help-19

[hollow quarry]

Lemme get my diagram rq

[mystic saffron]

i think we are right

[rough badge]

even using the diagram my professor gave me it’s still 24.9

[mystic saffron]

the correction is prolly wrong

ur teacher i mean

[rough badge]

you think? i’m gonna see him soon maybe ill bring it up with him

[mystic saffron]

yea i think u shold stop working on it rn

[rough badge]

yeah i feel like im out of options

and i only get one more try on the website

[mystic saffron]

bc at 3 ppl we found the same answer

[rough badge]

chatgpt also got 24.9 several times if that means anything

i think the website is wrong

[mystic saffron]

hmm chat gpt sucks at math

[rough badge]

sometimes

[mystic saffron]

closer to alway than sometimes

[rough badge]

eh it’s usually pretty good at kinematic stuff

i definitely take it’s answers with a grain of salt though

[mystic saffron]

big grain of salt

[rough badge]

but anyways i’m just gonna ask my teacher and hopefully get it figured out

thanks for trying to help

[mystic saffron]

np

[rough badge]

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[distant umbra]

how do i get rid of the - sign?

this is what I have done

2 = 20 e^-yt/2

where t = 20 s

now i am getting the right answer but i am getting y as -

[odd edge]

@distant umbra Has your question been resolved?

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@distant umbra Has your question been resolved?

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[celest bay]

The number of hours of sunlight in a day of a leap year, in part of Ohio, can be modelled by a sinusoidal function with a minimum of 8.9 on the 356th day of the year (December 21st), and a maximum of 15.4 on the 173rd day of the year
a. Find a sinusoidal function that models this relationship.
b. What days (on the calendar) are the closest to 14 hours in length?
c. How long is the 218th day of a leap year?

a)
f(x)=af(k(x-d))+c

For a. I got f(x)=3.25 sin⁡(π/183 (x-366))+12.15 , is this correct, I am unsure about the 366 number

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[jolly frigate]

i am confused on what i am being asked to do here

[forest sky]

imagine the boxes are replaced with nonzero numbers and the * are replaced with numbers (which can be 0). find whether the augmented matrix represents a consistent system, and if it does, if that system has 1 or infinite solutions

[jolly frigate]

so do i plug in numbers?

[forest sky]

you can if it makes it easier to understand

[jolly frigate]

how woudl you do it?

[forest sky]

use the same method to determine if a system is consistent or not and if it has unique solutions as you learned for any other linear system

[jolly frigate]

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[earnest nebula]

try to make some equations from the given data

[halcyon pond]

i tried but they arent working

these are the equations i have but i keep getting fractions

[earnest nebula]

x+y+z/3 = 53

[halcyon pond]

OH

wait

ur rigjt

holdo n

[earnest nebula]

k

[halcyon pond]

it still doesnt work

[earnest nebula]

it works

finally they say that 4 years ago thing

[earnest nebula]

z-4=4(X-4)

@halcyon pond

[halcyon pond]

wait why would it be z-4?

[earnest nebula]

cuz grandpa's age 4 years ago

[halcyon pond]

oh right

[earnest nebula]

got it?

[halcyon pond]

it says the answers are (180/7, 276/7, 636/7)

idk

the answers are supposed to be whole numbers

[earnest nebula]

Edwin's age is 24

father's age is 51

grandfather's age is 84

show ur work

of the simplifications

[halcyon pond]

give me a sec

[earnest nebula]

k

[earnest nebula]

z=4x-12

[halcyon pond]

y=64-5x right?

wait

i cant read my notebook wth

[earnest nebula]

huh?

