help-36

[proud echo]

👍

I get it

Thanks

Simple yet confusing

Should I close now?

[simple basalt]

Ye

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[faint locust]

#1195800467880558672 message

[upper sierra]

?

[faint locust]

Click it; it redirects to my thread

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[faint locust]

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[ebon sparrow]

Find the area of the figure bounded by these lines.

[ebon sparrow]

Is it right?

[feral ginkgo]

looks right

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[placid halo]

Geert has 12 pens in his pen pocket: eight blue, two red and two black.
Wim has forgotten his pen pocket and asks Geert to borrow a pen.
Geert takes 2 pens from his pen pocket without looking.
(a) He looks at the pens and gives Wim a black pen. Calculate the probability that Geert has another blue one in his hand?

[placid halo]

im confused when i have to do like

P(Blue given that Black) or when u can just do P(Blue)

[glad sundial]

try to visualize it with the tree gaph

you already know that geert gives wim a black pen

[placid halo]

yeah but why isnt it 2/12 * 8/11

like i get that you know that he has a black one as well

but sometimes youll still do P(Blue pen given that you got a Black one)

[glad sundial]

Why 2/12

oh

nvm

Ok

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[hazy turret]

what is the question?

[placid halo]

this

@hazy turret

.close

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[ruby lake]

can somone help me with this

i thought to do this P(abs(x-my) >1) = 0.05

[thorn shell]

oh my fucking god random variables

i was going to help you since our names are really similar but now i got ptsd, my bad

[ruby lake]

continuous random variables :/

even wors

how are our names similar?

[thorn shell]

my actual name is jordi

[icy glacier]

yes continue

[mental root]

yeah what critical value for z gives you that probability?

[icy glacier]

(and its mu not my)

[ruby lake]

so i divided it into P(x-mu>1) and P(x-mu <-1)

[ruby lake]

in the table i have in my book minimum is 0.5

so i was confused

[mental root]

hmm

well according to the 68-95-99.7 rule

[icy glacier]

thats not how you split it up

[mental root]

approxiamtely 95% of the data will lie within 2 standard deviations of the mean

[ruby lake]

sorry I forgot -1 at the second

[mental root]

the more correct number is 1.96 sigma

[ruby lake]

is it correct now?

[icy glacier]

Yes

And can you say anything about the value of P(x-mu>1) compared to P(x-mu <-1)?

[ruby lake]

they are equal?

[icy glacier]

indeed

So now you need to standardize P(X-mu<-1) if you want to use a z-table

[ruby lake]

why not use the one with >1

[icy glacier]

doesn't matter

just depends what your table uses

[ruby lake]

is z table defined only for things from 0 to some number

[ruby lake]

i'm not sure about this

ah ok i found it

it says to the left of x

so it means <x i think

[icy glacier]

yes

[ruby lake]

ok

i don't thave 0.05 in my table

[icy glacier]

You don't need 0.05

And have you standardized it yet?

[ruby lake]

yes i have

so mu is 0

i subtract mu from both sides and divide by sigma

to use the values from the z table

so i get P(X/s < -1/s)

is mu is 0

[icy glacier]

.

You said P(x-mu>1)=P(x-mu<-1). We are only looking at P(x-mu <-1)

[ruby lake]

i tried to standartize that

[icy glacier]

If you find sigma such that P(x-mu<-1)=0.05

does that answer the original question?

[ruby lake]

i don't understand

[icy glacier]

What was the original question?

How was it related to P(x-mu<-1)

[ruby lake]

find sigma

[icy glacier]

for what

[ruby lake]

for P(abs(x-mu)<-1) = 0.05

[icy glacier]

no

[ruby lake]

is this correct

[icy glacier]

yes and this?

[ruby lake]

you standartize it

[icy glacier]

no

[ruby lake]

?

[icy glacier]

what does P(X-mu<-1) have to do with the original question?

[ruby lake]

i am not sure

i don't know how to incorporate sigma into P(X-mu<-1) = 0.05

[icy glacier]

This is still not what you need to find

How did you start the question?

How did P(X-mu<-1) appear?

[ruby lake]

by solving absolute value

[icy glacier]

okay so whats the specific relationship

between that and the original question?

[ruby lake]

absolute value

[icy glacier]

????

