help-4

[twilit elk]

cool

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[muted eagle]

Pls help me

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[small heath]

Idk how far I'm correct but if the lines are tangent to the sphere with center I, then shouldn't the perpendicular distances from I to the lines be equal ( equal to the radius )

[muted eagle]

ye as i said

[muted eagle]

.

oh i forgot to forward the distances

these are equal to R^2

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[final steppe]

Help

[final steppe]

Can someone send me simple drawing of a graph edge being partitioned to form cycles

Just a drawing, i dont need help with the proof.

<@&286206848099549185>

[final steppe]

Can you partition it

Into cycles

About some arbitrary edge of ur choice

[final steppe]

You can just do that?

I thought a partition always must have a straight cut

Okay thanks

❤️❤️

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[drifting hornet]

i think that the cycles just cant share an edge

im not sure though

[final steppe]

Alright

Thanks alot

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[lusty dirge]

heyo! i wrote my question in purple

[lusty dirge]

im confused why we didnt change the gap

thing

because we did change x overall :(

[cinder creek]

As you wrote, for x-1, the domain of the function f(x-1) would be x > 4 and x <= 4. This also applies to the integral: x-1 requires 1 unit more than x, x requires 1 unit less than x-1, meaning the bounds 8 and 2 (for x-1) goes to 7 and 1 (for x).

[tepid wind]

Your method is to move the gap. Their method is to move the overall function (indicated by the change of bounds).

[lusty dirge]

woa so there's 2 paths?

[cinder creek]

1/1, 2/2, 3/3, etc. gives the same value.

[lusty dirge]

what i understood is moving the bounds is also changing the gap in a way?

[cinder creek]

More the opposite, when you change the gap, you also changes the bounds.

[lusty dirge]

thank you!!

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[tough burrow]

So I'm super unsure if I am even thinking in the right direction about this, I understand that a+b sqrt5 times the denominator should equal the numerator so I try factoring them but end up with something that looks nothing like it and I'm unsure if I even did it correctly?

[midnight pier]

a= -7 , b= -3

[next vortex]

hmm, try multiplying the left hand side by the conjugate of the denominator

[next vortex]

ah, please don't give any answers away

[edgy minnow]

better not gave the answer

[midnight pier]

Sorry lol

[next vortex]

the logic here is that if you do so, the denominator will reduce to a single number, which you can divide all the terms in the numerator by

one of the terms in the numerator will contain a coefficient and a sqrt(5)

[tough burrow]

yeah i already saw the answer on google, im more interested in understanding how to get there

[next vortex]

the others can be grouped together and labelled "a"

[tough burrow]

also conjugate would basically be flipping the positives to negatives and the negatives to positives right?

[next vortex]

no

[storm perch]

Also multiplying it out is quite inefficient

[next vortex]

the conjugate of a + bsqrt(5) is a - bsqrt(5)

multiplying both the denominator by its conjugate lets you take advantage of the difference of squares formula

(a + b)(a - b) = a^2 - b^2

this'll cut the denominator down to a single number (no square roots), which is why it's desirable to do this

let me know if something is unclear

I have no problem going through this again c:

[midnight pier]

system of equations and let’s go

[next vortex]

you probably won't even need a system of equations here

[midnight pier]

):

[tough burrow]

if im understanding right then i would be turning the left side into this? i mightve misunderstood still though

[next vortex]

it'll be 4 - 5 in the denominator

not 4 + 5

[tough burrow]

oh yeah duh

[next vortex]

(a - b)(a + b) = a^2 - b^2

[next vortex]

uhh, hm. how did you get 5sqrt(5)?

[tough burrow]

honestly not sure, it should be 3sqrt(5) shouldnt it?

or am i still missing something?

[next vortex]

[tough burrow]

okay lol, sorry my brain obviously isnt working at full capacity rn

so then once i have this do i need to do anything else to it?

[next vortex]

no worries, you're doing well

there you go!

now simplify that c:

[tough burrow]

when you say simplify it is this where i would wanna use long division for it or is there a different way im not thinking of?

[next vortex]

what's the denominator?

I promise you we don't need to long divide

[tough burrow]

OHHHH its one

[next vortex]

it's -1

[tough burrow]

wait

yeah

omg

[next vortex]

but even if it was 8712 or something, it wouldn't matter

,, \frac{a + b}{c} = \frac{a}{c} + \frac{b}{c}

[rocky lotus]

higher!

[next vortex]

because we can always do this!

in our case, it just happens to be a very simple number c:

[tough burrow]

so that would make this true then?

[next vortex]

a couple of comments

1. you should simplify the numerator as much as possible before breaking the fraction apart
2. it's -1, not 1

[tough burrow]

ugh youre so right, i keep making simple little hiccups bc im overwhelmed which probably means i should take a break soon but this is what you mean then i think?

[next vortex]

don't sweat it too much. make sure to give yourself enough breaks in between math, because it can be really stressful

your work looks great!

now just rewrite it a little and identify what a and b are :>

[tough burrow]

ohhhh okay so them being over the negative one just makes them negative and since they are over one they dont need to be changed so thats how a=-7 and b=-3 then?

[next vortex]

looks great!

[tough burrow]

so in the future with problems like this i should just multiply the top and bottom by the conjugate of the denominator and then simplify to solve from there?

[next vortex]

yeah

it's almost always a good idea to use the conjugate in problems like this

[tough burrow]

awesome!!! thank you so much, i really appreciate the hand

off to rest my brain a lil

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[next vortex]

get some rest c:

and have a wonderful day/night

[tough burrow]

you too!

