help-10

[subtle jetty]

How do you find the probabilities of 2 events

that happen back to back

say you roll a 6 twice in a row.

what are the probability of that happening

[fleet stag]

1/6 x1/6

[subtle jetty]

exactly

do you think we could use that here

[fleet stag]

were not given any value for the first coloum tho

[subtle jetty]

The first column is given to be a bus

[fleet stag]

wdym

[subtle jetty]

I defined the columns to be like this

[fleet stag]

ohhh ok

so what do we do from here

did they do 1-.4 to work out bus

but that dosent make sense

[subtle jetty]

Lets define
P(B) as the probability that Jean takes the bus
P(T) as the probability that Jean takes a taxi

So if Jean takes the bus on monday, the probability she takes a taxi on tuesday is 0.4

[fleet stag]

yh

[subtle jetty]

and the bus is 0.7

[fleet stag]

on monday its .7?

[subtle jetty]

The probability of her taking the same mode of transport the next day day would be
P(B|B) = 1 - P(T|B) = 1 - 0.4 = 0.6
P(T∣T)=1−P(B∣T)=1−0.7=0.3

To find the probability that Jean takes a taxi on Wednesday, we need to consider all possible paths she could take from Monday to Wednesday:

which are what

Monday is always the bus so

[fleet stag]

TB and BT

[subtle jetty]

Monday (Bus) -> Tuesday (Bus) -> Wednesday (Taxi)
Monday (Bus) -> Tuesday (Taxi) -> Wednesday (Taxi))

[fleet stag]

k i understand this bit

[subtle jetty]

So now we need to compute the probabilities for these paths

[fleet stag]

still not sure on this bit

[fleet stag]

isnt P(B|B) = P(B n B)/P(B)

oh u worked that out

mb

soz for interupting

[subtle jetty]

ok so getting back to computing the probabilities

i wrote it in python to be cool and i can explain the steps easier
First path
P(B) * P(B|B) * P(T|B) = 1 * 0.6 * 0.4
P(B) * P(T|B) * P (T|T) = 1 * 0.4 * 0.3

# Given probabilities
P_TB = 0.4  # Probability that she takes a taxi after taking a bus
P_BT = 0.7  # Probability that she takes a bus after taking a taxi

# Probabilities of taking the same transport the next day
P_BB = 1 - P_TB  # Probability of taking a bus after taking a bus
P_TT = 1 - P_BT  # Probability of taking a taxi after taking a taxi

# Probabilities for each path to take a taxi on Wednesday
# Path 1: Bus -> Bus -> Taxi
path1 = P_BB * P_TB

# Path 2: Bus -> Taxi -> Taxi
path2 = P_TB * P_TT

# Total probability for taking a taxi on Wednesday
total_probability_taxi_wednesday = path1 + path2
print(total_probability_taxi_wednesday)

Comes out to 0.36

[fleet stag]

ok so how do we work out the .6 and .4

thats the bit im confused to workuing out

[subtle jetty]

the notation im using is kind of off but

P(B) represents monday.

The probability of her taking the bus

Which is 1 because its given.

P(B|B) is the probability of Jean taking the bus on the second day after taking the bus

Which is 0.6 as seen in the chart

[fleet stag]

the chart is from the markscheme

[fleet stag]

that in the anwser not in the question

how did u work it out to be .6 on tuesday

[subtle jetty]

If she takes the bus on the first day, the problem reveals that the probability of the taxi ride on the second day is 0.4

So the bus ride is 1-0.4

Which is 0.6

[fleet stag]

omg

ok thank u

how did i miss that

😭

[subtle jetty]

shit happens I've been running on a quarter of my brain power for the past week

if you wouldve asked me this yesterday i wouldve been STUMPED

[fleet stag]

lool

btw u mentioned python are u in university?

[subtle jetty]

comp sci

well comp sci rn gonna be taking engineering once i finish this degree and some other shit next year

[fleet stag]

yh i applyed for comp sci for uni

[subtle jetty]

complicated

but at school the most ive done is effectively high-school level math...

[fleet stag]

dayum

[fleet stag]

apparently comp sci is kinda getting saturated

that what im worried about

i kinda wanna switch to maths for uni

[subtle jetty]

last year was bad but the job market is slowly recovering

[subtle jetty]

ive been considering this aswell

maybe a math teacher or something

[fleet stag]

yh maybe ur good at maths

nice talking to imma close the chat now

[subtle jetty]

alright

[fleet stag]

.close

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[timid silo]

Why is the answer x - 1 and not 1 - x ?
maybe because when it's squared it doesn't matter?

[latent walrus]

(1-x)^2=(x-1)^2 yeah

[timid silo]

oh okay

thanks

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[mystic ore]

.reopen

[safe horizon]

hello guys
this is the first time for me asking help from here
however, what are the advanced algebra tricks to solve limit, I mean sometime the limit is very complicated, and don't know how to start it?

[latent walrus]

#❓how-to-get-help

[obtuse pebble]

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[worthy forge]

.reopen

[grizzled bay]

Plainly, I don't even know where to start.

