help-0

[keen plinth]

ofc

[stable night]

ah

yes

OKAY

thank u sir

[stable night]

oh ye

i luv u

[keen plinth]

[stable night]

.close

[lone heart]

Channel closed

Closed by @stable night

Use .reopen if this was a mistake.

[lone heart]

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[night mirage]

How to do D) algebraically

[alpine sable]

ik how to solve just dk what to do when theres radical

[gray isle]

ik how to solve
...what would you normally do

don't let the radical intimidate you

[alpine sable]

not really but i dont see any examples with radicals yet (sorry im really dumb)

[gray isle]

don't overthink

[alpine sable]

do you simplify it?

[gray isle]

go through the first step like you would with all other questions

[fierce prairie]

create your own channel

[gray isle]

worry about simplification if needed after that initial first step

[alpine sable]

still cant get it

[gray isle]

you're overthinking

what did you mean when you said

ik how to solve

[night mirage]

Where the radical in d

[alpine sable]

hmmm

im overthinking ;-;

its ez im sorry

how do you close this

[gray isle]

.close

[alpine sable]

thanks man

[night mirage]

Oh my bad I thought this wa so pen

[alpine sable]

.close

[lone heart]

Channel closed

Closed by @fathom moss

Use .reopen if this was a mistake.

[alpine sable]

now it is

[gray isle]

wait for it to officially move back up

[alpine sable]

okok thx again

[lone heart]

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[raw citrus]

Hello again to whoever sees this. I am having trouble on starting this proof

[ornate condor]

ITS U AGAIN

[raw citrus]

HI

[ornate condor]

hii

[raw citrus]

lol I have 2 problems left to do on my assignment

then i can sleep

🥺

[ornate condor]

ok i quite like this diagram

so ill just use this again

um

i guess

[raw citrus]

then like before P(A n B) = P(A) + P(B) - P(A U B)

[ornate condor]

when u take

like

1-P(A') -P(B')

= P(A) -P(B')

[raw citrus]

OH SMART

[ornate condor]

and um

u can kinda notice these 2

when u minus u get that centre bit

but with more neg i guess

so like

u can rewrite it as

= P(A) -P(B')

[keen plinth]

[ornate condor]

wot

[keen plinth]

i dont like this approach

[ornate condor]

no

get out

u bad

[raw citrus]

👀

[ornate condor]

D:

snow gonna

nab my loot

[raw citrus]

[ornate condor]

[keen plinth]

can you see what you can do with this

[raw citrus]

kinda

[keen plinth]

A' and B' typically have overlap right?

so

[keen plinth]

left hand side just puts the two together with overlap

right hand side is considering the fact that theres overlap

[ornate condor]

:O

was my method morally wrong

[keen plinth]

so if we're doing 1 - (something)

then 1 - (something) ought to be less than 1 - (something smaller)

i.e.

[raw citrus]

Oh I see, would that then be P(A U B)?

[keen plinth]

the right hand side would then be P(A n B)

since

[keen plinth]

and

[keen plinth]

your method is asymmetrical

this problem is inherently symmetrical

[ornate condor]

what is that

[keen plinth]

so presenting a solution that doesnt prejudice either A or B is nicer

[ornate condor]

ohh

icic

ill learn to

prettify my stuff

mayb

[keen plinth]

most importantly tho

@raw citrus do you follow

[raw citrus]

Lol "prettify"

[raw citrus]

I do

[keen plinth]

wonderful

[raw citrus]

I totally forgot about how P(A) + P(B) >= P(A U B)

[keen plinth]

thats an inequality

its called the "subadditivity" of probability

[raw citrus]

I've seen that once but am not sure if we learned it

[keen plinth]

you have most definitely learned it

[keen plinth]

thats how you turn it into equality

but probabilities are always nonnegative

so the RHS is always <= than just P(A) + P(B)

[raw citrus]

Yes I've learned this

I'm flipping through my notes to see if my professor showed us the inequality

Isn't it for when it's mutually exclusive?

[keen plinth]

equality is mutually exclusive (usually called disjoint)

but inequality holds always

[keen plinth]

you can see from here theres the extra -P(A n B) term

so its necessarily smaller

[raw citrus]

I see, the most I've seen from P(A) + P(B) = P(A U B) is when my step says M.E. for mutually exclusive

[keen plinth]

subadditivity of probability is very useful

[raw citrus]

It seems so

[keen plinth]

usually its proved at the same time as this

because its just a direct consequence

[raw citrus]

I have a question

Say I'm doing it for three

This is a follow up with my last problem

this here

My professor gave us a hint in class and I'm not sure I follow what he says

Heres what I wrote down

[keen plinth]

not too sure how to interpret that

[keen plinth]

all i can really see is just this property being shown

[raw citrus]

I remember him talking about how P(A) = 1 and P(B)=1 but P(AB) can't equal 1

[keen plinth]

no it definitely can

if A = B then it can

even if A != B it still can

[raw citrus]

That's why it confused me

I wasn't sure why it's 2, it should be 1?

