help-0

[true cairn]

Hello

I need help with my homework

[alpine sable]

Send the question, if someone is available they will assist you

[true cairn]

Let g(x) be the transformation of f(x) translation 3 units to the left and up 2 units

How do I do this

[lusty plaza]

<@&268886789983436800> this dude's nickname

[sly mantle]

ty

[tropic ice]

do you use significant numbers in scientific notation

[glass lichen]

yes

you use sigfigs if you're asked to use sigfigs

[true cairn]

bump

[tropic ice]

but as a general rule

you should use sig figs on scientific notation

[placid zinc]

f(x - (-3)) + 2

[true cairn]

I get the 2 part

but not the 3 being negative

[placid zinc]

That's just the form haha
Going right by 8 would be f(x - 8)

[true cairn]

its going left tho

[placid zinc]

That's why I put -3

[true cairn]

g(x)=(x+3)+2

is what i got

[tropic ice]

left = subtraction right = addition

[true cairn]

isnt it the opposite

[tropic ice]

when you add to x

[placid zinc]

g(x) = f(x + 3) + 2 correct

[tropic ice]

which way do you go on a graph on the x line

[true cairn]

so i got it right?

[placid zinc]

Yes, except that you're missing f, but I assume that's a typo

[true cairn]

ye mb

[tropic ice]

@placid zinc why isnt 3 units to left be subtraction

[true cairn]

Vertical stretch by a factor of 3 followed by a translation down 3 units

how do I do this

[placid zinc]

g(x) = 3f(x) - 3

[true cairn]

so no reciprocal?

[placid zinc]

None

That's for horizontal

[true cairn]

what about bertical compression by a factor of 1/2 followed by a translationm left 6 unitw

units

[tropic ice]

?

[placid zinc]

If you do have the answer, I'll check it. If you don't, I encourage you to try and get it. You can do it with what we've already talked about

[true cairn]

I know its -2 amd +2

[placid zinc]

So if g(x) = f(x - 3)
Then g(x) is exactly the same as f(x), except translated 3 to the right.

If we plug in x = 4, we can see a concrete example:
g(4) = f(1)
That is, g stores the same info as f, except 3 points to the right

[tropic ice]

what

doesnt f go to the left of the x axis

so the original 4 point goes left to the new 1 point

[true cairn]

@placid zinc I got g(x) 1/2IXI+2

[placid zinc]

You are correct, that f is 3 points left of g

That's yet another way to show that g is 3 points right of f.

Remember, f is the "original function"

[tropic ice]

oh I thought g is the original function

[cloud zinc]

for question 18.c, how can we find one of the two pears are good

I tried doing 15/20 * 5/19

got a different answer from my textbook

would it be better to draw up a venn diagram?

[placid zinc]

You've found the probability that the first pear is good, and the second pear is bad

[cloud zinc]

yep

1/14 and 21/36

[placid zinc]

No, this specifically is the probability that the first pear is good, and the second pear is bad

Which is not what you want. You want the probability that one of the pears you draw is good, and one of them is bad

[cloud zinc]

aight, so is it better to draw a tree diagram?

[placid zinc]

Yeah! That will work for you

[cloud zinc]

nicee

I'll try that

[tropic ice]

4.66*10^-2 * 5.5 * 10^3 = 26. *10^-1

is the 26. correct scientific notation>

?

[scarlet atlas]

15 are good

[cloud zinc]

yep I got the answer

looks like drawing the tree diagram is more benefitical

[alpine sable]

Hey everyone. I dont get how Ln and Lim change places. Can anyone explain me this "rule"?

[open blaze]

Hmm, mind if you tell me the limit it is approaching to? @alpine sable

Wait...

It doesnt matter

since no matter what

[placid zinc]

lim can enter a function if the limit exists after doing so

[open blaze]

the limit would be something like N -> 123

so in which case, it literally does not matter

The logic is that as long as what Kaynex said is true

[alpine sable]

It is to + infinity

[open blaze]

it doesn't matter where the limit is, because the limit is just a statement evaluating a function when n approaches any number

in which case, it doesnt matter where the limit is

[alpine sable]

So, as both ln and lim approaches to + infinity, thats the reason why they can change places like that?

[placid zinc]

lim can enter any function if the limit exists after doing so

As for reasoning, well, see how both lines are basically saying the same thing, despite the order swap

[alpine sable]

Yh, I think I get it now, thanks!

why does f'(c)=0 at those 2 points

[snow nest]

the gradient of turning points, points of inflections, and (i think, endpoints aswell) are always = 0

[alpine sable]

In those points, the tangent lines are 0.

meaning the function is almost constant around the point (c)?

[snow nest]

how can you have c at two different points?

[alpine sable]

its just a way of making it simpler. we can call them different ones if u want

[snow nest]

oh okay, mb

wdym by constant

i'm new-ish to differentiation still

[alpine sable]

ah well, the derivative f'(x) is the rate of change of the value of the function relative to the change of x. so f'(c) (the second green point from the left) is at the local maximum, so its at a constant rate of change at the max point on that interval

therefore the derivative at that point (c) is = 0

fuck i answered myself

[hollow pelican]

hi guys does anyone know how to solve question3a

[placid zinc]

Note that 1/j = -j
Which is easy to show by taking j² = -1 and dividing both sides by j

[hollow pelican]

so i need to sub all j as squareroot -1 into this question?

[ocean tide]

Do here any russians?

[ocean tide]

I want to ask a terminology

[vale wigeon]

i am russian

what did you want to ask about

@ocean tide

[vale wigeon]

👻

[vale bison]

How did you reach from step 2 to step 3?

