help-13

[silent kelp]

its asking for f'(x)

[lusty grotto]

yes

[silent kelp]

do i do anything about that

[lusty grotto]

u will need f to get that

u need to know f as a piecewise function to get f' as a piecewise function

[silent kelp]

okay

[silent kelp]

is this right

[lusty grotto]

yes, and u can also write x != 2 in the top part

coz its undefined when x = 2

[silent kelp]

yea

[lusty grotto]

and u can simplify it

[silent kelp]

to?

[lusty grotto]

(x-2)/(x-2)

[silent kelp]

thats 1 right

[lusty grotto]

yea

[silent kelp]

and the other one is neg 1

[lusty grotto]

no

[silent kelp]

really?

-(x-2)/(x-2)

[lusty grotto]

$\frac{-(x+2)}{x-2}$ not $\frac{-(x-2)}{x-2}$

[wraith dagger]

SilverSoldier

[lusty grotto]

-x-2 = -(x+2)

[silent kelp]

i see

yeah

[lusty grotto]

right

so $f(x)=\begin{cases}
1, &x\geq0, x\ne2\
-\frac{x+2}{x-2}, &x<0
\end{cases}$

[wraith dagger]

SilverSoldier

[silent kelp]

yea

[lusty grotto]

now u have to differentiate these functions separately

[silent kelp]

okay

0, x>=0, x != 2
-(x+2)/x-2, x<0

wait

i didnt do bottom

[lusty grotto]

yes do the bottom too

[silent kelp]

4/(x-2)^2

0, x>=0, x != 2
4/(x-2)^2, x<0

[lusty grotto]

yes u r almost there, except ur function is not differentiable at x = 0

do u know that |x| is not differentiable at x = 0?

[silent kelp]

i didnt know that

so its just x>0

[lusty grotto]

well u know that the graph of |x| looks like a point at x = 0 right?

[silent kelp]

yeah

its a sharp turn

[lusty grotto]

so u cant draw a tangent there

[silent kelp]

yeah

[lusty grotto]

so its not differentiable

[silent kelp]

so just x>0

and x =! 2

[lusty grotto]

yes

[wraith dagger]

SilverSoldier

[silent kelp]

is what i got

[lusty grotto]

right

[silent kelp]

is d) 1/3

ok it is i think

thank you

.close

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[crimson sedge]

can someone explain to me the first sentence of the proof?

[gritty viper]

The distance function is continuous if only slightly changing its arguments slightly changes the result

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[midnight depot]

Hello, i need help with getting a proof for:

1. |f(x)| < g(x) ⇔ f(x) < g(x) ∧ f(x) > -g(x)
2. |f(x)| ≥ g(x) ⇔ f(x) ≥ g(x) ∨ f(x) ≤ -g(x)

I have tried solving the first one like this:
|f(x)| = max( f(x), -f(x) )
So, max( f(x), -f(x) ) < g(x), which means that f(x) < g(x) ∧ -f(x) < g(x), and that is f(x) > -g(x) if both sides multiplied by -1
I might have made a mistake, or did something incorrectly there for example with not enough evidence, so please correct me if im wrong
And please help me with the second one, im sure its similar, but i cant really understand why the sign ∨ in this case is this one, and not ∧.

[midnight depot]

my attempt for the proof for the first one might be entirely wrong though...

[cedar kiln]

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@midnight depot Has your question been resolved?

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[mellow pasture]

Could somebody explain how to integrate the above function?

[stark quest]

notice that the integrand is odd

that might be a helpful hint

[mellow pasture]

oh my

thanks alot..much appreciated

.close

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[frigid coral]

Silly question but I am confused on this quadratic method. [For partial fractions]

So I understand the GCF part, but how do you know if you pick -4x or 4x for GCF?

For example, let's take
2x^2-5x+2

The next step would be 2x2=4 and which factors into -4,-1 to add up to -5

Then it'd become

2x^2-4x-x+2

This part, how do I pick the GCF? 2x or -2x? It should be 2x but how about the 1, how is it not -1?

2x(x-2)-1(x-2)

How should I know if I should put 1 or -1 as GCF?

[digital cliff]

if you pull out -2x, you do -2x(-x+2)+(-x+2)=(1-2x)(2-x), if you pull out 2x you get 2x(x-2)-(x-2)=(2x-1)(x-2)

simple answer - it doesnt really matter

theyre equivalent

[frigid coral]

Alright, so basically just go for the one that is simplified further?

[digital cliff]

people just often prefer to pull out things that leave you with the x terms being positive in the brackets

but its all the same

[frigid coral]

Makes sense

Do you have any other quicker quadratic method in mind or should I keep on this one?

[digital cliff]

this ones generally quite good if youre just doing it without a calculator, its the one id probably go for anyway when dealing with a quadratic

unless i can just see it

[frigid coral]

Appreacite it, thank you

.close

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[unborn knot]

Hello I need help with math rnn

[dire geode]

!help

[cedar kiln]

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[heady drum]

I have an inequality

[heady drum]

i cant render it

(\frac{2n+1}{4^n} \lt 9 \epsilon)

screw it

[dire geode]

write it on paper and take a pic

[heady drum]

ok

[opal basin]

$$\frac{2n + 4}{4^n} < 9\epsilon$$?