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[wooden dock]

Can someone explain to me why the lamps flash? When unloading and unloading the capacitor? Does this have anything to do with the fact that lamps are not ideal R?

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[edgy minnow]

we don't understand the question

and we are lazy to use translator

[wooden dock]

Can someone explain to me why the lamps glow briefly?

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[sweet holly]

hi

[toxic ridge]

Could you perhaps translate the question?

[wooden dock]

Yes

I used Google translate

[toxic ridge]

Then pls translate it

[wooden dock]

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[clever sentinel]

Bro gave up

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[somber narwhal]

Hi I wanted help on the following question

[somber narwhal]

I know it's discrete probability. But idk if I should just use trial and error to find n from the binomial distribution.

<@&286206848099549185>

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[humble hound]

Hi, the task was: sketch the graph of the derivative function f′ of the given function f. The red sketch is from me, is my solution correct?

[turbid summit]

reading comprehension moment

okay

so like f(½) to f(2) its increasing

so f'(x)>0

not <0 as you've depicted

same for f(2) to f(4)

if you want the precise value for f' just calculate the slope using the point formula

[humble hound]

alr i think i got it thank you ❤️

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[wet tundra]

Can I pls have some help

[vale dock]

@wet tundra Has your question been resolved?

[copper stump]

find the movement of their center of mass

[wet tundra]

Im a bit confused

[copper stump]

where?

[wet tundra]

How do i find the movement

What do u mean by movement

[copper stump]

well, as the cats move away from the post, the center of mass is gonna shift

and once the cats move sufficiently apart, they would have shifted that com such that it lies outside the 0.5m wide section that rests on the post

and would make it unstable

[wet tundra]

oh

soo how do i calculate dis..

[copper stump]

assume that the unstable situation occurs when the cats have moved some distance x

write the center of mass equation

solve for x

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[thick rampart]

im lost

[daring depot]

can someone help me with factorization? i can't wrap my head around these 2 questions 💔

[hot tide]

!occupied

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[hot tide]

okay so

what's the degree of f(f(x))?

[daring depot]

oh ioops wrong place

[thick rampart]

4?

[hot tide]

yes

[thick rampart]

ive never done double functions before so i have no idea how to do this

[hot tide]

if you have that some function g has a double root r, then g(r) = 0 and g'(r) = 0

have you done calculus

derivatives to be specific

[thick rampart]

no, im in 11th class

our sir said this is done by quadratic equations and inequalities

[hot tide]

yeah we can do that

[hot tide]

this is a really weird question, there are multiple correct answers

[thick rampart]

there shouldnt be this was integer type qs so only 1 ans

[hot tide]

i found two examples of f where the discriminants are different and they seem to satisfy all the conditions

[thick rampart]

how did you do it?

[hot tide]

first has discriminant 4, the other has discriminant 16

[thick rampart]

oh you just graphed it

huh

maybe the question is wrong

how would we do this by hand though

answer key only says 4 @hot tide

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[viral glade]

Can someone help pls.I did it this way but I'm not sure if it's correct. What point in the hour does the fluidity of the body collapse linearly according to the law S=t^3-16t^2+64t (S - in meters, t - in seconds) before zero?

[safe fulcrum]

if you want S(t)'s derivative (the slope of the line) not to change at a certain point

isn't that S''(t) = 0 instead

I don't get what the fluidity of the body means at all

[viral glade]

sorry not corectly write the question

At what point in time is the velocity of a body moving rectilinearly according to the law
S=t^3−16t^2+64t (where
S is in meters and t is in seconds) equal to zero?

[safe fulcrum]

ohhhhh okay that makes much more sense

yes then I can just check the quadratic since that's correct

(you wrote -16t instead of -16t^2 btw for S(t))

(3t - 8)(t - 8) = 0, yep, all is good

[viral glade]

Ok thx for help

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[north scarab]

can someone check if I did 8. b) correct?

my working out is in purple pen (sorry for the mess)

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[urban kite]

why did it get mult by 1/3?

[urban kite]

isnt that only applicable for tan^-1 condition?

[glass kelp]

Why

[urban kite]

i mean , i might be missing something

[urban kite]

ok so its applicable for arc tan and arc sec

and cot and csc

[glass kelp]

Note arcsin

That u don’t need 1/a

But u do for other cases

[glass kelp]

I count arccos and arcsin

[urban kite]

yes its only sin and cos that are exluded from this case

got it

[glass kelp]

Ye u can prove the formula too

By factoring out a

[urban kite]

yeah

anyways thanks just needed a brush out

[glass kelp]

👍

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[tacit nest]

I need help with part b

[vale dock]

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

[tacit nest]

1

[mental notch]

Have you started writing things down?

In terms of a random variable?

[tacit nest]

I dont know how to start

[mental notch]

Okay, you can start by modelling the demand as given, say $X \sim \text{Poisson} (\lambda = 15)$

[rocky lotus]

jewels!

[mental notch]

X is the number of newspapers needed on a particular day

So if t is the number of copies needed you need to find t such that P[X = t] >= 0.99

@tacit nest That make sense?

[tacit nest]

i got the poisson lamda

[tacit nest]

i dont get this part

[mental notch]

X is the number of copies in demand, I think you get that part

[tacit nest]

yes

[mental notch]

I am introducing a variable t, which is the number of copies we need

[tacit nest]

ok

[mental notch]

So if we want to satisfy demand we need X = t

My bad I shouldn't have used an inequality

[mental notch]

And the probability of this is ATLEAST 0.99

[tacit nest]

i get the inequality

[mental notch]

So we have P[X = t] >= 0.99

[tacit nest]

at least means it must be greater than or equal to

[mental notch]

Yeah

That's what we're doing

Also t is the minimum which is why there's an equality inside the P[]

[tacit nest]

ok

so how do we find t?