@alpine sable

[gaunt magnet]

[astral dagger]

it's called partial fraction decomposition

[vale bison]

Oh

I didnt study about it thanks for the heads up

[astral dagger]

[tender star]

this emoji is golddd

[thin raft]

Hi! So I am struggling with recursive and explicit formulas. The formula is the previous term doubled +0.01, but I am unsure how to covey this is recursive/explicit formulas

[warped cave]

i need help i dont know what 9+10 is

[solar shore]

19 🙂

[quick surge]

can someone teach me this

i have no clue on how to do this

[rocky fossil]

@alpine sable what have you tried?

[rocky fossil]

That's the right line of thinking. Remember that you're assuming that f has roots in F_p, so there's some x such that f(x) = 0, can you show it must have another one?

there are a couple ways depending on what you want to use about F_p

one way is to say that if there is another root b, then you must have that b is plus or minus k

Try to show it

[quick surge]

oh my question got skipped

[rocky fossil]

not really, it's unclear to me how that implies that b is in the congruency class of either k or -k

I mean, you're assuming that sqrt(a) only has two solutions to say this

you know that b^2 = a (mod p) and k^2 = a (mod p)

this means that b^2 = k^2 (mod p)

[vale bison]

Its 910

[rocky fossil]

again, how do you show that square rooting both sides is valid?

[alpine sable]

Fractional decomposition

[alpine sable]

Do you know what's the union

[quick surge]

yes

i know simple stuff

my teacher is telling us to do something we dont know

[alpine sable]

Bruh

Ok wait

[quick surge]

A = {1, 3, 5, 8}

B = {2, 3, 6, 7, 8}

A U B = {1, 2, 3, 5, 6, 7, 8}

A ∩ B = {3, 8}

i know this

[alpine sable]

Exactly

[quick surge]

but

whats the n

[placid zinc]

Number of elements in set

[quick surge]

wat

can u give me an example

[placid zinc]

n({a,b,c}) = 3

Doesn't matter what a,b,c are

[quick surge]

ohhhh

to see how much stuff

are in there

is it?

[placid zinc]

Ye

Number of elements in the set

[quick surge]

ohhh

what does this mean

[placid zinc]

I'm guessing ξ is "the universe". So, there's 9 elements in total.

(A U B)' has 1 of those elements

[quick surge]

what

[placid zinc]

That means A U B has the other 8

Or, is there something else that explains what ξ is supposed to be?

[quick surge]

nono i dont understand what do u mean 9 elements

in total

[placid zinc]

So there's 9 elements.
ξ has them all.
A and B have some of them.

[quick surge]

ohhhh

[oak chasm]

It's for the universal set: https://en.wikipedia.org/wiki/Xi_(letter)#Pure_mathematics_2.

[placid zinc]

Cool good I assumed so

[quick surge]

what does this mean

i asked the question and u guys just discussed here

[placid zinc]

@quick surge
I'll meet you #help-8

[quick surge]

oh ok

[rocky fossil]

yeah this is right

[gaunt magnet]

hi

got 16x^3-3x^2/2

[rigid smelt]

Seems good

[sharp barn]

How do we solve this?

[placid zinc]

Note that the domain of f^-1 is the same as the range of f

So you really want the range of x² + 2, x ≥ 0

[sharp barn]

2

so that the inverse functions range are the same as the original?

[placid zinc]

The domain of the inverse is the range
The range of the inverse is the domain

[alpine sable]

I know I'm supposed to multiply the fractions somehow to cancel them out

dunno how

[sharp barn]

then what about b

[rigid smelt]

The range of the inverse is the domain

Works with the same logic

[sharp barn]

but for a its 2

[rigid smelt]

So?

b is different

For b you take the domain of the original function

That is the range of your inverse

[sharp barn]

the domain for be is x>= 0

so the range is 0?

[rigid smelt]

No...

You literally said the domain of the original function is x>=0

Does that looks like the range of the inverse should be y=0?

[sharp barn]

The range of the inverse is the domain thats what u said

[rigid smelt]

Yes thats true

But the range is not 0

The range is y>=0

[tough hatch]

they're referring to the set [0, infinity)

[rigid smelt]

Theres a very big difference

I know

But at least say it correctly

Because it will lead to many misunderstanding

[tough hatch]

well i tried many times, yet they persist with this "notation"

and see, they just ignored that

lol

[rigid smelt]

Referring to scroll:
The range and domain implies a set of values. If you say that the range is 0, people will imply that this set has only one element which is 0 and thats very not true.

Note that im not saying that the "phrase the range is 0" is not technically correct or sth, im just speaking on the behalf of your inaccuracy. (Also to scroll)

[tough hatch]

ig they are just lazy in interacting with people

[rigid smelt]

🤷‍♂️

[sharp barn]

wait so how doesThe range of the inverse is the domain

[rigid smelt]

Properties of inverse

Or maybe definition

Yeah actually thats just the definition lol

The inverse is defined to be a function that gives you back the input of some kind of function

You can think as such

Hence from that idea, you can pull out the conclusion that if it takes the output and it gives you the input of the original function, then that must mean the output/range of the original function is the input/domain of the inverse.

[gaunt magnet]

do u get -13 for this

[rigid smelt]

And likewise

[sharp barn]

we get the range for (a) by putting the 0 into the x of the original function

but what about (b) we dont need to put in 0 into the function to solve it?

[rigid smelt]

Yes, because you already have the domain

What else should you be solving for?

[sharp barn]

for (a) we dont already have the domain?

[rigid smelt]

you do....

the domain is listed as x>=0

for both a and b

[sharp barn]

yeah

[rigid smelt]

for a you dont need the domain of y

you need the range

but for b, you only need the domain

which you already had

could you see the difference?

[sharp barn]

we need the domain for b to find the range amiright?

