

if there were i would have said its a complex number or something else

[alpine sable]

ok

thx

[vale wigeon]

@alpine sable no, there is not even a complex solution.

e^z can return every complex value except 0

[alpine sable]

yes

[rigid island]

hello

question about logs

https://media.discordapp.net/attachments/573108797527031829/871330938834014278/unknown.png?width=953&height=451

why doesn't my method work

the method on the left is the correct working, however, why doesn't my method work?

[jagged imp]

who says your method doesnt work?

its incomplete so far but its not wrong

[rigid island]

i tried it

but it doesn't work out to be the right answer

[jagged imp]

uh

[woeful pulsar]

why did you write log(4^x)

[jagged imp]

the working on the left is diff to the q

yeah what element said just saw that

[rigid island]

i'm not sure , that's what the worked example said

[woeful pulsar]

check if your paper has a printing error

because the question is not 3^(2x+5)=4^x

[rigid island]

there is a printing error

my fault sorry i didn't think to check it

[woeful pulsar]

yeah there probably is

[rigid island]

the worked example has 4^x

however the actual question does not have 4^x

thanks

[merry coral]

I created an algorithm to look at the winning and losing streaks of ETH on the 1-hour chart.

Here are what they look like plotted. X being the streak (-4 means 4 negative closes in a row, 4 means 4 positive closes in a row)

The amount of winning streaks is higher than losers because the market was in an uptrend.

So, question:

What's the most accurate parabola or distribution that shows this? (5159 inputs checked, let me know if you need numbers)

[bleak hearth]

can some o1 help me do this question please

[vernal igloo]

These are contradicting statements. It says that every point on the gold line is a solution to the equation
y = 1/2x + 3
​
and every point on the green line is a solution to y = x + 1 So, the only point that's a solution to both equations is the point of intersection
??

There's no solution here. y depends on what x is, so any point on the line works.

There's not something called a "solution" here.. unless I am not understanding something

if there were equations like
2x + 3y = 50
4x + 9y = 43
then here there is a solution

[crisp grove]

do you know Cayley Hamilton theorem?@bleak hearth

[bleak hearth]

no

[crisp grove]

oke then computer pA+qI

[bleak hearth]

ik how to multiply divde matrics

[crisp grove]

and make them equal with A² elementwise

you'll get 4 equation in terms of p and q and solve them

[bleak hearth]

yea multply by itself

[crisp grove]

yes

computer the sum of pA+qI

and compare

@vernal igloo what seems to be your problem?

[bleak hearth]

ok so for multiplying ig tot (5 4 -4 -3)

[crisp grove]

ok

[bleak hearth]

but i dont know how to make it pA+qI

[crisp grove]

what's pA+qI?

[bleak hearth]

2 matrices

I is 1001

[crisp grove]

yes

you know A

[bleak hearth]

yea we just solved it

[crisp grove]

so what's pA? what's qI and what's their sum?

[bleak hearth]

?

ohh

gimme a sec

wait do i use A or a^2 when adding

[vernal igloo]

They say there's only one "solution" but in that case there isn't.

in slope intercept form, there's no "solution". y depends on what x is.

there's only a "solution" when it's something like 2x+6y = 45

like, "the only point that's a solution to both equations is the point of intersection" makes no sense there

[crisp grove]

why isn't there a solution in SI form?

[vernal igloo]

because you can pick any x, and find any y

you're not trying to find something

[bleak hearth]

umm i did what u said and got

[crisp grove]

all the slope intercept form, or ther form are just the representation, the line doesn't change

[bleak hearth]

(4 2 -2 0)

[crisp grove]

u get the same solution in every form

[merry coral]

lol what disribution is this

[crisp grove]

@merry coral Normal?

[bleak hearth]

ohh i can shsow it like this
(4 2)
(-2 0)

[merry coral]

ooo

[crisp grove]

@bleak hearth what's that?

[bleak hearth]

u said to add a and I

[vernal igloo]

like, "The only point that's a solution to both equations is the point of intersection" makes no sense there when they also say that every point on the gold line and the green line is a solution

[crisp grove]

no

they didn't say that

they said solution of L1 is gold, L2 is green

[vernal igloo]

every point on the gold line is a solution for the first equation

ye

and l2 for green

[crisp grove]

and the only point that is solution to both is the intersection

[vernal igloo]

how is it a solution when you're not trying to solve something??
in slope intercept form, you can just pick any x, and find any y, and you get your answer.

[alpine sable]

Can anybody tell me how he gets pi/2 here as a value that makes the function = to 0? I get the other two answers but not pi/2 UPDATE: Nevermind, he just added 2pi

[crisp grove]

ya but that method only gives the point on that line

[bleak hearth]

Ryuzaki how do i represent it as linear?

[crisp grove]

for ex y=x/2+3 will give u point in gold line only

if u want to find a point that both lies on gold and green as well, you have to look for common points in green and gold, whic is, in this case the intersection

[crisp grove]

you are supposed to find pA+qI elementwise

[bleak hearth]

when doing A+i do i use A^2

[vernal igloo]

calling it a "solution" is just weird unless the intent is to find one point that's both on the green and gold line

[crisp grove]

for example
p(1 2; 3 4) + (1 0; 01) = (p+1 2p; 3p 4p+1)

do similar to this with pA+qI

[bleak hearth]

ahh

ok gimme a sec

[crisp grove]

@vernal igloo that is a solution if the system
y=x/2+3
y=x+1

these are called system of linear equations

[vernal igloo]

yeah, I get that

well

[vernal igloo]

i might have got confused a lil bit, but i was more used to look at systems of equations like:

2x + y = 65
5x+6y = 90

[crisp grove]

equivalent

[vernal igloo]

because in here, you cant just pick any x, and find any y.

but in the one you posted, you can just pick any x, and find any y for both of them

[crisp grove]

u can, it requires a little rearrangement

x-2y=-6 is equivalent to saying y=x/2+3

[bleak hearth]

Ryuzaki i did what u said

but what do i equate it 1

2

[crisp grove]

A²

[bleak hearth]

ahhh

[crisp grove]

A²=pA+qI

solve for p,q

[bleak hearth]

ok i now have the values for q and p

@crisp grove

[crisp grove]

?

[bleak hearth]

ok i got it but 1 question @crisp grove why do we quate A^2 to pA +Qi

[crisp grove]

because question says write A^2 in the form pA+qI

so we are equating them and solving for p and q

[bleak hearth]

ahh ok tytytytytytytytyty ❤️

[alpine sable]

Can someone tell me how he manipulates this to remove the square root on the right? I can't quite figure it out:

[gray isle]

basics of combining fractions through addition or subtraction

common denominator etc

[alpine sable]

urgent question

what would the range be of the inverse?

would it be all real numbers or (3,infinity)

[glass lichen]

why urgency?

