help-39

[stone imp]

I got the complete wrong answer

[prime bramble]

can you show your work?

[stone imp]

The answe should be minus plus 3 I got this

Wait

It’s a bit messy cause I ran out of space

[prime bramble]

5*9 = 45, not 81

[stone imp]

Oh my god 💀

[prime bramble]

[stone imp]

Wait ill retry real quick 😭

[autumn fossil]

To avoid errors like this, its better to start with the simple stuff (such as addition)

[verbal plinth]

Why so mess when world gives u paper

[autumn fossil]

you can e.g. add 5 to both sides here

2x^4 / 9 = 18

[stone imp]

Cause I’m crazy lol

[autumn fossil]

now youll have to do just one multiplication

[stone imp]

This how little I write

[stone imp]

Oooooh

Yeah I have a test tmr I should keep this in mind thank you 🙏

[autumn fossil]

just make sure starting with addition doesnt break PEMDAS or sth

[autumn fossil]

here its completely fine, cause we are just doing the same thing to both sides

[stone imp]

What’s pemdas

[autumn fossil]

order of operations

[verbal plinth]

Parentheis exponent multi and...

[stone imp]

Ooooh

Sorry englihs isn’t my first 💔

Wait I’m gonna retry it rq

Okay i got a answer

Do any of you have any tips on how I can remember to do the minus plus symbol when the exponents are not odd

I keep forgetting all the time

And if I do a really hard question and get it right and don’t add the minus plus o don’t get the question right and I’m really struggling with remembering 🙏

[autumn fossil]

I used to keep a list of things i constantly forget

[verbal plinth]

Ig u mean u forget symbol of the term whrn there is power2 or 3 or 4 like that?

[autumn fossil]

just by writing it down before the test and reading it, i then remembered all of the stuff

[versed mica]

is this like a cheat sheet?

[stone imp]

I feel like when I finish the question I forget the last step of adding that little symbol

[versed mica]

why are you writing like that

[stone imp]

lol no that’s how I write

[versed mica]

🤔

[verbal plinth]

Paper crisis

[stone imp]

U like it organised and cramped together

[stone imp]

Trust I have a lot I just like who it looks like this 🙏

[verbal plinth]

Even i asked that to her

[verbal plinth]

Show ur working for que

[stone imp]

Wdym

I always switch pappers when I don’t write like this

Cause it triggers me 😭

[versed mica]

write horizontally

[autumn fossil]

writing equations horizontally must be pain

[versed mica]

like just move to the next line after you run out of space horizontally

[stone imp]

Ohhhhhhh

But like this I can look back to find questions easily

If I wrote horizontal I would look for hours

[autumn fossil]

Do you actually solve equations horizontally?

[stone imp]

That’s scary

[versed mica]

on paper

not when i type it up in latex

[autumn fossil]

that's crazy

[versed mica]

latex i use \begin{align*}

[autumn fossil]

i had never seen that before

[verbal plinth]

Are we discussing the que ever pls?

[versed mica]

who cares

didn’t they already solve it

[stone imp]

I just seen people write all over the place and

[autumn fossil]

that's me

[stone imp]

Yes o did I’m supposed to close it now

Bye bye tysm 🫶

.close

[pearl pond]

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[pearl pond]

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[exotic gale]

When a math problem says "rate of change of y with respect to x" does it essentially just mean the slope?

[wind robin]

It can also mean 1/slope

<@&268886789983436800>

[exotic gale]

wth

[wind robin]

Spammer.

[exotic gale]

oh ok

so back to the problem

it's basically dy/dx right

[verbal whale]

Yep

[exotic gale]

ok thnaks

thanks

.close

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[stone imp]

If a car passes three traffic stops that show red 60% of the time and green 40% of the time what’s the probability of the car passing a red one at least at one of the traffic stops

[stone imp]

I don’t know how to solve this

Like at all

Probability is not my strong side

[shrewd mist]

Find the probability that the car does not pass any reds first, then get its conjugate

[stone imp]

How do you mean

How do I do that

[peak cypress]

I dont want to answer straight up but since we do not know if stops are synchronized or speed of the car its probably 6/10 times 6/10 times 4/10

Fricking dc

Hold up

[stone imp]

Lol take ur time

[shrewd mist]

What is the probability that the car hits two greens* in a row?

[stone imp]

Why two 6/10

[peak cypress]

I put * to show multiplication and dc turned it into new font

[peak cypress]

60/100 possibility of them being green

[stone imp]

Yes

[peak cypress]

Is this like a beginning question

[stone imp]

It just asks what the probability of it passing at least one red traffic stop is

After sayinf he passes three

And that they are red 60% of the time and green 40% of the time

[peak cypress]

Oh

I am sorry

If it is red at least one of them

Then things change

I didnt quite read the question

I thought red on the last one only Idk why

[stone imp]

Ohhhh

It’s okay

[peak cypress]

Shoot I forgot how were we doing these

[shrewd mist]

^

[peak cypress]

I remember nothing about combination

[peak cypress]

Well this also works

[stone imp]

So 6/10 times 6/10

[shrewd mist]

For the car to not pass any red, it must be G-G-G

What is the probability that that happens?

[stone imp]

Ohh so 4/10 times itself three times

[shrewd mist]

exactly

[stone imp]

Okay wait

216/1000

Now what do I do

[shrewd mist]

there's a mistake here

[stone imp]

Oop

OH

Oh my goddddff

I did the red

Not the green

64/1000

[shrewd mist]

Yeah, 64/1000 or 0.064. That is the probability that the car passes through a green light on all three lights.