[rigid smelt]

yes

[sharp barn]

and we already have the domain

[rigid smelt]

yes

[sharp barn]

so b we can just write 0

as for a we need to find the domain

but a has already gave us x>= as a domain

[rigid smelt]

as for a, you need the range of the original function

not the domain

jsut remember, original turns -> inverse means domain -> range and range -> domain

like its just opposite

theres more to it

but i guess you will know that later on

[sharp barn]

The domain of the inverse is the range
The range of the inverse is the domain

so this is accutrate?

[tough hatch]

it's better to teach it step-by-step to them
speaking from experience

[rigid smelt]

i guess so

[tough hatch]

The domain of the inverse of f is the range of f
The range of the inverse of f is the domain of f

to be more precise and avoid repeated confusion

[sharp barn]

ok alright then thank you guys

[short spear]

y=-2x^2+4c

how am i meant to find the x int

[rigid smelt]

i suppose they want you to find it in terms of c

with an appropriate c ofc

[short spear]

i need to graph that equation

but idk how to find the x int

i know that i need to make y = 0

so -2x^2+4x = 0 but i don't know what to do next

[rigid smelt]

can you post the whole problem?

because there are infinitely many graphs of -2x^2 + 4c unless there is some kind of number restrcitions on c

[short spear]

question : sketch the following curves

[rigid smelt]

like for integer c in [1,2] or something

ok that looks nothing like you said

[short spear]

oh mb

i meant to say x not c

[rigid smelt]

anyway, see that you can factor x out of -2x^2 +4x

or you can use the quadratic formula

whichever you prefer

[short spear]

so it would become y = x(-2x+4)

[rigid smelt]

yes

x(-2x+4)=0

[short spear]

then i can find the x ints

[rigid smelt]

you can solve this now for x

yes

[short spear]

thanks :)

[alpine sable]

Hi

How do I even start with this

I have no clue

[alpine sable]

@oak chasm

Hey

Can u please help me too

That would be very much appreciated

[ionic jewel]

i don't even know what level of math this is but I imagine most people arent helping cuz they don't know how to do it

[oak chasm]

My guess would be, since the answers are integers, that p, q, and r might be integers.

There aren't too many triples of integers that fit the restriction in the problem.

[ionic jewel]

ah yes, guess and check

[oak chasm]

So, I'd try all of them.

[alpine sable]

Hmm

the negative is throwing me off here

[oak chasm]

@alpine sable Sorry, channel is busy.

#help-4 seems open.

[amber urchin]

Maybe right side can be used with newtons binominal theorem?

[alpine sable]

Hmmm

That is going to make this messy

[amber urchin]

True

Maybe finding actual value will work

[oak chasm]

You can also use the answers as restrictions on the values as well to get it below 56 triples.

[alpine sable]

Oof

What is that

This question was there in my number theory assignment

[amber urchin]

If that helps, it cannot be A cuz numbers have to be smaller than 10 and the answer is 31

[alpine sable]

Yeh

That’s a good point

[sharp barn]

How do we solve for (b)

[alpine sable]

Plug the value of x into f^-1 and solve the equation

Does this make it clear?

[marble hemlock]

You write out the inverse f (a) and then replace x with 5, then you have an equation with variable k to find out

[alpine sable]

Lol I didn't see the inverse

aleks keeps telling me I need to flip 4/-7 to -4/7

but providing zero explanation why as always with aleks

[covert berry]

Because negative sign is usually placed in the numerator instead of the denominator, as a convention.

[alpine sable]

why would it matter

I didn't do it and it made my answer wrong as a result

I tried doing
-(4/7) - 3/5
-(20/35) - 21/35

[covert berry]

Because it hasn't achieved its simplest form.

[alpine sable]

I'm saying my answer was totally off

it was opposite

something was being negated when it was supposed to be added or something

[covert berry]

$\frac{-31}{35}$ is the simplest form. $\frac{31}{-35}$ is not yet so.

[ocean seal]

moono

[alpine sable]

It shouldnt matter if you do the computation right

the conventions on negative signs in fractions

are making no sense at all to me

why do we have three ways to write the same thing

and if they are all equivalent

31/-35 is a negative number

why is only one of them the most simplifeid

so is -31/35

They are the same

[covert berry]

I like your questions.

Always question the man.

[alpine sable]

Most simplified is not a mathematical thing, just makes it easier to compute

Why is -31/35 more simplified than 31/-35

[icy trail]

i dont think it is? theyre the same

[alpine sable]

It's just notation

But I understand the confusion

[sudden tulip]

how do i even solve this

i tried finding coordinates of q by finding the length of the line

since the lengths are the same

but i always cancel out the values

[vale wigeon]

@sudden tulip you might find it useful to know that OQ is perpendicular to PR

[sudden tulip]

i cant tell

[vale wigeon]

OPQR is a kite. it is symmetric about PR.

[sudden tulip]

ok ao even if i know its a perpendicular

what do i do

[vale wigeon]

you can use this info to find the slope of OQ

[sudden tulip]

how i dont get it

[tough hatch]

m1 = -1/m2 where m1 and m2 are the slopes of perpendicular lines

[vale wigeon]

mr. unpingable-two-thirds has given you a formulaic reminder to that end.

[sudden tulip]

ok...

is it like a perpendcular bisector

[vale wigeon]

OQ? no, OQ is not the perpendicular bisector of anything in the picture.

PR is a perpendicular bisector of OQ though.

[sudden tulip]

i still dont understansd

[vale wigeon]

the slopes of a pair of perpendicular lines are negative reciprocals of one another.

surely you are able to at least find the slope of PR?

or, sorry, the GRADIENT as you'd rather call it

[sudden tulip]

yes i can i try now

[vale wigeon]

@alpine sable channel busy please move

[alpine sable]

My bad

[sudden tulip]

yo

its -2 for slope of pr

[vale wigeon]

PR

case-sensitive

but yes the slope of PR is -2

now what's the slope of OQ?