[dire geode]

or #latex-help / #latex-testing

[heady drum]

Like this

but 9epsilon*

[wraith dagger]

Jelle

[heady drum]

yep

[opal basin]

Do you need to solve this exactly or just find a value of n for which this holds (and for all n greater)

[heady drum]

all values of n

i need to prove a limit identity based on the limit definition, thats the background

but I need all values of n that holds true this ineq

[opal basin]

then you don't need all values of n, just the existence of a value N for which this holds for all n >= N

[heady drum]

yep

and this is where i got stuck

I tried logarithmation and stuff but it didnt work out

[opal basin]

You can make up some really loose inequalities like 2n + 4 < 9 * 2^n

[heady drum]

so what?

[opal basin]

Well if you solve (9 * 2^n) / 4^n < 9e, then you have also solved the original equation (not for all values though)

if the above holds, then the original inequality also holds

[heady drum]

ok

[cedar kiln]

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[cedar kiln]

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[crimson sedge]

Need help with this limit

[crimson sedge]

I can’t use l’hôpital

I separated it into two fractions

Then I did the conjugate for the first le I add one and removed one so I can use the conjugate

Then I simplified but still have IF

[crimson sedge]

why not?

[crimson sedge]

Cuz the teacher said so

Im not in university

So I can’t use it yet

Im in middle school

High school**

$\frac{\sqrt[3]{1+0} -(1+\frac{0}{3})}{0^2}$

[wraith dagger]

seymourdavison2201

[crimson sedge]

$\frac{0}0}$

[wraith dagger]

seymourdavison2201
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[crimson sedge]

indeterminant form

Yes I know

This already

oh ok

[crimson sedge]

ah

Do u have any idea ?

like except what I did

Cuz it’s not working

Should I do the conjugate

Without separating them into two limites ?

I can only think of l'hospital

<@&286206848099549185>

[echo quail]

Try multiplying by the conjugate of the numerator

[crimson sedge]

IT WILL BE TOO LONG

[echo quail]

Sometime in the future your math problems will take pages to solve....

[crimson sedge]

Well I’m 16 yo so I don’t think my maths problem should be long

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

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[bitter cargo]

The image shows a cobblestone pavement with a pattern composed of circular arches. In Figur 7, the geometry is shown with measurements in meters.

a) Determine the area of ​​the gray area.

[low grove]

hint:

[bitter cargo]

So i find area of the 1/4 og a circle then find the area of the grey circle. Then subtract the area of 1/4 circle from the grey circle?

Im confused

[low grove]

almost

split the shape like so:

[bitter cargo]

So I find area of the rectangle, find the area of the white area. Then subtract the two white areas from the rectangle, then i have the small grey area. Then i add that small grey area to half grey circle right?

[low grove]

yes

[bitter cargo]

Bro thank you so much man life saver fr

.close

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[cedar kiln]

@crimson sedge Has your question been resolved?

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[slate garden]

How do i do this?

[low trail]

sub (x+8) into y for the second equation

and expand

then u can complete the square and should get the answer

[slate garden]

I get

(x+1)^2 - 5

[low trail]

= 0 right

[slate garden]

yes

[low trail]

so now u send 5 to the other side

(x+1)^2=5

[slate garden]

omg thanks

[low trail]

yep hope u know how to do the rest

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[raven lodge]

I don't even know what my teacher wrote, but since you guys know the context, you can probably help me? Thanks. I have no idea what these 'letters' mean.

[royal loom]

$\in$ means is an alement of

[wraith dagger]

Austin

[royal loom]

$\mathbb{R}$ represents the set of real numbers

[wraith dagger]

Austin

[royal loom]

$x \in \mathbb{R}$ means that x is a real number

[wraith dagger]

Austin

[raven lodge]

theres an I looking thing for mine

[royal loom]

so the domain part is saying the domain is all real numbers

the vertical line

you can think of saying

such that

[surreal cave]

in essence, we can choose any x that is real as an input and the output will be real

x=1/2, -3, sqrt(2), pi, etc

[raven lodge]

so if the domain is negative infinity to infinity

it would be X | ER

?

[surreal cave]

if you mean -inf to inf, then yes, it is the same

[raven lodge]

yay thanks

tysmmm

wait so x | xER or just x|er

[surreal cave]

${x|x\in\mathbb{R}}$ means x such that x is an element of the real numbers

[wraith dagger]

FancyBredFries

[raven lodge]

my teacher had the vertical line tho

[royal loom]

the vertical line means such that

[surreal cave]

I did as well :)

[dapper raven]

the vertical line means 'where'

[royal loom]

same thing

[dapper raven]

not really

[royal loom]

the point is communicated either way

[cedar kiln]

@raven lodge Has your question been resolved?

[cedar kiln]

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[fervent crag]

hellooooo!! I am doing some related rates in calculus ab and I need to figure this out:
2 m/s / 5 degrees/second

[fervent crag]

relatively simple but damn I can’t figure it out

I got 5 degrees / 2m but that didn’t make much sense to me

[obsidian pasture]

so you are trying to divide (2m)/(second) by (5 degrees)/(second)

right

[fervent crag]

yes

[obsidian pasture]

how do u divide a fraction by a fraction

[fervent crag]

multiply by reciprocal

[obsidian pasture]

yes

so you have...