[alpine sable]

i got a test tomorrow

[glass lichen]

ok.. well range of f^(-1) is the same as domain of f...

[alpine sable]

i agree

by law

but

f(x) has a domain of all real numbers

therefore the range of inverse would be domain of non-inverse

but...

as u can see

no its domain

yeah

[gray isle]

misread

[alpine sable]

all good

so @glass lichen , ur saying this has a range of all real numbers?

[glass lichen]

yes

[alpine sable]

how so? it says its undefined at a certain point

[glass lichen]

I mean desmos also stops it randomly, so Im not trusting what desmos says

[alpine sable]

ok

thank u

[vale wigeon]

dunno i'm def not the person to ask

[halcyon geode]

Unless you're doing a PhD ain't no university program requiring 50/60 hours per week

Actually, I retract my statement cuz I don't know that much about programs outside Europe

Well, IMHO universities over here tend to try to get some resemblance of balanced workload, they tend to fail but not so miserably as to reach 60 hours. I did had a semester where I had 38hours of lectures+exercices, but for the most part it also meant we didn't had to put more than 2-4 hours in the weekend as exercices were done in those sessions

So up to 50,in particular semesters, I could see. But between universities trying to get a more or less standard level (with the whole credit system) and less of a workaholic culture I don't see going at that rate constantly

Unless you're going for 20/20, which is less of a thing over here so your mileage may vary

(to be fair, the only people getting 17+/20 on my program where people that kinda did work on their free time for fun, so maybe that's where the 50/60 hours comes from)

Which country is it?

Yeah no totally

Credits between different programs are not the same

I agree with that same here. But they give some amount of bounding. If the university goes too overboard, students will complain that it's requires significantly more time than whatever amount of credits is supposed to be worth it

Programs do vary, but in my experience is less "this program requires 60 hours of work" and rather "this program will have an 80% fail rate in the first year and then people will have to work 40 hours per week"

mmmh let's put it like this. Over here the med program is one of the hardest on the amount of workload, but each class is actually fairly easy (got friends there). Is just that they cover so much material that they do have 40/50 hours of workload

meanwhile there are certain first year courses on physics and math that are known to be grinders with incredible high fail rates

The thing is, the amount of material is not much, and grinding it wouldn't improve that much the results

rather, students just need to get more and more exposure thorugh long process to really get the material

because the exams require working and making proves about things tou haven't seen in class

Dunno if i make sense?

[wanton vortex]

me, someone who is interested in studying physics/math in college and is reading this:

[halcyon geode]

Mind you, i could be totally off mark

(Like, psychology has the same credits, but they probably put like 20 hours each week...)

I wouldn't say the harders, but one of the hardest yeah. They fight all the time with engineering and math/physics about who has it hardest xD

Belgium

The thing is, i do think that med, while being really hard, is also less prone to drop out exactly because most people can grind 40/50 hours for memory if they're motivated enough, which med students tend to be

So i don't think drop rates are the best indicators, in that case first year physics/math would take the crown with 80% drop rates

But....it's also because for a lot of students it will be the first real math physics exposure

When they realize physics is not nice simplifications and woah dude, and that math is not "i enjoy doing a bunch of calculations"

That's the thing, that's subjective

For example, i do think med students put more hours than math and engineering

like, probably for certain

But i don't think math students will win much by studying more, things require time to be really processed

So any more hours than that it will be a waste

Would be, if you could qualify that, and add "correct expectations" "same faculty culture"

Another thing that makes med super hard here is that second year has a limited number of places

so it doesn't matter if you pass, if you don't pass up to a certain spot in your class, you're fucked

which is a load of bullshit, but you know, happens

Which means math student here tend to help each other, med students tend to fucking compete against each other

Also that

Here a lot of people that failed the entrance exam for polytech go into physics and math thinking they'll tend simply transfer

and get thoroughly fucked xD

I have no idea where to get them sorry, it's also university based, so half of them will be in french, half in dutch, dunno if there are english versions

40 yeah, but there is a lot of difference betwen 40-45 to 50-55. because it mostly means you still get a semblance of personal life. 44 hours is 8h/day on weekday +2 hours saturday/sunday. Hard, lots of work, still allows you to have a life

after that, each freaking hour on top of that is a total pain

But yeah, i had 38h of lectures+excercies in my first semester and the third one

[lofty gorge]

To chip in I've had 40 ish hours of work a week in the UK.

[halcyon geode]

studying so hard that you dilate spacetime

Math physics minor

[lofty gorge]

Average

Maths

[halcyon geode]

But yeah, bottom line, 40 hours is definitely within the average of total work, some semester you might push 45, 50/60 is another level

[woeful pulsar]

looks at my expected weekly workload
70

i overloaded math by 40%

probably that i study at 140% speed

because courses at this level are easy

[halcyon geode]

Do you have the program?

like, what goes inside/exams or stuff like that?

[noble sinew]

50h expected work each week is pretty standard in Europe iirc

upper limit for yourself or expected on a course?

[halcyon geode]

yeah, still you're not getting multivariate calculus if the curriculum says "single variable calculus" :p

[noble sinew]

like my expected work is 50h each week (I'm not actually spending that much time) but that just depends on each person

undergrad

[halcyon geode]

same thing over here, i'm assuming the program is rigorous :p

[alpine sable]

i studied 3 h a day and got all high grades on math/physics/algebra but its my first year so it could be cus its easier material. it rly depends on the person (and yes its college

i think as u said w lectures n stuff its not like you /have/ to dedicate sm hours to study? cus you are also learnin those hours of classes

i did online school so i didnt rly have lectures

videos or stuff i watched were included on those hours

[heavy spear]

that is why ii am trying to finish ap calc ab and calc bc

in highschoo,

also take stats in 12th

in 10th rn

[alpine sable]

i think rather about time is u rly have to be jn the mindset to focus during that time

3h isnt a lot so i was able to turbo focus and get it all in

[halcyon geode]

states or europe?

[heavy spear]

states

[halcyon geode]

I meant starberry, i knew you were in the states since the ap thing is from there xD

[alpine sable]

oh im from argentina HAHA

studying at university of buenos aires uba

[halcyon geode]

programa de mates?

[alpine sable]

not precisely, but ppl who study math do the same programme yea

[noble sinew]

how tf do you not use more than 3h lol - I have 12h lectures each week+3 assignments each week + self study + excercises

[halcyon geode]

Is a bit different tho, here there is the 3+2 system, argentine is the 5 year program no?