[sudden tulip]

how

[vale wigeon]

@lament nimbus channel busy please move

@sudden tulip you've already been told exactly how

[vale wigeon]

here

[vale wigeon]

and here

[sudden tulip]

damn i forgot that

m2 is 1/2

therefore how do i find the equatin

[vale wigeon]

so the slope of OQ is 1/2 yes

notice also that OQ goes through O

the origin

[sudden tulip]

yep

so sub 00

damn im dumb

i have a problem

look at this

[vale wigeon]

this is a different question

ok

[sudden tulip]

ii is wrong omg

[vale wigeon]

you say the coordinates of D are (5, -3)

where did you get that from?

[sudden tulip]

i solved it on my own

[vale wigeon]

you will have to show the work that led to it, because i can say for sure you have made a mistake somewhere

and given that just now you struggled with recalling how the slopes of perpendicular lines are related, i'm almost certain of it

[vale wigeon]

,rccw

[vale wigeon]

what is this about?

you cannot conclude from a/b = c/d that a=c AND b=d.

by your logic, 1 = 5 because 1/2 = 5/10.

[sudden tulip]

y not they are parrallel

[vale wigeon]

you're trying to conclude that -5-y = 1-3 and also that 1-x = 3-7 just from the slopes being equal

im telling you thats wildly incorrect

forget about lines and parallelism

this is a matter of simple algebra

you claim that from the equation $\frac{a}{b} = \frac{c}{d}$ it is possible to conclude $a=c$ and also $b=d$. is that what you claim or not?

[ocean seal]

Ann

[sudden tulip]

yes

[vale wigeon]

then you are claiming 1 = 5.

[sudden tulip]

the answer for the first part is correct tho

[vale wigeon]

you

are

claiming

that

1

and

5

are

the

same

number

[sudden tulip]

theres an unknown

[vale wigeon]

you are claiming that 1 and 5 are the same number

[amber urchin]

@vale wigeon we can chill out

[vale wigeon]

by your logic, since 1/2 = 5/10, it must be that 1 = 5 and 2 = 10

[amber urchin]

We are here to help

[vale wigeon]

roxer99, would YOU like to explain to team bayern how nonsensical their reasoning is?

[amber urchin]

If they stick to "their" method and don't give in for the facts, then it is better to step away

No I would not

And I don't recommend

[sudden tulip]

say that i did not say th denominators and numerators are the same

am i still correct like the fraction

[vale wigeon]

i wasn't contesting the equation (-5-y)/(1-x) = (1-3)/(3-7).

i was contesting what you derived from it.

if you hadn't done this bullshit step, you would have ended up at the equation of AD. you would not get the coordinates of D, but there is nothing wrong with that.

[sudden tulip]

ok so how should i get the coordinate

[vale wigeon]

do parts i and ii first

get the equations of AD and CD

D will be at their intersection

you know about AD that it passes through A and has a slope equal to that of BC

you know about CD that it passes through C and has a slope equal to the negative reciprocal of that of BC

[alpine sable]

how to solve this?

[amber urchin]

Are calculators allowed?

[alpine sable]

what do you mean?

[amber urchin]

Well, I want to know if you are allowed to use the calculator to solve this question?

[alpine sable]

ya sure

[amber urchin]

Ok, palindromic number is the number that remains the same when written out forwards and backwards\

For example 101, 1221 and 123454321

[alpine sable]

ok

[amber urchin]

So, to find out, take a square root of the answers and with that you can find out which answer is a palindromic number

[dull onyx]

how would i go on abt solving this 😵‍💫

$\lim_{x\to 0}[(x+1)\frac{x}{x^2-1}]$

[ocean seal]

mario

[dapper tendon]

can someone teach me calculus out of good will ;-; ( i mean ig u ll have a good revision teaching too) BUT I REALLY REALLY NEED HELP PLEAASSEE

[dull onyx]

um

khan academy

[tough hatch]

notice that x^2 - 1 factors into

___ and _____

[dull onyx]

oh sorry i should’ve deleted it bc i kinda figured it out @tough hatch

i factored it into x-1 x+1 then got x over x-1

and i got 1/2 idk if its correct doe!

[tough hatch]

why 1/2?

0 / (0-1)

does that look like 1/2 to you?

[dull onyx]

what

omg

HELP

i wrote the wrong thing here im so sorry

$\lim_{x\to -1}[(x+1)\frac{x}{x^2-1}]$

[ocean seal]

mario

[dull onyx]

thats what it is</3 sorry

[small bear]

what is x^2 - 1 equal to?

do you know how to factor it

?

[stone scroll]

It is not, cube root of 144 =5.24

[dull onyx]

yes i already said i solved it

i just wrote the wrong number on the limit

[alpine sable]

Just wondering. Is L'Hopital's rule just that you turn f(x)/g(x) to f'(x)/g'(x) and keep derivative the numerator and denominator until the lim x->0&infinity is defined?

you dont want 0/0 or infinity/infinity since that is not defined (in calculus math)

[tough hatch]

u mean differentiating the numerator and denominator

until the lim x->0&infinity is defined?
what do you mean?

the limit should always exist

and both f and g must be differentiable on the interval of interest

and continuous

@alpine sable

a limit resulting in the indeterminate form (0/0) or (infinity/infinity) does not imply that the limit doesn't exist

[dusk solstice]

I need some help

[tough hatch]

stick to one channel only

[dusk solstice]

Ok

[alpine sable]

Okay. I am currently studying on this and trying to understand the idea. So what you are looking for i the limit

When you use the rule

[tough hatch]

and you can only use lhopital's if f and g are both continuous on the interval

[alpine sable]

okay

and if they are not, is the problem then undefined?