[fervent crag]

so did my earlier answer work?

[obsidian pasture]

(2m)/(second) * (second)/(5 degrees)

I think u have it backwards cus ur 2m should be in the numerator... see?

[fervent crag]

do you flip the top or the bottom?

[obsidian pasture]

um

let me find a picture

[fervent crag]

ohhhh

new wallpaper just dropped

thanks slappo!

[obsidian pasture]

lol!!

[fervent crag]

so would it follow that 2/5 meter per degree

would be right

[obsidian pasture]

uh

2m/5deg

yeah

[fervent crag]

thanks!!!!

[obsidian pasture]

I mean idk when you will encounter m/deg but that looks like it should work

[fervent crag]

.close

[cedar kiln]

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[fleet turret]

Hello, I’m working on number 17, the converse part. I know the answer is when s and t are co primes but I don’t know why that’s the case.

[glad folio]

Hello my friend

[fleet turret]

Hello

[glad folio]

Well

The thing about

[fleet turret]

Yes I remember I appreciate your help

[glad folio]

if s and t are not coprime

Ummm I'm thinking how to phrase this as well

[fleet turret]

No worries. I know st=lcm(s,t) if s and t are co primes

[glad folio]

Yeah no sorry I've tried to follow up on your case and it took me over 15 mins

I'm sorry

<@&286206848099549185>

[fleet turret]

It’s ok thank you for your help

[glad folio]

Assume s and t are not coprime

that s = mx and t = nx

where m and n are coprime

a-b = 0 (mod s)
a-b = 0 (mod t)

a-b = pmx = qnx

where p,q are some integer constants

pmx = 0 (mod nx)

hence n | p

same setup for another side and

m | q

hence

a-b = cmnx where c is not divisible by s nor t

a-b = c (lcm(s, t))

when lcm(s,t) unequal 0

a-b does not equal 0

Proof by contradiction that s and t has to be coprime

It may be a bit more complicated than optimal but a few tweakings will make it work

or so I think lol

Not a specialist in number theory

[fleet turret]

Ok I think I see what you’re saying. I’m going to digest this a bit and attempt it again with these ideas. Thank you again for your help.

.close

[cedar kiln]

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[glad folio]

Hey

[fleet turret]

Yes?

[glad folio]

Just wondering

How old are you?

Nvm if that's sensitive

[glad folio]

Just curious from this

[cedar kiln]

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[unique gust]

any idea here?

uni level prob and stats

[woeful barn]

anyone that can help with conversion factors

[unique gust]

<@&286206848099549185>

.close

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[cedar kiln]

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

[grand forge]

First

figure out how they would make 0 dollars

the probability

X = 0

[cedar kiln]

@long swan Has your question been resolved?

[long swan]

beef

[cedar kiln]

@long swan Has your question been resolved?

[cedar kiln]

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[lavish dome]

I am a little confused about this problem and not sure how to prove this directly

[lavish dome]

any advice

I began with the definition of surjective and at this point i would try composition of functions but thats not really what is happening here is it?

[royal finch]

I'm not sure why you are thinking of function composition as a first step.

[lavish dome]

well i know thats not the correct

direction

[royal finch]

Can you explain what a surjection is

[lavish dome]

onto. if f is surjective this implies that for every $y\in \mathbb{Z}$ there exists a $x\in X$ such that $f(x) = y$

[wraith dagger]

BockLobster

[royal finch]

So if that is true for f and g

and h(x,y) = f(x) + g(y)

What does it mean for h(x,y) to be a surjection

[lavish dome]

if $h(x,y)$ is a surjection this implies that for every $z \in \mathbb{N}$ there exists an $x,y$ such that $h(x,y)=z$

[wraith dagger]

BockLobster

[lavish dome]

in my head i can construct why this is true tho im just struggling with the formal proof ig

[royal finch]

So you know that z is a natural number, and it is equal to some f(x) + g(y)

[lavish dome]

yes

[royal finch]

where f(x) and g(y) are integers

[lavish dome]

where f(x) and g(y) are integers

yep haha

[royal finch]

Lets say z = 5, can you tell me a f(x) and g(y) both in Z so that f(x) + g(y) = 5

[lavish dome]

yes, there are many correct, f(x)=5, g(y)=0, f(x)=8, g(y)=-3 ect

[royal finch]

Okay, so we only need one pair, lets start with f(x) = 5 and g(y) = 0

Is there an (x,y) so that f(x) = 5 and g(y) = 0?

[lavish dome]

by our definition of surjectivity there is

call them x^* and y^*

[royal finch]

but what if z is a natural number other than 5? Can you always do this?

[lavish dome]

yes

[royal finch]

Well, that's your proof

[lavish dome]

hmm i guess

[royal finch]

Notice that because there are many that are correct, you will fail when it's 1-1

[lavish dome]

and i guess i see that if g is not surjective then h is not onto

[lavish dome]

yes

[royal finch]

The idea is that there is no need to compose and functions

[lavish dome]

yes agreed

[royal finch]

You are just studying whether the f(x)+ g(y) part inherits the property you want by virtue of f and/or g having that property

[lavish dome]

that makes sense

[royal finch]

or if the natural numbers/ Z part, or the additional part somehow meses with it

[lavish dome]

yes

thank you!