I think it has something to do with the standard error of the mean (2.214 I think)

If someone could point me in the right direction, that would be great

[obtuse pebble]

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[brave moth]

Hello i just have some questions regarding derivatives as someone just looking into it for fun

[brave moth]

so don’t get mad if i don’t fully have a deep understanding of the concept

[proud mulch]

ofc

[brave moth]

but i don’t understand how you get the slope from a given point

[fathom flicker]

Slope is a measurement between points

There is no slope of a point

The derivative try’s to measure what would be, if it existed

[proud mulch]

it is generally known as Difference in y over Difference in x

[fathom flicker]

Do you know the definition of the derivative using the difference quotient?

[proud mulch]

so it can never get to a singular point

[brave moth]

no, i don’t really have a definition i just understand the concept

[proud mulch]

its just that the difference gets extremely small

[fathom flicker]

Didn’t you just say you didn’t understand the concept and that’s why you’re asking this question?

Look at the definition

It will help you understand the concept

[brave moth]

can you tell me how i would graph a visualization on desmos?

wait so is a derivative also a function?

[fathom flicker]

Sometimes

[brave moth]

or ig something i can shove numbers into and get something out of it

[fathom flicker]

Sometimes

[proud mulch]

There is a video series on youtube by 3blue1brown which is very good for beginners and visualises everything needed. here's a link: https://youtube.com/playlist?list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr&si=0fNoQ5PUEozJNAOy

[brave moth]

thank you

[proud mulch]

watching this will clear up a lot of your questions

[brave moth]

alr

ty!

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[dense schooner]

im trying to use the alternating series test for this but one of the requirements is that bn is decreasing on the interval but the problem is that its actually not decreasing from 1 to 2?

so like what do i do

[zenith raft]

b_n is decreasing on what interval?

[dense schooner]

heres the graph

[robust raven]

Show that your series is absolutely convergent, and then it follows that it converges, that's all.

[dense schooner]

so should i just ratio test it

[zenith raft]

for convergence, it only matters what's happening "eventually"

[dense schooner]

oh ok

[robust raven]

no, please use comaprison test for absolute value of the geenral term

[zenith raft]

it doesn't matter what's happening for the first finitely many terms

[dense schooner]

so you mean if absolute value of the series converges then its absolute convergence

and if it doesnt then its conditional?

[robust raven]

yes, if absolute value series is convergent then yours is absolutely convergent hence convergent

[dense schooner]

ok let me do

@robust raven is this what you mean

[dense schooner]

yes thats what i did

[robust raven]

write in a such way

[dense schooner]

oh

ok

[robust raven]

then 1/n^2 is very knwon seris convergent harmonic of an order p =2

so veryone accepts it

[dense schooner]

yeah

i shouldve just wrote 1/n^2 for the right side comparison

[robust raven]

yes

hence your series given oen is absolutely convegeent, and then

it implies convegrence

no need to mention about conditonal convergence here

[dense schooner]

right

ok got it ty

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[charred ledge]

Confused with both questions

This is my working

[obtuse pebble]

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[charred ledge]

.reopen

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✅

[charred ledge]

<@&286206848099549185>

[obtuse pebble]

@charred ledge Has your question been resolved?

[charred ledge]

<@&268886789983436800>

<@&286206848099549185>

[slim cove]

(Please don't ping Moderators for math help, only for server-related issues)

[obtuse pebble]

@charred ledge Has your question been resolved?

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<@&286206848099549185>

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[pastel lichen]

so i been stuck on this for the past hour

[pastel lichen]

honestly its too much to type so nvm

.close

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[dense imp]

if it's on computer, take a screenshot, if it's a problem in a book, you can take a photo?

[pastel lichen]

its more of the work i got like 3 pages of messy notes XD

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[pastel lichen]

hmm

[pastel lichen]

i solve for dv/dt first

and get roughly dv/dt = 9.81-1/3 v(t) then im suppose to solve for v(t) and it shows me some expnential and idk how to get to that

[brisk matrix]

what do you mean it shows you some exponential

[pastel lichen]

there is like a example problem to show you the steps

but idk what it does to go from that

[brisk matrix]

it is a differential equation

[pastel lichen]

to v(t) = 32.7-32.7e^ (-(3t/10))

[brisk matrix]

do you know about differential equations? specifically first order linear nonhomogeneous diffeqs

[pastel lichen]

not the same numbers but looks simmiliar

[brisk matrix]

y' + p(x)y = q(x)

does that form look familiar

[pastel lichen]

and tbh yes but my brain is fried and i keep getting an answer like only off by .7 or so at the end

[pastel lichen]

and yee ya take the integrating factor by getting integral of pxdx to e

[brisk matrix]

yes

if you are getting the wrong answer, show your work

[pastel lichen]

okie dokie gimme a min to re write it to not be a complete mess lmao

yeaaa im lost lmao

tried reworking it

and just following their problem

dv/dt = 9.81-3/10 v(t)

says use separation of variables to determine velocity equation

and they get v(t) =32.7-32.7e^ (- 3t/10)

also not helpfull that this problem has 19 parts in the view an example 😭

[brisk matrix]

show your work

or show where you are confused in their explanation

[pastel lichen]

dv/dt = 9.81-3/10 v(t) idk how to go from this to v(t) =32.7-32.7e^ (- 3t/10) like i understand the concept of e ^ intergral pxdx = u and v(t) = 1/u integral u qx dx

but i got no clue how to actually do that here

[brisk matrix]

i would appreciate if you showed a picture

[pastel lichen]

There is where I’m at and that’s what the steps I’m attempting to follow

[obtuse pebble]

@pastel lichen Has your question been resolved?