[halcyon pond]

like im doing the math rn

but i tried like a lot of times and now i just see my old work lol

[earnest nebula]

haha

[earnest nebula]

first multiply both lhs and rhs by 3 for this equation

then u get $x+y+z=159$

[clever fjord]

Bihandu

[earnest nebula]

now substitute $z=4x-12$ to $x+y+z=159$

[clever fjord]

Bihandu

[halcyon pond]

wait

i got it

omg

[earnest nebula]

cool

[halcyon pond]

thanks

[earnest nebula]

no worries

[halcyon pond]

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[south dirge]

okay

[south dirge]

simple unit conversion

i have 40nano coulumb /cm

i need to convert to coulumb meters right

so thats 40x10^-9 for the nano

but how do i do the cm aswell ?

am i tripping or its normally one thing

so do i do 40x10^-9 /100 ?

[steady tide]

yes you are correct

[south dirge]

hm

i appear to have gotten the answer wrong

can i send the full question to get some feedback?

When a potential difference of 156 V is applied to the plates of a parallel-plate capacitor, the plates carry a surface charge density of 40.0 nC/cm2. What is the spacing between the plates?

is my question

so i start by writing the formulas i believe are right for this problem

that

so i have the forumla for v=Ed tryingto find d E=charge density over epsilon nought

im given charge density episolon nought and v

so i solve for E and plug that into the formula v=ED so i know v i know e solve for d i get 3.45*10^24

m

which i have to convert to micro meters so i just times that answer by 10^-6 ?

so doing it step by step i get 40x10^-9x10^-2 divided by Eo 8.85x10^-12

[alpine mango]

$$ 40*10^{-9} \frac{C}{Cm} \frac{100Cm}{M} = 4010^{-7} \frac{C}{M}$$

[clever fjord]

Sevchenko

[serene lark]

I need help

À French speaker

[south dirge]

so i get e being 4e-10 / 8.85e-12 getting 45.2

i take e plug it into v=ED

and get 156/45.2 = 3.45

[south dirge]

go to help 10 or 11 or 32 or 37

the ones without names are not taken

[serene lark]

Thx

[south dirge]

np

[alpine mango]

$$ \sigma =4010^{-9} [\frac{C}{Cm^2}] = 410^{-4} [\frac{C}{M^2}]$$

[clever fjord]

Sevchenko

[alpine mango]

To convert coulomb over square centimeter you must multiply by 10,000 to have coulomb over square meter

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[west hull]

What do you need help with

[sterile wadi]

how did it become 0-? i dont understand

am i just supposed to memorize that

[lyric dust]

what is sin(pi)

[sterile wadi]

0, but why the negative superscript

[gleaming turtle]

x (the angle) is approaching pi from above

[lyric dust]

ok

so if it is x approaching pi+

it is slightly over

[sterile wadi]

OH I THOUGHT IT WAS THE OTHER WAY AROUND

thanks guys

like i thought

[sterile wadi]

welp

[gleaming turtle]

yeah that can be a bit confusing

in this case bigger angle means lower down on the circle, since we're on the left side

[sterile wadi]

thank you

i hope you get good food everyday

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[grave plank]

I not sure how to do this as when i plot it out its not a parralelogram

[lyric dust]

is this in context of only highschool vectors or have u learnt something beyond that

[grave plank]

this is the start of my calc 3 class lol

[lyric dust]

im australian highschool curriculum so idk what calc 3 really means

[grave plank]

second year university course

[lyric dust]

ok

u can apply either matrix method or vector method directly

[grave plank]

what would be the vector method?

[lyric dust]

cross product and dot product

im not sure if scalar triple product is what it is called in US

@grave plank

matrix method is arguably bit easier if u have taken linear algebra

[grave plank]

i have not heard of that term so far

[lyric dust]

u just have to find determinant

[grave plank]

we have only learned cross products and dot products

[lyric dust]

scalar triple product is a combination of those 2 things

ok

what i will do is try to make u understand why it works

and then apply it to this question

[grave plank]

👍

[lyric dust]

so

if u have paper or any drawing surfaces, it would help

just draw any parallelpippened

with arbtirary vector vertices

[grave plank]

sounds good

done

[lyric dust]

give me a sec to draw mine as well

sry

[grave plank]

np take your time

[lyric dust]

ok my drawing looks bad but might have to bear with for now

so let vectors a, b, c represent arbtirary vertices

what vector does a x b give?