[alpine sable]

yes! 6 years

[halcyon geode]

In south america we tend to have a year to put people up to speed cuz our schools suck ass

[noble sinew]

ah lol

[halcyon geode]

I don't know about argentina in particular

[alpine sable]

i dont have lectures and i didnt have to give in assignments (i still did em

[halcyon geode]

But that's my experience back home and friends from colombia

[alpine sable]

cus i took online classes

[heavy spear]

lol

honestly i can blame online classes for ruining my life xd

cause i dont understand anything i learned so im strugling this year

but lifes life

[alpine sable]

online classes jus means u gotta self study

sadly:(

[noble sinew]

Atleast you don’t have my prof - he was new at the course and decided he wanted to make the exam totally different and harder. Result? 50% of class failed the exam (around 80 ppl).

[heavy spear]

wait a min if u take calc in highschool and pass you dont need to in college from my understanding that iis the main reason im taking calc xd

[halcyon geode]

Definitely not true

You neeed a strong background of algebra, if you are confortable with the practical aspects of limits and derivatives is a big plus too

[alpine sable]

you should probably continue this discussion in #math-discussion or the like

[halcyon geode]

True, sorry

[heavy spear]

true xd

[alpine sable]

literally why would he do that HDJD

people be like: imma become a prof to shit these students!

[noble sinew]

Lmao ye idk - however the Uni decided that the questions weren’t solveable in the given timeframe and offerered everyone another exam if they wanted to

[alpine sable]

hell yea thats epic!

[heavy spear]

wait a min does anyone have a idea what they could mean by odd or even

[vale wigeon]

@heavy spear have you ever worked with the concepts of "odd function" and "even function"?

[heavy spear]

no

[vale wigeon]

and you haven't been introduced to them in class either?

[heavy spear]

no

[vale wigeon]

then you are being asked a question which you don't have the right tools for

[heavy spear]

oh rip

i guess the internet is going to help me

[vale wigeon]

i mean, you're being given homework on something you haven't been taught.

unless you were expected to learn about it yourself? in which case you should study the section(s) of your textbook which talk about odd and even functions.

[heavy spear]

we dont have a text book

it is so stupid

like i have to use khan academy to learn concepts since the teacher is kinda lazy and it is inperson learning not even online

[vale wigeon]

you should talk to your teacher and make them actually do their job i think

[heavy spear]

ik im pretty sure the teacher hates me since i ask about 20 question on the hw every day

lmao

some times she just gives me answers

withought explaining

[vale wigeon]

yikes

[heavy spear]

ye

[vale wigeon]

i mean ok like

[heavy spear]

well i am tryign my best so

[vale wigeon]

i could either tell you the actual definition

of odd and even functions

but this will take some time getting used to

[heavy spear]

ok

[vale wigeon]

or i could tell you a shortcut trick which works for this exercise in particular but won't give you a true understanding

[heavy spear]

nah i want to understand it cause ill prob need it for the test or somthing

[vale wigeon]

okay

we say that a function f is odd if f(-x) = -f(x) for all x, and we say it is even if f(-x) = +f(x) for all x

in terms of graphs, odd functions have 180° rotational symmetry about the origin while even functions have reflection symmetry about the y-axis

examples of even functions include: |x|, x^2, 1/(x^4 + 1), cos(x), etc.

examples of odd functions include: x, x^7, sin(x), 1/x^3, etc.

[heavy spear]

k

i think that first part should help me get the answer to the question just plug and chug lmao

[vale wigeon]

it is just plug and chug yes

[heavy spear]

thx btw

[vale wigeon]

a lot of students find themselves confused by it

which is why i was initially apprehensive about giving it to you

[heavy spear]

are you a teacher you said students ?

[vale wigeon]

i'm not a teacher, though i do tutor one on one occasionally

i mean students in a broad sense

like, school students who come here

[heavy spear]

nice

[astral dagger]

Hello, I was trying to solve a question that defined a piecewise function f(t) and found some answers that I don't know if are correct or not. Either way, what I want to know is if there's a proof to this:

[crisp grove]

proof of?

[ocean seal]

Ryuzaki

[astral dagger]

indeed, I tried to solve another related question that the answer doesn't seem to satisfy it

like, maybe it has to do with how the function was defined

[crisp grove]

this statement is indeed true, u sure what you did was right

[astral dagger]

,tex (f(x)=\begin{cases}1,~\text{if}~0\leq x< 1\0,~\text{if}~x\geq 1\\end{cases})

[ocean seal]

SubGui

[astral dagger]

but it seems that

(f\ast f=2-x,~\text{if}~1\leq x\leq 2)

[ocean seal]

SubGui

[astral dagger]

if it indeed satisfy the statement, then I was just using it wrong

[crisp grove]

how's f*f /=2-x?

[vital sleet]

y did the Y(5) change into 10?

[vale wigeon]

Y(5)?

i don't see a Y anywhere in this picture

[twin nimbus]

I believe he means V(5)

[vale wigeon]

did you mean V(5)?

@vital sleet

[vital sleet]

oops

[vale wigeon]

V(5) is 10, as you can calculate for yourself.

[vital sleet]

yes

wait what

[vale wigeon]

V(t) = t^3 - 6t^2 + 35

[vital sleet]

mhm

[twin nimbus]

\begin{align*}
V(t) &= t^3 - 6 t^2 + 35 \
V(5) &= (5)^3 - 6 (5)^2 + 35 \
&= 125 - 150 + 35 = 10
\end{align*}

[vale wigeon]

V(5) = 5^3 - 6 * 5^2 + 35

[ocean seal]

OmnipotentEntity

[vital sleet]

ohhhhhhhhh

im dumb

ok thx

[twin nimbus]

Not dumb.

just learning

[vital sleet]

lol

ez

[twin nimbus]

Is there an established inverse function for $y = x - \sin x$?

[ocean seal]

OmnipotentEntity

[twin nimbus]

I know it's not elementary.

But is there a special function? Something with properties I can reference somewhere?

[warped phoenix]

I know how they solve A because I know the formula

but I don't really know what anything means

could someone ELI5? google's not being that helpful LOL, what exactly is the margin of error? For a., it's +/-34.81, what does that 34.81 mean

[twin nimbus]

The 34.81 is the amount above and below you have to go to make a range where there's a 50% chance the true value falls within the range

[warped phoenix]

50% chance that what value falls within that range?

any given number? or the 1800

or the 7950 😅

[pine cipher]

someone please help 🥺

[warped phoenix]

channel in use

[pine cipher]

😭

[twin nimbus]

So if you have an average loan value of $7950, and you pick someone randomly within the population, what is the probability that this person will have a loan of exactly $7950?

Very low, surely.

[warped phoenix]

ohhhhhh

ok i follow

[twin nimbus]

What is the probability that person will have a loan between $7900 and $8000? Higher.

Margin of error gives us a way of formalizing it.

Also, I'm not certain your values are correct for the record.