[stone imp]

So

The probability of red

Is

[shrewd mist]

Now, logically, if this doesn't happen...

It must end up passing through a red at least once

[stone imp]

1000-64=936 which is 93,6%

[shrewd mist]

Yeah exactly

[stone imp]

oooooooooooh

Tysmmm

I feel so dumb it seems easy now

[shrewd mist]

happens. the conjugate trick (find the odds of the thing not happening) comes up often. you could solve this without it (ie. add 0.6 * 0.6 * 0.6 for RRR, 0.4 * 0.6 * 0,6 for GRR and so on) but it would take ages

[stone imp]

Ohhhhhh

Thanks I’ll keep in mind 🙏

.close

[pearl pond]

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[stone imp]

I don’t understand what’s going on

I thought

Maybe I was gonna do the whole sum times the interest rate and then divide it by the amount of months

But the answer is completely different

<@&286206848099549185>

Anyone? 😭

Anyone know how many times I’m allowed to ping..

[desert birch]

ones

[stone imp]

While ur here maybe u can help me 🙏😭

I beg🙏🙏🙏🙏

[desert birch]

wait until someone who knows helps you
if i could i would

[stone imp]

U sure I can only tag once…

Eff it whos gonna jail me

<@&286206848099549185> pls

[teal plume]

How

[stone imp]

Hiiii

I need help.

[teal plume]

Hi

For

[stone imp]

It’s almost been half an hour

This

[teal plume]

Question plz

[teal plume]

Did you ai search

[stone imp]

Ai?

I translated it in google translate the original question is in Swedish

[desert birch]

we dont recommend ai

[teal plume]

Ok

[stone imp]

🥲

[solemn terrace]

the first thing to note is the amount of payments

[stone imp]

I think it was 60

[solemn terrace]

• equal
• monthly
• 5 years

yes correct

oh wait i think i did the wrong thing when trying to solve through this myself 💀

nvm

[stone imp]

Did u do it like me🥲

I have the answers if u wanna check urself

[versed mica]

do you know the formula?

[stone imp]

OMG

HI

PLEASE

HELP

[versed mica]

💀

[stone imp]

I BEG

[versed mica]

^

[stone imp]

NO

I DONY

DONT

[versed mica]

🤔

does this look familiar

[stone imp]

What the hell

No it does not.

[versed mica]

are you sure?

[stone imp]

what is that 💔

Yes I’m so sure

[versed mica]

what formulas were you given?

there are equivalent representations

[stone imp]

I wasn’t given any

Ykw

What are the chances

Of this

[versed mica]

in notes

[stone imp]

Coming on the test

[versed mica]

high

[stone imp]

I mean come onnnnn

[versed mica]

this is pretty common

[stone imp]

DONT SAY THAT

[versed mica]

i took a financial math class last year

we did this often

[stone imp]

oh hell

Kill me now

[versed mica]

do you have lecture notes?

[stone imp]

No we haven’t been through how to solve this

[versed mica]

🤔

is this homework?

[stone imp]

It’s preparations for final math exam tomorrow.

[versed mica]

yea but if it’s on a practice test that they gave you then surely you would have done something similar by now

maybe you saw this version?

it’s the same thing

r/n = i

[stone imp]

I don’t think so

I’m not sure this is a part of my course

I think it’s Over course

[versed mica]

where did you find the practice test

[stone imp]

My teacher sent it out and said that the test won’t have anything that’s not on these sheets

[versed mica]

hmm

i don’t see how you’re going to do this without having these formulas

😭

these aren’t easy to derive

[stone imp]

I’ll skip it thanks anyway 🙏

[versed mica]

🤷🏼‍♂️

check your lecture notes or something

should be in there

what was the answer btw?

[pearl pond]

@stone imp Has your question been resolved?

[stone imp]

It was 500 on A and 6250 on B

[pearl pond]

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[versed mica]

oh wait this is simple?

[versed mica]

that’s just from principal payments then?

[stone imp]

How

Huh

[versed mica]

well you have 300,000 principal (before interest) and 5 years so 60 payments so 300,000/60 =5,000

i think you meant 5000

[stone imp]

Ohhhhhhhhhh

So when does the interest rate come it

In

[versed mica]

this formula incorporates interest

so if you wanted equal payments while considering interest

youd use that

[stone imp]

Oh god

[versed mica]

but since you’ve never seen it i think it’s safe to assume you won’t

well now for part b you have the annual interest rate but we want the monthly

so divide it by 12

[stone imp]

Yes

[versed mica]

and then do you remember the formula for interest?

simple interest here

guess not

I = P * r * t

t here is in months

and we just adjusted our rate to be the monthly rate

[versed mica]

^

then since you only care about the first month you let t = 1

where P = 300,000

[stone imp]

Ohhh

[versed mica]

,calc 300000 * 0.05 /12

[jolly parrot]

Result:

1250

[versed mica]

then add that to the answer from part a

which was the principal

to get the total payment

@stone imp make sense?

can i close this?

[stone imp]

Then I add 5000?