I suggest you start over

Figure out exactly what it has to do with the original question

[ruby lake]

X-mu is Y

man don't take this as an offence but try answering your questions by my perspective

you ask me a question which might have a thousand answers

[icy glacier]

it doesn't

[ruby lake]

well the way tou say it yes it does

at least from my perspective

because you already know the answer

and expect me to give the same answer

[icy glacier]

Because if you redid what you did

before you asked for help

you could answer

[ruby lake]

while i'm lost because you make me a few consectuive answers like that

[icy glacier]

legit look ur 1st three messages

and you get answer

[ruby lake]

can somone help me with this
i thought to do this P(abs(x-my) >1) = 0.05

this were my first 2 messages

[icy glacier]

three then

[ruby lake]

this was 3rd

continuous random variables :/

[icy glacier]

obviously the one related to the question

[ruby lake]

never mind

please don't try to help me anymore

you really destroy my mood

.close

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[elder vine]

I am struggling with the second part of this question, I already know that the angle inside is 90 because it is a rectangle, but how do I find the rest of the bearing?

[final saddle]

@elder vine Has your question been resolved?

[echo torrent]

What does it mean by hearing?

Bearing?

It was ages since I did these so I need a refresher hahaha

[elder vine]

its like the angle from the north pole of a point to another point

I hope i explained it well

the blue angle

in this case this is the bearing from A to D

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[mild osprey]

Hello! I need help with this convergence problem:

[mild osprey]

the answer is expressed in terms of k.

I’m not sure how to start

.close

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[smoky siren]

hello, i recently started reading about laplace transform but im confusing with the frequency domain the laplace transform has! , could anyone suggest me a intuitive source or book?

[smoky siren]

?

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@smoky siren Has your question been resolved?

[smoky siren]

<@&286206848099549185>

[hazy turret]

what

[smoky siren]

any source or book to suggest me what book should i read?

about laplace transform etc

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[graceful sand]

anyone know how to do this part i? I tried resolving horizontally and vertically but didnt seem to get anywhere

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[hollow cairn]

If |x + 1| < 1
10 , prove that |x3 + 1| < 0.331

[granite heath]

not rlly sure what you're asking

are you asking if
|x + 1| < 1
then prove
|3x + 1| < 0.331

x / 3?

[tulip coyote]

x^3 I'm guessing(?)

[granite heath]

oh

[tulip coyote]

And is that 1/10 or?

[granite heath]

1/10?

prolly

[tulip coyote]

Is the question "if $\abs{x + 1} < \frac1{10}$, prove that $\abs{x^3 + 1} < 0.331$", or?

[soft zealot]

@tulip coyote

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@hollow cairn Has your question been resolved?

[hollow cairn]

yes..thats the question

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[latent fractal]

what have you tried?

[random flame]

p(AnB) is the part that A and B have in Common

unlike others P(AUB) has formula and it is : P(AUB) = P(A)+P(B)-P(AnB)

[next lance]

so A would be 57?

how do you get A

[random flame]

ok I misunderstood a about your question P(A) is 57

and P(B) is 61

P(AnB) would be 10

[next lance]

I don't think P(A) is 57

[random flame]

and P(aUb) would be 61+57-10

[next lance]

its supposed to be some kind of decimal i can't remember how to do it but when i did know how it usually was a decimal answer

it was something like number of favorable outcomes/Total possible outcomes

to find P(A)

[random flame]

so you wanna find U right?

in that case it would be (A-AnB) + AnB +(B-Anb) + (AUB)' = U

[next lance]

No im trying to find P(A) rn

ohhh wait i just remembered how

ok so P(A) is .33 and P(B) is .35

not sure how to do the last 2

[light violet]

Is P supposed to mean power set?

[lethal estuary]

no, probability

[lethal estuary]

how did you get these?

[light violet]

Oh okay lmaooo

[next lance]

For A its (57 + 10)/(57 + 10 + 61 + 75)

and B is 71/(57+10+61+75)

[final saddle]

@next lance Has your question been resolved?

[next lance]

<@&286206848099549185>

[hushed apex]

I think I know this, what is your question?

[next lance]

I don't know how to find the answer to the last 2 questions

[hushed apex]

Ok, the 3rd question is P(A intersection B), which means what both sets have in common

4th question is P(A union B) which is the totality of what both sets include

found a photo of this, maybe helpful

you can remember it like this: the one that looks like a U is a Union, the other one is an intersection

or in this way: an open hat will get more things than a closed hat, the U is open and the intersection is closed

does this help?

[next lance]

yea thanks so much

[hushed apex]

Np have a great day

@next lance if you don't need help anymore, make sure to type in ".close"

[next lance]

this is the last question i need

not really sure how to start it

[hushed apex]

this one I'm not sure of, good luck

try pinging helpers in 15min if nobody figures it out

[next lance]

kk thx

[hushed apex]

👍

could you please ping me once you got a solution, I'm kinda curious

ty

[next lance]

sure

[shell cove]

48 times 78% = 37.44
So there’s 37.44 of them survive their first year of life in math
But 0.44 eagle is not possible so you should just count 37.44 to 37of them survive their first year of life and then answer those questions

@next lance

[next lance]

im confused

[shell cove]

About what

[next lance]

what would the equation be to get a

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@next lance Has your question been resolved?