[keen plinth]

it should

the bound is just bad

in that chain of inequalities the bound is very bad

i think if P(A) = 1 and P(B) = 1 then P(AB) necessarily = 1

[keen plinth]

anyhow this is all i feel like it could lead to

[keen plinth]

this can be proven in exactly the same way

[raw citrus]

In one go?

Or I have to apply it twice?

[keen plinth]

technically twice

but morally its in one go

[keen plinth]

since this inequality holds for an arbitrary number of events

even infinitely many

[raw citrus]

Oh I see

So it's the same exact way as the previous one, but instead with P(C) being involved

[keen plinth]

yes

but de morgans still holds

and everything proceeds as before

[raw citrus]

Also

I think I found like an opposite way of doing this problem

[keen plinth]

opposite?

[raw citrus]

Not really opposite but using the other side to start

[keen plinth]

yes you can start on either side

[raw citrus]

Couldn't I do DeMorgans law on (AB)?

[keen plinth]

the way i showed is possibly easier to motivate

but you can do demorgans on the intersection first

and then proceed from there

[raw citrus]

Alright

Thank you!

I think I got it from here

[keen plinth]

wonderful

[raw citrus]

.close

[lone heart]

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[orchid python]

A batch contains 36 bacteria cells, in which 12 are not capable of cellular replication. Suppose you examine 7 bacteria cells selected at random, without replacement. What is the probability that exactly 3 of them are capable of cellular replication?

[orchid python]

I am stuck with this one, please help

[vale wigeon]

find the number of ways to select 7 bacteria from your batch of 36
find the number of ways to select 3 good ones and 4 bad ones, given that the batch contains 24 good bacteria and 12 bad bacteria

(bad = incapable of replication, for short)

[orchid python]

yeah

I will try, thanks

will this be (24C3 + 12C4) / 36C7

this is not

[orchid python]

is this binomial distribution

[vale wigeon]

no to both

24C3 times 12C4 on the top.

and no, if you want to view this as having to do with a distribution, it's hypergeometric.

[orchid python]

oh yeah

how can I solve this without using the hypergeometric formula?

[vale wigeon]

well you just did

except for the mistake you made

the probability you're looking for is (24C13 * 12C4)/(36C7)

[orchid python]

yeah thanks

According to the 2003 National Survey on Drug Use and Health, 55.3% of males have never used marijuana. Based on this percentage, what is the probability that more than 50 males who have used marijuana for samples of size 120?

is this one related to normal distribution?

[vale wigeon]

what use is it to tell you a problem is related to some or another distribution if all that's going to happen is that you will go into overthinking mode?

[orchid python]

i'm in the overthinking mode?

The probability of a successful optical alignment in
the assembly of an optical data storage product is 0.7. Assume
the trials are independent. What is the probability that the first two successful alignments require exactly 4 trials?

Wh this one the answer is not 0.7^2 * 0.3^2?

[lone heart]

@orchid python Has your question been resolved?

[orchid python]

is this 0.3 + 0.4 - 0.6?

how can i do this?

Is this Bayes's theorem

how can I get the P(A) in this case?

[ornate condor]

um

these r 2 diff problems?

[orchid python]

yeah

[ornate condor]

oh ye they r

try writing out the formula for given

[orchid python]

the first one the second one?

P(B'|A) = (P(B') * P(A|B')) / P(A)

hi?

i only have 1h left to prepare

😦

[keen plinth]

no

[keen plinth]

the denom can be written as P(B') P(A|B') + P(B) P(A|B)

[keen plinth]

you can calculate P(A n B) = P(A) + P(B) - P(A u B)

then P(A n B) + P(A n B') = P(A)

[orchid python]

ok

let me try

but what is P(A n B)? or P(A n B')?

[keen plinth]

you calculate P(A n B) from here

you know P(A) from the question

you solve for P(A n B')

[keen plinth]

this is for this one

[orchid python]

ok oki

so it will be 0.3

[orchid python]

please help me with this one

[keen plinth]

use this

you know all of the values

[orchid python]

why the denom can be rewriteen like this?

[keen plinth]

because of the total probability formula

P(A) = P(A n B) + P(A n B')

P(A n B) = P(A|B) P(B)

P(A n B') = P(A|B') P(B')

[orchid python]

but why P(B) P(A|B) exists in the denom

but when P(A n B) = P(A) + P(B) - P(A n B)?

or it's just a different representation?

[keen plinth]

diff representation

P(B) P(A|B) you can calculate

cuz you have the values given to you

P(A) + P(B) - P(A n B) not really

[orchid python]

ok I got it

yeah the answer is 0.75 thanks

[orchid python]

can you help me with this one?