[versed mica]

yes

[stone imp]

I get it tysmmm

[versed mica]

Total payment = principal + interest

you’re welcome

[stone imp]

This should not have taken me an hour ten mins oh my god

My bad 🙏

I’ll close it

[versed mica]

lol no worries

[versed mica]

nah it’s my channel i have to close it

[stone imp]

Oh right

[versed mica]

.close

[pearl pond]

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[eager jewel]

can someone help me understand the question

not able to understand what is g(A)

[merry carbon]

Using "g(A)" instead of "f^{-1}(A)"

[eager jewel]

sorry what?

[merry carbon]

The set they're calling g(A) is basically the set of all things that when you apply f to them, they "land" in your set A

[merry carbon]

(it's just me complaining about them using non standard notation, usually this set, the preimage of $A$, is denoted by $f^{-1}(A)$)

[jolly parrot]

@merry carbon

[eager jewel]

huh oh...i sort of understood that..
so how do i find g(S)?

[eager jewel]

i agree this notation is not common where i study either which is why im struggling to understand it

[merry carbon]

In this case, for S as what they gave you, you're considering the (real) numbers such that when you square them, they're between 0 and 4 inclusive

[eager jewel]

yeah so f(S) = [0,16]

g(S) = {x belongs to R,f(x) belongs to S}

Oh

are they just trying to say g(S)={f(x) belongs to S}

that x belongs to R is kind of irritating

ohk

thanks man

just needed to familiarize myself with the notation

[merry carbon]

For that, they're just trying to be a bit more clear, so that e.g. you don't start including complex numbers

[eager jewel]

oh right

[merry carbon]

Without them specifying that, then asking what g([-1, 0]) is will depend on whether you wanna include complex numbers, or not (if you don't, it would just be {0} only)

[eager jewel]

👍 got it

<@&268886789983436800>

.close

[pearl pond]

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[solar coral]

A question on geometric method for first order pdes

[solar coral]

Wifi is dying I’ll be back 😭

I tried understanding why u(x,y) = f(bx-ay)

But my brain keeps thinking u(x,y) = bx-ay should be the general solution

<a,b> dot <ux, uy> = 0 implies directional vector is is 0, i.e u must be constant along lines parallel to <a,b>

I derived that the set of lines parallel to <a,b> follow bx-ay = c

Now I'm sitting there staring at this diagram

if 1 of these lines is the particular solution, isn't the set of all lines the general solution?

i.e shouldn't the general solution of u(x,y) = bx-ay? why is it f(bx-ay)?

[vital estuary]

for any line bx-ay=c, we can pick the value of u on that line

[solar coral]

could you go into more detail? my peanut brain isn't working :(

[vital estuary]

u(x,y)
=f(bx-ay)
=f(c) by above, bx-ay=c
f(c) does not change wherever you are on the line, i.e. f(c)=k for that specific c

k is constant

because c doesnt change, f(c) doesnt either

[solar coral]

OH

[fluid axle]

the xy-plane is only the domain of u right
u is a 2-input 1-output function, so if you want to draw it, you need 3 dimensions
this diagram you're staring at only talks quite indirectly about the values of u, think of a contour plot

[solar coral]

OHH I THINK SOMETHINGS CLICKING

FWKA

ITS CLICKING

wait it clicked :oo

thank u

weeeeeeeeeeeeeee

.close

[pearl pond]

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[solar coral]

wait im actually so happy thank u guys i was losing it

[pearl pond]

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[scarlet radish]

wait why doesnt $\sum_{n=2}^{\infty} \frac{1}{log n}$ converge

[jolly parrot]

astral

[scarlet radish]

cant you use ratio test which gives $\frac{log n}{log (n+1)} < 1$

[dense jasper]

$\log n < n \implies \frac{1}{\log n}>\frac{1}{n}$ for sufficiently large $n$, hence divergence by comparison test.

[jolly parrot]

astral

Civil Service Pigeon

[dense jasper]

The limit of that is 1

ratio test is indeterminate

[scarlet radish]

oh

i see, i misunderstood ratio test

you have to take the limit

[pearl pond]

If you are done with this channel, please mark your problem as solved by typing .close

[scarlet radish]

so the r here is fixed

[dense jasper]

yes it's a constant

[scarlet radish]

.close

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[pearl pond]

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[karmic pollen]

What would be the integral of ( ((x-a)^n)/x ) dx where n and a are constant real terms?

[cobalt hinge]

Term by term integration on the binomial expansion

This feels sus

Yeah if n is real you have to invoke the infinite binomial expansion

[pearl pond]

@karmic pollen Has your question been resolved?

[pearl pond]

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[silver oracle]

Base graph*

[earnest finch]

If you have $y = 2^x$, then I agree with $(x, y) = \qty(-2, \frac14)$ as one of the points.

[jolly parrot]

@earnest finch

[silver oracle]

The base graph before any transformations should be 2^x right?

[silver oracle]

Is this correct for after all of the transformations?

[earnest finch]

✅

[silver oracle]

Okay

It's annoying when your teacher does stuff wrong just cuz then it confuses you

Glad I caught it

Tysm 😊

[silver oracle]

Sorry it's messy

But is this graph correct

(obv my placement isn't perfect I forgot my graph paper at school)

[earnest finch]

You should draw a dashed line for your asymptote.

[silver oracle]

My teacher doesn't require that

Nice to know though

[earnest finch]

I’ll look at the rest in a few minutes, if no one else does.

[silver oracle]

Okay thanks

[pearl pond]

@silver oracle Has your question been resolved?

[earnest finch]

It looks about right, but you forgot the arrow.

[silver oracle]

Okay thanks

[pearl pond]

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[fading nexus]

I lost my chat so I’m just going to open a new one but how do I find the y values on the circle.