[tough hatch]

not necessarily

there may be other methods to evaluate the limit and get a value

depends on the problem

[alpine sable]

okay

I am watching a khan academy video and Sal repeats the rule

[tough hatch]

iirc, khan also has a chapter which includes a flowchart for evaluating limits

[alpine sable]

does that only work if f(x) and g(x) are continues on the interval

[tough hatch]

yes, i just said that.

[alpine sable]

I meant for repeating the rule

[tough hatch]

huh?

are you asking about lhopital's, or the flowchart i mentioned?

[alpine sable]

f'(x)/g'(x) -> f''(x)/g''(x)

[tough hatch]

their limits are equal if f' and g' are also differentiable

on the same interval

as for f and g.

[alpine sable]

okay

I think I got it

thanks 🙂

What would happen with
lim n->infinity (a+b)^n

I kinda forgot how this worked

[median tendon]

If a +b is smaller than one, what do you think the limit would reach?

Then, if a+b is larger than 1, would would thr limit reach

Lastly, if a+b =1, what would the limit reach?

[alpine sable]

0?

[alpine sable]

Infinity right

[median tendon]

Seems like it

And the last condition?

[alpine sable]

0?

because both a, b < 1

[median tendon]

1 x 1 x 1 x 1..... =?

[alpine sable]

1

[median tendon]

There we go

[alpine sable]

Wait what

[red phoenix]

But a+b < 0 if a+b < 1

or atleast can be

[median tendon]

Oh yes

Put abs signs on the conditions ig

[alpine sable]

o i thought a, b could go from 0 to 1 only

idk how to express that

[small bear]

does it specifically say what a and b are in your problem?

[median tendon]

In your question u did not specify any boundaries

[alpine sable]

right

[median tendon]

If you want stability, then yes, a+b<1

I.e. limit goes to zero

[alpine sable]

No i mean

If (a+b)²= a² + 2ab + b²
i was wondering what would happen when n is incredibly big in (a+b)^n

probably couldve worded my question better

[small bear]

A couple of things would happen, first let x=a+b

we want the limit of x^n as n goes to infinity, but we must consider cases first

what do you think we would get when |x|<1, or simply, 0<=x<1?

(first the positive part)

to help you out, we have some small number x raised n-times, so x multiplied by itself many times keeps getting smaller right?

[alpine sable]

Yeye

Sorry for answering late, had to go do smthn

[small bear]

no worries, that means that for x between 0 and 1, x^n goes to 0

now, consider what happens when x=1

x^n = 1^n which is just one

[alpine sable]

Yes

So far so good

[small bear]

when x>1, the number would then get bigger, x^n -> infinity

[alpine sable]

oh yea

[small bear]

great, those are all the positive numbers of x

for the negatives we have something different (since the sign can create a problem)

[alpine sable]

let x ∈ N

the n of natural numbers

idk how to type it

[small bear]

alright

then we only have two cases

x=1 meaning x^n = 1^n = 1

[alpine sable]

awesome awesome

[small bear]

and x>1 meaning x^n -> infinity

I want to go back to the a+b thing

if a,b ∈ N

[alpine sable]

i see i see

[small bear]

we would always have (a+b)^n -> infinity

[alpine sable]

o makes sense

ty for ur help

[small bear]

np

[alpine sable]

similar to the (a+b)^n thing

Is there a formula for it

like

[small bear]

yes there is

the binomial formula

[alpine sable]

(a+b)^9199 besides using pascal triangle

DAMn fr?

[small bear]

yup, you can check it out here https://en.wikipedia.org/wiki/Binomial_theorem

[alpine sable]

Daaamn

Tyty

[small bear]

instead of pascal, you just use the binomial coefficients which are easy to calculate

[alpine sable]

I thought that there could be a hyper mega complex formula using series with the sigma notation

[small bear]

(well, relatively easy for smaller numbers since they contain factorials)

[alpine sable]

I see i see

Ty again

[quaint pond]

hello i have question about the solution to the following problem:

i know the answer is binom(52 + 10 -1, 10)

but like

why not

(520, 10)?

[small bear]

Pretty tough problem, but it wouldne be 520 choose 10 since we would overcount

[quaint pond]

how so?

[small bear]

for example, 520 choose 10 would count the same deck because of the repetitions, choose 11112222AA, but you could also count choosing a different A in that set (there are 10 total)

[quaint pond]

so basically 520 10

will count this: 1,1,2

the same as this: 1,1,2 (the 2 is from another deck)?

[small bear]

yes, and also the different 1's from other decks

[quaint pond]

aha

so then

why binom(61,10)?

that's the answer according to the book

[small bear]

here is an idea but I must first explore it in depth to understand it

the reason is, for example, pick A

you can match A with the 52 other cards + the 10 other from the deck

however we already picked A, so we cant pick it again, remove it -1

[quaint pond]

yes but then we add it back

+10

its one of those 10, no?

[small bear]

it allows us for each card, to match it up in a group with 60 others, in order for no repetition to pop up

it isnt, there are 10 A's for example, but one A is also matched in the 52 standard deck

we have 1111 (all different colors) 2222 3333 ... QQQQ KKKK AAAAAAAAAA

wait I didnt account for the different colours

yeah, since initially in the first set there are 52 cards right, when adding the other 52*9 cards it means there are 9 other A's

we wouldnt add 10

[zenith spruce]

1+1=2!

im bad at math someone help lol

[alpine sable]

x! factorial is basically

1*2*3*4*5.......*x

it can also mean the number of ways to permute x objects among themselves

[alpine sable]

and 1*2=2=2!

x ≡ 25 (mod 33)```

what is this inspection?