[mental notch]

Do you know the pmf for the Poisson distribution?

[tacit nest]

what does PMF stand for

[mental notch]

probability mass function

[tacit nest]

I use my calculator to find poisson, I got a CG50

[mental notch]

Uh

Is there an inverse poisson pmf on it

[tacit nest]

I dont know

[mental notch]

Well I guess you can just guess and keep tweaking your answer

Chuck in a few numbers and see the smallest one such that the probability is over 0.99

[tacit nest]

gimme me a sec

[tacit nest]

I think it does

I got 7

[mental notch]

Hmm I expected it to be over 20

Is that the inverse cdf or pmf

[tacit nest]

is it 25?

[mental notch]

,calc 1 - (15^24)e^(-15)/(24!)

24 seems to be it

[tacit nest]

but its less than 0.99

[mental notch]

thats 23

[rocky lotus]

Result:

0.99170020589953

[mental notch]

24 is above it

oh does your calculator say 24 is below

,w 1 - (15^24)e^(-15)/(24!)

[rocky lotus]

Results provided by WolframAlpha

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

Requested by jewels9006

[mental notch]

¯_(ツ)_/¯

[tacit nest]

what calculator do you have?

[mental notch]

Just using this one lol

[tacit nest]

ok

In my school there was another method which i just found

thank you for your help, I understand the concept of the question more

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[signal loom]

dont tell me what to do or anything

just a hint

nothing more

i wanna have fun with this problem cuz i have fckin failed for 2 hours now

[tacit moon]

e^x=t

wait no

(e/2)^x=t

[signal loom]

ok bet

thanks

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[stiff lily]

not an equation

[tacit moon]

guessing it = 0

[signal loom]

wait why is it e/2 ^X

all my atemps i have done e^x

[tacit moon]

cause there is 4^x in there too

take 4^x common

first term will have ((e/2)^x)^2

t^2

[signal loom]

oh ok

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[signal loom]

BRO this question hurting my head, wdym its (e/2)^2 = t, may i know your thought proccess behind this what observation made you think this, cant u just break down the 4^x to 2^2x

[wraith heart]

,tex .exp rules

[rocky lotus]

riemann

[wraith heart]

power of power and 4 = 2^2

[tacit moon]

wait

[signal loom]

funny thing is this question requires theese rules only

and lns

[signal loom]

ok

[tacit moon]

3e.e^2x-(e^4+9)(2e)^x+3e^2.2^(2x)=0

take 2^2x common

[signal loom]

the fist term doesnt have 2^x in common

[tacit moon]

2^2x(3e.(e/2)^2x - (e^4+9)(e/2)^x+3e^2)=0

2^2x can never be zero

[tacit moon]

multiply divide

2^2x in first term

[signal loom]

ohhhhhhhhhh

ok thanks

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[livid pier]

I did the first part, but I don’t see any connection with the second part

I should understand it like: $x’=x_{n+1}$ and $x=xn$? Then what should be $f{n+1}$ and $f_n$? Also $f’$ and $f$?

[rocky lotus]

Aruseq

[fair wing]

oops

[vale dock]

@livid pier Has your question been resolved?

[gritty sinew]

@livid pier you know euler's method for numerically solving DEs right ?

[livid pier]

yup, I do

[gritty sinew]

yeah so we're trying to solve some 1st order DE $\dot x = f(t,x)$ with this method

[rocky lotus]

aPlatypus

[gritty sinew]

1st derivative is allowed to depend on time and the function itself, that's what the DE means in english

and to get an approximate solution to that DE with euler's method, you need

• an initial condition x(t0) = x0
• a time step h
  and then we'll be computing approximations of x(t0+h), x(t0+2h), x(t0+3h), ...etc on time step after the other

these approximations we call them x1, x2, x3, ...etc for each time step, one approx value of x

[gritty sinew]

can you explain how we get from one time step to the next in euler's method then ? [just use your words or your notation first if you want, then I can translate to the notation used in your exercise]

[livid pier]

so in my example I probably should get $x$ from $x'=x+t$, it would be:
$x(t)=Ce^t-t-1$
using $x(t_0)=x_0$ I can get C
and in Euler's method I would get:
$y_{n+1}=y_{n}+hf(t_n,y_n)=y_n+hy_n$

[rocky lotus]

Aruseq

[gritty sinew]

last equality is wrong

f(tn, yn) ain't just yn

but yeah the rest is fine

[gritty sinew]

and in their notation f_n is just f(tn, yn) really

[livid pier]

hmmm.... okay.
\so I have $x(t)=Ce^t-t-1$
\and in the first step I can calculate
\$f_0=x_0+t_0$
\then I get:
\$y_1=x_0+hf_0$
\and now I can use it for:
\$f_1=y_1+t_1=y_1+t_0+h$ and
\$x_1=x_0+h/2(f_0+f_1)$

[rocky lotus]

Aruseq

[livid pier]

smth like that?

[gritty sinew]

yeah well be careful you're mixing the x and ys, there's just xs here, should have paid more attention to that

otherwise yes

we aren't solving for two functions, there's only one function we're trying to find and we call it x

[livid pier]

ye ye, I know it, I just wanted to introduce an auxiliary variable

to be more clear

[gritty sinew]

so what does your y1 mean then ?