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[woven wigeon]

.reopen

[covert nimbus]

how do I answer this

[covert nimbus]

Coordinates of Vertex
Y-integer
X-integer
Sketch parabola
Domain and range

Those are what I need to solve

[upper sierra]

Hi

Do you know graph of quadratic equation?

There is a general graph for

[covert nimbus]

Barely

[upper sierra]

$y=ax^2+bx+c$

[soft zealot]

Monarch of Eternal Night

[upper sierra]

For this equation, first find the roots

[upper sierra]

So what are the roots

[covert nimbus]

What are roots again?

[upper sierra]

The values for which y=0

[covert nimbus]

Sorry but I am not sure

[lethal estuary]

set the equation equal to 0, solve for x

[upper sierra]

I gtg so can you cover from here?

[lethal estuary]

sure

[upper sierra]

@covert nimbus

[covert nimbus]

ah thanks for the help though

[covert nimbus]

I might be wrong here but I dont think I am supposed to solve anything

[lethal estuary]

then what is the objective?

[covert nimbus]

Coordinates of Vertex
Y-integer
X-integer
Sketch parabola
Domain and range

[lethal estuary]

y-integer?

what does that mean

[covert nimbus]

My abd

bad

I meant intercept

Confused the terms lol

[lethal estuary]

ok well there is a formula for the vertex

the y-intercept is where x=0, and the x-intercept is where y=0

[covert nimbus]

so 0,-4?

[lethal estuary]

that's the y-intercept, yes

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[lean basalt]

Can someone help me on where I am fundamentally messing up the signs?

No matter how I re-write this problem I end on 1 + cos(4x) instead of negative

I think in the pink highlights are where I am misunderstanding but idk

OMG NVM I figured it out

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[keen shard]

would the answer to this be E according to riemann tables

[young verge]

i think its already 82

using a right rieman sum i got 90

and then 75 with a left one

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@keen shard Has your question been resolved?

[midnight prawn]

you could use integration to find the area under the graph ig

[young verge]

but you arent explicitly given the function

[midnight prawn]

ye i realised

its 82

[vital surge]

no

also no need to use a riemann sum

[midnight prawn]

cause 15 - 20 is 15 cm of growth

which already makes it 75

10 - 15 is < 5cm of growth

but less than 25 cm

so answer is D

because the first box under 10 - 15 is 5cm

making it 82

and the triangle formed under the line is less than 5

closer to 2

making it 80 + 2 (or 2.5) = 82 (or 82.5)

thus answer is D

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[mystic dune]

Can someone explain how to answer this question.

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[unique pendant]

help

[final saddle]

Please don't occupy multiple help channels.

[unique pendant]

what do i to?

im very dumb at math

pls help

[robust coyote]

im very dumb also but i think this is how the drawing would look like

[unique pendant]

so i find the x?

[robust coyote]

yes, by doing tan

[proven solstice]

angle of elevation, change the angle to the other one

[unique pendant]

bruh

just just say the formula or something

[proven solstice]

no?

[robust coyote]

tan= opposite/adj

try to find it

mb

[proven solstice]

change the diagram dw we all make mistakes

[robust coyote]

do tangent

do you know which is the opp and which is the adj?

[unique pendant]

Ah okay...

30tan(55)

[robust coyote]

yes

did you understand?

[unique pendant]

yeah

do i make a drawing or something?

[proven solstice]

mate, angle of elevation from the ground, that’s the wrong place to put the angle

[robust coyote]

OH WAITTT

OKAY ONE SEC

[unique pendant]

XD

[proven solstice]

lmao

[unique pendant]

it should be there

[robust coyote]

itll be like this

😅😅😅

[unique pendant]

now its fix

whats this all about?

[unique pendant]

so the answer is 21?

[robust coyote]

yes

[unique pendant]

hello anyone there?

[umbral pulsar]

yes

[unique pendant]

how to solve this?

[umbral pulsar]

which grade?

[unique pendant]

9

[umbral pulsar]

I mean they've already give angle a and b so why are they asking for it in the question?

[unique pendant]

idk

error or something

[umbral pulsar]

Okso they're asking for sides b and c not the angles

so law of sines

Use the formula

U there bro?

First of all we have to find angle c

Which is 107

Cuz sum of angles is 180 in a triangle

[unique pendant]

yeah

[unique pendant]

C not c

[umbral pulsar]

yea C

now we know angle A and side a and Angle B but not side b

So we use first part of law of sines

[unique pendant]

ok

[unique pendant]

?