[oak chasm]

@quaint pond It's stars and bars technique.

[alpine sable]

I don't see how they come up with x ≡ 25 (mod 33)

[oak chasm]

You have 52 bins for cards.

You have 10 cards to choose.

[quaint pond]

yeah i know that technique

but like

[oak chasm]

You can put the 10 cards in any of the bins.

[quaint pond]

how

[oak chasm]

So, there are 10 cards and 51 separators as locations in a row and you choose the 10 card locations.

61C10

[quaint pond]

ahaaaa

[quaint pond]

could you elaborate

im kind of starting to get it but not so much

[oak chasm]

Well, let's do a smaller problem.

Let's say you have 3 bins and 2 items.

X X | |
X | X |
X | | X
| XX |
| X | X
| | XX

Those are the ways you can put the two items into three bins.

[quaint pond]

yeah

[oak chasm]

So, that's four positions.

[quaint pond]

stars and bars thing

right

[oak chasm]

OK, now the bins in your card problem are the card values.

You have 10 cards. They have a rank and suit.

You can put them in a bin that's labelled with that rank and suit.

So, you put the 4 of clubs in the 4 of clubs bin.

Well, that's 52 bins or 51 separators.

And 10 cards to put in the proper bin.

Does that make sense so far?

[quaint pond]

yes

[oak chasm]

OK, so it's the same as our three bin two item thing.

We have 51 separators and 10 cards to place in a row.

We pick the locations of the 10 cards or the 51 separators and the other positions just go to the other thing.

61C51 = 61C10 = answer

[quaint pond]

ok so is that the same

[oak chasm]

With our three bin two item thing, we had 6 possibilities.

[quaint pond]

as thinking about the problem

that way:

[oak chasm]

Same as what way?

[quaint pond]

so we have 52 cards and basically when we pick one card, we add space for it back form where we picked it from and we add the same card on that free space just from another deck

or maybe no

[oak chasm]

No.

[quaint pond]

idk

[oak chasm]

It's more like we have 10 cards.

We have 52 labelled bins.

We look at the cards and place each card in the right bin.

Let's do that smaller example again.

Three bins, two items.

. . . .

We have four positions and we need to choose two of them for the items.

Let's choose the second and the fourth positions.

. X . X

Now the other positions are just separators.

Whatever positions are left over.

| X | X

[scarlet atlas]

can someone help with this?

[oak chasm]

And now we have three bins with two items.

@scarlet atlas Sorry, channel is busy.

[scarlet atlas]

oh sorry

[oak chasm]

@quaint pond The items are in bins two and three.

[quaint pond]

ok i think that makes more sense now

51 separators for the different cards

and 10 cards to deal with

would've never thought of that on my own lol

[oak chasm]

Yeah, it's a nice technique to learn 🙂

[glacial tiger]

Need help on this question :)

[oak chasm]

@glacial tiger Hint: angle ABD is a right angle.

And so is angle ADC.

[glacial tiger]

im deeply confused

like i get the right angle part

but besides that wat

[alpine sable]

Angle A is equal to itself

[glacial tiger]

so aa?

[oak chasm]

Yes, if two angles are the same, all three are.

[glacial tiger]

also how do i prove that they are right angles?

[oak chasm]

This is because of the 180 degree sum rule.

Thales' theorem for angle ABD.

[glacial tiger]

I dont think i learned that

yet

is there a different way to know they are right angles?

without like you saying it

[alpine sable]

since DC is tangent to circle O, at D

and line AD is the diameter

you know that ADC is right

[glacial tiger]

ahhh

yes

t

y

what abt abd ttho?

[gray isle]

they probably don't teach it as Thales theorem,

but just explicitly state the property of the theoren

[alpine sable]

it looks like an 8th/9th grade geo question ^^

[gray isle]

i.e angle at the circumference subtended by diameter is 90°

[glacial tiger]

yep

[glacial tiger]

how do we prove this

[gray isle]

(which is an application of inscribed angle theorem)

[glacial tiger]

wat

is ABD a right triangle bc of inscribed angle thm?

[oak chasm]

Yes.

[glacial tiger]

o

[oak chasm]

The angle at the edge of the circle is half the angle at the center of the circle.

angle ABD is half angle AOD

Angle AOD is a straight line or 180 degrees.

So, angle ABD is half that, or 90 degrees.

[glacial tiger]

I see

Last one

[sage bronze]

given $\angle Q \cong \angle R$, what can you say about the triangle PQR?

[ocean seal]

HELLOBELLO

[glacial tiger]

Its isoceles?

[sage bronze]

yes

can you identify which sides 2 sides are equal

[glacial tiger]

pq and pr?

[glacial tiger]

?

[sage bronze]

yes

[glacial tiger]

but what does the circle

have to do with anything

i thought there was some random meaning or smth

[glacial tiger]

also, what is the reason in which PQ and PR are equal? like what is the reason

doing two statement proofs

[sage bronze]

as base angles are equal, the sides corresponding to these angles will be equal as PQR is isosceles

[glacial tiger]

o

i c

[sage bronze]

now you prove that arc PR = arc PQ using the fact that PQ=PR

[glacial tiger]

k

what would be the reason

behind that

[sage bronze]

If two chords of a circle are equal, then their corresponding arcs are congruent

[glacial tiger]

tysm

[sage bronze]

no problem

[lament nimbus]

Idk what to do after finding the partial derivative of F in respect to L and setting it to 0

[zenith spruce]

O thanks

now im math pro

[icy trail]

venn diagram time !