[pastel lichen]

<@&286206848099549185> can someone show me how to work this out

like better than the example lol

[obtuse pebble]

@pastel lichen Has your question been resolved?

[brisk matrix]

oh sorry i missed this

we have
[\dv{v}{t} + \frac{3}{10}v(t) = 9.81]

[warm shale]

maximo

[brisk matrix]

we let
[\mu(t) = \text{exp}\left(\int \frac{3}{10},\dd t\right) = e^{\frac{3}{10}t}]

[warm shale]

maximo

[brisk matrix]

and then we can write the diffeq as
[\dv{}{t} \left[v(t)\cdot e^{\frac{3}{10}t}\right] = e^{\frac{3}{10}t} \cdot 9.81]

[warm shale]

maximo

[brisk matrix]

@pastel lichen if this is not obvious let me know, but it is just part of the method for first order linear equations

[pastel lichen]

where does the 32 come from ?

[brisk matrix]

what 32

if you are talking about the answer

i am not there yet

so i have no idea

[pastel lichen]

this part

[brisk matrix]

i am working this question out for your benefit

actually i'll let you integrate and find out where the 32 comes from

[brisk matrix]

go from here

[pastel lichen]

not sure aint e to anything just e

i honestly dont know ima just take the l for this homework problem

[brisk matrix]

no

[pastel lichen]

then i got no clue

ill have to settle with me being dumb and learn it later

[obtuse pebble]

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[pastel lichen]

.close

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[grand umbra]

I need help learning right triangles and trig

[fiery sorrel]

!status

[obtuse pebble]

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

[grand umbra]

1

I missed like 4 days and she gave me a quiz and got a 3.5/18 now i need to do correctins

[fiery sorrel]

Do you have any work you want help with?

[ember frost]

ask your question

[ember frost]

practice

and open help channel if you have a problem you stuck on

[grand umbra]

so i got this triangle

its a right triangle

45-45-90

i only have hyp

whcih is 10

!close

.close

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[odd sleet]

.open

i have a question on my homework

[odd sleet]

i got a which equal a = 5
(0,5)
but can't figure out how to get b

this is pre cal

[dense imp]

use the (1, 2) point, plug in 1 for x and 2 for y

(and now that you know a, plug in 5 for a)

[odd sleet]

so 5 times 2^(2)(1)

[dense imp]

hm wait wait why are you putting a 2 in the exponent there?

[odd sleet]

2=5 times 2^b(1)

sorry my mistake

i was wondering the same

[dense imp]

yep so 2 = (5)2^b do you know how solve this for b now?

[odd sleet]

would i log it?

[dense imp]

yeah exactly but start off by dividing by 5 on both sides first to just ahve the 2^b isolated on one side, then log as you say

[odd sleet]

so 2/5=2^b

[dense imp]

yep, now time to log, which base should the log be?

[odd sleet]

10

[dense imp]

you need the same base as the exponenial part youre trying to reverse (2^b) so base 2

[odd sleet]

b=log2(2/5)

[dense imp]

assuming you're writing a base 2 log there, yes correct

$b=\log_2(2/5)$

[warm shale]

Soosh

[odd sleet]

how do you think i should input this since we are not suppose to enter log but a number

[dense imp]

well if you wanna estimate it on a calculator, you can use a change of bases thing since most calculators will only do base 10 or natural base (e)

[odd sleet]

ok thank you

ok got it right

[dense imp]

so to write it in terms of a new base c (say we want 10), it would end up as:
$\frac{log_{10}(2/5)}{\log_{10}(2)}$

[odd sleet]

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[warm shale]

Soosh

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[timid silo]

help anyone??

[twilit meteor]

write root(-x) as i X root(x)

and simplify

[last pilot]

note: $\sqrt a \cdot \sqrt b = \sqrt {ab}$

[warm shale]

ren

[obtuse pebble]

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[merry girder]

ive found one root

which is 1.3

1/3

how do i find the others?

[whole dock]

How did you find the root?

[merry girder]

here

[whole dock]

You can use rational root theorem

[merry girder]

whats that

[whole dock]

https://www.cuemath.com/algebra/rational-root-theorem/

[merry girder]

thats really long lol

[whole dock]

Here $a_n = 12, a_0 = 1$

[warm shale]

ColdTee

[whole dock]

n = 3

[obtuse pebble]

@merry girder Has your question been resolved?

[merry girder]

alr ty

.close

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[stiff remnant]

How can I find the exterior angle of a shape?

[stiff remnant]

.close

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.reopen

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[timid silo]

send question

[obtuse pebble]

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[haughty hamlet]

Hey

[haughty hamlet]

I need help with this question

f(x) = 0.5 (x-4)² - 2

As well as 3x² + 2x - 8 = 0

[timid silo]

what's the question

[haughty hamlet]

One sec

Determine the vertex and the direction of opening for cach quadrau
function. Then state the number of zeros.