[keen plinth]

oof

that one looks like a negative binomial

except my memory of that is terrible

[orchid python]

I think it's geometric

oh yeah it's negative

how can I do this?

[keen plinth]

independent trials

30% of the time its green

what do you think the distribution is

[orchid python]

negative?

[keen plinth]

negative counts how many trials before the nth success

not what we're doing here

we have a fixed number of trials

and we're counting successes

thats binomial

[orchid python]

ok

[keen plinth]

anyway i gotta dip

hopefully someone else can help

[orchid python]

yeha thankyou

[lone heart]

@orchid python Has your question been resolved?

[lone heart]

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[dim oracle]

Hi, potentially a silly question, but is the directional derivative in the direction of vector [1,1] just df/dx + df/dy?

[vale wigeon]

yes

[dim oracle]

I thought as much... I'm overthinking questions again, thanks Ann, have a good one <3

.close

[lone heart]

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[quasi rivet]

hi

this is linear programming problem for me

i need to solve it using spreadsheet

this is what i do

but i have difficulty on interpreting it into a spreadsheet and uses Opensolver

The thing is, it had constraints, variables and we must find objective on maximizing profits

does anyone knows how?

[next zodiac]

is it a surjective function?

[quasi rivet]

well maybe?

but i dont think it is

linear programming

[noble sinew]

#❓how-to-get-help find your own channel

[quasi rivet]

@strange sleet

[quasi rivet]

this the problem

<@&286206848099549185>

[strange sleet]

@quasi rivet for screensharing DM @fierce herald

[quasi rivet]

@strange sleet

https://docs.google.com/spreadsheets/d/1KnnvXPoDKWMbqThejN_U2jpQx9sBVV34cA3DMK7EcRg/edit?usp=sharing

@strange sleet

[lone heart]

@quasi rivet Has your question been resolved?

[quasi rivet]

@strange sleet

[lone heart]

@quasi rivet Has your question been resolved?

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[spiral thunder]

Hi guys, I'll just say sorry now if I do ask too many questions

I remember something being on the board to solve it using integration and substitution method(?) But I'm not sure with my solution:

[nimble fern]

hello there! I have been reading your solution since you posted it

[dry rune]

your method is right.

[nimble fern]

what's giving you trouble?

[spiral thunder]

hello people for visiting my help channel T_T

see now on the textbook exercises and examples there always seems to be a "let x = ?" which I guess is for substitution so I'm not really confident if I got it right

[spiral thunder]

Ohhhhhhhhhh even if I did not show the let x = thing?

[dry rune]

let x equal what

[spiral thunder]

the substitution thing

[dry rune]

nope. just get the primitive F(x) and let value of the upper limit, 8 in this case, plug in the primitive, u can get F(8) and value of the lower limit does same,u can get F(2) . Finally F(8) - F(2) is ok

[dry rune]

maybe your textbook is so friendly to beginner that lists each step in detail

[dry rune]

oh, maybe it uses other method to solve this problem.But I think your solution is the easiest. Can I have a look at your textbook if I may?

[lone heart]

@spiral thunder Has your question been resolved?

[spiral thunder]

Wait give me asecond.

Yes you may

[spiral thunder]

@dry rune

It's cut off but it's like that

[nimble fern]

hello again abendita,
i think your solution is correct and you need not to use substitution method, but incase your teacher do require you to use substitution, you can try
Let u=x^(1/3)

[spiral thunder]

henlo, yeah I think we're required to do so

[nimble fern]

hmmm

if so, I'll start with
Let u=x^(1/3)
then u³=x
hence 3u²du=dx

[spiral thunder]

Okokok wait let me get a pen and paper

Go on

[nimble fern]

it's your turn afterwards 👍

[spiral thunder]

Ok sec

[lone heart]

@spiral thunder Has your question been resolved?

[lone heart]

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[hard raptor]

Does anyone know the answer to this?

[slender gull]

Anything you've tried?

[hollow inlet]

definetely a test, quiziz

@hard raptor

[hard raptor]

It’s an assignment 👍

[slender gull]

Graded?

[hollow inlet]

We won't provide any help with that.

[hard raptor]

My teacher assigns assignments on quizziz

since I’m virtual

[hollow inlet]

yeah graded?

[hard raptor]

it’s graded by leaderboard on quizziz so i guess so

[hollow inlet]

No sorry, we can't provide any help 😔

[hard raptor]

damn thanks

[hollow inlet]

.close

[lone heart]

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[devout zinc]

i didn't understand anything about this

[gray isle]

wtf is this

it makes no sense

[tawny condor]

2 = 2pi?

[gray isle]

is there more context?

[tawny condor]

2 is an irrational number... I didn't know that

Thanks

[hollow inlet]

it is bro.

[gray isle]

value of a blank void is 3.1415

[hollow inlet]

"two" can't be represented on number line.