[livid pier]

I wrote it: y_1=x_0+h*f_0

[gritty sinew]

that's the euler's method 1st approximated point ok

why are you reusing it in the trapezoid rule computation tho ?

they're two seperate methods

one important thing about the trapezoid rule is that it's an implicit method

$x_{n+1} = x_{n} + \frac{h}{2}(f_n + f_{n+1})$

[rocky lotus]

aPlatypus

[gritty sinew]

the thing is f_n+1 also depends on x_n+1 in general

so it's not as straightforward as just using the last point like you do in euler's methods

you actually have to solve an equation to get x_n+1 out of this

that's what they mean by finding an explicit formula for x_n+1

it's not completely immediate what it is

[livid pier]

I dont know if its that hard or I just cant get in intuitively, for what can't even do it 😭

[gritty sinew]

there's a lot of moving parts that's all

[livid pier]

yeah... I see

[gritty sinew]

so we have $f_n = f(t_n, x_n)$, $f_{n+1} = f(t_n + h, xn+1)$

[rocky lotus]

aPlatypus

[livid pier]

yeah, at least I get this part xd

[gritty sinew]

if you use f(t, x) = x+t [from the equation the question is about] what do you get for these two guys

[livid pier]

Do you want me to just substitute?
\$f_n=x_n+t_n$
\$f_{n+1}=x_{n+1}+t_n+h$

[rocky lotus]

Aruseq

[gritty sinew]

yes exactly

[gritty sinew]

now if you plug these two guys in the trapezoidal rule iteration what do you get ?

[livid pier]

$x_{n+1}=x_n+h/2*(x_{n+1}+x_n+2t_n+h)$

[rocky lotus]

Aruseq

[gritty sinew]

yep exactly

as I said earlier x(n+1) is on both sides of the equation

that's what makes this method implicit [instead of explicit like euler's method]

at least here the example is nice enough that you can solve easily for x(n+1) in terms of everything else

[livid pier]

should I do it?

[gritty sinew]

well that's what the question asks of you

"find an explicit formula"

how to compute x(n+1) in terms of the previous data

[livid pier]

okaaay, I thought explicit means without x_n xd then euler wouldnt be explicit either

so I get
\$x_{n+1}=\frac{2x_n+h(x_n+2t_n+h)}{2-h}$

[rocky lotus]

Aruseq

[livid pier]

and that's all?

prbbly not, I didnt even use x(t0)=x0

[gritty sinew]

it's just the starting point really, it's not that important overall

[gritty sinew]

what you/the computer is gonna spend most time on is the iteration there

[livid pier]

okay... so thats everything?

[gritty sinew]

yeah

[gritty sinew]

that's the formula you'd plug into your computer to get the next point from the previous one using the trapezoidal rule for that specific ODE given

[livid pier]

ye ye, I get it

[gritty sinew]

most times you can't even solve that equation algebraically like we just did

as wiki says

[livid pier]

okay, I see it

thank you so so much for spending so much time here, it's priceless ♥

.close

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[obtuse palm]

This is math question from a CSEC Past Paper (Caribbean Secondary/High School Math).
The answer is as in the picture. I would like to know and for someone to go through with me how do we arrive in that answer.
I understand the concept (or think i do) of y = mx + c
y being the y value, x being the x value, m is the gradient and c is the y intercept. (please correct me if im wrong). But i just dont quite understand how the answer is C. Help is very appreciated thank you.

[compact spindle]

You add 7y to both sides

Divide by 7

And you got it

[obtuse palm]

Hey! I still dont quite understand

[paper verge]

you need to leave y alone to reach ur y=mx+c equation

you will try to make that equation look like y=mx+c basically

[obtuse palm]

Hey! I still dont quite understand when it comes to this. Like where or how do i plug in the right figures etc.

[paper verge]

you have 3x-7y-9=0

[obtuse palm]

Yes

[paper verge]

no plug ins, you will just change places of the numbers

we need y value to be by itself right?

so separating it and sending it to the other side you get 3x-9= 7y

[obtuse palm]

Yes so it can be alone in y = mx + c

[paper verge]

yes

[obtuse palm]

Okay i understand that part

from -7y it becomes positive since we change sides

to a positive 7y

[paper verge]

okk now we just need to get rid of the 7 in the front of y

[paper verge]

exactly

[paper verge]

any ideas how to do it

[obtuse palm]

is the 3 in the equation representing the m in mx + c?

[paper verge]

no not yet

the equation isnt there yet

[paper verge]

?

[obtuse palm]

we need to take the 7 and place it on the other side. However im unsure where to put it. Its suppose to be dividing something correct?

[paper verge]

lemme draw it real quick

you divide it with 7 on both parts

[obtuse palm]

ok i understand that part

what are the steps we now need to take to get the gradient

[paper verge]

now u use the mx+c=y formula

the m is ur answer

[obtuse palm]

how do we use it then?

[paper verge]

what do u mean

i mean use as in it fits the criteria for the formula

[vale dock]

@obtuse palm Has your question been resolved?

[obtuse palm]

Hold on

I believe i understand

Just let me piece it together

ok, ive come up with the answer to it. So its asking for the gradient. Which is m. Using that since we put 7 on the left side it becomes what you see in the picture, therefore making it 3/7. Which is the answer for the gradient

Is this correct?

If they asked for the c which is the y intercept it would be 9/7?

[rigid whale]

y = (3/7)x - 9/7

y = mx + c

m = 3/7, c = -9/7

[vale dock]

@obtuse palm Has your question been resolved?

[vale dock]

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[midnight pier]

find the derivative of log(sin^2(x)) wrt sin(x)

[midnight pier]

it was on an exam but none of the options could match my answer

[green trail]

what did you get?