[pearl pond]

Please don't occupy multiple help channels.

[fading nexus]

How do I close the other one it does not appear for me

[dapper kraken]

".close" on the channel

[fading nexus]

I cant find it it does not show up on the side bar for me

[dapper kraken]

#help-25

[fading nexus]

Now I’m even more extreamtly confused cus it says graph time as the vertical coordinate so the y coordinate but now we have two y values and no X values

We have the ft value which I don’t undestand what that value represents and the time value I understand but now that’s y instead of X but the ft cannot be y because it’s kinda like height but then it it not height

And I understand how to graph equations I have no problem with that

I just don’t know how to find the mad midline or min

All I need is one

<@&286206848099549185>

[dapper kraken]

which part are you stuck on

[fading nexus]

I don’t understand how to find the mid max and min aka the points around the circle and Now I also don’t understand how to graph it because our period is in seconds. But now it says we have to put time units on the y axis. But in order to graph it I need the period on the X axis

I know the amp value the period and the b value

[dapper kraken]

ok first of all it wants in the function for time, so time is the x axis and the vertical coordinate is on the y axis

[fading nexus]

So the X values are 0,2.5,7.5,10

[dapper kraken]

you can see the max/min is at the top point and the bottom point

[fading nexus]

Cus it says “ sketch a graph of the vertical coordinate of Jada location as a function of tjme “

[dapper kraken]

which happens at 1/4th and 3/4th of the rotation specifically

[fading nexus]

Wait I’m confused

R we only using two points

[dapper kraken]

you wanted to know what the maximum and minimum of the function is no?

[fading nexus]

We still have to plot all of them tho on the circle

[fading nexus]

I mean yea but I also have to plot the main points around the circle

[dapper kraken]

its continuous, it uses all the points, you wanted the maximum and the minimum as it was important to graph it yes?

actually for starters, do you know what the graph would roughly look like?

[fading nexus]

I need the 4 intersection points

[fading nexus]

I know what a sin and cos graph looks like

Idk what this one looks like yet tho

[dapper kraken]

ok good

[fading nexus]

I have no problem graphing equations

But I cant get the info I need to graph it

[dapper kraken]

lets focus on the graph, can you fill in whats known with what information you have currently?

[fading nexus]

That’s all I have

I cant plot anything since I don’t have a min max or midline value

I know at 2.5 there will be a min or max, at 5 it will be at the midline, at 7.5 it is a mid or max value and at 10 it is on the midline

[dapper kraken]

yes thats good

[dapper kraken]

going back to this, what point would t=2.5 represent?

[fading nexus]

Do u know if we are rotating counter clockwise or clockwise

[dapper kraken]

its given its rotating counterclockwise

[fading nexus]

2.5 seconds after the carasol started

[fading nexus]

So I think the first mid/max value would be max

[dapper kraken]

so your saying when t=2.5 it reaches the maximum?

[fading nexus]

Yea

Then at 5 it reaches its midline and at 7.5 it reaches its min

[dapper kraken]

ok good

ok for t=5 it reaches the midline yes? what would the vertical coordinate be when t=5

[fading nexus]

Wouldent the height always be the same since it is a carasol

That’s where I’m getting confused

If I was thinking like it was a unit circle it would be -20

Wait

0

(5,0)

But that doesn’t make sense with the context of the story

[dapper kraken]

ok i should probably change it to "vertical coordinate"

the vertical coordinate is refering to the y value of the carousel graph (the one thats a circle)

[fading nexus]

Yea

I have no idea what it would be

Cus if it was the distance away from the midpoint it would always be 20, if it was in terms of a unit circle one of the values would have -20 which does not make sense

[dapper kraken]

when t=5, on the graph of the carousel do you know what point its refering to?

[fading nexus]

Yea it would be at pi if it was a unit circle

[dapper kraken]

so this blue point right?

[fading nexus]

Yea

[dapper kraken]

ok, what would its y coordinate be?

[fading nexus]

I thought it would be 0 or the midline value in this case

But I’m not sure how to get the midline

[dapper kraken]

it is 0

[fading nexus]

Wait how do we know?

What happened to the 20

[dapper kraken]

20?

[fading nexus]

The radius

The amp

I just don’t understand how we found zero

[dapper kraken]

this point is the origin, as you can see the vertical coordinate of the blue point is 0

[fading nexus]

Ohhh kk

So since our midline is zero our max is 20 and our min is -20

[dapper kraken]

close, remember the origin is at the center and the radius is 10

[fading nexus]

Wait is says the radius is 20 tho

I highlighted it

[dapper kraken]

oh

mb

[fading nexus]

so would our max and min values be 20 and -20

And we would have no h value?

[dapper kraken]

this is correct

congrats

oh wait

for c, when t=0 the y coordinate is 20

[fading nexus]

Why?

The midline is 0 and the amp is 15

And we are on the midline so wouldn’t y = 0

[dapper kraken]

for part c, t=0 is over here?