[grave plank]

the area of the surface

oh wait

[lyric dust]

no

not the magnitude of it

just the direct cross product

oh

sry

i mislabelled my diagram

one sec

[grave plank]

oo ok np

[lyric dust]

o is just origin for convenience

[grave plank]

would give a vector pointing up towards C i believe

[lyric dust]

yep

so maybe something like this

[grave plank]

yes

[lyric dust]

the length of the vector is not known but that is fine

now, can you think of a way to find the length of a x b such that it is the same height as vector c

[grave plank]

hmmm

[lyric dust]

for starters, let the angle between a x b and c be theta oir whatever variable u prefer

so something like this

[grave plank]

ohhh you could use the dot product right?

[lyric dust]

u could but there is even an easier expression

it sounds kinda counter intuitive but it is just |c| cos theta

we are only interested in length

so the volume is actually base parallelogram area x height

or rather

|a x b| |c| cos(theta)

[lyric dust]

now this is really familiar to something else u know

what does it look like?

[grave plank]

dot product formula

[lyric dust]

yep

so really the volume of parallelpippened is just (a x b) * c

• = dot, idk how to write it on keybaord

oh wiat that did it

[grave plank]

how would we get the angle theta tho? or would we just compute it using the components

[lyric dust]

dont need theta

its eliminated when u just do (a x b) dot c

[grave plank]

how is it eliminated?

[lyric dust]

there is no theta or any angle in (a x b) * c

[grave plank]

oh wait by * do you mean dot product or simply just multiply them

[lyric dust]

dot product

because we have the vectors a, b and c

we dont need theta

[grave plank]

right

[lyric dust]

i think u are confused because in the derivation process the angle theta was involved

but when we rewrote the final expression as (a x b) * c there is no angle involved

[grave plank]

yeah

[lyric dust]

it might help if u spend a little time looking into the geometric intuition behind dot product but just for now u will have to trust the angle isnt involved

[grave plank]

we just apply the formula

[lyric dust]

yep, note that because a x b is a vector

and c is a vector

(a x b) * c will give u only just numbers

not another vector

which is ur volume of the paralellpippened

[grave plank]

yes

[lyric dust]

a thing to note is that this gives you the signed volume

meaning it can be negative, which isnt alarming

it being negative indicats which direction the object is actually pointing

it is just a property of dot product because it signs the direction,

[grave plank]

oh ok

[lyric dust]

since we are only interested in volume and not the direction as well, we can just slap an absolute value around it

ok so back to the original question

so if it helps u understand, we can reconstruct our parallelpippened

[grave plank]

that would be helpful

[lyric dust]

now we just have to find the 3 vectors representing the vertices, a b c

doesnt really matter which order u do it or which one u let equals to which

[grave plank]

so when it says adjacent vertices how do we know where to place them?

[lyric dust]

there are only 3 adjacent vertices

any corner has only other 3 adjacent corners

[grave plank]

like for example we have (1, 2, -2) placed and they give 3 other coords how do we know which coordinate corresponds with each of the other 3 corners

[lyric dust]

it doesnt matter

a really simple geometric explanation is because

regardless of which 2 vectors u decide to cross

then dot with the third

u are always doing any of the parallelogram faces multiplied by perpendicular height

since every face is a parralelogram

[grave plank]

oh so we can just place them wherever on the parralelpiped?