[devout zinc]

no

[devout zinc]

wtf?

..?

[slender gull]

3.1415 is rational.

[devout zinc]

bro what the fuck

[gray isle]

the image if plagued with errors

[devout zinc]

that literally makes 0 sense

blank void???

[tawny condor]

At first it seems legit, until you actually start reading it.

[hollow inlet]

✅

[gray isle]

that's my point

the image is plagued with errors

[devout zinc]

yeah prob

okay that was all

thanks

[gray isle]

and we're all crapping on it

[devout zinc]

.close

[lone heart]

Channel closed

Closed by @devout zinc

Use .reopen if this was a mistake.

[hollow inlet]

who wrote this?

[gray isle]

like based on the values present
the best we can infer is that this was supposed to be some sort of proof that 2pi is irrational

but there was some type set screw up along the way

[devout zinc]

Are you familiar with NCERT?

Its a question from NCERT, but the website I'm using messed up

[hollow inlet]

I am familiar with NCERT

it's the org who write books rigt?

[lone heart]

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[limpid plover]

Hello. I am trying to learn partial fraction decomposition and having trouble applying what I learned from a khan academy video to my equation: 1/(4y^4-5y^3).

[vale wigeon]

you do not have enough terms

you have a repeated root (in the form of y^3, which gives 0 as a triple root)

so you need A/y + B/y^2 + C/y^3 + D/(4y+5)

[limpid plover]

amount of terms should be the same as the degree of the denominator?

[vale wigeon]

yes

[limpid plover]

thank you

[lone heart]

@limpid plover Has your question been resolved?

[lone heart]

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[mental umbra]

2*11^x - 8^x - 3^x = 0 help

[mental umbra]

answer is 0 obv

but idk how to get to it

at all

[mental umbra]

basically find x

[trim wagon]

[mental umbra]

really a thinker innit

its supposed to be decently simple

since it doesnt involve logarithms

like you cant use them for it

[trim wagon]

i might have an idea

let’s say if we prove f(x)>0 for x>0 and f(x)<0 for x<0 then we can show that there is only 1 real root, and that is x=0

well i was able to see that thru graph tho

,w plot 2*11^x - 8^x - 3^x = 0

[ocean seal]

Results provided by WolframAlpha

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

Requested by Deep.#0001

[trim wagon]

@mental umbra

[mental umbra]

oh my bad i wasnt looking

[sullen dome]

Best option here since we have no similar bases

[mental umbra]

ok i see it

but i wouldnt really have the option to have a graph of my problem would i?

in a test i mean

[sullen dome]

Nope then you just have to see that 2*1-1-1=0

[mental umbra]

i did see that

im not sure if im gonna be given a point for that tho

i already did the test earlier today

and only found the answer without solution

[trim wagon]

i mean yes, but idk how i would solve that in test, well now we can have liberty to use graph, so maybe use that

[mental umbra]

i guess so

but it is meant to be possible in other ways

which is what confuses me

[trim wagon]

hmm 🤔

[hollow inlet]

[trim wagon]

if we solve this maybe we might get better insights

idk

[mental umbra]

hard one

[trim wagon]

f(x) >0 can be shown by for example AM-GM inequality ig

we have

$2\cdot 11^x +( - 8^x) +(- 3^x) \ge 3( \sqrt[3] {2\cdot 11^x ( - 8^x) (- 3^x)})$

[trim wagon]

for x>0

so clearly rhs is >0 so lhs is >0

umm did you get this?

hmm now that i think about it we can maybe use arithmetic progressions or something

2b = a+c

wait nvm

idts that helps

[lone heart]

@mental umbra Has your question been resolved?

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[waxen seal]

does set of real numbers has a least upper bound property?

[tawny condor]

yes

[waxen seal]

how should i approach proving this?

this is my first take

[royal meadow]

huh

i thought it was an axiom

[waxen seal]

completeness axiom?

[royal meadow]

i thought the least upper bound thing was an axiom

[waxen seal]

what is it called?

[royal meadow]

i'm not sure

it was just like

'any nonempty subset of R with an upper bound has a least upper bound. axiom, bang.'

[waxen seal]

R is a subset of R

[royal meadow]

R doesn't have an upper bound

[waxen seal]

then R does not have least upper bound property?

[royal meadow]

it does

R has the least upper bound property

[waxen seal]

how?

[royal meadow]

however, R does not have a least upper bound

[waxen seal]

oh i see it's 2 different things

[royal meadow]

yes

[waxen seal]

how should i prove this though?

wait i'll try

<@&286206848099549185>

[lone heart]

@waxen seal Has your question been resolved?