[umbral pulsar]

now we just solve this

[umbral pulsar]

Yes

[unique pendant]

cross multiply?

this the example i found

[umbral pulsar]

yes

We get 16.1005

Now do the same thing for the last part of the equation

[unique pendant]

am i getting it wrong or something?

thank you for the help

i think i will seek help from my mom

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[clear spade]

This is a civil engineering question. it involves maths but the part i'm struggling with is mainly the steps to get to the answer. any help would be appreciated

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@clear spade Has your question been resolved?

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@clear spade Has your question been resolved?

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@clear spade Has your question been resolved?

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@clear spade Has your question been resolved?

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[clear spade]

.close

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[signal citrus]

hello, can someone explain to me how P(A intersection B)= 1/36?, shouldn't it be 2/10 when a+b=10/36 since there's two outcomes for A and B being the same number (5,5) and (6,6)?

[lethal totem]

a + b > 8, b = 3, so a must be 6. (6,3) forms a unique pair
As in there is only one way in which to have a+b > 8 AND b = 3

[signal citrus]

i got it, thank you

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[clever solstice]

how do i calculate the integral between the intersection of 2 functions in wolfram alpha

[mossy shore]

what is congruent

[final saddle]

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).

[clever solstice]

i need to check my results

[celest crane]

-> ,w int_a^b (f(x) - g(x) dx)

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[echo torrent]

How do we prove this? Let f(x) = x if x is rational, f(x) = 0 if x is irrational. Show that f is continuous at x = 0 and nowhere else.

[magic sparrow]

use epsilon delta

[echo torrent]

How though

I know the definition

But then how do we use it

Can we just show that rationals and irrationals are dense in R?

[autumn geode]

it's immediate

and the choose of lambda is obv

[echo torrent]

you mean delta?

[autumn geode]

yea

[echo torrent]

ok ill try

[autumn geode]

just write it out

it's really easy

[echo torrent]

u mean the def?

[autumn geode]

just write it all out

you will see

[echo torrent]

aight mind if I stay here for a while

Ill do it now

[autumn geode]

take your time chef

[echo torrent]

bro u r the one thats super smart

How do we show that it is discontinuous anywhere using the def?

Do we use the negation?

sry @autumn geode can u gimme some hints plz

or @magic sparrow hahaha

would rlly appreciate it

im struggling to show that it is discontinuous everywhere

other than the origin

[magic sparrow]

split it into cases

suppose you're at x=p/q

in reduced form

where p!=0

then show it's discontinuous there

suppose instead you're at x=an irrational value, not 0

[echo torrent]

do i use the negation

[magic sparrow]

sure

[echo torrent]

but then how do I show that it is continuous???

at x=0

I get that |x|<delta

and then i wanna make |f(x)|<epsilon

[magic sparrow]

Showing it's continuous at 0 should be easy just by the definition

write it out

[echo torrent]

omg

I forgot that 0 is rational

lol

right i finished this part

what about the second part?

[final saddle]

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[tranquil pine]

Hello there, I could really use some help with this binomial expansion question please

[warm ether]

okay, what do you have thus far

[tranquil pine]

Well, I change it to (x^2 + 2x^3)^1/2 to get it into the form (1+x)^n

[young bridge]

you need to factor out an x^2 to get it into the correct form

[tranquil pine]

Carried out the expansions and got 1,2x^3,1/2x^6

[warm ether]

an x*

[tranquil pine]

Ok thank you

[young bridge]

x^2 from the square root but yes

[tranquil pine]

So I got

X^2(1+2x)^1/2

Then just carry it out now right?

[young bridge]

$\sqrt{x^2+2x^3}=\sqrt{x^2(1+2x)}=\sqrt{x^2}\sqrt{1+2x}=x\sqrt{1+2x}$

[soft zealot]

Obotron

[tranquil pine]

I need to get rid of the square root right?

[young bridge]

what do u mean?

[tranquil pine]

To carry out the expansion

[young bridge]

i was saying this isnt quite correct

[tranquil pine]

Ah so it would be

X(1+2x)^1/2

[young bridge]

yep

then u can use binomial expansion on the (1+2x) term

leave the x factored out for now

[tranquil pine]

👍

So I got

1,x,-x^2

Then just times by x right?

Each term

[young bridge]

yep

how many terms u need?

[tranquil pine]

Just the 3

[young bridge]

ok nice

[tranquil pine]

Then I’m not sure about where it converges either

Third term is /2 as well sorry

[young bridge]

for any binomial expansion of the form: (1+bx)^n, the radius of convergence is given by |bx| < 1

[tranquil pine]

So

2x < 1

X < 1/2

Thanks a lot mate I appreciate the help

.close

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[tranquil pine]

Hello, I could use some help with this binomial expansion question please

[final saddle]

Please don't occupy multiple help channels.