[midnight pier]

1/sin^2(x) * 2sin(x)cos(x)

[green trail]

how did you get that?

[midnight pier]

chain rule

and it was wrt sin(x)

[green trail]

that lets with 2/sinx

[midnight pier]

d(sin^2(x)) / d(sin(x))

[river adder]

Ig here we might need sin^2 (x) = t

Differentiate it

[green trail]

sinx=t

[river adder]

Nah

[green trail]

is the same

but yours is longer

[river adder]

dx/dt

[midnight pier]

i dont understand what you guys are hinting at

[green trail]

subtitution is your ally

[frozen zodiac]

what's the ques..?

[green trail]

reading is understimated

[midnight pier]

can you please first point out my mistake

because i remember learning it this way

and i want to know where i've gone wrong

[polar oxide]

send your work maybe ?

,, \frac{\dd}{\dd{sin^x}}\log(sin^2(x))

[midnight pier]

wrt sin(x) and not x

[midnight pier]

i didnt really have any steps i didnt show here

i just used chain rule

[green trail]

[
\frac{d}{d(\sin x)}\log(\sin^2 x)
]

[rocky lotus]

Samuel

[midnight pier]

and consodering that it was wrt sinx

[midnight pier]

yes

[green trail]

[
\log(\sin^2 x) = 2 \log(\sin x)
]

[rocky lotus]

Samuel

[midnight pier]

i will be back in 10

oh

why was what i did wrong?

[green trail]

who knows, whenever you show your work we can see

igtg now

[vale dock]

@midnight pier Has your question been resolved?

[midnight pier]

Please reply ping

[charred nacelle]

@midnight pier

@midnight pier you there??

[midnight pier]

yes

[charred nacelle]

Ok so

[midnight pier]

yes

[charred nacelle]

Anyways

How did you get that cosx to cancel with

[midnight pier]

derivatrive of sin^2(x)

oh that one

thats derivation of sin(x) wrt x

[charred nacelle]

check the derivative again

[charred nacelle]

.

[midnight pier]

2sin(x) * cos(x)

[charred nacelle]

exactly

now look what you sent

[midnight pier]

oh

ohhhhh

i got too carried away

thank you so much

.close

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[quaint kelp]

Hello, is there anyone that can help me with quadratics, final is next week and I'm waiting for one neuron to like click and understand it. So please, anyone?

[glass kelp]

Do u have like specific questions

[quaint kelp]

yes, in standard form, ax^{2}+bx+c if I remember right, what does the "b" veriable do. (as I may or may not forgot).

[silent fox]

the 2 numbers that myltiply to c need to add up to b

[quaint kelp]

may you explain furthermore please?

[silent fox]

yea

so if u hhave

x^2 + 7x + 10

what numbers multiply to 10

but add to 7

[quaint kelp]

5 and 2

[silent fox]

yea

so that means 5 and 2 add up to the b variable

(7)

[quaint kelp]

oh, ok thanks

[silent fox]

no prob

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[midnight pier]

i need help with arithmetic in general

[drifting hornet]

any specific question?

[midnight pier]

equations with congruence and diophantine equations

how to solve them

[obsidian cypress]

the exercice usually helps you with that

they give you the necessary steps to make it easier for you to solve it

but it depends in what type of equation

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[midnight pier]

Thx a lot

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[vital moon]

Hi

[vital moon]

I have a question regarding a mathematical philosophical question: Am I allowed to ask about this? It is regarding mathematical models and their usage

[drifting hornet]

ask, at worst you get redirected

[digital vapor]

yay summer is here

[vital moon]

Okay, so does anyone know anything about epistemic and non-epistemic values when you try to model something? It is related to for example mathematic modelings

[drifting hornet]

(in case you wont have luck here, you could try one of the advanced channels, e.g. #modeling or #foundations , depending on what's better suited for your question)

[vocal tusk]

yes someone knows

just ask ur question

[vale dock]

@vital moon Has your question been resolved?

[vale dock]

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[halcyon lintel]

whats the correct of order of operation when solving cosine law

r^2=650^2+550^2-2(650)(550)cos50?

[stiff lily]

the same as any other equation

[halcyon lintel]

im getting a different number though from what its suppoesd to be

not sure if i wrote down my notes wrong or what

[glass kelp]

show plz

[halcyon lintel]

650^2+550^2 = 725000

then i do the second part...

[stark wedge]

550^2 or 350^2?

maybe you are typoing it?

[halcyon lintel]

2(550)(650)cos50
= 247473.22

725000-247473.22

= 7002526.78

is that right?

[glass kelp]

,calc 650^2+550^2

[rocky lotus]

Result:

7.25e+5

[glass kelp]

,w 2(550)(650)cos(50 deg)

[stiff lily]

is that supposed to be 350 or 550

[rocky lotus]

Results provided by WolframAlpha

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

Requested by nuclearinteraction

[halcyon lintel]

its 650 and 550

[glass kelp]

is it 50 degrees

or radians

[halcyon lintel]

deg

[glass kelp]

u sure ur calc is in deg?

[halcyon lintel]

what answer are you getting?

[glass kelp]

.

[halcyon lintel]

that's your final answre? that's even more off

[glass kelp]

not my final

[stark wedge]

725000-247473.22
= 7002526.78

sus

how are you subtracting two 6-digit numbers and getting 7 million and change

did you do it by hand and screw it up

[halcyon lintel]

2(550)(650)cos50
does this not equal to 459593.1409??

[glass kelp]

u said it was this?? 😭

[stark wedge]

hold on so like, are we having a master class in how to use a calculator or what

[halcyon lintel]

725000-459593.1409

=265406.8591??

is that the answer?