[lyric dust]

yeah as long as it is adjacent

algebraically u will find that sometimes ur volume will be negative or positive and again, that is simply becausae it is a signed volume but we end up putting absolute value around it at the end so it doesnt matter

now

think of (1, 2, –2) as a base vector or a new origin if that makes sense

[grave plank]

yes

[lyric dust]

so your vectors for each vertex has to be subtracted by that

[grave plank]

right

[lyric dust]

and then just apply the result above and u should get an answer

[grave plank]

so i would just pick one to be my B then another to be my C

and one as A as well

[lyric dust]

yeah, a b c doesnt really matter which order u pick

u can spend sometimes redrawing the diagram and doing different combinations if you aren't convinced

if u have learnt linear algebra

u can apply a matrix approach as well

by simpliy taking determinant of all 3 vectors which gives you the volume of the 3 dimensional object

[grave plank]

i have not yet, this is for my multivaribale calculus course which im taking at the same time for linear algebra

[lyric dust]

mhm ok

well for future reference

u might find it interesting to learn what determinant represents geometrically

also if u are confused later on, just search up 'scalar triple product'

[grave plank]

sounds good

[lyric dust]

there hsould be more than enug hresources online for it, it is a pretty commmon approach

[grave plank]

thank you for the help

[lyric dust]

np

have a good day

[grave plank]

you 2

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[marsh fox]

have you heard of euler's formula

Alright,
so we have

e^ix = cos(x) + isin(x)
and
e^-ix = cos(x) - isin(x)

try subtracting both equations

e^ix - e^-ix

and show what you get

great now divinde both sides by 2i

Do you see what we're left with

oh sorry I didn,t see that text above

ok well we recall cos(z) = e^iz + e^-iz)/2

so plugging in cos(z1 + z2) we get what

also sorry for bad grammar english isn't my first language

now with property of exponents

cos(z1 + z2) = (e^i(z1 + z2) + e^-i(z1 + z2))/2

woops nothing did

My bad

ah t francais!

Ok ben déso je déteste te laiser comme ça mais je dois vrm y aller

[lavish slate]

Bro is here as well

Euler’s formula should work here, idk what you can do other than that

I have no idea then, probably try pinging again after a bit

Apologies

[rigid dragon]

Have you tried starting with the right hand side

Like start with cos(z1)cos(z2) - sin(z1)sin(z2)

And use the identities on that

And try to reach cos(z1+z2)

[odd edge]

@ashen holly Has your question been resolved?

[rigid dragon]

so the key here is to add and subtract terms in sch a way that things cancel nice

alternatively i guarantee you didnt go far enough when you expand the RHS

basically you need to in a sense complete the square

but i highly recommend starting on the right hand side and trying to go towards the left

you expand the cosines and sines

then multiply both terms out

and you'll see that all the cross terms cancel

yeah i know

but it also not THAT horrible

because a lot of it cancels

note that the only difference between the first term and the second is the minus sign in between the exponentials

so you end up with the same expression in both terms but with signs flipped on some of them

figure out which signs flip

then you can determien what cancels

a tip that actually would make it a lot easier to handle is to rename your variables

like W_1 = e^{iz_1} and W_2 = e^{iz_2}

or something like that

and the same for e^{-iz_1}

etc

terms should cancel

and you should be left with almost exactly what you need

as long as you did the expansion carefully

and dont forget about the 1/2 factors all over the place

yeah cause you have 1/2 times 1.2

1/2*

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[twilit oak]

I can send my work if wanted

<@&286206848099549185>

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[upper pasture]

Did I do the formula correct

<@&286206848099549185>

[quasi sparrow]

!15m

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Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[upper pasture]

Mb

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[odd edge]

Please don't occupy multiple help channels.

[jaunty minnow]

I need some help with these physics problems

[quasi sparrow]

!1c

[odd edge]

Please stick to your channel.

[quasi sparrow]

Oh did you close your other channel

[jaunty minnow]

yes

I can close this one, one sec

.close

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[warped glacier]

write the first one as $\frac{1}{(x + 1)^2 + 1} \ dx$

[clever fjord]

south

[warped glacier]

similarly, complete the square of 8 - 2x - x^2

you can get the 2nd integral into this form

[shut ember]

Is the answer arctan(1+x) +c

?

[warped glacier]

,w integrate 1/(x^2 + 2x + 2) dx

[clever fjord]

Results provided by WolframAlpha

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

Requested by sooouth.