[tranquil pine]

So what I did was expand the brackets

To get (1+x)/(1 + 2x) * (1+x)/(1 + 2x)

Which gave me

(1 + 2x + x^2) / (1+2x)^2

Which I change to 1 + 2x + x^2(1 + 2x)^-2

Carried out the binomial expansion on (1+2x)^-2

And times the terms I got by 1 + 2x + x^2

However what I got was not right and I’m not sure where I went wrong

<@&286206848099549185>

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[tranquil pine]

.close

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[late pasture]

How do I convert this to expontial form, I'd need the same theta. Cos(theta) + isin(theta) = r^i(theta).

[late pasture]

It's cos(5pi/6) + isin(5pi/3)

[quiet ermine]

cos (pi - pi/6) = -cos(pi/6)

-sin pi/3 = sin(2pi - pi/3) = sin(5pi/3)

oh wait

No actually it worked

[late pasture]

I'm confused why you did that

[quiet ermine]

I am trying to convert it into a e^ix thing, so I'm getting out anything I can from the angle side

Notice that cos pi/6 and sin pi/3 are both half of square root 3

[late pasture]

Could I add a full rotation of the unit circle to isin to try to get the same angle as cos?

[quiet ermine]

So you "factorize" it kinda

[quiet ermine]

You can do that as well tbh

Both ways solve it

I was going to write it in a form Re^{i(3pi/4)}

Because -1 - i lies on a line with 135° inclination

[late pasture]

I'm not sure how many rotations to do tbh

Pi + 2pi/3 ?

Oh wait nvm

That wouldn't work

[quiet ermine]

$2^8\left(\cos(\frac{5\pi}{6}) + i\sin(\frac{5\pi}{3})\right) = 2^8\left(\cos(\pi - \frac{\pi}{6}) + i \sin(2\pi - \frac{\pi}{3})\right)$

[soft zealot]

Riku

[late pasture]

When adding rotations to the isin would I try to get the result of 5pi/6?

[quiet ermine]

Do you follow this?

[late pasture]

Imma look at it rn

Ah k

I think I get it

[quiet ermine]

Good

[late pasture]

Wait I just realized something.

[soft zealot]

Riku

[late pasture]

Aren't both theta supposed to be the same to convert to expo form?

[quiet ermine]

It becomes like that after you go through

When you factor out the half of sqrt(3) , -1 - i remains

[soft zealot]

Riku

[quiet ermine]

If you'ree not convinved, just expand the right side

[late pasture]

Ah okay one sec imma type it out to make sure I'm understanding correctly

[quiet ermine]

I can write down a handwritten short note for you if you have trouble following this

[late pasture]

Sure I'd appreciate it

[quiet ermine]

Cool, lemme whip it up

[late pasture]

Here is my understanding: so we have cos(pi - pi/6) + isin(2pi - pi/3).... we can get rid of the pi and 2pi (because of rotations).. leaving us with pi/6 and pi/3... so we find the angle related to them on the unit cirle then factor... it would be: root(3)/2 and 1/2

but it's negative pi/6 and pi/3 which I forgot how to deal with

[quiet ermine]

I was wrong, trivial mistake on my part. The angle is 5pi/4. Look here

I hope my handwriting is legible.

[late pasture]

ah okay okay that makes sense. what is the also part

is that you converting back to polar

[quiet ermine]

That's the justification for why I put the sqrt(2) thing in place of -1 -i all of a sudden

[late pasture]

ahhh okay

[quiet ermine]

I'm sorry if I wasn't clear before because intuitive ideas are very hard to convey

[late pasture]

no you're good! thanks so much!

[quiet ermine]

You're welcome

[late pasture]

thanks again, have a great day!

.close

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[steel kite]

help

idk where to start

[thorn shell]

oh this one is interesting

[final saddle]

@steel kite Has your question been resolved?

[steel kite]

yeah idk

[spare jewel]

well

for one, you could count

but it seems interesting

ask your teacher

not even gauth helped me. it did step 1,2,3 and said forget it let's just count it up

or someone smart enough could come

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[muted prairie]

Unless you want to try to learn generating functions, this is brute force

Of course, there is still some skill in finding the best way to brute force it. I would start by considering the case where there are no 20s, then one 20, then two 20s

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[latent spindle]

can someone help with this word problem? “One group of workers completes a job in 10 days, a different group finishes in 15 days. The work was completed in 12 days after hiring a third of the first group and a part of the second group. What part of the second group was hired?” i feel like it looks simple but i keep getting the wrong answer

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@latent spindle Has your question been resolved?