[stark wedge]

yes that's the value of your expression

if this came from applying the law of cosines -- which it really looks like it did -- you'll want to take the square root of that in order to get back to the third side length.

[halcyon lintel]

that's still not the answer that was given in class

anyway...somebody is wrong

thanks

[stiff lily]

that'll be r^2

you're not quite done

assuming the end goal is to get r

what's the expected answer?

[halcyon lintel]

1,184,602

then you square root it, so final answer should be 1,088

[stiff lily]

did you copy down the question correctly?

can you take a pic of the original

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@halcyon lintel Has your question been resolved?

[vale dock]

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[halcyon lintel]

Yea sorry....I just realized it's cos130 not cos50... I'm getting correct answer now thanks!

[fickle quiver]

so close the chat

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[pseudo oak]

Hi, i just joined this server, because i just finished my pre-calc class this year, i would like to start learning calculus for my own, does anyone have any recommendation of what i should learn or memorize as a beginner?

[flint sparrow]

I would either use a textbook or Khan academy

[pseudo oak]

okay, i currently have (Calculus by Larson Edward, the ninth edition), is that one okay?

[faint ferry]

Hello, I am new to the server and I am at the end of grade 8, anything that I could do for high school like topics (I am doing physics on khan academy atp but any math topics would be helpful and suggestions).

[flint sparrow]

!occupied

[vale dock]

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).

[flint sparrow]

Looks pretty good

[pseudo oak]

thanks, also just in case, do i have to memorize all the basic derivatives and integrals, and if that is the case witch ones are the most relevants?

[raven oriole]

don't memorise. the best way to learn maths is by doing it so prioritise thinking deeply about a problem given what you've learned rather than try to memorise answers or formulas. knowing formulas from first principles is more powerful than just being able to recall without derivation

[pseudo oak]

thanks

[flint sparrow]

I would say that most students eventually do have them memorized, but start by deriving them with the definition

And as you do practice problems, you'll probably naturally memorize them

[faint ferry]

Someone help please.

[pseudo oak]

thank you so much you two for the help, I'll just start with the textbook, to see how it goes. 👋

[flint sparrow]

Use an unoccupied channel

[faint ferry]

where

[flint sparrow]

such as #help-28

or any of the 5 available ones

[raven oriole]

https://www.wolframalpha.com/problem-generator/

chatgpt can generate problems too

[pseudo oak]

you can use those avobe the ones that say occupied, gook luck with physics

[pseudo oak]

thanks you

[faint ferry]

physics aint that hard

good luck with calculus btw

[pseudo oak]

is not, i took honors in high school and is mostly know some algebra

good bye to you all, and thank you

how do i close the chat?

[faint ferry]

.close

that

[pseudo oak]

.close

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[wet tundra]

how do i do a?

[novel canyon]

use the properties of the integral that you can split it up

[rocky lotus]

water beam

[wet tundra]

what whys it equal c and a

[novel canyon]

bru

did they not teach you this

actually u dont even need to be taught this u can intuitively see for ur self why this is the case

[wet tundra]

why

[novel canyon]

look

[wet tundra]

shud i just graph a random func in my calc

to see

[novel canyon]

this is the graph of x^2

no

[wet tundra]

yes

[novel canyon]

no calculator

just look

what happens if you add the area from a to b

then add the area from b to c

[wet tundra]

idk it gets bigger

[novel canyon]

..

[wet tundra]

oh then it goes from a to c

[novel canyon]

yes it is the same as the area from a to c

[wet tundra]

what about psrt ii

[novel canyon]

same property

[vale dock]

@wet tundra Has your question been resolved?

[raven oriole]

fundamental theorem of calculus would certainly help

F'(x) = f(x). integral of f(x) from a to b is F(a) - F(b)

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[mortal sluice]

Can I get some help with a Janestreet Puzzle? It's just for fun so if somebody else needs help give them priority.

[mortal sluice]

The 11-by-11 grid above is divided into several regions. Place positive digits (1-9) into the cells. Every cell within a region must contain the same digit, and orthogonally adjacent cells in different regions must have different digits.

After doing this, place some tiles into the grid. Tiles are represented by blacking out a cell, and no two tiles are allowed to share a common edge. When a tile is placed on a cell, it displaces the value (digit) in that cell. That means the orthogonally adjacent cells, collectively, must be incremented by that displaced value. (For instance, in the example the rightmost tile displaces a 5. That displaced 5 results in increments of 1 for the cells below and to the left of the tile, and an increment of 3 for the cell above it.)

Digits may not be incremented any higher than 9. Incrementing digits may cause neighboring cells from different regions to contain the same value – this is fine. Some cells have been highlighted: these cells may not contain tiles and may not be altered by any of the increments.

And finally! Each row has been supplied with a clue. Every number formed by concatenating consecutive groups of un-tiled cells within a row must satisfy the clue given for the row. (As in the example.) Numbers must be at least two digits long and may not repeat in the grid.

The answer to this month’s puzzle is the sum of all the numbers formed in the completed grid. (As in the example.)

[mild kernel]

they mention an example?

[mortal sluice]

let me getthe picture

[mild kernel]

well what have you tried

they make it sound like you should be able to fill in all of the cells before placing tiles, but when you do this then the hints dont apply?

that doesnt make any sense to me

how are you supposed to know if youve placed them correctly or not without any other restriction

[mortal sluice]

the approahc ive been taking is to place the tiles as you go

and sometimes u just bump into contradictions

[cloud coral]

Product 25/product 20 seems to be the restriction to look at first

[mortal sluice]

right thats what i thought too but i didnt know where to go after that

like the (col, row) = (6, 6) could be a 1 or 5

*must be

[cloud coral]

Product 25, third square needs to be a tile

Otherwise too large i guess?