.close

[cedar kiln]

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[tame jasper]

https://i.imgur.com/3U8nXKm.png

[tame jasper]

Is this a valid formula for standard deviation?

I thought this was the right formula and I thought the top most picture is wrong

since I thought you can't just split up the summation into 2 separaet summations since the result is being squared after you subtract them

so sum of (x-mean)^2 /=/ sum of x^2 - sum of mean^2

[cedar kiln]

@tame jasper Has your question been resolved?

[neat dune]

Ir right but that's not what's happening harry

[tame jasper]

Oooh so it is the same then

[neat dune]

Ye

[cedar kiln]

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[plush wharf]

Help

[cedar kiln]

@plush wharf Has your question been resolved?

[cedar kiln]

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[thick heart]

how would i do this?

[thick heart]

for a i know how but idk how to get b

[cedar kiln]

@thick heart Has your question been resolved?

[thick heart]

<@&286206848099549185>

[tiny gale]

You can use synthetic division

[cedar kiln]

@thick heart Has your question been resolved?

[thick heart]

i know but what else r u supposed to do fete

<@&286206848099549185>

[mossy lichen]

A

B

c

D

@thick heart

[thick heart]

thank you!

[verbal compass]

how does this work

how foes factoring -2 from -10 give (4x^2-21)

also when you expand the favtored form you get

4x^3 -8x^2 -21x +42?

[verbal compass]

also for this expanding gives:
x^4 -x^2 +6x +x^3 -x +6
x^4 +x^3 - x^2 +5x +6
unless i made a mistake i dont got paper

[verbal compass]

this gives:
x^3 -2x^2 -x + 2

how does factoring (x-2) out of:
x^2(x-2) -1(4x-1) give
(x^2 - 1)(x-2) ?

[verbal compass]

this is correct

[verbal compass]

the solutions even for the wrongly factorised equation js wrong 🤔

[verbal compass]

i think almost all of them are wrong unless i’ve severely misunderstood the assignment

[verbal compass]

idk what AI you used but it sucks. also dont do this; just post answers, especially if they’re wrong answers. I don’t suggest you use this AI again it doesn’t seem to know math well. it only got 1 question right

@thick heart the screenshots are wrong, don’t do what they say

[thick heart]

oh okay!

thanks for informing me

[thick heart]

would you be able to help me out with B then?

[thick heart]

nvm it's ok i got it

.close

[cedar kiln]

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[vital mason]

Instructions say “Solve the exponential equation algebraically”. Would this be how I solve it?

[dreamy pendant]

yeah thats one way to solve it

[peak minnow]

shouldnt it be natural log , cuz ln(e) = 1

[dreamy pendant]

yeah thats the more formal way to do it

but log base 10 works too, since he justs wants the exponent x to come out

[vital mason]

So its good?

[dreamy pendant]

wait no its not

you took loge of left side but did not make any changes to the right side

[peak minnow]

he took log on both sides

[dreamy pendant]

oh shit u right

im tired af

nvm u good lol

[vital mason]

Oh ok thanks 👍

When I plug in x to the problem it ends up being a negative. Im not to sure what I did wrong though

Unless I just can’t solve this one

[dreamy pendant]

u cant take x out from log(3e^x)
im pretty sure the law was that everything needs to be to the power of x
e.g. log((3e)^x) = xlog(3e)

[vital mason]

I don’t think I’m understanding to well I got -10 somehow

[dreamy pendant]

can you show your steps on how you got -10?

[vital mason]

Well I just did log(25)/ log((3e)^x) hoping that would work

It in fact made it worse

[dreamy pendant]

log((3e)^x) does not equal to log(3e^x)

what you want to do is get rid of the three before logging both sides

[vital mason]

Would i do log 3 + xlog e?

Is = log 25

[dreamy pendant]

yes you can do that

[vital mason]

Do I divide next?

Or would I subtract because it is adding them together to move log 3 to the right

[dreamy pendant]

you would subtract

i.e., xloge = log25 - log3 => x = (log25-log3)/loge

[vital mason]

Ok thanks for the help I got it now 👍

.close

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[red gulch]

i would like help on this problem please

[cedar kiln]

@red gulch Has your question been resolved?

[red gulch]

<@&286206848099549185>

[gritty viper]

Can you find their normal vectors?

!status

[cedar kiln]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[red gulch]

1

[cold ibex]

Is that $n_{1}* n_{2}= n_{1} n_{2} cos \theta$

[wraith dagger]

him

[red gulch]

i think so?

[cold ibex]

Are P and Q vectors or points

[red gulch]

points?

[cold ibex]

In that case you need to do the cross product to get a vector normal to the plane

[red gulch]

ok

so would i try to find the vectors PQ and PR

and cross product them?

[cold ibex]

Exactly

[red gulch]

i got <40,16,10>

do i plug that into the formula shown earlier?

[cold ibex]

Is that the result from the cross product

[red gulch]

yes

[cold ibex]

When you get a normal vector then you can use the formula

When you do the cross product it’s normal to the plane

[red gulch]

does normal mean orthogonal ?