[timid silo]

you can find vertex of the second equation by doing -b/2a, to get the x value of the vertex, then plug that into the equation to get the y value.

openings depend on the "a" part, if "a" is positive it opens up and if it is negative it opens down.

[haughty hamlet]

I need help

[timid silo]

i'm doing the same stuff in math rn lol

[haughty hamlet]

U think u can write it down?

[haughty hamlet]

Oh

What grade r u in?

[timid silo]

10

[haughty hamlet]

I'm in grade 11 studying rn for a quiz

[timid silo]

nice

lol

[haughty hamlet]

I forgot what I did since grade 10

[timid silo]

no worries

basically

you're familiar with ax^2 + bx + c = 0 right

@haughty hamlet

[haughty hamlet]

Yea ofc

[timid silo]

yeah so

a is 3

[haughty hamlet]

Can u do It for me rq? 😭

Ok a is 3

[timid silo]

yeah hold up

[haughty hamlet]

k ty

[haughty hamlet]

...

Smart

K tysm fr

[timid silo]

can you factor that equation?

if you can lmk

[haughty hamlet]

Wdym

I'm lost lowkey

I also need help

With

f(x) = 0.5 (x-4)² - 2

[timid silo]

working on it

[haughty hamlet]

Ok thanks

[timid silo]

do you know what factoring is

[haughty hamlet]

Yea

[timid silo]

can you factor the equation 3x^2 + 2x -8

[haughty hamlet]

Yea

[timid silo]

what is it

[haughty hamlet]

Idk

I'm fucking lost

[timid silo]

i don't think you can factor it unfortunately

[haughty hamlet]

Alr

[timid silo]

you just need to remember

the vertex is a coordinate, and the x-value is always -b/2a in a question like that

then when you have that x value you plug it in for x in the equation and you get your y value

also since it's just asking you how many x intercepts (or zeroes) there are, you can put two

this is the graph for the equation, it crosses the x-axis two times, therefore there are 2 zeroes.

[haughty hamlet]

I see

Thank you

[haughty hamlet]

Yeah I understand that part

[timid silo]

here's the second equation hope this helped

vertex is always (h,k) in that type of equation

in "a(x-h)^2 - k"

[haughty hamlet]

That does that say?

The last part

Something opens up

So?

A = 0 . S, which is positive so it opens up?

Correct?

@timid silo

[timid silo]

0.5

sorry my handwriting is bad

it says since a = 0.5, and it is positive, it opens up

basically whenever "a" is positive it opens up, when it is negative the graph opens down

[haughty hamlet]

Ok perfect

Tysm

[obtuse pebble]

@haughty hamlet Has your question been resolved?

[haughty hamlet]

Yes sir

[obtuse pebble]

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[silver cove]

I don’t understand this, this is theorem 4.

[silver cove]

What is really the central angle here??

[inland matrix]

It's the angle formed at the center when end points of the arc are joined to the center

[stark thorn]

Ig an angle formed at the centre
like with the centre as the corner

[silver cove]

the central angle is supposed to be MAT right?

or MT

[inland matrix]

It is, but not the only one

All the three angles are central angles

[silver cove]

oh..

HOW come

T-T

How am I supposed to know the central angle

[stark thorn]

cuz there are infinitely many possible central angles

cuz the the end points can be any two points on the circle

[silver cove]

wth

that's complicated

what if the question was "Find MTP" what's the central angle for it?

[stark thorn]

i mean u can define a unique central angle for a given pair of points lying ON the circle

[silver cove]

oh how

[stark thorn]

If the points are say M and P
And centre is O,

Central angle is angle MOP

[silver cove]

OHHHHH

OK I lowkey get that one

[silver cove]

so the central angle here would be MAP?

[stark thorn]

u can in technical terms say it's the angle subtended by 2 points at the centre

[stark thorn]

i mean u mentioned 3 points so if u consider central angle for M and P, it's MAP

[silver cove]

oohh

so like

the center will always be the letter in the middle?

[stark thorn]

yup

any angle like that is a central angle

[silver cove]

oohhh and then what about the intercepted arc? is it the looking for ? like "find MT" will it be like "MAT is the central angle and MT is the arc intercepted by the central angle" ?

[stark thorn]

yup

[silver cove]

OOH OKI I GET IT

but how about the computation

T-T

[stark thorn]

what do u want to compute

oh the arc length?

u need to know the radius for that ig

[silver cove]

hmm I wanna compute the " find m TP "

[stark thorn]

Could u tell me what u mean by that notation? cuz i noticed u wrote an angle as the answer

are u referring to the central angle of those 2 points or the arc length?

[silver cove]

huhh...😭

Wait

the arc length

[stark thorn]

oh okay

um do u know about radians?

[silver cove]

radians are degree right

[stark thorn]

not really

[silver cove]

oh.

[stark thorn]

nvm i'll tell u another method

the perimeter is 2 pi r

[silver cove]

2pir?

[stark thorn]

so considering the central angle is say x
we get (x/360) * 2 pi r as the arc length

[stark thorn]

mb xD

[silver cove]

pi??? as in 3.14??