[lone heart]

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[grizzled elbow]

Hello, I have a question which looks simple but I can not find a way to work it out without a calculator

[grizzled elbow]

Oh it’s sideways

Anyways, it’s a non calc question so I struggle to just turn the decimal into a fraction

[alpine sable]

,rotate

[alpine sable]

Way better

[grizzled elbow]

Lmao

,rotate

[grizzled elbow]

,rotate

[grizzled elbow]

It might have something to do with square rooting something

[alpine sable]

You can write (101/100)²-(99/100)² if you want a fraction

[wanton tusk]

a^2 - b^2

[royal meadow]

a^2 - b^2

[wanton tusk]

yepp ^^

wait

no

[wanton tusk]

I wouldn’t recc this

leaving it as decimal wld make it easier for u to see

[grizzled elbow]

Ah yes turning it into fractions would mean simplifying it?

[wanton tusk]

unless ure okay w fractions

[grizzled elbow]

Eh I don’t mind either

[wanton tusk]

do u know the formula for a^2 - b^2?

[grizzled elbow]

No...

[wanton tusk]

(a-b)(a+b)

[grizzled elbow]

Ah like a quadratic?

[wanton tusk]

look at the third one

[grizzled elbow]

So just factorise?

[wanton tusk]

yes

[grizzled elbow]

Okie dokie

[wanton tusk]

okiee!

[grizzled elbow]

Thanks!

[wanton tusk]

welcc!

[abstract rivet]

serious question. Do"animation" can relate to mathematics? If so, how ?or does mathematics can relate to animation? If so, how?

[lone heart]

@grizzled elbow Has your question been resolved?

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[lone heart]

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[leaden fulcrum]

I cant isolated or reduce the equation to just only sin or cos term , i try using trig identity and cos+cos

[royal meadow]

angle addition formula

cos(x+a) = cos(x)cos(a) - sin(x)sin(a)

[leaden fulcrum]

Man i tunnel vision so much on those equation i forget this exist , thank for the help i got the answer.

.close

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[mellow skiff]

(64^1/3)^1/2

[mellow skiff]

What can I do

[keen pasture]

(a^b)^c = a^[bc]

[mellow skiff]

Yeah but

1/3 times 1/2 idk

Like it doesent have same deniomator

[gray isle]

its multiplication, doesn't matter

you could also first evaluate the cube root of 64

and then take the square root of that

[mellow skiff]

Perhaps i should do 8^3 *1/3?

[gray isle]

where's 8^3 coming from

[keen pasture]

8^3 = 2^9=512

[mellow skiff]

From 64

[gray isle]

8^3 isn't 64

[mellow skiff]

What should i do

[gray isle]

two approaches were provided for you

[mellow skiff]

Cuberoot 64 is 8

[gray isle]

(there are more)

no

are you implying that the cube of 8 is 64?

i.e are you saying that 8^3 is 64?

[slender gull]

,calc 888

[ocean seal]

Result:

512

[mellow skiff]

No that squareroot 64 is 8

[slender gull]

yes

[gray isle]

using that would be another approach

(64^(1/3))^(1/2) = (64^(1/2))^(1/3)
=8^(1/3)

[keen pasture]

You're not "active" anymore?

[slender gull]

Yeah

Been a while.

[gray isle]

and take the cube root of 8 for the final answer

[mellow skiff]

Wait what Did you do

[gray isle]

who

[mellow skiff]

What happen to 1/3

[gray isle]

(64^(1/3))^(1/2) = (64^(1/2))^(1/3)
=8**^(1/3)**

${({a^b})}^c = a^{bc} = {({a^c})}^b$

[ocean seal]

ℝamonov

[mellow skiff]

So you add squareroot to 64 and its 8, why is 1/2 gone

[slender gull]

Because you've already computed 64^(1/2)

[mellow skiff]

Oh

I thought it was just a add on

[gray isle]

since you were able to recognise the sqrt of 64

instead of the cube root

[slender gull]

It's like (2+3)5
You can either do 10 + 15 or 5 * 5
If you do 5 * 5. You don't say, "why is 2 or 3 gone" that's because you've performed the operation already.

[gray isle]

i tailored an approach that utilises that

[mellow skiff]

Never learned the other option at school

That’s not even in my books

[gray isle]

${({64^{\frac13}})}^{\frac12} = {({\underbrace{64^{\frac12}}_{8})}}^{\frac13} \
= 8^{\frac13}$

[ocean seal]

ℝamonov

[gray isle]

Never learned the other option at school
its just the distributive properly and/or basic simplification

something you should be familiar with if you're doing stuff with exponents

[slender gull]

“it's not in my books"
Well definitely not anymore, it should have been taught to you long time ago.

In any case, the 1/2 isn't gone

64^(1/2) is replaced with something equivalent

[mellow skiff]

Yeah im aware power of 1/2 is same as square root

Or power of 0.5

[gray isle]

power of

crucial words you're missing there

[mellow skiff]

I have one more question

Or 2

(9)^-1/3

And (-27)^1/3

I was doing
(9)^-1/3= 1/9^1/3 3^2 )1/3 but seem wrong here

And here I do And (-27)^1/3 = -9^3 )1/3 -9^3/3 = -9

.close

[lone heart]

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[hot bison]

Can someone explain how I know the limit exists In this?