[cold ibex]

Yes

So any vector on the plane is normal to that vector. That equation I showed relates two normal vectors

Solve for cos(theta)

You will use your normal vector and the yz plane vector

[red gulch]

could you explain what the yz plane vector is

sorry

[cold ibex]

(1,0,0)

Yz means normal to yz plane which is the x axis

[red gulch]

got it

so it would becross product = dot product of the yz plane vectors X cos(theta)?

[cold ibex]

Cos(theta) = n1 dot n2/n1n2

Where n1n2 is the product of the magnitude of both vectors and the numerator is the dot product

[red gulch]

okay

[cold ibex]

I am going to sleep apologies feel free to ping more helpers

[red gulch]

its okay

thank you very much for the help

<@&286206848099549185>

im having a bit of trouble since my professor showed us this formula in class

never mind i solved it

.close

[cedar kiln]

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[cedar kiln]

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[crimson sedge]

This is what the question is asking

do you have an idea of what to do?

I tried to isolate for t, however, I did not know how to take the inverse sin of (x-1)/2

this is a very bad way to go about it

[foggy merlin]

its better to square it I think

(x-1)/2 = sint

and u use the fact that sin² + cos² = 1

🤔

[crimson sedge]

Ohhhh okkk

Im gonna try that out, give me one second

Okk i got it now

Thank you!

.close

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[quartz bloom]

this is my working so far

but i think i'm missing something as wolfram alpha says 1

.close

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[scarlet rover]

hello, need help w limits

[scarlet rover]

1.1

my workings so far ^

is it possible to evaluate the 2nd part first? but it seems like it should be indeterminate

cuz 2^n tends to inf while the recursive sqrt thing tends to 0

and idk how i would apply lhopital on the recursive part

[cedar kiln]

@scarlet rover Has your question been resolved?

[scarlet rover]

😢

[royal finch]

That's a famous problem, I don't know how you solve it other than using the "trick". Namely you make an observation like that $\cos(x/2) = \sqrt{\frac{1+\cos(x)}{2}}$ is similar visually to $a_n = \sqrt{2+a_n-1}$ and massage it a bit to come up with a trig substitution.

[wraith dagger]

JessicaK

[cedar kiln]

@scarlet rover Has your question been resolved?

[scarlet rover]

what the, trig sub 😭

hmm ill see what i can do

the only recurring thing i see is this x.x

[cedar kiln]

@scarlet rover Has your question been resolved?

[autumn tendon]

HELP ME

[primal gust]

Mr fizz

How would u like me to help

[cedar kiln]

@scarlet rover Has your question been resolved?

[cedar kiln]

@scarlet rover Has your question been resolved?

[cedar kiln]

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[torn dock]

Why is this person using P=3pi/(1/3)?

[torn dock]

Isn’t the formula T=2pi/B?

Why 3pi instead 2pi

[digital cliff]

if P is the period, then yeah, should be 2pi/(1/3)=6pi

they may have got enthralled by all the 3's on the screen

[torn dock]

I see, so that’s an error on the vid?

[digital cliff]

i believe so yeah

[torn dock]

Ok, thx

.close

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[acoustic iron]

can anyone help me understand these type of combinations?

[acoustic iron]

this is a screen shot from my lecture

there are 9 people. creating teams of 5

how many teams have at least 1 faculty member

i am LOST

[violet flume]

the writing is horrible

[acoustic iron]

ahah

[violet flume]

theyre all faculty members or what

its illegible

[acoustic iron]

this is order doesnt matter... no repetition btw

[violet flume]

who is faculty

[acoustic iron]

nahh he was writing out all the diff combinations of having atleast 1 faculty member on a team

its too bad this is a pre recorded lecture

and i have no option to ask him whats up with these problems

[violet flume]

you havent given enough info

who is faculty

[acoustic iron]

so theres 9 people

9 total peoples

that could be faculty or students

attempting to make teams of 5 of those poeple

[violet flume]

how many are faculty

[acoustic iron]

that is for us to decide

we are just trying to see how many combinations we can make

[violet flume]

then the problem has no answer

[acoustic iron]

maybe thts why im so confused

but still i dont understand how he is writing the combination formula

this deals with combinations and permutations

[violet flume]

it looks like hes saying 5 are faculyy

[livid crescent]

how many teams have atleast 1 faculty member

[acoustic iron]

n!/(n-k)!k!

[violet flume]

and 7 are students

for a total of 12

where are you getting 9?

[acoustic iron]

one sec

re winding

to make sure

[violet flume]

if we pose the problem that way its well-posed i think

[acoustic iron]

holy crap i am losing it

you are right

sorry guys the previous problem was using 9 people

so yea

12 people

5 faculty

7 students

teams of size 5

how many diff combinations can i make with each team having atleast one faculty member

and im assuming this formula is being used... n!/(n-k)!k!

[violet flume]

it is, yea

theyre just splitting it into cases

based on the number of faculty present

so like, if you have one faculty, you can choose 5 ways

then however many ways you can pick four students out of the 7

[acoustic iron]

so the first case

1 faculty and 4 students

that still leaves 7 people not on a team

[violet flume]

sure

every case leaves 7 people though

[violet flume]

doing okay?