[warped phoenix]

wdym

for the z-score?? thats what was given to us in the question, idk what a z-score is but my teacher said we dont need to know cuz we'll learn it later

but everything else you see is what my teacher wrote out and said was correct

[twin nimbus]

the margin of error is the standard deviation * the z score

I don't think you divide by sqrt(n) here.

that should have already been done for you in calculating the standard deviation

[warped phoenix]

thats what my teacher said to do :/

so when the confidence level is 50% they want to know the probability of having a loan between, 3975 and 11925?

since thats 50% and 150% of 7950

that sounds wrong hahaha

[twin nimbus]

No, use the stdev

.67 * 1800 = 1200

[warped phoenix]

what does the standard deviation mean

we're told that it's 1800

[twin nimbus]

It's the square root of the variance.

[warped phoenix]

does that mean that most loans will be 1800 more or 1800 less than 7950

[twin nimbus]

it means that, on average, the total loan amount will be different from 7950 by 1800

in this case, "on average" is doing a lot of work.

But that kinda gives you a feeling for the idea behind standard deviation

[warped phoenix]

so on average, if i were to pick a random person of the sample, their loan might be 9750 OR 6150?

[twin nimbus]

not quite.

[warped phoenix]

😦

[twin nimbus]

Let's say I choose a loan at random, and its amount is 8000. The difference in this case is 50.

I choose another loan, this time the amount is 10,000. The difference is 2050.

Then I choose yet another loan, this one is 2500. The difference is 5450.

I do this a whole bunch of times, then I take the average.

This is kind of what the standard deviation is trying to do.

The mathematics is different behind the scenes, though, for rather complex reasons that you'll learn about in a college statistics course.

so you get slightly different answers, but they're morally similar.

Does this help @warped phoenix ?

[dapper tendon]

yes pls u can share it!!

[warped phoenix]

1 sec

soooo

the standard deviation of this example means that the typical difference of a loan given will vary by $1800?

so the individual loan someone gets wont be a difference of 1800, but the average difference of the entire sample would be $1800

[twin nimbus]

Yes. And the distribution of that difference is assumed to be normally distributed (which is why you're using a z score)

So there will be more people close and fewer farther away in a very specific sort of sense.

[warped phoenix]

ok so ive got the stdev down, but the margin of error of 34, what does that mean in accordance to this

the deviation is a difference of $1800, does a margin of error of 34 mean that

idek tbh what it could mean

[twin nimbus]

Again, I don't think that the MOE of 34 is correct.

[warped phoenix]

ahahahha thats what my teacher is sticking with ig 😅

but even if its wrong, what does it mean?

that the stdev of $1800 is off by like 34% or something?

idk thats my best guess

[twin nimbus]

It means, that, because your confidence level is 50%, there is a 50% chance that if you selected someone at random, their actual loan value would be in that range.

7950 +- 34

or 7916 - 7984

[warped phoenix]

ohhhhhhhhhhhhhhhhhhhhh

so there's a 50% chance that a random person's loan, when there is a difference of 34, will be within the range of the stdev?

(i think...? 😅 )

[alpine sable]

hi all how would i set up this integral?

[warped phoenix]

channel in use

[twin nimbus]

Let's say you have a bin of balls. And half of them are blue and half of them are red. And you pick a ball and then put it back and shuffle it around each time. You'd get a series of random blue and red ball pulls. You might get 0001000001000111 (where 0 is blue and 1 is red). But each pull has a 1/2 chance of coming up either blue or red.

[alpine sable]

Two angles of a polygon are right angles and every other angle is 120 degrees. Find the number
of sides of the polygon.

can someone help

please

i have an exam tomorrow

pls

[warped phoenix]

channel in use dude

[alpine sable]

wtf does that mean

[twin nimbus]

Now we apply this logic to your MOE example. Let's say 0 represents a value within the MOE and 1 is a value outside of it.

[warped phoenix]

#❓how-to-get-help #rules

[twin nimbus]

It's still 1 in 2.

instead of picking balls directly, you're picking a value and then examining it to determine if it's inside or outside of the MOE

So if you pick someone and their loan is 7000, it would become a 1. And 7943 would become a 0.

and the assertion is that this MOE gives the range such that whether you get a 1 or a 0 is 50%.

[warped phoenix]

so there is a 50% chance that we pick someone who's loan is in that range of -34/+34?

[twin nimbus]

Yes

[warped phoenix]

then what was the point of the stdev range?

[twin nimbus]

and if you make the range bigger the chance goes up

if you make the range smaller the chance goes down

[warped phoenix]

but regardless of the range, it will be within the diff. of 1800?

is that what the stdev is for here @twin nimbus

[twin nimbus]

Why do you think that?

It's not impossible for there to be a loan of $40000

[warped phoenix]

well then idk what the stdev is for then 😦

because the MOE is already the important range for us

[twin nimbus]

You can find any MOE using the stdev

[warped phoenix]

ohhhhhhhhhhh

wait yeah the stdev is kinda irrelevant here outside of the fact that it's used for the formula

🤦‍♂️

i see

ig i understand then, ty!!!!!!!!!!!!!!!!!!!!!

i love the hat in time pfp btw 🙂

[twin nimbus]

thx.

Bumping my question again. Does anyone know a special function or a combination of special functions that is the inverse function of y = x - sin x ? I'm trying to analyze cycloid behavior and I keep running into situations where I need to work around being unable to invert this.

[alpine sable]

are you a mathematician

[twin nimbus]

no.

[alpine sable]

ok

[warped phoenix]

its been more than 15 minutes since ur original question has been posted, i think ur free to tag helpers now 😄

sorry i cant help im in 10th grade lol

[twin nimbus]

Ok, I'll put a little bit more work into my question and ping.

[velvet forum]

is the inverse not just y = -x + sin(x)?

[twin nimbus]

The functional inverse

x = f(y) = something in y

[alpine sable]

What would be the most effective/fastest way to solve this problem?: One of two pumps takes 24 minutes longer than the second to fill a container. In 35 minutes, both pump the tank full at the same time. How many minutes does it take for the first pump to fill the container?

[placid zinc]

Think of the rates as "containers per minute", not "minutes per container"

[clever locust]

So basically you want to solve the limit

$$\lim_{n\to\infty}\frac{n^{1000000000}}{2^n}=\lim_{n\to\infty} \frac{n^{10^9}}{2^n}.$$

We start by noting a few properties of this which are really easy to prove (for example the first two derivatives can be proven using induction). So if we differentiate the function on the same form as those in the numerator and denominator we have that

$$\dv[m]{x}x^m=m!,$$

$$\dv[m]{x}a^x=\ln^m(a)a^x,$$

where $m$ is a positive integer and $a$ is a positive real number. Now we also note that if $a>1$ we have that

$$\lim_{x\to\infty} \dv[m]{x}a^x=\infty,$$

and if $k$ is a positive integer strictly smaller than $m$ we also have that

$$\lim_{x\to\infty}\dv[k]{x}x^m=\infty.$$

Using what we have now established we can easily see why we can use L'Hôpital's rule $10^9$ times, as we would have $10^9$ instances of an $\frac{\infty}{\infty}$ indeterminate form. Do doing this we get

\begin{align*}
\lim_{n\to\infty} \frac{n^{10^9}}{2^n}&=\lim_{n\to\infty} \frac{(10^9)!}{\ln^{10^9}(2)2^n}\
&=\frac{(10^9)!}{\ln^{10^9}(2)}\lim_{n\to\infty}\frac{1}{2^n}\
&=0
\end{align*}

and thus the limit equals zero.