[hot bison]

Am I just supposed to use direct substitution of 3 for both equations and see that they have a value

I feel like that is wrong

Limit to 3 btw

Sorry

[echo socket]

Well yes you can do that since the functions x^2 and 6x - 9 are continuous, if you need a more rigorous proof then you'd need to show why these are continuous

Or just prove the side limits nromally

[hot bison]

They are not contunous at xx =3 though?

Cause the answer key says a is the answer

So do I jut say the limit exists for both since for x^2 you get 9 and for 6x - 9 you get 9?

[tall topaz]

6*3 - 9 = 9

[gray isle]

are you looking at the correct answers?

[hot bison]

Oh wait what

It says they are correct

Is it not a?

[tall topaz]

Do you know the answer key?

[hot bison]

It says this

1. Is a, 2. b, 3. D and 4. E

There are 4 questions

But I only need help with the first one

[gray isle]

answer to this isn't A

[hot bison]

Interesting

So how do I find if it’s continuous

Just plug the things in?

The teacher made a mistake then

[tall topaz]

Continuous at a point if the limit from left side = limit from right side.

[echo socket]

If $\lim_{x\to{3}}g(x)$ exists, then $\lim_{x\to{3^{+}}}g(x)$ and $\lim_{x\to{3^{-}}}g(x)$ both exist and are equal, now notice that these limits are equal to $\lim_{x\to{3^{+}}}(6x - 9)$ and $\lim_{x\to{3^{-}}}x^2$ correspondingly

[ocean seal]

A Lonely Bean

[gray isle]

Continuous at a point if the limit from left side = limit from right side.
that's just existence of limit

[hot bison]

Ok

Is II also true

It should be right

?

You plug in both with direct substitution and they both = 9

[gray isle]

continuous would be function evaluated at that point is the same as limit

[tall topaz]

Yeah

I forgot that part

[echo socket]

Yes, g(3) = 9

[gray isle]

yes, limit is 9 and g(3) is also 9

so its continuous at 3

[hot bison]

Ok differentiable means you can take the derivative right?

[gray isle]

yeh

[hot bison]

Do the derivatives of both functions have to be equal?

[gray isle]

differentiate each piece and consider the one sided limits again

[hot bison]

I think its 2x and 6

Ok and then at 3 they are equal again??

[gray isle]

yes

[echo socket]

Yes, so it's differentiable

[hot bison]

So does that mean it is also differentiable?

So the answer is E then?

[gray isle]

yes

[echo socket]

Yes

[hot bison]

Alright thankyou so much, I’m gonna talk to my teacher about this.

.close

[lone heart]

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[grizzled crystal]

Is anyone able to help me with these? I’m having trouble on the first finding them to start

[lone heart]

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[grizzled crystal]

Having trouble on the first one

Made a venn diagram for it

[autumn pasture]

hellooo

do you know where A’ intersecting B’ is

in the Venn diagram

[grizzled crystal]

Everything that is not in a or b right

[autumn pasture]

yes

what’s the probability that you get an element in either A or B

[grizzled crystal]

Would it be a + b

[autumn pasture]

it’s in the question

[grizzled crystal]

.48

[autumn pasture]

yes

so probability that you don’t get anything in either A or B

is 1-

I think

[grizzled crystal]

So would that be in the intersect?

Bc we’ve been told to make Venn diagrams

[autumn pasture]

yes

can you share the area

[grizzled crystal]

And find for a and b then the intersect

[autumn pasture]

A’ int B’

shade

[autumn pasture]

yes

[grizzled crystal]

So would I write .41 in the A circle

Or would I have to do math to find A to complete the diagram

[autumn pasture]

so the P(A’ int B’) is 1- 0.48

[grizzled crystal]

Okay yes

Would this be correct? Or would they have to be subtracted for something to find them. Bc I thought they all have to add to 1

Not above

[autumn pasture]

no I don’t think so

because there is an intersection

[grizzled crystal]

But .41+.23+.48 is over 1

[autumn pasture]

they gave you the union right

A U B = .48

[autumn pasture]

do you know that P(A) + P(B) - P(A and B) = P(A U B)

[grizzled crystal]

Wouldn’t a + b have to add to 48? Bc I put outside the circles

For the area

[autumn pasture]

this

[grizzled crystal]

Okay yes I forgot

So my whole Venn diagram is incorrect?

[autumn pasture]

hahah it’s okay

yes

[grizzled crystal]

Ok

[autumn pasture]

once you’ve found P(A and B) after solving the equation above

you should be fine :))

[grizzled crystal]

So .41+.23 - .64 ?

Wouldn’t t it just be 0

[autumn pasture]

how did you get .64?