[acoustic iron]

losing my mind

[violet flume]

what has you tripped up?

@acoustic iron theres 2 pieces here, enumerating the cases, then enumerating each case

are you convinced of the 5 cases?

that the number of faculty can be 1 2 3 4 or 5?

[cedar kiln]

@acoustic iron Has your question been resolved?

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[tepid grail]

i have the answers but i dont get it

the explaination is so confusing?

[cedar kiln]

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[crimson sedge]

suffering and confusion

[deft saddle]

$rotate

.rotate

!rotate

[crimson sedge]

idk why my phone likes to post documents sideways

i cannot for the life of me understand how to solve for x let alone z

So you need x and z?

[crimson sedge]

pretty much

[desert cedar]

Both of those two lines intercept with each other making them opposite and making them the same

[crimson sedge]

oh :tired:

[desert cedar]

3x - 56 = x + 2

Solve for x

[crimson sedge]

doing math homework after writing a 3 page essay for general papers is not a great formula

i have the rest myself

[desert cedar]

Mood. I’m too tired to do my own homework. Might as well help while I wait for help on my post

[crimson sedge]

yeah thats literally all i got stuck on since all i remembered today was supplementary and complementary so i was looking for 90 and 180 degrees to solve it

[desert cedar]

Nothing makes sense, its too late for coffee and I have a test soon

[crimson sedge]

Find x first

[crimson sedge]

Start with this

yeah yeah brain doesnt brain at 8 pm after 4 hours of sleep and 3 pages worth an essay written in one sitting for college credit classes

.close

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[torpid urchin]

how can i show these are a linear transformation

i know i have to show its closed under addition and scalar multiplication, but im not sure how i should do that with generic polynomials

i tried something like this but clearly it didnt work

[silver parcel]

5. T is the linear map that sends the polynomial function f(x) on xf(x)+f'(x)
   Take two polynomial function f and g
   T(f+g(x)) = T(f(x)) + T(g(x)) = xf(x)+f'(x)+xg(x)+g'(x) = x(f+g(x)) + (f+g)'(x)

[torpid urchin]

ok that makes sense using those

but how am i supposed to find a basis for the nullity and range with just f(x) and g(x)?

can i do that using generic polynomials?

i tried something like this but once again doesnt make much sense here

the answer says the nullity is 0, which should mean 0 is the only thing in the basis for the kernel, but im not sure how to get there

[cedar kiln]

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[idle lava]

can someone help me on these statistics questions

[idle lava]

i dont understand why i got themm wrong, all calculations add up

my work for the first one is E(X) = np = 19 * 0.8 = 15.2

my work for the second one is sqrt(19 * 0.8 * (1-0.8))= 1.74

[upper abyss]

15.2 ≠ 15

I agree with 15.2

[idle lava]

wouldnt itt be 15 since it is talking about the number of survivors?

[upper abyss]

It's talking about the expectation, which is not quite the same. This can be a decimal

[idle lava]

ok, what about the second one tho

[upper abyss]

,calc sqrt(190.80.2)

[wraith dagger]

Result:

1.7435595774163

[upper abyss]

I agree with your answer. Maybe more decimal places?

[idle lava]

i hope so

[idle lava]

anyways, here is another question that I got all parts of wrong.

here is my work:

b: P(X=5) = C(6, 5) * (2/3)^1 * (1/3)^5

P(X=6) = C(6, 6) * (2/3)^0 * (1/3)^6

then adding them together makes

0.351 @upper abyss

<@&286206848099549185>

.close

[cedar kiln]

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[idle lava]

.reopen

[cedar kiln]

✅

[upper abyss]

Yeah I like that strategy

[idle lava]

but ig its wrong

[upper abyss]

Oh whoops I'm looking at successes

[idle lava]

huh

[upper abyss]

0.018 for "less than 2 successes"

[idle lava]

so

[upper abyss]

C(6,1)(2/3)¹(1/3)⁵

• C(6,0)(2/3)⁰(1/3)⁶

Which is what you've got above, isn't it

[idle lava]

yeah

[upper abyss]

So I accidentally calculated "more than 4 successes" and got an answer pretty close to what you selected

I think you accidentally calculated "more than 4 successes" too

[idle lava]

oh I see

[idle lava]

does the calculator show failures too

[upper abyss]

"more than 4 failures" = "less than 2 successes"

[idle lava]

so it would be 0.018 then

for the first one

and 0.650 for the third one

what about the second one

@upper abyss

yo

[upper abyss]

It's easier to do
1 - "5 or more successes"

1 - 0.351

[idle lava]

ah so thats it?

[upper abyss]

Should work

[idle lava]

damn

wound it be 2-5 or more

@upper abyss

[upper abyss]

2,3,4,5 successes

Might be easier to consider
1 - "0,1,6 successes"

[idle lava]

so how would i solve that

this is what my prof said

so 5-1?

[upper abyss]

Why 5 - 1?