[tidal grotto]

a^2 + b = b^1999 what are positive integers of a,b

[arctic blade]

I have some financial data, that is a vector of trading volumes. It's a time series, with equal time period between values. Given a new trading volume, after the same fixed time period, I want to find how 'different' this value is from what would be expected. How should I best go about this? It could be just a general good way to quantify the change in a trend
@alpine sable I tried fitting an equation with least squares but it just isn't accurate enough

[outer isle]

I think it’s 75

[prime wigeon]

https://t.me/joinchat/nVr3tQpcmTlkMTY0

[candid sluice]

sus link

[tidal grotto]

a little help appreciated

[alpine sable]

so sir I get confused again, can you help me for Number (1) until bottom one
<@&286206848099549185>

[worthy moat]

Hi mathematics community. I need help with this.(hope I am not interrupting anything)

[alpine sable]

do you have to show how you solved it

[worthy moat]

I am just sending

[alpine sable]

i would just use a math computation program to do it for me if you dont have to show how you solved it

cause its long

[worthy moat]

I have done till

[candid thistle]

If I find the radius of the incircle of an isosceles triangle. Is it possible to find the area of the triangle as a whole?

I also found one side length of the triangle.

[worthy moat]

I got a hint from the prof that its an algebric answer

[alpine sable]

If my order is too much, you can give me an example for number (i) only

[candid thistle]

I think I may have gotten something for this.

[timber pendant]

Can someone help me out

[tight locust]

$x^2(x-1)^2(x+2)$

[ocean seal]

EndTimes

[tight locust]

qed

[elfin talon]

Lmfao I though it was simultaneous for a sec

I would of laughed hard

[ionic jewel]

no solution means the rref has a row of the form [0,0,0, c] where c is not 0

infinity many solutions means a free variable

i imagine you can but i don't really know what Cramer's (rule?) is

there's like 50 billion ways to solve any given linear algebra problem like that

[alpine sable]

why would you do it with cramer's rule

cramer rule is always less efficient than gauss

cramer rule is only interesting in theory, but really is never useful in practice

[strong carbon]

9 people in a group, 3 rooms in a hotel which respectively have a capacity of 2 , 2 and 5 people. Distribute these people in groups in which two already picked (for example a person and b person out of these 9) people won't be in the same room.

What I did was all ways to distribute - the ways these 2 will be in the same room

Which led to (9c2).(7c2).(5c5) - (7c2).(5c5) - (7c2).(5c5) - (7c3).(4c2).(2c2) = 504

But 504 isn't even an option + the answer key shows 252

(We don't need to pick 2 random people out of 9 since they are already set)

[oak chasm]

,w Binomial[9, 2]Binomial[7, 2]Binomial[5, 5] - 2Binomial[7, 2]Binomial[5, 5] - Binomial[7, 3]Binomial[4, 2]Binomial[2, 2]

[ocean seal]

Results provided by WolframAlpha

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

Requested by Chai T. Rex#7323

[oak chasm]

For some reason, it's divided by 2.

[strong carbon]

If you do the other way you get 504 again

[alpine sable]

can someone explain what you did

cause i can't deduct it just from the equation

first you determined how many choices are there if no one chooses beforehand

but what did you substract?

[strong carbon]

I calculated how many ways you can distribute these 9 people without a rule

then I deducted in how many ways these 2 set people will be in the same room

So in none of the remaining ways will they be in the same room

[alpine sable]

i'm confused sorry for my poor english

but are they in the same room

or do we not know that

[oak chasm]

Why not just use your number for when they're in the same room?

[alpine sable]

do they just pick a room, and we don't know if they are in the same room or not, or do we know something more?

[oak chasm]

,w 2Binomial[7, 2]Binomial[5, 5] + Binomial[7, 3]Binomial[4, 2]Binomial[2, 2]

[ocean seal]

Results provided by WolframAlpha

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

Requested by Chai T. Rex#7323

[strong carbon]

What did you do here

[oak chasm]

The same thing you did for the second part.

You took the unrestricted and you subtracted the restricted.

But the restricted is already the answer.

[strong carbon]

How...

[oak chasm]

You had - 7C2 5C5 - 7C2 5C5 - 7C3 4C2 2C2, right?

@elfin talon Sorry, channel is busy.

[strong carbon]

Yeah, that's in how many ways they'll be in the same room

[oak chasm]

Looks like #help-9 is open.

[strong carbon]

The opposite of what we want

[oak chasm]

Oh, never mind.

It's probably 504. Let me write a computer program to check everything.

[strong carbon]

Wow that's sounds so cool lol

Thanks and also I checked a few same question type with different numbers so maybe it's just a mistake?

They all apply the same rule

You were told to move channels since this one is busy use #help-9 please @elfin talon

[elfin talon]

Sorry brother I didn’t pay attention

[oak chasm]

@strong carbon Yeah, 504 is the correct answer.

ghci> let ok [a, b, c, d, e, f, g, h, i] = [a, b] == sort [a, b] && [c, d] == sort [c, d] && [e, f, g, h, i] == sort [e, f, g, h, i] && not (a == 1 && b == 2) && not (c == 1 && d == 2) && not (e == 1 && f == 2)
ghci> length . filter ok . permutations $ [1 .. 9]
504

So, we go through the permutations of 1 through 9. We ensure that each room has the people in numerical order and throw out other lists of people that are out of order, leaving us with one permutation per combination, giving us a count of all the combinations in the rooms.

Then we throw out any with rooms that start with people 1 and 2, since those people will be the first people in the rooms if the rooms are in numerical order.

Then we count the remaining room fillings.

Which is 504.

[strong carbon]

Thank you so much

[oak chasm]

You're welcome.

[strong carbon]

A very well deserved very cool ppl role 😎

By the way I understood everything but the "We ensure that each room has the people in numerical order" part

[oak chasm]

Well, let's say room one, with two people has people (1, 5).

It can also have people (5, 1).