[ocean seal]

Lorago

[clever locust]

It's a really stupid solution but it works lol

Hopefully I typed it up correctly, I was kind of in a rush

[ionic jewel]

10^9 lhopitals in one problem I'm a fan

[lofty gorge]

The usual method is done by considering the 10^9+1th term in the series expansion for 2^n

[ionic jewel]

wait how does that help?

series expansion for solving limits?

[lofty gorge]

2^n is greater than just that term, so you sandwich with that

[ionic jewel]

,w series expansion for 2^x

[ocean seal]

Results provided by WolframAlpha

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

Requested by 兔子#6562

[ionic jewel]

2^x = sum_(n=0)^∞ (x^n log^n(2))/(n!)

[lofty gorge]

https://cdn.discordapp.com/attachments/717123612125167628/871476534786015252/365017527484416001.png

(with an n in the denominator whoops)

[ionic jewel]

yeah i was going to point that out but seemed obvious enough

[astral dagger]

the user that answered used the convolution defn. to show that (f\ast f = \int_0^t f(\tau)\cdot f(t-\tau),d\tau), such that (0\leq \tau<1) and also (0\leq t-\tau<1), in which (t-1\leq \tau<t), but then for the first integration, the integrand would be (1) and the for the second, would be (0). That part is the easiest to understand, but then he said when (1\leq t\leq2), the integral must be (f\ast f=\int_{t+1}^{1}1,d\tau=\tau~\biggr|_{t-1}^1=1-(t-1)=2-t), so (f\ast f=\begin{cases}1,~\text{if}~0\leq x<1\ 0,~\text{if}~x\geq 1\2-x,~\text{if}~1\leq x\leq 2\\end{cases}). These limits of integration didn't make sense to me.

[ocean seal]

SubGui

[astral dagger]

that t is a dummy variable

[quick fox]

Are you alllowed to cancel 3x+2 in this expression

In the question it does not say that x does not equal -2/3

[austere bridge]

you can cancel them out, but you have to keep track of the fact that you did, so the answers you get might not all be valid

it depends on the context

[quick fox]

If the question was simplify

that ^

[austere bridge]

then yeah I would cancel them out and specifically say "assuming x does not equal -2/3"

[quick fox]

Ok cool ty

[nocturne bronze]

oka so what are 12(fiften)-25(twentifive) and tgen plus fore?

<@&268886789983436800> is it ok to mention=

[tame falcon]

Do you want to report something?

Or are you asking for help on your problem?

[nocturne bronze]

no thank

[tame falcon]

For the latter, please read #❓how-to-get-help .

[nocturne bronze]

this is bothers account

ok thank

[digital raft]

Hey , i'm trying to understand what this is

its the mean square difference

but why would they divide by Y_n

[digital raft]

where Y_n is the actually value

as far as i know , the mean square difference is the sum of the difference squared of the actual value and the predicted value

<@&286206848099549185>

[verbal gull]

https://gyazo.com/ecadfddb55ce7167c057be0f79dc20ae

Here’s what I have so far

[austere bridge]

if $g(x)$ and $f(x)$ are inverses, then $g(f(x))=x$. We can take the derivatives of both sides to get $g'(f(x))\cdot f'(x)=1$, or $g'(f(x))=\frac{1}{f'(x)}$

[ocean seal]

cgodfrey

[austere bridge]

so if you can find an $x$ such that $f(x)=26$, then the answer you want is $1/f'(x)$

[ocean seal]

cgodfrey

[verbal gull]

so then 1/3x^2 is my final answer?

[austere bridge]

no, but you're on the right track

now you have to find the right number to plug in for x

[verbal gull]

So would x be 3 then?

[austere bridge]

yep

[verbal gull]

So my finally answer is 1/27

[austere bridge]

yes

[verbal gull]

Thank you

I can see where I didn’t clarify the answer now

[hardy geyser]

https://gyazo.com/cb694b693c01f4b0bd980cdcce35d9dd

help idk wha tto do with the -8x

[slender forge]

U factored the top wrong

@hardy geyser

[hardy geyser]

how

-4 -4 = -8

right

[slender forge]

Yes

[hardy geyser]

wait

(x-4) (x-4)

[slender forge]

Yes good job

[hardy geyser]

oh i alreayd factored the -8 right

burhhhhhh

[slender forge]

Ya there is no -8x when factored

[hardy geyser]

ooops

[slender forge]

U can foil ur factorization to check it

U would have gotten something like -8x^(3)+…

Which obviously is not equal to any of the original terms

[hardy geyser]

for the top i was thinking of perfect squares too thats why

ty

[slender forge]

Np

Did u get a final answer?

[hardy geyser]

yes its k

[slender forge]

Good job

[digital raft]

Any help on this ?

[hardy geyser]

@digital raft r u in college

[digital raft]

@hardy geyser yes

[halcyon geode]

Uh, weird, dunno why they're dividing either. The difference divided would give you a relative error, but never heard about that being used for the squared deviation

Maybe try #probability-statistics

[winter salmon]

what did i do wrong here

oops forgot to put the mininum

sqrt 2/2

but its still wrong

[obsidian cave]

Wierd why does the range option let you pick the type of bracket?

[winter salmon]

[obsidian cave]

Is it supposed to open with a square bracket? and close with a regular bracket?

[winter salmon]

i checked my answer in a calculator and i was right in every area but idk why it is still saying its wrong

[obsidian cave]

Isnt the minimum supposed to be -7/2?