[fading nexus]

Oh wait whoops

Wait

What c r u talking about

There’s two question Cs

Wait

[dapper kraken]

the one with noah

[fading nexus]

Wdym by t=0

[dapper kraken]

when it starts, cause noah starts at N right

[fading nexus]

Yea

It’s a horizontal shift of 2.5

[dapper kraken]

so his vertical coordinate when he starts (aka t=0) is +20

[fading nexus]

Oh wait he start at the max

So it’s a cos not a sin

Well it is still sin

But it looks more like cos while drawing it

[dapper kraken]

cos is just a shifted sin

you can use either

[fading nexus]

Is this better

[dapper kraken]

like you said noah starts at the max

but the graph shows that noah starts on the midline

[fading nexus]

He starts at the max at 2.5 since there is a shift

Oh wait I did it wrong again

[dapper kraken]

perfect

[pearl pond]

@fading nexus Has your question been resolved?

[pearl pond]

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[sullen oar]

can someone help with SOPS, Sequence of Partial Sums, im in precalculus and this is how we are ending the year i cannnot figure out this problem and another

[sharp vigil]

can you post a picture of the instructions?

[sullen oar]

i have the answer key if you'd like I understand sequences but the sum of the infinte series is very hard

[sharp vigil]

are you given any indication of what the formulas for the sequences being summed here are? it doesn't seem especially clear from the terms

[sullen oar]

no, our instructions are find an expression for Sn, the nth partial sum, and then take the limit of Sn as n goes to infinity

[blazing breach]

oh in that case

sum the first term

the first two terms

etc.

try to find a pattern

i think that's why each term looks so contrived

[sullen oar]

yes but I can't figure out the pattern

[blazing breach]

for the first one: write each partial sum as a fraction (even the integer ones), see if that makes it clearer

[sullen oar]

sorry let me fix that

I think I have the wrong thing because they must be negative right

[blazing breach]

take out the plus signs but what you have is fine

ok see that 2/1?

can you rewrite that in an equivalent form that gives a pattern across the partial sums

what do you notice about S1 and S2, and S4 and S5?

[sullen oar]

oh the denominator goes up by 2

[blazing breach]

and the numerator?

[sullen oar]

by 3

so its 10/5

[blazing breach]

yep

so what's the general form of the partial sum S_n

[sullen oar]

4+(n-1)3 all over 1+ (n-1)2

[versed mica]

what

[sullen oar]

and then distribute

[blazing breach]

(3n+1)/(2n-1)

i think you're missing a few plus signs there lol but

yea

[sullen oar]

oh yea

[blazing breach]

as n gets super super large what happens?

[sullen oar]

3/2

yoooo

[blazing breach]

nice

and the other one you sent is solved the same way

[sullen oar]

ok thank you man that's all the help I need how do I end this

[versed mica]

type .close

[sullen oar]

.close

[blazing breach]

np

[pearl pond]

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[pearl pond]

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[sharp vigil]

<@&268886789983436800>

[pearl pond]

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[muted sierra]

4 (cos ( π - c)/4) .cos (( π -b)/4) .cos (a- π )/4 = 4 (cos( π -c )/4). cos (( π + b)/4) .cos (( π+ a)/4), is this true?

[muted sierra]

'4' is as denominator for the angles

its given that a+b+C =pi

[pearl pond]

@muted sierra Has your question been resolved?

[slow grove]

it does not hold for a=c=0, b=pi

[pearl pond]

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[sharp smelt]

This is probably a wrong idea, but I was thinking each v in V can be mapped to that element whose abcissa is translated by v?

[woeful torrent]

abcissa?

can you explicitly write the ismorphism you are proposing?

[sharp smelt]

like each element in V/U is a set

so

$v \to (x, {v+U}); x \in U

[woeful torrent]

but which x, specifically😄? right now as you have written it there may be more than one x, so your mapping will not be a function much less an isomorphism

[sharp smelt]

I see the issue now, it is not a bijection

[sharp smelt]

yea, I see the issue

[woeful torrent]

as i see it, there is a natural mapping 🤔, namely:
||hint: something like (u, v+U) -> v + u||

[sharp smelt]

right

that works

Thanks!

I'll close this now?

[woeful torrent]

well, you should atleast check it is an isomorphism😄 0) it is well defined 1) it is linear 2)it has trivial kernel 3) it is surjective
infact, there is a small problem with this as written which you need to fix

[sharp smelt]

There is?

hmm

I'll think about this and reopen if required

Thanks so much!

.close

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[pearl pond]

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[swift spindle]

hi can anyone find whats wrong with my working out

[woeful torrent]

how is integral of cos(2x) = -sin(2x)/2?

thats wrong, remove the negative sign 😄

i think you have confused it with the derivative

[rough forge]

It seems you wrote sin(π) = -1

[swift spindle]

ohhh yeah your right

sin pi isnt -1?

[rough forge]

No, it's 0.

cos(π) = -1.

[swift spindle]

sin 0 is 0?

[rough forge]

,w plot sin(x)

[jolly parrot]

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[woeful torrent]

yes, to remember this you can imagine a right angled triangle with one angle going to 0

[rough forge]

For integer multiples of π sin(x) = 0.

[woeful torrent]

taylor expansion of sin x also gives you easy way to remember this

[swift spindle]

i lowkey just do hand thingy so when it comes to like 0, pi/2, 3pi/2, pi

i like imagine the circle

[pearl pond]

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[golden ice]

i know the answer but i dont get how

what i thought it was was 120

because it says the ratio initially is 3 : 4 : 2

but then it says debbie gets 120

and then hers change from 4 to 5

so doesnt that me 1 = 120

and then chris gives 1 to errol

so 1 = 120

[obsidian steppe]

what is the total money that all have in the starting case

[golden ice]

is that relevant tho

[obsidian steppe]

because the total money doesnt change

they only exchange the money right

what answer did you get

[golden ice]

21

[obsidian steppe]

yep

[pearl pond]

@golden ice Has your question been resolved?