[grizzled crystal]

41+23

Then subtract a and b

[autumn pasture]

we are trying to get the Probability for P(A and B)

so 0.41 + 0.23 - P(A and B) = 0.48

solve for P(A and B)

[grizzled crystal]

So .64 - p(a and b) = .48

Would these be right? I’m not sure bc obv I’m having trouble figuring out Venn diagram

[autumn pasture]

it’s okay

where did A’ U B’ come from?

[grizzled crystal]

Oh I did that wrong. Just did .48 from what it gave me

It would be opposite

Bc it’s asking for everything not in a and b right

[autumn pasture]

A’ U B’ is basically excluding the intersection only

[grizzled crystal]

But we still haven’t found intersect rjght

[autumn pasture]

so it’s 1- P(A and B)

oh you haven’t solved it yet

[autumn pasture]

this one

[grizzled crystal]

No I’m having trouble with the initial findings of the actual Venn diagram

After that it would be easier

[autumn pasture]

okay

[grizzled crystal]

A and b I have to find

[autumn pasture]

let’s let (A and B) be x

[grizzled crystal]

Ok

[autumn pasture]

0.41 + 0.23 - x = 0.48

[grizzled crystal]

Would I subtract .23

[autumn pasture]

solve for

yes

subtract 0.23 both sides

[grizzled crystal]

.41+x=.25

[autumn pasture]

yes

what would you do now? :))

[grizzled crystal]

Subtract .41 right? But it would be negative

[autumn pasture]

yes

don’t worry

[autumn pasture]

no

it’s .41 - x

not +x

[grizzled crystal]

So 66

.66

[autumn pasture]

yes

wait

how .66?

you had .41 - x = .25

[grizzled crystal]

Add .41

[autumn pasture]

subtract

if you add .41 it’ll become .82 - x = .66

[grizzled crystal]

Ok so -.16

[autumn pasture]

yes

so -x = -0.16

[grizzled crystal]

Just inverse it right

[autumn pasture]

what is x

what do you mean by inverse it?

[grizzled crystal]

Turn it positive?

[autumn pasture]

yes

[grizzled crystal]

It can’t be negative right

[autumn pasture]

good :))

[grizzled crystal]

So .16

[autumn pasture]

yes

so that’s P(A and B)

basically the intersect

[grizzled crystal]

Would that go in the middle of the circle

[autumn pasture]

yes

[grizzled crystal]

But a and b are wrong right

[autumn pasture]

.41 and .23 are wrong

[grizzled crystal]

Yes

[autumn pasture]

yes

since you found the intersect

you can find P(A only)

and P(B only)

[grizzled crystal]

Yes

Would I just subtract by .16

Each?

[autumn pasture]

yes

[autumn pasture]

B

why 0.32?

[grizzled crystal]

.48-.16?

[autumn pasture]

what was P(B)

[grizzled crystal]

.23 omg sorry

[autumn pasture]

hahah it’s ok!

happens

[grizzled crystal]

So .07?

[autumn pasture]

yes

now add everything up

does it give 1

[grizzled crystal]

.25+.16+.07?

[autumn pasture]

and the outside

the one that’s not in A or B

remember we found that earlier

[grizzled crystal]

.52

Yes it does

[autumn pasture]

yes so it checks out I think

[grizzled crystal]

Awesome

[autumn pasture]

now it should be ok 👍

[grizzled crystal]

So to find Union of a’ and b’

I would maybe add .52 to something

[autumn pasture]

not needed

do you know which part is A’ U B’

[grizzled crystal]

Intersect?

But wouldn’t that mean it’s in both a and b

[autumn pasture]

no

it just excludes the intersect

everything else is included

[grizzled crystal]

So .25+.07+.52

[autumn pasture]

sure

that’s fine too :))

[grizzled crystal]

P(A’ Union B’) = .84

[autumn pasture]

u could also consider 1-0.16

[grizzled crystal]

Ok true

[autumn pasture]

but it’s the same :)) so whatever is more comfortable for you

[autumn pasture]

yes

[grizzled crystal]

Okay and to find P(A’ Union B ) I would add .07 and .52?

[autumn pasture]

and .16

[grizzled crystal]

But isn’t that inClyde’s in a

Included *

And .16 is intersect

[autumn pasture]

this is how A’ U B looks like

[grizzled crystal]

Ahhhh okay

You’re right

I think this is all correct now

[autumn pasture]

second one haha

0.16 is the intersect

A’ U B’ excludes the intersect

[autumn pasture]

^ didn’t you do this haha

[grizzled crystal]

Oh it’s .84

[autumn pasture]

yep!

[grizzled crystal]

I forgot to write

[autumn pasture]

hahaha it’s okay

[grizzled crystal]

Thank you!

[autumn pasture]

welcome!

[grizzled crystal]

Should I close this out now?