[latent spindle]

nvm i solves it lol

.close

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[unkempt seal]

can someone tell me why the saddle point is wrong

for (0,0)

why can’t i plug it into y=3x/2

to get y=0

[unkempt seal]

this is the key btw

[formal trail]

for something to be a critical point, fx and fy must both be 0 for the same (x, y) pair

if you plug in (0,0) for fy, you find that it is not 0

[unkempt seal]

i isolated y in the first eq’n and plugged it into the second to solve

oh

wait how does that work then

y=3x/2 can’t be (0,1)

wait is it cause i factored out an x and divided 0 by x to cancel it out

[formal trail]

if x= 0 then there's no restriction on y from the fx equation

[unkempt seal]

oh

so to know what equation to solve i plug it in to both and get the value that is nonzero?

pick the value that’s nonzero*

[formal trail]

so from the fx equation you can conclude that either x = 0 or y = 3x/2, so you plug in both of those restrictions separately to the fy equation

[unkempt seal]

ah i see

so i shouldn’t divide the x to the other side to get rid of it

[formal trail]

yes, that loses a solution (since you can't divide by 0)

[unkempt seal]

is this statement valid ? plug to both fx and fy and use the nonzero answer

[formal trail]

you can check your results by plugging in a potential critical point (x,y) to fx and fy and making sure they're both 0

[unkempt seal]

ok i think. i get it thanks

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[floral atlas]

Did I do sum wrong

[floral atlas]

Wtf

<@&286206848099549185>

[delicate gulch]

What are you trying to do?

[floral atlas]

Finding the

Derivative of

V

Should be v(x)

But yea

[delicate gulch]

Oh sorry idk derivatives I haven’t interacted with them yet

[floral atlas]

Okay

[barren hound]

looks right to me

[floral atlas]

Yeah exactly

It is right

😭

[barren hound]

,w d/dr 2πr²√(a²+r²)

[soft zealot]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by kitten.in.a.teacup

[floral atlas]

Sigh

My textbooks wrong

[barren hound]

off by a sign somewhere?

oh

i am

,w d/dr 2πr²√(a²-r²)

[soft zealot]

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[floral atlas]

nope

they js dissapeared the denominator

💀

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[severe timber]

can someone help me with a basic imperfect bifurcation
I know what the bifurcation looks like, but Im not really sure how to do the regions for it, and I also dont know how to get the stabilities in a). Or maybe it's just asking me to plot and that's it

[mint orbit]

have you made a bifn diagram before?

[severe timber]

yeah

[mint orbit]

its been a while for me but i might be able to help

which part are you on

[severe timber]

I have r = x - h/x. I just plot this for h<0, h=0, h>0

this part is easy

but how do i find the stabilities of these plots (im not even sure if im required to)

[mint orbit]

so i guess you examine the flow of a point near the fixed point

if they tend to be dilated or compressed

you could check out like, a bifn plot maker that does this automatically

to get an idea

but i could be interpreting the problem wrong

you are talking about b yea?

[severe timber]

No idea what that means. How do i find how many fixed points there are for each case

i think that's what its asking?

[mint orbit]

a bifurcation diagram is a fixed point plot

its the fixed points versus the bifurcation parameter

[severe timber]

no im talking about part a)

[mint orbit]

at least, thats the curve you plot

so maybe we do uhh

well hold on, lemme make a plot

im gonna do h=0

then we can see if were on the same page or not

alright?

[severe timber]

yeah

[mint orbit]

so, i think youre intended to use the second derivative

but i just look at a perturbation lol

but, typically i believe youd look at $\ddot x$

[soft zealot]

jan Niku

[mint orbit]

and if $\ddot x < 0$ then you have stability

[soft zealot]

jan Niku

[mint orbit]

but perturbations are more immediate if slower IMO

[severe timber]

if it has no fixed points (h<0) do we graph stability? (dotted = unstable, solid = stable)

With intuition i can see how h<0 has no fixed points, h = 0 has one, and h>0 has two if you look at h+rx = x^2

and set r = 0

and then look at y = h

[mint orbit]

h = 0 has one?

[severe timber]

yeah

[mint orbit]

well it depends on the value of x, right

sorry, of r

actually it has 2, almost everywhere

[severe timber]

yeah but the bifurcation represents 0, 1 or two fixed points

[mint orbit]

right

[severe timber]

the 1 fixed points represents the tangent line in the \dot(x) vs x graph

two is almost everywhere bseides when h<0

[mint orbit]

the transcritical bifurcation for h=0 occurs where the stability of the two fixed ... idk what you call them, flip

[severe timber]