[idle lava]

idk

[upper abyss]

Consider the work you've done previously

[idle lava]

yeah

would it be (6,2)⋅(2,3​)2⋅(1,3)4+(6,3​)⋅(2,3​)3⋅(1,3​)3+(6,4​)⋅(2,3​)4⋅(1,3​)2+(6,5​)⋅(2,3​)5⋅(1,3​)1

I got 0.444 @upper abyss

@upper abyss yo

hii

I got 0.350

when i solved it agian

@upper abyss yo

[cedar kiln]

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[crimson sedge]

use the disk method for the curve then what?

[tepid urchin]

idk

[cedar kiln]

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[stoic thorn]

I setted up as w x 2(2w+11) = 63 and just got lost after

[amber ridge]

solve for w?

[stoic thorn]

yeah

[cedar kiln]

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[lucid path]

w (4w + 22) = 63 just keep expanding

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[sacred jolt]

helop

[sacred jolt]

this

it is yes cuz each output has input

but what is the domain?

it should be xer. x<-3 and greater than 7?

how

rite?

[carmine whale]

No

[sacred jolt]

rite?

[carmine whale]

Yep

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[fresh gazelle]

does anyone know if its possible to calculate area of trapezoid only having all its sides?

[proven fable]

Yes you can

@fresh gazelle you can do it by diving it in rectangle and triangles

[cedar kiln]

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[fresh gazelle]

can u show me an example?

ive got something like this

and what do i do with it now

[cedar kiln]

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[fresh gazelle]

.reopen

[cedar kiln]

✅

[fresh gazelle]

is that correct?

not the calculations

i mean the method

[cedar kiln]

@fresh gazelle Has your question been resolved?

[cedar kiln]

@fresh gazelle Has your question been resolved?

[fast relic]

Still need help?

@fresh gazelle

You might want to check this
https://www.quora.com/How-do-I-calculate-the-area-of-a-trapezium-when-the-sides-are-given

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[azure sedge]

do anyone know how to convert km/h^-1 to m/s^-1

[azure sedge]

?

[tough sage]

Use dimensional analyisis

[feral coyote]

umm, maybe km h^-1 and m s^-1?

[tough sage]

Km is 1000m/km

[feral coyote]

is it $\frac{km}{h}$ or $\frac{km}{h^-1}$?

[wraith dagger]

TimK

[azure sedge]

okay

km/h^-1

[feral coyote]

...

[azure sedge]

so just convert??

[feral coyote]

weird units

[azure sedge]

yea

physics

[feral coyote]

yeah

[azure sedge]

so for example 1 km/h^-1

[feral coyote]

1kmh = 1000m min*60?

[azure sedge]

equals

0.277 m/s^-1

?

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[undone grove]

How do i derivative this?

[tropic oxide]

you again only need the power rule for this

and also knowledge of how to write roots as fractional exponents

[undone grove]

So x^3 + 3/x^4?

what do i do then

[tropic oxide]

$\sqrt{x} = x^?$

[wraith dagger]

Ann

[undone grove]

okay but what about the 3 on the outside?

[tropic oxide]

answer my question first.

[undone grove]

1/2

[tropic oxide]

yes

so the first term is $3x^{1/2}$

[wraith dagger]

Ann

[undone grove]

ohh okay

second one is 4x^1/3?

[tropic oxide]

yes

[undone grove]

is that solved or do i have to do anything else

[tropic oxide]

well you have to take the derivative actually

[undone grove]

so the formula now?

[cedar kiln]

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[undone grove]

.close

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[iron loom]

What the main diffrence from the uniform convergence and pointwise convergence, I don't get it:
$limn->infinity fn(x)=f(x)$ and
$limn->infinity sup{abs(fn(x)-f(x))}=0$

[iron loom]

$lim(n->infinity) fn(x)=f(x)$ and
$lim(n->infinity) sup{abs(fn(x)-f(x))}=0$

[wraith dagger]

Giannis

[tropic oxide]

$\lim_{n \to \infty} f_n(x)=f(x)$

[wraith dagger]

Ann

[iron loom]

oh nice

[tropic oxide]

vs. $\lim_{n \to \infty}\sup |f_n(x) - f(x)| = 0$

[wraith dagger]

Ann

[tropic oxide]

ie pointwise vs uniform convergence, is what you're asking.

...ok right you said that

yeah so.

to put it informally, uniform convergence means the function sequence converges 'synchronously' at all points

or like, that there are no points near which the convergence is "lacking behind"

if that makes sense

[iron loom]

I know the difference on what they represent but how does that translate to the definition, it looks like you are saying the same thing twice

how do they converge uniformly by taking the absolute value and the sup?

[tropic oxide]

im not talking about pointwise here at all

sup |f_n - f| is basically the farthest distance that f_n ever gets from f

[iron loom]

oh I never thought of it like that...
that makes a lot more sense now

thank you

.close

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[sterile fulcrum]

How to do 9b

[slate lintel]

did you do 9a?

[sterile fulcrum]

Yes

[slate lintel]

what did you get for 9a?

[sterile fulcrum]

@jovial glacier use one of the available channel to ask for help

[jovial glacier]

Took awhile to type and didnt realize, sorry about that

[cedar kiln]

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[slate lintel]

okay... does that expression look familiar?