[winter salmon]

[winter salmon]

wait wut how did you get that

[obsidian cave]

I assume its asking for the y value at the vertex

And you put the x value

[winter salmon]

oh i used wrong formula for it

ty

[obsidian cave]

np

[digital raft]

@halcyon geode okay thanks will do

[gloomy lintel]

In interval notation, a square bracket means these values are included but a normal bracket means these values are not included, eg an asymptote

so like (2,5] means 2<x<=5

[obsidian cave]

Oh cool

So that explains why infinity had a normal bracket

[gloomy lintel]

Yep

[obsidian cave]

I watched Veritasiums newest video yesterday and though there were many interesting parts I was confused about one, the one at the 7:56 timestamp (here https://youtu.be/094y1Z2wpJg&t=476 ) (PS if you didnt watch the full video you definitely should)
He says that (using 3n+1,) on average an odd number is multiplied by 3/4 to get to the next odd number, and apparently does that by getting the geometric mean, he shows the sequence he uses so I drew the pattern from it (it can also be drawn from his
explanation)
3/2 * 1/2 + 3/4 * 1/4 + 3/8 * 1/8 ....
Essentially each term is 3/(2^(2n)) and it is summed from n=1 to infinity, evaluating it numerically as well as on Wolfram Alpha shows it equals 1. Even ignoring the geometric sequence and brute forcing the original problem as such (in python)

def next_odd(num):
    """Returns the factor multiplied by to reach the next odd with 3n+1"""
    num0 = num
    num = 3 * num + 1
    while not num % 2:
        num //= 2
    return num/num0

# get factor multiplied by for 100,000 big odd numbers
L = [next_odd(i) for i in range(100001,200001,2)]

# get average factor
print(sum(L)/len(L))

shows that on average going from one odd to the next multiplies by 1. What am I doing wrong? How did Veritasium get 3/4? Clearly he must be right because odd numbers do eventually drop to 1 with 3n+1

Sorry for the wall

[austere bridge]

you're calculating the wrong thing. You should find next_odd(i) / i, and find the average of that

[ionic jewel]

also this the heuristic approach to the collatz conjecture, and you can read that relevent part of the Wikipedia page if you are so inclined

[austere bridge]

oh nvm I misread the code

[alpine sable]

Enclose code with code

Makes it easier to read

[obsidian cave]

How do I do that?

[alpine sable]

```

[obsidian cave]

Alright thanks

[ionic jewel]