[pearl pond]

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[rustic zealot]

This question is just confusing me. Uniform circular motion in physics

[iron basin]

period of an object in circular motion is the time it takes to complete one revolution

[rustic zealot]

Yeap ive got that part

[iron basin]

so answer for part a is given in the qn

[rustic zealot]

9 seconds yeah?

Yeah simple

[iron basin]

yeah

[rustic zealot]

ive done b and c but not sure if im correct

but d and e im really hazy on

b i got 0.7rad/s

c i got 1.6m/s for horse a and 2.9m/s for horse b

[iron basin]

both are right

[rustic zealot]

oh great

what about d and e how do i go about doing them?

[iron basin]

magnitude of centripetal acceleration is $\omega ^2 r$, $\omega$ is the angular velocity of the object in circular motion

[iron basin]

do you know about this?

[rustic zealot]

hmmm i think i recall

Learning about it at some point

So i use that for 4.

I get 1.127 ill round to 2 sig figs so 1.1m/s^2?

[iron basin]

yeah

[rustic zealot]

great

for the last one

would i use F=ma?

[iron basin]

yes

[rustic zealot]

to find the force apploied to the 50kg rider?

[iron basin]

a is the centripetal acceleration

[rustic zealot]

i got 100N

i recalculated the centripetal acclerationb ecause hes on the outer ring

[iron basin]

correct

[rustic zealot]

oh great

thanks so much

[iron basin]

welcom

[rustic zealot]

.close

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[humble basin]

https://youtu.be/og0FtoaYRM4?si=PReIH4dm3OID-oHH

[latent quail]

Hi, do you have any questions to be solved?

[pearl pond]

@humble basin Has your question been resolved?

[sweet gorge]

hey so i'm in ninth grade and i have a test on math coming up and i'm way behind. could i have some help?

[desert birch]

!occupied

[pearl pond]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[desert birch]

||that what happens when you dont lock in||

[pearl pond]

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[sweet gorge]

hey so i'm in ninth grade and i have a test on math coming up and i'm way behind. could i have some help?

[light helm]

send specific questions you're struggling with

[pure rapids]

@sweet gorge

[sweet gorge]

i would like some help with goeagraphy

[pure rapids]

wrong server blud

Unless you mean geometry

[sweet gorge]

yup

[pure rapids]

this then

[sweet gorge]

could you teach me similar triangles?

[pure rapids]

oh ok

what is your current understanding

https://en.m.wikipedia.org/wiki/Similarity_(geometry)

[pearl pond]

@sweet gorge Has your question been resolved?

[sweet gorge]

yes

.close

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[indigo urchin]

Helo can anyone help me on how to draw the level curve i dont rlly understand

[brave hawk]

No way it's ryan gosling

Wait but I'm ryan gosling so who are you

[indigo urchin]

oh wait nvm so do i just plug in random values for x and y and then plot it

[fluid axle]

you found y=6/x, level curve is a hyperbola

[fluid axle]

sure

[indigo urchin]

the real ryan gosling

THANKS

.close

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[exotic gale]

Is the inequality for the picture below: y≤-2/3x+2

[exotic gale]

Please check

[dense jasper]

Yes

,w y \leq -2x/3+2 graph

[exotic gale]

ok thanks

[jolly parrot]

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[exotic gale]

.close

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[sick grotto]

My question is why do the different approaches give different answers? Is it because of the cancellation in the AM-GM square root, or have I missed a condition for it?

[plush bramble]

some algebra mistake somewhere if you get different r

[sick grotto]

This one is for the calc approach and the bottom one for the am-gm approach
The ratios are different, so even if there was an algebra mistake we'd still get different surface areas no?

I can show how I get to each r brb

This is it for the calc approach

And this is the one for the am-gm approach

the inequality is x+y>=2sqrt(xy) for any real numbers x and y, yes?

[plush bramble]

your very first lines for the two are contradictory

is h = 2r or h = r?

[sick grotto]

no from the AM-GM approach we got h:r = 1:1, and from the calc approach we got 2:1, i.e. we got two different ratios/results form the different approaches

h = 2r for the method that used differentiating and h = r for the one that used the inequality

[pearl pond]

@sick grotto Has your question been resolved?

[plush bramble]

yea h=r is wrong because the assumption in AM-GM is x and y are independent variables. both surface areas have r as a variable in common.

Use V=1 to get an equation for h in terms of r before using AM-GM

[sick grotto]

I still get r = (1/pi)^(1/3) from it

[plush bramble]

oh i see. my suggestion doesn't remove the dependence on each other since 2/r still has an r in it

another approach would be to use a trick and switch the surface area to a sum of 3 terms using 2/r = 1/r + 1/r

see example 9 here: https://www.whitman.edu/Documents/Academics/Mathematics/2016/Greff.pdf

[sick grotto]

looks interesting i'll take a look

thank you

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[broken chasm]

not sure how to correct this or if i did this right

[broken chasm]

all the other theorems i cited are like basic properties of integrals and stuff like you can add integrals

[wet osprey]

Where is the start

The 3rd picture?

[broken chasm]

oh hold on

[pearl pond]

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@broken chasm Has your question been resolved?