.close

[lone heart]

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[errant stone]

Two people throw a 6-sided dice, and the person with the larger number wins $1. No reward if equal. How much are you willing to pay for this game? If you had another option, and spent $0.25 to add 2 to the number you got, how much would you pay to play the game now?

[echo socket]

The probability of winning from just throwing the dices is (5 + 4 + 3 + 2 + 1)/36

[errant stone]

the first question would be $0.42 right?

[errant stone]

yup and multiply that by 1 right?

to get $0.42

[echo socket]

Well multiplying by 1 won't change it so yeah

[echo socket]

Approximated or not?

[errant stone]

ye

approx

[echo socket]

Well it's asking the reader so idk

[errant stone]

the second one would be approx $0.47 right?

[lone heart]

@errant stone Has your question been resolved?

[errant stone]

<@&286206848099549185>

[lone heart]

@errant stone Has your question been resolved?

[potent garnet]

Well, $0.47 > $0.42 so it does make sense on that part...

Becuase higher chances -> more money willing to gamble

[lone heart]

@errant stone Has your question been resolved?

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[nova sandal]

9x9=81

[lone heart]

Please don't occupy multiple help channels.

[trim wagon]

please stop trolling if you are

[trim wagon]

<@&268886789983436800>

[wise thistle]

ayo mods just to be safe its not me lmao

[trim wagon]

oh i thought they posted gif

anyways

[wise thistle]

bruh dont frame me i need this server

[wary stream]

.close

[lone heart]

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[trim wagon]

thanks

[wary stream]

Gasp

Awesome

[wise thistle]

why is it dark green bruv

[wary stream]

#info Explains the roles

[worn fox]

Save the planet

[wary stream]

Helpful role

[wise thistle]

thought it was lifht green

[wary stream]

There's helper and helpful

[wise thistle]

damn

[wary stream]

Basically, the people who were helping, who weren't helpers (like me) didn't want to be a helper and get pinged all the time but have helper powers, that's what they did

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[nocturne kelp]

oop

this one pls ^^

I tried it but was kinda hard

[fallen verge]

if you have a function y=mx+c, m is slope, y-intercept is c

[nocturne kelp]

so m is 3

we have that

and so y=3x+b

uh

f(0)=1 ?

[gilded vessel]

at x = 0 the y intercept occurs

so solving for b is quite trivial here

but you can plug in the provided values for any arbitrary X value

for this example you plug in zero for x and 1 for y and solve for b

y = 3x + b

1 = 3(0) + b

[lone heart]

@nocturne kelp Has your question been resolved?

[lone heart]

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[cyan rapids]

Hello. I am just completely lost on this problem. No clue what I'm doing with limits anymore

[fresh parcel]

well think about what happens when v approaches c from the positive side

[cyan rapids]

Well how am I supposed to know what happens

There's like no numbers here

[ornate condor]

ok so

when v is close to c

what happens to

v/c

[cyan rapids]

It's close to 1?

[ornate condor]

yes

and what if v is a bit more than c

[fresh parcel]

well square roots arent defined for negative numbers

[cyan rapids]

It either doesn't exist or the value is 1

(I'm aware of imaginary numbers, they don't apply for this class though)

[ornate condor]

anw

so

[cyan rapids]

It approaches from the left though so v would have to be less than c right?

[ornate condor]

yess

but

[cyan rapids]

Yeah it wouldn't be that simple lol

[ornate condor]

what happens if we approach from the right

[ornate condor]

ye

the

[cyan rapids]

Why would that matter if the question only asks for the left side? Anyways, then the number would exist

[ornate condor]

lim exists when v<c

[ornate condor]

nono

when approaching

c+

[cyan rapids]

I do not understnad

[ornate condor]

when v->c+

whats the lim

[cyan rapids]

If v is negative than the sqrt fails

[ornate condor]

w8w8

wdym v is neg

no

[cyan rapids]

Right here

Wait I read it wrong

[ornate condor]

mhmm

[cyan rapids]

When v is approached from the left going to when c is approached from the right?

[ornate condor]

omg

im

confused by u

[cyan rapids]

I am confused by the problem

[ornate condor]

just

[cyan rapids]

My apologies

[ornate condor]

if weve

v->c+

what would the lim be

[cyan rapids]

What in the world does "v->c+" even mean

[ornate condor]

like

lim v->c+ L

[cyan rapids]

Gotcha

Wait hang on

[ornate condor]

as v approaches c from the right

whats L

[cyan rapids]

You were making an arrow I thought that v was being approached from the left

bc the - is part of the arrow

I thought it was part of v

My b my b

[ornate condor]

im

so confused

by what u cobfused abt

hahaha

but u got it

so

[cyan rapids]

I got it now though don't worry I understand what you mean

[ornate condor]

allg

[cyan rapids]

Just have to figure it out now

If v approaches c from the right it should be positive?

[ornate condor]

ok so