[stark thorn]

yeah

cuz what fraction of the perimeter is the arc length?

x/360 r8?

taking angles in degrees

[silver cove]

Help my teacher doesn't apply that in our lesson tho..

😞😓😓

its like you just minus and add here

[stark thorn]

uh i think ur teacher wants the central angle then maybe?

as far as ik the m MT isn't a 'standard' notation, but i'm checking right now to be sure

[silver cove]

ok so like im finding m TP here

[stark thorn]

yeah but is m TP the length of TP or the angle subtended by T and P at the centre?

[silver cove]

whaaaaatt !! T-T

[stark thorn]

uh what grade r u in?

[silver cove]

10th help

[stark thorn]

oh okay

um if m TP means the length of TP, u need to find what fraction of the perimeter TP is

does that make sense?

[silver cove]

yeah but why fraction

[stark thorn]

um cuz or else how will u find the arc length?

[silver cove]

by degrees?

[stark thorn]

like we know how to find the perimeter

so the arc length is some fraction of the perimeter

[stark thorn]

uh that's the angular length then
so the central angle of the 2 points

[silver cove]

oh okay

so how to do that

[stark thorn]

the angle in a straight line is 180 degrees

uk that right?

[silver cove]

mhm

[stark thorn]

so the sum of the 2 angles must be 180

uk one of them, so find the other

[silver cove]

145+35?

[stark thorn]

yup

[silver cove]

oh so

m TP is = 145 degrees?

I mean

180?

wait what

[stark thorn]

yeah

[silver cove]

THANK U T-T

but how are u supposed to know if youre going to add or subtract it

[stark thorn]

can u elaborate?

[silver cove]

ah

its nothing

Im so sleepy i cant comprehend anything anymore

thank you so much btw !!

[stark thorn]

my pleasure man o7
it's ok dw if u get confused

[silver cove]

Huhu I'm actually anxious

I have a quiz tomorrow about this

[stark thorn]

oh dw it'll be fine

[silver cove]

HWAKLDKSALDJ I hope so

[stark thorn]

just remember to visually understand the problems

all the best for ur test o7

u should close this if ur done

[silver cove]

thank u, I appreciate !

.close

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[patent oasis]

mplicit differentiation of x^2y=y-7
im stuck at 2xy+x^2y'=y'

[high lily]

what's your issue with solving for y' here

[patent oasis]

i dont know what to do after

[high lily]

after you've isolated y', nothing, ur done

[umbral torrent]

are you solving for y' ?

[obtuse pebble]

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[ivory quartz]

Exercise from my Topology and Metrics lecture notes that I am trying to prove. My idea is to show that there exists an N such that K_n \subset U_0 for every n > N and thus that all by finitely many K_N are covered by U_0, and thus construct the rest of the finite cover by taking the covers of the finite number of remaining K_n, but cannot seem to prove that, presumably because it is false?

[ivory quartz]

alternative directions are to show closed and bounded, or sequential compactness, though I have had no success in these avenues either.

<@&286206848099549185>

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[hoary idol]

AB is the chord the length of the chord is the same as a inscribed triangle what is the area of AOB if AB is 5

[fierce elbow]

u mean its an equilateral triangle?

[stark thorn]

wdym by the length of AB being the same as an inscribed triangle?

[hoary idol]

Yes

Not prove it this triangle is not inscribed

As you see

The inscribed triangle is not in the drawing

[stark thorn]

could u plz restate the proble,

[iron edge]

It’s just a formula

You an go slower if you wants to

The result remains the same

@hoary idol

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[formal violet]

I'm confused, not sure where to start.

[latent walrus]

create the augmented matrix

then row reduce it

[formal violet]

the augmented matrix

as in [4.5, 3.1 = 19.249]
[1.6, 1.1 = 6.843]

and then row reduce that?

[latent walrus]

[4.5 3.1 | 19.249]
[1.6 1.1 | 6.843 ]

then row reduce

[formal violet]

understood

so

then what is w1

will it be the row reduced matrix of the augmented?

[latent walrus]

i dont know what w1 is

[formal violet]

no as in how would i find w1

will it be the row reduced matrix

[latent walrus]

again, i dont know what w1 is

[formal violet]

oh

my bad

[formal violet]

w1 is the solution to the system

[latent walrus]

alright, when you row reduce
if you get the left two columns to be the identity matrix then the last column is w1

[formal violet]

oh ok

thanks

[obtuse pebble]

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[obtuse pebble]

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[timid silo]

How did they get that?

[tardy epoch]

there's d_i

and there's dbar

[timid silo]

Oh they used the previous result

[brave bramble]

Imo, wikipedia has a much cleaner derivation of this fact:

Actually, this only really works for random variables, which might not work here. Nvm, ignore me

[timid silo]

Oh

So there’s no simpler way?

I have to just memorize the formula because it’s unlikely im going to be able to derive this whole thing during a test

[brave bramble]

I guess if you think of E[X] as "mean of the data set X" and recognize that E[A + B] = E[A] + E[B], then the above still works

[timid silo]

I find that notation really confusing

[brave bramble]

Basically, Var(X) = (mean of X²) - (mean of X)²

Where X is a data set, and X² is the same data set, except all points are squared

Is a generally easier way to think of variance

[timid silo]

Oh

Okay

I’ll try to keep that in mind

Thank you

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[fading herald]

How would you solve this?