[mortal sluice]

hmm let me think i havent tried that yet

[cloud coral]

And hence can only push the extra value up

[mortal sluice]

wait y would that be the case?

im not seeing it

[cloud coral]

Obviously cannot have 1 digit numbers

[mortal sluice]

right

[cloud coral]

But 5 means "at least 5" or tile

But 25 has no bigger factors <=9

[mortal sluice]

wait sry im a bit slow rn bc ive been staring at this

can u use the cell number?

[cloud coral]

C6

[mortal sluice]

so we're assuming the left region starts with 5s?

[cloud coral]

If that region has 5s then this is a tile

[mortal sluice]

mm okay

checks out

wait couldnt a6 be a tile meaning c6 isnt necessarily a tile

[vale dock]

@mortal sluice Has your question been resolved?

[vale dock]

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[woeful latch]

I can't think of a less brute force method to figure this out, anybody have any tips?

[wraith heart]

What even is the question

[woeful latch]

Make an equation to be able to do this faster

[wraith heart]

What is "this"

[woeful latch]

I'm trying to calculate what the new weeks total distance would be if a runner should be able to run the previous week's distance multiplied by 1.1 or 110%

[wraith heart]

Oh

,calc 1.1^5

[rocky lotus]

Result:

1.61051

[woeful latch]

I can't think of a less brute force way other than to just do it manually

[wraith heart]

The operation you're looking for is called exponentiation

There are computer algorithms that calculate fast exponentiation

[woeful latch]

I officially feel dumb now 😂

Thanks for the help

.close

[vale dock]

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[vale dock]

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[clever sigil]

So, Just to be clear...I am not in a quiz rn, this is me studying. And I need help because I don't understand why the other base is equal to x but on the right it's 15-x...why is it just x and not 15-x???

[clever sigil]

So is it because, x=part of 15, let's say 15=y+x? so y=15-x?

[next vortex]

so the length of both bases combined is 15, and the length of the left base is x

so the length of the second base has to be 15 - x so that we can get 15 when we add em together

[vale dock]

@clever sigil Has your question been resolved?

[tired phoenix]

Yup that's right

[tepid wind]

Please don't multipost; this makes it clear to helpers what progress was made on a question.

[vale dock]

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[silent fox]

Hi

[silent fox]

How do i do this 🙏

[gloomy harness]

$\frac{1}{\frac{a}{b}} = \frac{b}{a}$

[rocky lotus]

Flatus

[golden gate]

!status

[vale dock]

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

[silent fox]

i factorised the right

idk how to do the 3 part

[gloomy harness]

$\frac{1}{\frac{a}{b}} \cdot \frac{b}{b} = \frac{b}{a}$

[golden gate]

!showyourwork

[rocky lotus]

Flatus

[vale dock]

Show your work, and if possible, explain where you are stuck.

[gloomy harness]

that's the proof

[silent fox]

ohh

[gloomy harness]

do you know what to do next?

[silent fox]

yes

ill do it rq

[gloomy harness]

alr bet

if u still got a problem ping me

[silent fox]

nvm i dont get it @gloomy harness

[neon summit]

${x}^2 - 1 = {x}^2 - 1^2 = (x+1)(x-1)$

[rocky lotus]

Astar777

[silent fox]

.. .o

i don get it

[neon summit]

$3 - \frac{(x+1)(x-2)}{x^2-1}$

[rocky lotus]

Astar777

[neon summit]

$3 - \frac{(x+1)(x-2)}{(x+1)(x-1)}$

[rocky lotus]

Astar777

[gloomy harness]

where are you up to

[gloomy harness]

ur js giving the answer..

[neon summit]

i mean

he didnt get the previous hint

this was the next step

i didnt give more after that

[vale dock]

@silent fox Has your question been resolved?

[vale dock]

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[cunning ruin]

Hello

[cunning ruin]

I want to find the continuity of the greatest integer function

using mathematical arguments

I have tabulated the graph, and observed that the graph breaks at integral variables

I do not wish to proceed with the diagram

There are two cases:

Case 1 is for interior points

Case 2 is for integral points

I can complete case 2 with ease, but I'm facing troubles with case 1

Please help

[timber burrow]

What are those interior points?. Points other than integral points?

[cunning ruin]

Right, they are those points.

[timber burrow]

U know the graph right

[cunning ruin]

I know the graph

[timber burrow]

There is no discontinuity in the graph at interior points.

[cunning ruin]

Can you prove it mathematically?

[timber burrow]

Like not graphically

[cunning ruin]

Right

[timber burrow]

Do you know the condition for continuity. Lhl=rhl=f(x)

[cunning ruin]

I know it. Continuity at a point

[timber burrow]

Then use it

[cunning ruin]

I need some help with the general expressions required to use it

[timber burrow]

Let a be any non integral number between n and n+1

Where n is an integer

[cunning ruin]

Right

[timber burrow]

gif(a)=n

Lim h tends to 0 gif(a-h)=n

Since a-h is very close to a.(Only just smaller)

[cunning ruin]

Right

[timber burrow]

Similarly lim h tends to 0 gif(a+h)=n

[timber burrow]

So this condition is satisfied.

[cunning ruin]

What about the point just to the left of n+1

[timber burrow]

a+1??

[timber burrow]

Why are you looking into a+1?