```py
code here
```

py for python

[topaz scaffold]

Ohhhh

That's what I was missing all this time

[obsidian cave]

Ah there we go

Thanks bunny

[austere bridge]

@obsidian cave I think you want the geometric mean, not the arithmetic mean

instead of $S=\frac{a_1+a_2+\cdots+a_n}{n}$, you want $M=(a_1\cdot a_2\cdots a_n)^{\frac{1}{n}}$

[ocean seal]

cgodfrey

[obsidian cave]

Ohhh

Wow I just assumed I knew what geometric mean meant

[austere bridge]

you might have to get clever about trying to calculate it in python, though

[obsidian cave]

Any idea why use this over arithmetic mean? I mean the statement "on average an odd number is multiplied by 3/4 to get to the next odd number" seems to more apply if an arithmetic mean was used

[austere bridge]

I'm not completely sure why

oh wait I just realized I wrote that wrong

$M=(a_1\cdot a_2\cdots a_n)^{\frac{1}{n}}$

[ocean seal]

cgodfrey

[austere bridge]

oh the two are the same lol

but you might run into trouble naively trying to compute that in python

[obsidian cave]

I think it could work with mpfr using gmpy2

It has arbitrary precision floats

[austere bridge]

yeah, doing something like that would also work

[obsidian cave]

I'm trying it with 100000 bit floats and as n increases the mean just constantly decreases, down to something e-300 at n=1000

Increasing precision isnt helping

[thorn kindle]

Just a simple 2liner. Take an arraylist, find the product, then raise it to the power of 1/size

[keen saddle]

An arc is basically a line segment limited between 2 points of a circunference?

[glass lichen]

it's the section of the circle defined by those 2 points, yes

line segment would be the chord

[austere bridge]

@obsidian cave

def next_odd(num):
    num0 = num
    num = 3 * num + 1
    while not num % 2:
        num //= 2
    return num

L = []
for i in range(1,2001,2):
    L.append(next_odd(i) / i)

prod = 1
for i in L:
    prod *= i
prod = prod ** (1 / len(L))
print(prod)

the following gives a number close to 0.75 in naive python

but it breaks if you make the upper bound much larger

[obsidian cave]

Why next_odd(i) / i ?

[austere bridge]

I moved the division out of the next_odd function

[austere bridge]

otherwise it should be called next_odd_ratio or something like that

it's the same code

[obsidian cave]

Oh my bad didnt see that

Alright thanks I see then

I wonder if theres a way to get the geometric mean from the terms 3/2 * 1/2 and 3/4 * 1/4

[twin nimbus]

You mean a weighted geometric mean?

Or?

[shut rampart]

a bit confused on which one i got wrong and why

[twin nimbus]

Please don't ping helpers if it hasn't been 15 minutes

[shut rampart]

sorry botu that

didnt know the rules

i think it has something to do with the horseshoe lookin thing on the bottom

but idk

[twin nimbus]

Independence is when P(A|B) = P(A)

If you rewrite the intersection in terms of the conditional probability you can figure out the second. But the first is clearly dependent

[shut rampart]

yes

oh

yeah

just realized how dumb i am lol

i forgot that the | line means given

[shut rampart]

what abotu this tho

i thought that 3 to 2 odds means that out of 5 possibilities it will be 3 the one way and 2 any different way

[lofty gorge]

"against"

[shut rampart]

oh so its 2/5

ok

i am terrible with actually reading questions

how about this

@lofty gorge

i know that A is right

[lofty gorge]

What did you do for c

[shut rampart]

and that B is 0,08

but i forgot the formuila for C

[shut rampart]

i added the probabilities of both of the things

and averaged it

i think

[lofty gorge]

winning with rain and winning without rain?

[shut rampart]

yup

[lofty gorge]

you have to multiply those terms by the chance of it raining

[shut rampart]

oh

so

um

wait how does that make sense @lofty gorge

i got 3/25 and 8/25

and i added them

but if i multiplied both by the chance or it raining it would be tiny

[lofty gorge]

I forgot to write something down

My bad

It's P(rain)*P(winning with rain)+P(not rain)*P(winning with no rain)

However you say that in words

[shut rampart]

ok

let me do that rq

[lofty gorge]

("or not, respectively" should be at the end of what I said initially)

[shut rampart]

so it has to be .28

28 percent chance of winning

[lofty gorge]

0.8*0.35 + 0.2*0.6 = 0.4?

[shut rampart]

that isnt the right calculatoin

its 0.8x0.32 + 0.2x.12

[lofty gorge]

By winning with no rain I meant the 60% in the question

My bad I was ambiguous

[shut rampart]

oh

[lofty gorge]

I would write winning and no rain if I meant the 0.12

[shut rampart]

but then shouldnt the second one be .4

instead of the other thing

.32

[lofty gorge]

b is P( losing n not rain)

[lofty gorge]

.

where the n is that

I'm asking for P(rain)P(win | rain) + P(not rain)P(win | not rain), and 0.12 is P(win n not rain)

[shut rampart]

uh

huyh

huh

ok

nvm

so then it is .26

wiat no

.3

.,4

.4

yeah it s .4

[lofty gorge]

The values given in the question are "if it rains, this is the probability of winning after that". Part b is asking for "not raining and winning", not "if it rains, what is the probability of them winning". For the formula you need in c, you need the first, not the second kind

Is that clearer?

[onyx chasm]

is this chat occupied?

[viscid topaz]

Open

[onyx chasm]

okay well

$$\text{where did I go wrong?}$$
$$\lim_{n\to\infty}dx\Sum[i=1]{n}f\left(a+i\cdot dx\right) \mathop{=}\limits^{set} \lim_{n\to\infty} \Sum[i=1]{n} f(i)$$
$$dx=1\text{, a=0} \implies b=n \because dx=\frac{b-a}{n}$$
$$\implies \lim_{n\to\infty} \Sum[i=1]{n} f(i)= \lim_{n\to\infty}\int_0^n f(x) dx$$

[ocean seal]

Pedrosso

[onyx chasm]

and if you're gonna tell me it's because dx=1 and dx should approach 0, tell me why that would mess it up

[astral dagger]

https://tenor.com/view/krach-boursier-calculate-monkey-silly-gif-14808948

[astral dagger]

maybe it'd be ok to say dx = 1 if that limit was not there, cause then you'd be talking about a Riemann sum using partitions with size equal 1

[onyx chasm]

unless of course I'm not wrong but Im just assuming I'm wrong because I'm always wrong

[astral dagger]

that's kinda sad

[onyx chasm]

I actually haven't proved myself wrong and I'm trying to find a convergent series to try to prove it wrong. But it looks wrong

[onyx chasm]

well, yeah

O:

Illegal xD

[alpine sable]

i know test are not allowed but are u guys allowed to help on a task that is both assessment + assignment or is it not allowed

[glass lichen]

if it's an assessment no

[alpine sable]

ok

[red lagoon]

anybody know what property the 2nd line used to get f = l/2T_s

[ionic jewel]

i don't see that being done anywhere

of course I don't really understand the problem z but the 1/2T_s i think you mean was in front of the sum before

[astral dagger]

that star means convolution or is another property?

[restive glacier]

dy/dx=(dy/du)(du/dx) can I cancel the du?

[placid zinc]

That equation is true, and we call it the chain rule

Be aware of "cancel the du" as these aren't fractions, but notations for derivatives

[restive glacier]

So (dy/du)(du/dx)=(dy/1)(1/dx) is false?

[ocean seal]

Pedrosso

[restive glacier]

@placid zinc is this false?

[rigid smelt]

that is false

[placid zinc]

dy/1 is jibberish

[rigid smelt]

that is like saying derivative of y wrt 1 where 1 is a variable

[restive glacier]

Ok thanks

[echo aurora]

hey can i get help

dm me soon plz if u can help

[rigid smelt]

why not just post it here?

and dont ask to ask

just ask

[echo aurora]

cause i dont wanna post the questions in here

[rigid smelt]

oh well too bad then

[echo aurora]

its like college questions

[rigid smelt]

no one is judging you

if you cant post here then you are the oen with disadvantages

[echo aurora]

im not worried abt judging im worried abt the questions being leaked getting traced

like the college seeing it

[rigid smelt]

🤷‍♂️

that means you are cheating or something

[echo aurora]

nah im not

[rigid smelt]

sounds very suspsicious

[echo aurora]

im just tryna relearn how to do piecewise functions

A car company charges $35 a day to rent a car for the first 6 days. The charge then drops to $25 a day for each additional day up to 6 days. After that, the rate drops to $12 a day. The rental company does not allow you to rent a car for longer than 3 weeks. There is also a one-time rental free of $40. Define a piecewise function

this is an example

how would u turn that into a piecewise function

[rigid smelt]

so what have you tried?

[echo aurora]

i barely remember it, as far as i got was 35b and 1 </ b </ 6

but i fr dont remember any of it

[rigid smelt]

first of what is b supposed to represent?

[neat rose]

can someone help me

distributive property is hard

for me

[rigid smelt]

secondly, what does </ supposed to represent

channel is busy

[echo aurora]

days

[rigid smelt]

please move

[alpine sable]

what is 444,214,773,035,046,582,606 divided by 2?

[echo aurora]

</ is less than or equal to

[rigid smelt]

ok

well i mean

[echo aurora]