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[sharp smelt]

Just to be sure, here when we say's in invarient, we mean T(v)=u; v,u \in U

right

[tropic saddle]

no

T(u) in U for every u in U

you need to out quantifiers for your variables

your statement doesnt mean anything without those

[sharp smelt]

Got it

Thanks

.clos

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[wind robin]

Solve the functional equation:
f(xy) = f(x^2) + 2xy

[hollow cobalt]

Any progress?

[wind robin]

Nope.

!status quo

[pearl pond]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[hollow cobalt]

Typically plugging some values of x or y in which simplify the equation is a good start for solving functional equations

[hushed oxide]

try subbing vals in

[acoustic path]

let x = y

[wind robin]

f(x) = f(x^2) + 2x
f(1) = f(1^1) + 2 * 1
0 = 2

I put y = 1 and x = 1

[hollow cobalt]

Good, that means there are no solutions

[wind robin]

.close

[pearl pond]

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[wind robin]

great

thanks y'all

[pearl pond]

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[young gate]

given that i know the graph of the RHS how can i get conclusion about the following expression?
$$\frac{\text{sign}\left(k\right)}{j}\left(\frac{a_{k-500}}{2}+\frac{a_{k+500}}{2}\right)\stackrel{?}{=}\frac{1}{j}\left(\frac{a_{k-500}}{2}-\frac{a_{k+500}}{2}\right)$$
i have the following plot for RHS

[jolly parrot]

Henry_quite_hungry

[pearl pond]

@young gate Has your question been resolved?

[young gate]

<@&286206848099549185>

[pearl pond]

@young gate Has your question been resolved?

[olive finch]

im just learning about differentiation... this looks hauting, but fascinating, how many years does it take to learn this stuff?

[junior loom]

in one dimension, its one semester

in multiple dimensions, 2 or 3 semesters

[broken chasm]

My first year doing this, it’s been quite painful

[olive finch]

wdym multiple dimentions??????

theres 3d and 4d calc?????

[compact ridge]

if you're in Europe they start off first semester with proof-based real analysis

real analysis is just calculus with proofs and rigour

[olive finch]

it does look painful and hard

[olive finch]

oh im a year 10 in australia LOL

still in high school

[compact ridge]

so for the US you'd do the calc 1/2/3 sequence first, so 3 semesters
and then if you take intro to proof-writing in one of those semesters, you can take a first course in single-variable real analysis in your 4th semester

[compact ridge]

PERFECT

yeah okay so you'd have maths 1A and 1B at uni

that's basically calc + linear algebra both semesters

[olive finch]

damn

[compact ridge]

then you'd have to look at your uni's availability for when you can take RA

[olive finch]

i wanna do this stuff man

[compact ridge]

our uni sucks so we can only take it in 2nd year 2nd sem

[olive finch]

oh...

[compact ridge]

1st sem we take intro to absalg

[olive finch]

i se

thanks]

[compact ridge]

yeah um you can also take headstart

if you take maths 1A in Year 12, then you can take maths 1B in 1st sem

that allows you to take real analysis in your 2nd sem if you want to

check your uni's handbook of course for the exact prereqs

[compact ridge]

I didn't do high school in Aus but I basically did a version of this by taking maths 1A and 1B concurrently

if you have the ability it's not that hard

but yes they do teach you useful foundational knowledge

those courses are computational-focused but when introducing key topics, your course notes will have the full details of the proofs

oh and you'd probably be taking the advanced version of 1A and 1B which is going to be more proofs-focused

but if you don't want to you're not exactly missing out

[pearl pond]

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[remote current]

not a single person did this person for hw and my teacher re assigned it with hardly any help so idk what to do from where im at

[remote current]

ik the trapezoids lengths but then im stuck

[autumn fossil]

okay so what exactly do you know?

Can you put every length you know in the diagram?

And every angle

[remote current]

here one sec lemme edit the pic

top is rounded

but its rly close to that

[autumn fossil]

okay cool

how did you calculate the top?

[remote current]

made a triangle and did pythagorean

[autumn fossil]

ah okay i see

,calc sqrt(25^2 - 5^2)

[jolly parrot]

Result:

24.494897427832

[autumn fossil]

well it appears to be incorrect

[remote current]

oh shi

24.5

[autumn fossil]

oh okay then

[remote current]

mb

[autumn fossil]

anyway, we wont probably even need tha

can you spot 2 similar triangles there?

[remote current]

yes

the small and whole thing right

[autumn fossil]

yes, right

and similar triangles have equal ratios of sides

[remote current]

yes

[autumn fossil]

so use that to make an equation

perhaps label some side with x

I'd label this one

[remote current]

okay

[autumn fossil]

now you can make an equation by comparing the ratios

once you figure out x, you can just use pythagoras to figure out VW

[remote current]

ik the ratio is 1.5 or sm but idk how it is that

like idk how to find it

[autumn fossil]

the ratio?

It's 15 / 10

and it should equal VY / VZ

[remote current]

so in any problem like this is it the biggest radius over smaller radius

[autumn fossil]

its more related to the sides of the traingles

[remote current]

wdym

[autumn fossil]

the triangles are similar

[remote current]

like how xy is 15

ohh i see it

ty

[autumn fossil]

if the smaller one has side lenght 10, and the larger one 15, the ratio must be 15 / 10

[remote current]

yea

i see that now

ty man

[autumn fossil]

and in the same way, VY / VZ must also be 1.5

and VY / VZ = (x + 25) / x

use that to calculate x

ill have to go for a minute or two, try working it out

i will then check it

[remote current]

ok that works im about to change periods ty ill lyk what i get

[remote current]

does x=50

?