[sterile fulcrum]

Yea

Thanks

[cedar kiln]

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[crimson sedge]

how do i approach a problem like this

[jaunty pumice]

This is of olympiad

You can watch solution to understand this problem

[crimson delta]

at first you just try examples

see if you find some pattern

could you have predicted that 8 is not beautiful in some way without finding those two options

stuff like that

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[crimson sedge]

did u give ioqm?

[jaunty pumice]

Yes

[crimson sedge]

what was your marks

[cedar kiln]

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[dusty lodge]

vs. √21

[dusty lodge]

(√54*350)/(√21)

I wonder how to use bot for that, any idea?

[primal socket]

,calc (sqrt(54) * 350) / sqrt(21)

[wraith dagger]

Result:

561.24860801609

[primal socket]

Or

,w (sqrt(54) * 350) / sqrt(21)

[wraith dagger]

Results provided by WolframAlpha

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

Requested by _uss_enterprise

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[heady spindle]

Proposition 2.1.11. If A is finite and B ⊆ A, then B is finite.

Proof. If B is empty, the conclusion is immediate. Suppose that
B is not finite. By the hypothesis, there exist n ∈ N and f: A → Jn bijective, and consequently,
f(B) ⊆ f(A) = Jn. By the previous lemma, f(B) is finite. Since
f|B : B → f(B) is bijective, then f(B) ⊆ B, and therefore, B is finite.

I don't understand the underlined part, If I restricted my function f, it will be f|b : B --> Jn, how can I conclude the f(B)?

[heady spindle]

Also why the conclusion is immediate if B is empty?

[south tundra]

No, here f is defined as the mapping from A to Jn, it's not necessarily true that f restricted to B gets you codomain Jn

E.g. if I took A = {a, b, c}, B = {b, c} and f: A -> {1, 2, 3} given by f(a) = 1, f(b) = 2, f(c) = 3

Clearly, f|B is a mapping B -> {2, 3} rather than B -> {1, 2}

And, continuing, f|B: B -> f(B) is bijective since f is injective everywhere (even if we restrict the domain, injectivity remains) and it is surjective by definition

[south tundra]

The empty set is finite

Ah wait I think I understand what you meant

Sure, you can say that f|B: B -> Jn

But they also restricted the codomain to simply be the image of B under f

(This is a valid step in general as far as I am concerned)

It's so that surjectivity is guaranteed

[cedar kiln]

@heady spindle Has your question been resolved?

[heady spindle]

I don't understand why they decide that the codamain will be f(B), when I restricted a function, can I change the codomain?

[south tundra]

You can restrict the codomain as long as you make sure that the image of the domain is a subset of whatever you are setting your codomain to be

So you can always set your codomain to be just the range of your function

This will make your function surjective

E.g, when you have g: R -> R given by g(x) = sin(x), you can define h: R -> [0, 1] given by h(x) = g(x)

h is basically the same as g except it's surjective

You can think of what they did here in the same way

We have f: A -> Jn

f(B) is some set, right?

Let's use it to define g: B -> f(B) given by g(x) = f(x)

g is injective since f is injective

And

g is surjective by definition of f(B)

[heady spindle]

I'm lost, I don't if maybe my english isn't working :c I watched this video, and they doesn't change the codamain

[cedar kiln]

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[heady spindle]

.reopen

[cedar kiln]

✅

[south tundra]

Well, what stops you from redefining the codomain of f to be R^{>=0} as well?

You have real numbers in your domain so x^2 >= 0 and f(x) >= 0 clearly

[heady spindle]

Mmm so, I have a function f: X --> Y, if I want to restricted it to some set A, A must have to be A ⊆ X, then I will get f|A : A --> Y

Now, I also can redefine my codamain to some set B, if it also is B ⊆ X? And, I have another question, Have I to restrict a function to redefine the codamain? or can I redefine the codamain without restrict the function?

[gleaming cloud]

you can redefine the codomain without restricting the function

[cedar kiln]

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[hidden lion]

HELP

[hidden lion]

I have a question concerning proba basically when throwing 2 dices

[tropic oxide]

!da2a

[cedar kiln]

No need to ask "Can I ask...?" or "Does anyone know about...?"—it's faster for everyone if you just ask your question! See https://dontasktoask.com/

[hidden lion]

If two dice are thrown, what is the probability that at least one of them results in the number 6? Two different forms of reasoning are proposed and lead to different results (the correct solution, 11/36, and the incorrect solution, 6/21)

how did we obtain the 6/21 and how for the 11/36

its the problrmatic posed by Henri poincaré

[slim jasper]

Same problem asked in #help-37, apparently from an alt account.

Answers should go there.

.close

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[tropic oxide]

!status

[cedar kiln]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[tropic oxide]

mkay

so judging by your "how the actual fuck" reaction, you're having trouble deciphering the problem statement?

i beg your pardon?

are you saying i made a south park reference?

coincidental at best.

you have a right triangle
one of its legs is 3cm shorter than its hypotenuse
the other leg is 8cm shorter than the hypotenuse
you need to find the hypotenuse

does this make more sense to you?

you're gonna need that, yeah.

what's wrong?

is this your first pythagorean theorem problem?

k

myeh

ok fine so like

the first obvious move would be to make a variable to represent the length of the hypotenuse