I think i got it now, but im not even sure if a) cares about stability

[mint orbit]

presumably youve seen the actual diagram

like something like this

so you need to know where stability occurs

[severe timber]

yeah thats a transcritical bifurcation

that's already given in the problem

anyways this is the finished result

h(r) = (-r^2)/4

[mint orbit]

sure

because $x^\star = \frac 12 \qty( - r \pm \sqrt{ r^2 + 4h } )$

[soft zealot]

jan Niku

[severe timber]

ok what do you do with that

[mint orbit]

they say fixed points, right

fixed points are solutions of $\dot x = 0$

[soft zealot]

jan Niku

[severe timber]

ok i get that

[mint orbit]

solutions of $\dot x = 0$ are $x^\star$ solving $h+rx -x^2 = 0$

[soft zealot]

jan Niku

[severe timber]

but the problem doesnt not state i need fixed points

[mint orbit]

i imagine this is for part b

[severe timber]

Ok here's how I actually did the problem. I got h + rx - x^2 = 0 <=> h+rx = x^2. I differentiation both sides to get the tanges which yield r = 2x <=> x = r/2. I also wanted to get a graph of r vs. x to graph the diagrams for h>0, h=0, h<0 in which i got r = x - h/x. From x = r/2 i plug is back into \dot(x) and get h(r) = (-r^2)/4 which is the bifurcation diagram. To figure out the regions I graph y = h and y = x^2 for r = 0. This help me show that for h<0 there are 0 fixed points, for h=0 there is 1, and for h>0 there is 2 fixed points. and done

[mint orbit]

I don't understand what you are asking anymore

[severe timber]

no im done

[mint orbit]

oh

[severe timber]

i solved it

[mint orbit]

congrats

im sorry if i didnt help lol

[severe timber]

but in case there is a more complicated problem i do gotta use the quadratic thingy

[mint orbit]

yea

[severe timber]

its okay

[mint orbit]

or sometimes you get weird implicit equations

[severe timber]

.done

[mint orbit]

those suck a lot more to graph

[severe timber]

idk how to close

[mint orbit]

i mean im sure you know bifurcations can get screwy

.close

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[mint orbit]

[severe timber]

yeah it sucks

im hoping my exam doesnt have a stupid one

[mint orbit]

there arent very many simple ones

you can learn them all quickly

i believe in you

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[short anchor]

Hi I need help figuring out how to find the prime power factorization of 36 for my discreet math class

[rocky tusk]

keep dividing by primes

36 is even so divide by 2 to get 18 this is also even so divide by 2 again to get 9 this is divisible by 3 so you get (2)(2)(3)(3)

[short anchor]

Thank you I appreciate it

May I ask another question

I need help applying the division algorithm, the question is express the GCD (15,17) as a linear combination of 15 and 17

[final saddle]

@short anchor Has your question been resolved?

[short anchor]

<@&286206848099549185>

[frosty cedar]

To express the GCD of 15 and 17 as a linear combination of the two numbers, you can use the Extended Euclidean Algorithm.

Starting with (17 = 1 \times 15 + 2), we find (2 = 17 - 1 \times 15).

Next, (15 = 7 \times 2 + 1), which gives (1 = 15 - 7 \times 2).

Substituting the expression for (2) from the first step, we have (1 = 15 - 7 \times (17 - 1 \times 15)).

Solving, (1 = 8 \times 15 - 7 \times 17). Hence, the GCD of 15 and 17 expressed as a linear combination is (8 \times 15 - 7 \times 17).

[soft zealot]

evil murkius

[trail mango]

!nogpt

[final saddle]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

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[barren crescent]

what exactly is modular inverse used for in number theory

[final saddle]

@barren crescent Has your question been resolved?

[desert mantle]

its a very fundamental concept so its a bit hard to give specific examples where its used

a lot of questions can be framed as solving ax=b mod n for example, and if a is invertible you can multiply by its inverse to get x=a^(-1)b mod n

[barren crescent]

i thought it was used for coprimes

is it just solving for a number in the extended euclidean algorithm?

[desert mantle]

the eea is an option to calculate the modular inverse, sure

it doesn't tell you how that inverse is then used

[barren crescent]

in terms of gcd and eea how would the inverse be used

like what is the purpose

[desert mantle]

the gcd tells you whether the inverse exists and the eea gives you an option to compute it. neither of them tell you how to use it

[barren crescent]

inverse only exists with coprimes?

[desert mantle]

the inverse of a mod n exists if and only if a and n are coprime, yes

[barren crescent]

i dont understand this problem, does it use inverse>?

[desert mantle]

yes

[desert mantle]

its this

[barren crescent]

what is the equation asking, is it 13 times what (mod 37) = 6 mod 37

?

[desert mantle]

yes

[barren crescent]

how would i go about solving it?

[desert mantle]

by reading

I have to go

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[glass ocean]

Help

[glass ocean]

Anyone

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@glass ocean Has your question been resolved?

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@glass ocean Has your question been resolved?

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@glass ocean Has your question been resolved?