But that counts twice the combination we want to count only once.

Does that make sense so far?

[strong carbon]

Ohh like shaking hands

[oak chasm]

What do you mean?

[strong carbon]

Sorry, we don't divide by 2 in shaking hands

I mixed up

[oak chasm]

Similarly, with the 5-person room, you can get 120 different ways for the same five people to show up.

So, we throw out every one of them except the one where they're in numerical order.

That way, we only get one result per combination.

[strong carbon]

What will we get for that occasion if they are in numerical order?

Or are they already in

[oak chasm]

Well, let's say you have people 3, 6, 7, 8, 9 in the 5-person room.

If we only accept (3, 6, 7, 8, 9) and throw out (9, 7, 3, 6, 8) and so forth, we'll only count that situation once.

Which is what we want.

[strong carbon]

Oh, we'll also throw out 6,3,7,8,9 okay I get it now

This one and 1,5 5,1 example made it clear thank you

[alpine sable]

Why is this wrong

I did -2 * -9 * 8 = 144 for numerator

then 5 * -3 * 8 = 120

-144/120 simplifies to -6/5

[strong carbon]

Why did you multiply the denominator with 8?

[alpine sable]

oh

yeah should have been 1

is that the only error I made?

[strong carbon]

👍

[alpine sable]

thanks

[ashen agate]

in the formula nPr what does n and r stand for?

[red phoenix]

What is the formula about?

usually i think it corresponds to n!/(n-r)!

[ashen agate]

probability

permutations

[red phoenix]

yeah, i think it means n!/(n-r)!

[ashen agate]

but what does n and r stand for?

[red phoenix]

those values right there

[jagged raptor]

you can think of n as the number of items in the entire set and r as how many you're using at a time

[ashen agate]

ty

[meager leaf]

Guys

When I want to find a perimeter of a triangle

Don't I add all 3 distance?

Here are the 3 coordinates

[jagged raptor]

yea

the side lengths

[meager leaf]

(2,3) (2,-1) (-3,-1)

The distance of each one of them are

4, 5 and 41 Square root

When I add them up it be 15.4

Mathway is giving me 18

When I saw the steps, they weren't familiar what I was taught

@jagged raptor any idea if it's 15.6 or 18

[jagged raptor]

are those the coordinates of the vertices

[jagged raptor]

yeah its this

9 + sqrt(41

[scarlet heath]

Can I get some help with solving this?

[meager leaf]

Uh

I assume that's Alegbra 2

[scarlet heath]

its uh pre calc work

atleast its in my pre calc packet rn

[ashen agate]

can i get some help with this

[candid thistle]

If I have the semiperimeter and the inradius of a triangle. Is it possible to find the area of it?

[candid thistle]

A should be farely simple.
Do you replace the tiles every time, or do you keep them out of the box?

Read on permutations, that will help.

(That is what E is asking for, actually)

[ashen agate]

keep em out the box

so would it be 1?

[candid thistle]

no

how many tiles are there to choose from for the first tile?

If there are 5 tiles, how many can you choose from

[ashen agate]

5

[candid thistle]

If there are n tiles, how many can you choose from?

[ashen agate]

n?

[candid thistle]

Yes

Now for part B

How many can you choose from now (for your second tile)

[ashen agate]

n-1?

[candid thistle]

And continue

[ashen agate]

wdym

[candid thistle]

Now you continue on for part C and D

[ashen agate]

how does d work?

[candid thistle]

Think about it

[glass lichen]

do C then notice the pattern..

[candid thistle]

[ashen agate]

is it n-1-1-1

[glass lichen]

is what n-3?

[ashen agate]

yea

question d

[glass lichen]

no

cause 3 isnt general

what's the pattern?

[ashen agate]

you lose a tile each time?

[glass lichen]

yes

1st choice has n possibilities
2nd has n-1 possibilities
3rd has n-2 possibilities
etc

so the rth choice has how many possibilities?

note n=n-0

[ashen agate]

so its not n-3?

[glass lichen]

it isnt.

Like I said already

[ashen agate]

n-r?

[glass lichen]

im asking about the rth choice

no

what's the pattern?
1 and n-0
2 and n-1
3 and n-2

[ashen agate]

im lost

[glass lichen]

0 is 1 less than 1

1 is 1 less than 2

2 is 1 less than 3

[ashen agate]

n-4?

[glass lichen]

no

im asking for the rth, so your answer needs r somewhere in it

[ashen agate]

r-4?

[glass lichen]

no

Like I really cant spell it out much more.. it's a pattern and you notice it

[candid thistle]

At this point its just giving the answer

Think about it, if you have n items and you want to take out the rth one, how many can you choose from

[glass lichen]

I've literally spelled out the pattern at this point as well

[candid thistle]

so you have already taken out how many before your rth one

[ashen agate]

3

[candid thistle]

Not your 4th one, your rth one

[glass lichen]

stop guessing and think

[ashen agate]

i mean havent i taken out 3?

[glass lichen]

No

[candid thistle]

No, for your rth one

[glass lichen]

you're on your rth picking

[candid thistle]

r as in the variable

[glass lichen]

not your 4th...

[ashen agate]

r-n?

[glass lichen]

no

[candid thistle]

No?

[glass lichen]

again.. I've literally spelled out the pattern

as well as part A to C were to have you discover the pattern yourself

[candid thistle]

Also can anyone help?

[ashen agate]

n-r?

[glass lichen]

no

[ashen agate]

is it n-2-r

[glass lichen]

no

[candid thistle]

Again, you are guessing

[glass lichen]

stop guessing.

[ashen agate]

i dont get it thats why im guessing

[candid thistle]

Then think

[ashen agate]

if its n-1, n-2 shouldnt it be n-3

[glass lichen]

NO