[fading herald]

I’m forgetting how to do this

[gilded needle]

you type 13 as follows: 13

😁

or, if you really want to know how to do it, try factoring the numerator

[obtuse pebble]

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[timber pine]

i think u can look at DF vs AC

DF * factor = AC

[grim glacier]

idk how to do this tho

[timber pine]

what is the length of DF and AC

u can find it yourself

[timber pine]

then do this

[grim glacier]

ok nevermind that

i need help with 9 then 8

but

i got 10,8 for 9

this is for 9

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[regal zephyr]

Could anyone explain this?

[frigid goblet]

this is a ED separable

so you can put all Y or in this case m(x) and the X on the other

[regal zephyr]

And integrating infinitely small x (dx) gives me simply an integral of 1?

[frigid goblet]

on the left you see a dx standing alone after integrating $\int_{.}^.{1dx}=x$

[warm shale]

nico

[frigid goblet]

$\frac{dm(x)}{dx}=\sqrt{...}\
\frac{dm}{\sqrt{...}}=1dx$

[warm shale]

nico

[regal zephyr]

So what this dx means is solely an indicator that the integral if calculated in respect to x?

[frigid goblet]

yes

witch is why we isolated each indicator seperatly

[regal zephyr]

Ok, it makes sense. Thank you

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[dry crown]

Hello!

[versed pier]

hellooo!

[dry crown]

Can someone let me know whether or not I’m doing this right?

[tardy epoch]

unfortunately no

the hypotenuse of the triangle is a straight line

since width and length are the axes, straight lines are described by something like
length = (slope) * width + (y-intercept)

[dry crown]

Im… not following

So there needs to be a slope in the inequality?

[tardy epoch]

i'm only describing the hypotenuse

you figure out the inequality later

[dry crown]

So I put it in the formula y=mx+b?

[tardy epoch]

find the slope and y-intercept

yea m = slope, b = y-intercept

[dry crown]

Uhhh lemme know if I’m doing this right so far

(less than or greater to) 1/2x + 65

[tardy epoch]

nope

again, find slope

[dry crown]

Actually that’s definitely not 65

[tardy epoch]

65 is the correct y-intercept

[dry crown]

Really??

[dry crown]

Is the slope 1?

Nvm

It’s not

I know it’s less than one, but I don’t know how to decipher the numbers less than one on the graph

-5/5?

[tardy epoch]

-5 / 5 = -1 is the slope yes

[dry crown]

Nice, so it’s
(less than or equal to) -1 + 65?

I know that’s not the whole inequality

[tardy epoch]

where did your x go

[dry crown]

But so far?

[tardy epoch]

use this

[dry crown]

Wait yeah it’s c

[dry crown]

X=-1w+65?

Wait no

It’s mx

<@&286206848099549185>

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[tepid sedge]

I need someone to explain why those are the answers

[tepid sedge]

A means always, S means sometimes, and N means never

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[tawny kite]

is there an easier way to do this other than by inspection like the example from the textbook?

[tawny kite]

also, extend to form a basis means you have to keep these original vectors still right?

I tried turning each vector in S to form columns in a matrix.. and then see if its linearly dependent

if it is thats means I still gotta get rid of a vector

but Im still taking out the unnecessary vectors out by inspection...

[tawny kite]

Also, this is an example that is unrelated to 45.

like its related but not same question

[obtuse pebble]

@tawny kite Has your question been resolved?

[tawny kite]

i guess by inspection is the only way, but its so easy to miss one

also, I think you can have different answers but still be a basis

for example,

I had the same thing with E22

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[snow egret]

Hi, I have a set of 2D data points that I'd like to calculate the PDF for. I've tried applying the PDF for all the X data points, then for all the Y data points and tried summing the PDF of X & Y. I was wondering if this is the right approach? Any guidance would be highly appreciated

[obtuse pebble]

Please don't occupy multiple help channels.

[hybrid gull]

.close

[obtuse pebble]

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[hybrid gull]

stop opening so many

[snow egret]

Hi sorry for the trouble, Im new to discord. I see that my query is being closed, could you please let me know why?

[inland matrix]

!help

[obtuse pebble]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[inland matrix]

!onechannel

[obtuse pebble]

Please stick to your channel.

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[summer estuary]

does this seem right?

[cunning burrow]

have you tried using a derivative calculator?

[summer estuary]

not yet

[cunning burrow]

So do it. You will get fully worked solution step-by step. If you still have a question I will take a look

[summer estuary]

got it

[willow gorge]

supamen

[last pilot]

okay firstly

don't do that

this is a differential equation, it's something else

secondly, you can't just move the xy out from d/dx; since y is a function of x (i'm assuming that, otherwise this is just basic linear equations) you can't do that. use the product rule for (xy)'

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[floral estuary]

hi, i thought i had the right idea for part (a) but i guess not. does anyone know why my method was wrong?

[floral estuary]

non-pdf version

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[obtuse pebble]

@floral estuary Has your question been resolved?

[floral estuary]

<@&286206848099549185> ?