[cosmic bolt]

!status

[final saddle]

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

[cosmic bolt]

also good to say what exactly confuses you or show your work so far

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[west yoke]

So right here

I take the derivitive of 3t+4t^2

and get 8t+3

sub in 2 and get 19

right?

[heady otter]

yup!

[west yoke]

Marginal cost is stated as C'(x)

Thought process is

take deriv.

21x^2/10000-4x/25+7

sub in 100 and get 12

[west yoke]

this look good?

[heady otter]

yeah if the marginal is the derivative

[west yoke]

thanks

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[tranquil pine]

Solve for x.

[tranquil pine]

It's 7 or 8

I think 8

[mental root]

what did you do?

[tranquil pine]

[ 9x = 6(x + 4) ]
[ 9x = 6x + 24 ]
[ 3x = 24 ]
[ x = 8 ]

[lofty sinew]

That method and that result both look right to me

[onyx peak]

No idea how that was done, but it's correct

[tranquil pine]

Ive been known to be crazy

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[fading hamlet]

$mn=xy$ and $m \ne x$ and $n \ne y$, then $(m-1)(n-1) \ne (x-1)(y-1)$

[soft zealot]

CalicoJackRackham

[fading hamlet]

Sorry meant $m \ne y$. How do I go about proving the latter?

[soft zealot]

CalicoJackRackham

[fading hamlet]

Mnxy are all positive integers

[hybrid heath]

proof by contradiction feels like a good option to explore

[fading hamlet]

Thanks - I will look into that

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[clever canyon]

hello

[clever canyon]

how can i start solving this?

[abstract bramble]

it asks you to type the exact value

-sqrt(2)/2

[clever canyon]

right

i solved the first two

but idk how to answer the third one

what does it want?

what is it asking here?

i look at 225 since its equal to 135

i put in -sr2/2

but wrong

nvm i answered it on my own

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[amber plover]

Hi guys iw this solution correct? The task is Calculate the addition and subtraction of radicals

[tranquil pine]

,rcw

god fucking dammit

why is it always upside down

[tranquil pine]

alright

[amber plover]

Taken from phone camera dxd

[fierce prairie]

check how you did sqrt(8) again

[amber plover]

Ehat does sqr8 mean?

[fierce prairie]

$\sqrt{8}$

[soft zealot]

MerryTacoGamerCat

[amber plover]

Oh alr

Aint it right? Like 8 equals 2^3 so it cancels out the root and it ends like 2^1 but one cant be a exponent so i think its right?

[fierce prairie]

it should be $18\sqrt{2}$

[soft zealot]

MerryTacoGamerCat

[amber plover]

Aaaa, ty bro

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[wispy panther]

can i get a hint for this one please?

[wispy panther]

I got 1/5 but I'm not quite sure

[restive cosmos]

||consider which of the colors are repeated||

[wispy panther]

The numeratoe is the 3 unordered sets of 3 different colours
i think i got the denominator wrong though

would something like this be better?

@restive cosmos how would you work out the denominator?

would using ordered sets be better?

[distant shoal]

Just use permutations and combinations

[restive cosmos]

i would casework on the number of blue marbles and use unordered sets like you did

for example, if there was 1 ble marble, then there are 3 options, 0, 1, 2 red marbles

the denominator is ||11||

[wispy panther]

ty

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[lyric lichen]

I am trying to do syntehtic division to get the factors

[lyric lichen]

,rotate

[lyric lichen]

this is what I got

the problem is I have an extra -36

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[peak ruin]

Hey, i would recomend you checking out this video from this timestamp as it explain the method quite well https://youtu.be/JUClZR66U1g?t=139

[lyric lichen]

gotha watching it rn

I know how to do all that but

https://www.youtube.com/watch?v=D_I11k2DfCg

following this video

It has 3 factors for the factored out polynomail

but in mine it has 4

so idk how to proceed

[peak ruin]

could you write out the polynomial?

[lyric lichen]

yes it is written on paper in the image above

[lyric lichen]

this one

problem 1.)

[lyric lichen]

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[slender cargo]

for part d wouldn’t it be changing at a decreasing rate

since C’>0 and C’’<0

[rocky tusk]

ap calc bc

ay

[short skiff]

C' < 0

[rocky tusk]

so i put changing at a decreasing rate since C is decreasing and concave up

the slopes of the tangent lines approach zero

so it’s changing at a decreasing rate

[slender cargo]

same

[rocky tusk]

and it makes sense

if you think about newtons law of cooling

[slender cargo]

some people are thinking that it’s increasing rate cuz C’’>0

[rocky tusk]

nono

increasing as in becoming less negative

is C’’>0

[slender cargo]

ye

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[tranquil pine]

[timid sinew]

Try plugging in values

thats what I would say

[tranquil pine]

ok