[cunning ruin]

The function isn't continuous at that point, intuitively

But there's no way to prove it using my basic mathematical knowledge

[timber burrow]

Forget about a+1

[cunning ruin]

No, the point just to the left of n+1

It is an edge point

[timber burrow]

We just proved function is continuous at a
Where a is an interior point

You understood that part??

[cunning ruin]

I made a typing error

Edit: What about the point just to the left of n+1

The function isn't continuous at that point, intuitively

But there's no way to prove it using my basic mathematical knowledge

It is an edge point

[river adder]

Depends on the function

[timber burrow]

Greatest integer function

[cunning ruin]

The function is the greatest integer function, f(x)= [x]

<@&286206848099549185>

[river adder]

Obviously it will be n
Like for example if u put n= 3
So left of n+1 will be 3

[cunning ruin]

No, the discussion is about the point that lies just to the left of 4

The point which we can't locate

[river adder]

It's ans Will be 3 ofc

[cunning ruin]

But, to the right the answer will be four

[river adder]

Yes

[cunning ruin]

So, the limit does not exist at this theoretical point

[river adder]

It's greatest integer function so yeah

[river adder]

Do u know it's graph

See that u will understand

[cunning ruin]

But books say there is only one kind of point of discontinuity

For this function

The integral points

[river adder]

Yes

All of them

4 is too

Tats why

[cunning ruin]

But there is another kind: all points that lie just to the left of the integers

[river adder]

For them there actual no. Or integer will be answer

Like left of 4 and right of 3 all will get same answer 3

[cunning ruin]

They are not the same kind of points

Right

Left of 4 makes the function discontinuous, as does 4 itself.

[river adder]

Discontinuity at integers

[cunning ruin]

Discontinuity at points to the left of integers

[river adder]

Nah its discontinuity at integers

See graph first

[cunning ruin]

A graph is a slow and imprecise form of mathematics

[river adder]

U will not get that without graph

[stark wedge]

it's kind of silly to completely eschew graphs though

[cunning ruin]

I have despised drawing since childhood

Tbh

[river adder]

@stark wedge what will graph of it

[cunning ruin]

I know it

It is a bunch of steps

[river adder]

It's like leader (what's that called)

[cunning ruin]

They start at integral points

[stark wedge]

it's like a staircase is how i would describe it.

[cunning ruin]

Would you say that the function is discontinuous at points just to the left of the integers

[river adder]

No

[cunning ruin]

I've taken a mild liking to drawing as an adult though

why not?

[viscid sedge]

discontinuous at integers

[river adder]

It's at integers as i said earlier

[cunning ruin]

@stark wedge what do you think?

[viscid sedge]

continuous elsewhere

just plot it

[stark wedge]

wdym "just to the left"?

[cunning ruin]

Of course it is integers

[viscid sedge]

,w plot floor(x) from x = -10 to 10

[stark wedge]

how far left?

[cunning ruin]

The point that lies immediately to the left of the integer

It is a theoretical point

[rocky lotus]

Results provided by WolframAlpha

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Requested by _nofluxgiven

[cunning ruin]

@stark wedge

I know that it is discontinuous at the integers

[stark wedge]

there's no such point in the real numbers that i know of

what is this point "immediately to the left of" 0, for example?

[cunning ruin]

But what about the points that lie immediately to the left of the integers

I have assumed it exists

[stark wedge]

tell me what this point is called -- i don't know of one.

[cunning ruin]

I don't know what it is yet

[stark wedge]

are you positing that there exists some number $u$ exists that $u < 0$ but there aren't any numbers between $u$ and $0$?

[rocky lotus]

Ann

[cunning ruin]

Right

I want to assume that there exists such a u

[stark wedge]

u/2 would like to know your location

[cunning ruin]

I assume that the number is indivisible

I am thinking of it to be like an indivisible subatomic particle

[cunning ruin]

Let this number be the only number that cannot be divided further

and every number lies at u distance from the neighbouring number

[stark wedge]

so you assume that some numbers cannot be divided by 2...?

this is no longer real numbers you're talking about

there are no subatomic particles in the reals!

[river adder]

Huh

I'm offended

[stark wedge]

are you serious or joking @river adder

[cunning ruin]

I am assuming that it cannot be divided by any number greater than 1

[river adder]

Serious ig
Ok I'll take it as a joke

[stark wedge]

well you can assume anything you want if you are ok staying in fantasy land

[stark wedge]

aight off to #serious-discussion we go

[cunning ruin]

If you keep on probing you will finally hit an indivisible quantity. I am not sure if the indivisible quantity will always stay the same...

It is natural

Why isn't there a branch of mathematics that makes this assumption?

[stark wedge]

dude it's not even true in rational numbers

[cunning ruin]

Mathematics is supposed to mirror the physical world

[pine prairie]

no math is made up jargon for lunatics

[cunning ruin]

I say that mathematics needs rethinking

[pine prairie]

it just so happens to sometimes approximately describe the physical world

[sharp whale]

something is happening? its time to investigate

[cunning ruin]

But assuming that such a point exists, the function is discontinuous at two types of points

[sharp whale]

hey do you want to hear something crazy

[cunning ruin]

What are you going to talk about?

[edgy meteor]

wtf is happening here

[sharp whale]

@cunning ruin there are such things as sets that have no beginning nor end, but are bounded

these are an unfortunate consequence of infinite sets

[pine prairie]

there are even sets with no meaningful measure of length too

[sharp whale]

for example, consider the set of proper fractions

[pine prairie]

[river adder]

Tell me first what do u mean when u say function is continuous at this point

[sharp whale]

for any number you can name, you can divide it by 2 and get a smaller number