[small rover]

I also got the same 💀

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[fading sigil]

hello

[fading sigil]

find the volume of the solid of revolution obtained by rotating the region bounded by y=√x and y =1 about line y = 1

can anyone help with this

[obtuse pebble]

@fading sigil Has your question been resolved?

[obtuse pebble]

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[frosty parcel]

Hi!, im studying basic limits and I came accross this question. Ive asked websites, and the hints should be Limit chain rule and exponent rule. Can someone explain it?

[strong ermine]

Is that

💀

[versed pier]

aight

for this question you wanna rewrite $(1+65/x)^{3x}$ in terms of e

[warm shale]

nosqldb

[frosty parcel]

yes it is.

[versed pier]

in general, we can do this for $a^b$ with $e^{bln(a)}$

[warm shale]

nosqldb

[frosty parcel]

so it should be $e^{3xln(1+65/x)}$,? Then how do I apply the chain rule?

[warm shale]

GiddyBassoon535

[versed pier]

well make it into a fraction first

you want $\frac{ln(1 + \frac{65}{x})}{\frac{1}{3x}}$

[warm shale]

nosqldb

[frosty parcel]

ok that's a new thing. What's next?

[versed pier]

try to evaluate

[frosty parcel]

just change the x with infinite?

[strong ermine]

Ok @frosty parcel I’ll try my best

Uhh ok lets start over

Like nos here said, we are able to rewrite our exponent as an exponent of e

[strong ermine]

This right here

Also I apologize for the bright light, its the best Ive got

See how in the limit we have e, which is a constant

So we can move that outside the limit indicator

I should remind you that the reason we placed e in here in the first place is because we need to find k, which e is raised to the power of.

Great.

So now in this limit, we can see 3 being multiplied by the other factors.

And 3 is a constant, so again we’ll move it outside the limit indicator.

Now say we use direct substitution

Inserting inf into the limit. Let’s see what we get.

We get inf * 0. Indeterminate form for an exponent.

Meaning that we can use L’H for exponents.

So now we have to rewrite our exponent in such a way that L’H will solve it.

So we put it as a fraction.

Again, nos was ahead of me.

We turn the x in the exponent into a 1/x

As done here.

[strong ermine]

.

However, they did not pull out the 3 (constant), which may make things a bit tricky as we go on. So I’ve done that for you.

Now, we can use L’H.

[versed pier]

Wow good job Saturn

[strong ermine]

I assume you already know what L’H is. So I’ll just take the derivative of the numerator and denominator and put them back in the fraction.

[strong ermine]

Thanks

This would be the numerator:

[tardy epoch]

,rotate

[strong ermine]

(Chain rule just so you dont get too confused)

[strong ermine]

Youre right I should probly rotate these things

,rotate

[strong ermine]

Numerator.

[strong ermine]

Denominator

Now our fraction looks like:

Now make it a bit easier on the eyes, and add the limit.

Simplifying, we get:

Notice the 65 in the numerator. That is a constant, so we can place that outside the limit.

Oh hold on

I made a mistake

[strong ermine]

Here the x in the numerator shouldn’t be squared. It should just be x.

[strong ermine]

Here too.

Sorry

Now lets divide the entire fraction by x.

This shouldnt change the value of the fraction, since we’re dividing it by 1 (written as x/x)

Doing this we get:

And with direct substitution, we have:

Now, replacing all this back into our original equation.

[strong ermine]

Here.

We now know that everything after 3 in the exponent has a value of 65*1 = 65, as we have just calculated above.

So, we have: e^3*65

Which is…

Hope this solves it @frosty parcel

Also please tell me the game you found this in.

🧐

[obtuse pebble]

@frosty parcel Has your question been resolved?

[obtuse pebble]

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[potent bramble]

i could not solve this problem, i have the solution but i did not really understand the idea behind it for example in the solution i see a pattern in the * and | so for example (2,3,6,9) = ∗ ∗ | ∗ | ∗ ∗ ∗ | ∗ ∗ ∗ |∗ and i see 2 stars than a bar then 1 star event tho it is 3 in the list so here i noticed that it is adding up 2+1 = 3 and 2+1+3 = 6 finally 2+1+3+3 = 9 and then the thing that i also dont understand is why there is another bar and star ?

[potent bramble]

solution:

for example what i thought about is +++ | ++ | +++ | ++ and this is wrong as the condition is not respected so why use 4 bars | ??

[brave bramble]

There's another star, but not another bar

[potent bramble]

4 bars ?

[brave bramble]

You need 10 stars, as the bars' positions within those stars are what you care about

[brave bramble]

Why is this wrong?

Oh it's wrong because there's 3 bars

[potent bramble]

its (3,2,3,2) and we must have w<=x<=y<=z

[brave bramble]

It's not. It's (3,5,8,_)

Every bar prints out a number. That number is the star count to the left of the bar

[potent bramble]

Oh ! i see but wait i just noticed this ? how did i solve the multi-set problems without this knowledge !

or is there another way to count the stars or am just out of my mind ??

I thank you Mr.@brave bramble for your help, that widened my knowledge and flattened the land that is yet to be explored. Good-bye!