i have multiple questions to go thru and i dont really have time to fully learn it but if you can give me the equation for the first 6 days and then how to connect that to the next time frame i should be able to do the rest

[rigid smelt]

technically you just have to divide it into two cases

like how you did, in the case with 1<=b<=6

tho im having a bit of trouble analysing the question

they are asking to draw a piecewise function for the rent?

and what is the condition for the one-time rental fee?

how long is that one-time rental?

and also, how long of a period do they want us to draw the piecewise function over? 3 weeks?

[echo aurora]

thats all it gives me, im not sure

maybe we can move to a different question?

[rigid smelt]

why?

i mean if you want to

but the question does seem to be a bit ambiguous

[echo aurora]

thats why i wanted to skip it till maybe we do other questions and maybe we might learn what its asking for from doing other stuff first

[rigid smelt]

since we are goign to be graphing money against time but they didnt tell us how long of a period we should graph it

sure

[echo aurora]

ok so im given a parent function, given a transformed function

it says to write the transformed function in terms of the parent function but i thought thats already done when u make a transformed function>

[rigid smelt]

yeah it is

weird

or did they just tell you the transformation?

[rigid smelt]

ah ok

so basically, they want you to write it in terms of f(x)

and not in terms of x

for example, a transformation h(x)= x^2 + 2 where the parent function is f(x)=x^2 can be written as h(x) = f(x) + 2

[echo aurora]

oh ok

let me see if i can do it and u can tell me if im right

[rigid smelt]

sure

[digital radish]

Hey guys can I have some help

[echo aurora]

g(x)=3f(x-2)+4?

[digital radish]

Uh

I have a question

Can I ask here?

[rigid smelt]

its currently occupied

[digital radish]

Fuck

[rigid smelt]

yes good

[digital radish]

I'm new here

Can questions be asked in general

[rigid smelt]

#❓how-to-get-help

[echo aurora]

\

how about that one

[rigid smelt]

what are you tasked to do here? write the transformation in terms of x?

[echo aurora]

same thing as before just different ones to fill out

gives u different info

that second box is the parent function, 4th box is the way it changes

[rigid smelt]

yeah just write out what h(x) would be

what do you think h(x)=?

[echo aurora]

g(x)=.75(x+1)^2-2?

[rigid smelt]

not 0.75

oh wait

nvm, sorry miscalculated

but the constant is not -2

remember, f(x) = 3x^2 -5

[echo aurora]

so +3?

[rigid smelt]

no

[echo aurora]

or -7

[rigid smelt]

f(x+1) is multiplied by 0.25

dont forget that operation

[echo aurora]

20

[rigid smelt]

no...

5 * 0.25 -2 is not 20

[echo aurora]

18

i was just doing the dividing first

to make sure i was doing the right thing

[rigid smelt]

no 18 is not correct

0.75 * (x+1)^2 is correct

now its just the constant that you are wrong

[echo aurora]

5 x .25

is 20 right

minus 2 is 18

what am i missing

[rigid smelt]

no

you do know that 5 * 4 is already 20 right...

[echo aurora]

Where’s the 4 coming from

Bro ur making me feel stupid just help me out 🤣

[rigid smelt]

no im just giving you an example of why 5 * 0.25 is not 20

this is just simple multiplication....

ok instead of writing 0.25, i will write 1/4

can you do 5 * 1/4 - 2 now?

[echo aurora]

Wait I swear u said 5/.25

So -.75

[rigid smelt]

not that either....

idk you but theres no way to read * into /

oh didnt see you wrote -0.75

yeah its -0.75

[echo aurora]

Ok one sec

ok so i did the rest of the other questions for that

so now i have a composite function

and i have to turn it into f(m) and m=g(x)

[rigid smelt]

right

do you have a specific problem?

[dull oak]

someone help pls

[fringe robin]

9=10-1 99=100-1 and so on

[dull oak]

?

how does that help

[fringe robin]

use that to add

[placid zinc]

Add 1 to every term, ez sum

[dull oak]

oh i see

[placid zinc]

Then subtract after

[ionic jewel]

eg 9+99 = 110-1-1

[fringe robin]

ye

[ionic jewel]

yes

[placid zinc]

But that's a large number isn't it

[dull oak]

so would it be

11111111...(2020 times) - 2020?

so it would be 2016 ones?

[ionic jewel]

not quite

notice 9+99 isn't 11 (2 times) - 2

[dull oak]

wait

so how would i do it

[ionic jewel]

1111(2020 times) then a 0 - 2020

[dull oak]

wouldnt that lead to 2016 1's?

[ionic jewel]

kinda thinking it was 2017 or 2018

[ivory crypt]

you should consider how many 1 in 11110-2020, then add 2016,I think answer is 2016

[inland horizon]

i think it's 2016 ones too but never saw a problem like that so i'm no t sure

[ionic jewel]

,calc 11110-2020

[ocean seal]

Result:

9090

[ionic jewel]

don't mind me, i can't do mental math

2016 looks good then

[dull oak]

yeee

ty

very helpful perspective

[cerulean vine]

Yo

Can anyone help me

If possivle

Possible

[steel horizon]

dont ask, just put the question 😉

its a helping server matey

[night geyser]

[cerulean vine]

Here they are

[steel horizon]

wait

these are not english

[cerulean vine]

It is?

Looks like its not dual lang

[steel horizon]

OOH

YEAH I SEE

I SEE

sorryy

[inland horizon]

Posting in different channels is not allowed kingarthur

[cerulean vine]

I found these online

[steel horizon]

btw im not a genius so i cant help 😦

[cerulean vine]

Ohh

Its on gradient of a straight line

If thar helps?

@inland horizon what do you mean

[inland horizon]

the rules of the server to ask for help

[crisp grove]

slope = rise/run

u can count the run and rise so

[cerulean vine]

Yez

I asking for solution and explanation

[plush wagon]

What is Derivative of sin^2y = 0?

Is it " cosy.2siny y' " or just "2siny y' "

[ionic jewel]

wait with respect to what?

[plush wagon]

dy/dx

[ionic jewel]

2sin(y)cos(y)y' then, yes

chain rule important

[plush wagon]

Q7

[ionic jewel]

here's a Wolfram for your problems

[plush wagon]

But answer doesn't include cosy

[ionic jewel]

,w derivative of sin^2(y(x)) wrt x

[ocean seal]

Results provided by WolframAlpha

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

Requested by 兔子#6562

[ionic jewel]

yep, answer is correct

it probably gets cancelled with the other term or something?

[plush wagon]

No i don't think so

[carmine lion]

https://cdn.discordapp.com/attachments/269573202018041856/871626685609545768/unknown.png

wait is this channel occupied

[ionic jewel]

,w derivative of sin^2(y(x))+cos(xy(x)) = k

what is that k thing?

[plush wagon]

a constant

[ionic jewel]

fine Wolfram if you don't want to be useful

well anyways let's do the second part

derivative of cos(xy)

-sin(xy)(y+xy')

[plush wagon]

Yes that's what I got

[ionic jewel]

2sin(y)cos(y)y'-sin(xy)(y+xy')= 0

[plush wagon]

Yes

[ionic jewel]

y'2sin(y)cos(y)-ysin(xy)-y'xsin(xy) = 0

y'(2sin(y)cos(y)-xsin(xy))= ysin(xy)

cos doesn't go away as far as I can tell

unless there's some magical trig identities

expand our sin(xy) and it magically cancells?

[cerulean vine]

Imma learm herons formula because of this discord

I needa understand derivatives

[ionic jewel]

,w y'2sin(y)cos(y)-ysin(xy)-y'xsin(xy) = 0

[ocean seal]

Results provided by WolframAlpha

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

Requested by 兔子#6562

[cerulean vine]

Am i to young to to be learning derivatives

[carmine lion]

age don't matter

all that matters is that u can understand the concept

[ionic jewel]

also i don't think herons formula has derivatives

isn't it something with geometry

[cerulean vine]

Ohh wait im dumb

[ionic jewel]

and yeah idk @plush wagon either book is wrong or there's some weird trig tricks i don't want to work out

[carmine lion]

@ionic jewel can u help with my question pls

[cerulean vine]

Sin cos and tan come under geometric transfo?

[ionic jewel]

sin cos and tan are trigonometry

[plush wagon]

Answer written in book is wrong , i think so

[carmine lion]

those are trig funtions arthur

sine cosine and tangent

https://cdn.discordapp.com/attachments/269573202018041856/871626685609545768/unknown.png

how can i do part (c), i've done (a) and (b)

[ionic jewel]

oh

hmm let's see

[carmine lion]

if i solve for the intersection i get this

,tex x^3-(m+1)x+(3-2m)=0

[ocean seal]

abe
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[ionic jewel]

first of all the derivative is 3x^2 -1

[cerulean vine]

This discord server makes me feel dumb

[ionic jewel]

we want the slope of the line at a point such that it goes through point P

[cerulean vine]

Im 14 and in the uk you finish school at 17

So we gonna learn this stuff like next year

[ionic jewel]

so assuming we are finding the x value where this is true, we need the line to satisfy,

slope is 3x^2-1, goes through (x,y), and goes through (-2,-3)

[carmine lion]

sooo

$3a^2-1=m$

[ionic jewel]

so what's the general form of a line that goes through (x,y) and (-2,-3)?

[ocean seal]

abe

[carmine lion]

thats 1 right?

[ionic jewel]

what?

why is it an a?

[carmine lion]

if a is the x-coordinate

of the intersection