[autumn fossil]

Yes

now you can just pythagoras it

[remote current]

51?

it matches with the other triangle

[autumn fossil]

,calc sqrt(50^2 - 10^2)

[jolly parrot]

Result:

48.989794855664

[autumn fossil]

no, why?

[remote current]

i did sqrt5850 - sqrt650

[pulsar pilot]

Might I recommend:
VX / VW = 15/10 (similarity)
=> (VW + XW)/VW = 3/2
You have XW

[remote current]

51s xw?

[pulsar pilot]

It comes out to be 2root(600)

[remote current]

how do i get 51

[pulsar pilot]

Waht

[remote current]

im doing sqrt2600

[pulsar pilot]

Why

[remote current]

bc 50^2+10^2

[pulsar pilot]

Does this make sense ^^

VW comes out to be 2 × XW

XW is just the DCT and is equal to root(600)

[remote current]

why doesnt pathagorean work

[remote current]

whats dct

nvm im a dumbass

[autumn fossil]

you just took the wrong sides

50 is the hypotenuse

[remote current]

i thought the top was the hypotenuse

[autumn fossil]

10 is the leg

[remote current]

yea

woopsies

i get it now ty guys

[autumn fossil]

you should be doing VW^2 + 10^2 = 50^2

[remote current]

yea

ima keep it open bc theres another i may not figure out

.close

[pearl pond]

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[pearl pond]

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[somber locust]

Hello, I am no expert in Maths by any means and i am having a discussion with a friend who has a degree in mathematics. If this question is not meant for here that is completely fine. To put it into context (I will try my best), We have a population size of 10 (Because we are referring to a number of usages a key has in Escape from Tarkov, this room behind the key can spawn valuable loot that can be sold) and we want to find the mean (mean being money made per run to know if it is worth spending x amount on the key (28 million) and work out the average per key usage). My friend is saying that it is statistically accurate to have a sample size of 1 with a population of ten (ten being the maximum as there is ten uses of the key) due to the 10% rule. I am saying that the 10% rule would not apply to this size of a group. Happy to go into further discussion but I do not see why it is stastically accurate to have a sample size of one just because of the 10% rule? I have tried to keep it to a minimum, sorry for long message.

[pearl pond]

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[pearl pond]

@somber locust Has your question been resolved?

[pearl pond]

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[pearl pond]

@somber locust Has your question been resolved?

[junior loom]

you seem to be asking about when you can approximate the sampling distribution as a normal distribution

you can't assume that if n is small unless the population is distributed normally, which it is not here

the 10% is for sampling without replacement, though. in this scenario you're sampling with replacement so it's not relevant

you can still do statistics on this study, but not by the central limit theorem

[somber locust]

Hi, thank you for your response, looking at what CLT means, I think yes, it wouldn’t apply to this study as the sample size is not large enough (from what I can understand). Are you saying he is using CLT when this would be the wrong maths to apply?
I do want to ask, what statistics can be done? I am not understanding why my friend insists that a sample size of 1 can be considered statistically accurate whilst trying to work out a mean when the population is 10. He starting pulling out graphs with confidence and margin of error but none of it seems to answer how can you work out an average when you only have one result and the 9 other results would have a significant impact on the actual mean as there are so many variables (some valuable loot might spawn, some might not, some are very very expensive and some aren’t)
Sorry for the long message, look forward to hearing from you

[pearl pond]

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[dense arrow]

Hi! I'm pretty laic in advanced math and till now I wan't agile in the average level math neither, but I would like to deepen my knowledge.

In short words: any idea how he calculated that?
https://www.psychologytoday.com/us/blog/the-skeptical-sleuth/201103/did-a-study-really-show-that-abstinence-before-marriage-makes-for
"After controlling for religiosity, length of relationship, number of sexual partners, and education, whether participants had abstained from premarital sex only **accounted for less than two percent of the variance **in sexual satisfaction after getting married. "

He's talking about the results of this research: Dean M. Busby, 2010 "Compatibility or Restraint? The Effects of Sexual Timing on
Marriage Relationships"
DOI: 10.1037/a0021690
The research has three tables with data I send in the attachment.

[pearl pond]

@dense arrow Has your question been resolved?

[dense arrow]

<@&286206848099549185>

[long briar]

bro i cant understand question

[dense arrow]

Uhm, okay, I can provide you more data or maybe clarify something? English is not my native language, so maybe I formulated sth wrongly.

[long briar]

mine too i m pakistani

[dense arrow]

I'm wondering what's the method Coyne used to conclude that the result obtained by Busby "accounted for less than two percent of the variance"

How does he know that it's less than 2% if in all the Busby's article that's written nowhere?

[pearl pond]

@dense arrow Has your question been resolved?

[dense arrow]

<@&286206848099549185> 👀

[frigid lark]

war

waht

[dense arrow]

hi

[dense arrow]

.

that

[pearl pond]

@dense arrow Has your question been resolved?

[wet osprey]

I’m gonna guess this is anova

Anova looks at how much each factor contributes to explaining the variance in a data set

[dense arrow]

Hmmm, interesting

Thanks:) I'm reading about it

So it would be one-way Anova, not the one with replication?

[wet osprey]

Yea

[pearl pond]

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[pearl pond]

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[final citrus]

im looking for an accessible proof of the basel problem, something that wouldnt require digging deep into calculus and stopping at limits and series, does anyone have any ideas?