[brave bramble]

I mean different problems might count things differently

[potent bramble]

.close

[obtuse pebble]

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[potent bramble]

.reopen

[obtuse pebble]

✅

[potent bramble]

what about this one huh ??? @brave bramble

.close

[obtuse pebble]

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[obtuse pebble]

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[zealous peak]

Hi, I'm getting true for this, but my answer key is saying false - any ideas? Current thought process is if f(n) is in O(g(n)), it must be at least as large as g(n), which should hold true as 2^f(n) and O(2^g(n))

[versed pier]

Wym

Consider said 3lg(x) and lg(x)

[zealous peak]

oh

[versed pier]

Yeah…

[zealous peak]

would turn to (2^lgx)^3 and O(2^lgx) eh

tuff

thanks 😭

[versed pier]

I mean simplify it

X and X^3

[zealous peak]

yeah

[versed pier]

Mhm

The coefs matter a lot when ur raising to an exponent

[zealous peak]

makes sense

ty

.close

[obtuse pebble]

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[sly matrix]

im not sure how to do this. my thinking is that i can flip the sign on the last three elements in the given vector to create 3 new ones for each sign flipped. then use the gram-schmidt process to orthonormalize them

[brazen viper]

That should work, provided that the vectors have no zero elements in the last three places.

[brave bramble]

Why can't we just apply Gram-Schmidt directly to the given vector?

[timid silo]

you don't need to do that

what you should do is first normalize v

[brave bramble]

Oh we do need four vectors.

[timid silo]

then look at the eigenvectors of I - \hat{v}\hat{v}^t

and that's it

[brazen viper]

Why not just use 3 of the standard basis vectors?

[timid silo]

where \hat{v} is the normalized v

they won't give you a basis

[brazen viper]

If the given vector happens to equal one of the 4, use the other three

Then apply gram-schmidt

[timid silo]

i feel this is easiest and probably what they were looking for but idk

[sly matrix]

i was told that the 3 other vectors im supposed to make shouldnt be parallel to the given one or eachother

[brave bramble]

Right. You need a linearly independent set of vectors to start. Problem is, flipping the coordinates of your vector is not going to guarantee this

[sly matrix]

yeah ive been spending a lot of time thinking abt that. not sure how im supposed to make 3 new ones which are linearly independant. apparently theres a pattern.

[brazen viper]

Again, why not just choose the first 3 of the 4 vectors standard orthonormal vectors that aren't parallel with the given?

[obtuse pebble]

@sly matrix Has your question been resolved?

[sly matrix]

not sure how to do this in python. is there an easy way to check if two vectors are parallel? i assume you mean vectors like [1,0,0,0] right?

[obtuse pebble]

@sly matrix Has your question been resolved?

[brazen viper]

@sly matrix two vectors are parallel if their dot product is the product of their lengths.

[sly matrix]

that makes sense ty. I should be able to solve the problem now. Would the given vector and the 3 other standard vectors be linearly independent just out of curiosity?

[brazen viper]

Ah, good point, it is possible that there would be no component in the other direction, like the vector is [0, 1, 1, 1] and you use the last three

In that case the simpler method would be, choose the first non-zero component of v, then choose the basis vectors that are zero in that component.

@sly matrix ^

Those will definitely be linearly independent and span the space

[sly matrix]

The first vector is complex. Should fix this problem no?

[brazen viper]

Remember that because this is a vector backed by complex numbers, your scalars are also complex. If your bases are e1, e2, e3, and e4 then vectors will be ae1 + be2 + ce3 + de4 with a, b, c, d complex

Like if your vector v = [1+i, 3+2i, 0, -4i] and you pick e1: [1, 0, 0, 0], e2: [0, 1, 0, 0], and e4: [0, 0, 0, 1] as the other 3 basis vectors, we can see v = (1+i) e1 + (3+2i) e2 - 4i e4

So they're not linearly independent

But if we chose e3 instead of e1. Then we'd never be able to make the (1+i) part of v with e2, e3, and e4.

[brazen viper]

@sly matrix ^

[obtuse pebble]

@sly matrix Has your question been resolved?

[obtuse pebble]

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[red ice]

You've misunderstood the question

They have already given you the solution of the DE to you

So you just need to substitute x = 0 and y = -1/4 to find c1

But yes c1 = -5 is correct

So just substitute c1 back in and you have your particular solution

[agile girder]

I plug in c1 into y?

[red ice]

Yes, $y = \frac{1}{1 + c_1 e^{-x}}$

[warm shale]

south

[red ice]

Yep

[agile girder]

That’s it?

[red ice]

Yes

[agile girder]

So I didn’t need to find y prime

[red ice]

No, you didn't at all

[agile girder]

Damn

Ok then thank u g

[red ice]

No worries man

[agile girder]

.close

[obtuse pebble]

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[obtuse pebble]

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[robust locust]

tried using power of a point only to get a quadratic equation

[fallow reef]

Before I start to look too hard into this one, be aware that sometimes you will get two possible answers that satisfy the mathematics, but the physical geometry will rule out one of the answers

If you solve for the quadratic you got, what two answers do you get?

[red ice]

What quadratic equation did you get?

[robust locust]

i did

i tried the positive answer

it is wrong.

[red ice]

Cool, probably just a sign mistake or something then

Ah did you do AB * AC? Hopefully you did