[warped glacier]

yes, to check your answers you can use the bot like this

[shut ember]

Ok

Hep close

[warped glacier]

.close

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[ashen ether]

Hello

[ashen ether]

_Question b solution

I don't understand this notion of right-continuity on the right here. I can't understand what they're doing for question b)

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@ashen ether Has your question been resolved?

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[mystic saffron]

yo whoevers reading this

[mystic saffron]

i got a diagnostic (ungraded but im tryna score well) in a bit so whoevers open to help ur welcome to

[wet raven]

Do you have a question?

[mystic saffron]

not rn, im just doing a bit of practice before the "test" opens up

if i have any ill send them over

you mind if i ping you when i have a question?

[wet raven]

Sure, but I don't think assistance on a test is allowed here

[mystic saffron]

thats why im calling it a "test"

its not actually a test

[wet raven]

Alright

[mystic saffron]

thanks brother, ill ping u when im ready

[regal wren]

I may also help.

[mystic saffron]

i appreciate that

[odd edge]

@mystic saffron Has your question been resolved?

[mystic saffron]

ok guys im ready @wet raven @regal wren

[wet raven]

k

[regal wren]

Ok.

[mystic saffron]

starting off basic questions

so u guys r porlly gonna have to wait for later for the tough ones to come u

p

this ones simple but ill solve other questions cuz i dont wanna use up too much time

[regal wren]

Have you already learn trigonometry?

[wet raven]

you'll need to know this triangle to solve that

[mystic saffron]

yeah, i know most of this stuff but this "test" is on old lessons

so id need to refresh to remember how to solvve

[mystic saffron]

i found the bottom side to be 7.4 through pythag but im not sure what im supposed to do with it

im pretty trash at geoemtry so thats why im not the best at these

[wet raven]

Can you use calculators in this test?

[mystic saffron]

yeah

[regal wren]

Alright, then can you also use the trigonometric functions like sin, cos, tan,etc?

[mystic saffron]

ohh right

sin

3/8

22.02

so ill choose 22

[wet raven]

arcsin(3/8) tbf

but yes

[mystic saffron]

i got 10.89 for this one, so i should round down to 10 since thats the maximum under 100

[mystic saffron]

yep i did that i was just speaking out loud

[regal wren]

Do you know the arithmetic sequence formula for terms?

[mystic saffron]

yeah i did it

and got 10.89

just wanna make sure that rounding down is the correct choice

[wet raven]

yes

[mystic saffron]

ok good

i left taht other geometry question

wsill come back to it later

not quite sure how to do this

but i can just sub in x values into the f(x)'s they gave us and see which one matches the graph right

nvm that doesnt make sense

cuz no function provided

[wet raven]

have you learn transformation of functions?

[regal wren]

Do you know the transformations of function?

[mystic saffron]

im pretty sure i did but it was a couple of years back

i remember doing a bit of it in APs

[regal wren]

So, what difference do you see in the photo?

[mystic saffron]

oh its the complete opposite

[regal wren]

Not quite there yet.

[mystic saffron]

oh

i thought cuz

the dashed one starts going straight up

and the normal ends going straight up

what should i be looking for

[regal wren]

Did you notice that the other function is a bit pushed to the side horizontally?

[mystic saffron]

oh

that means its x-2

because - means shift to the right

f(x-2)

[regal wren]

Yes.

[mystic saffron]

ok perfec

ill choose that

about halfway thru now

i hate log questions so much lol this whole section is based on them

i havent tried the question yet tho just wanted to complain about log

[regal wren]

What is the law of divison for logs?

[mystic saffron]

minus

so log2x^4 - logyz

4log2x - logy + logz

[regal wren]

What about the law of multiplications?

[regal wren]

Ok, great!

[mystic saffron]

oh ok

is there more to it?

[regal wren]

Yes, log2x.

[mystic saffron]

where from

[regal wren]

4log2x

[mystic saffron]

oh

log2 + logx

so its a

like the first choice

[regal wren]

Wait, 4log2x = log16x^4

[mystic saffron]

yes but they didnt simplify the 4

[regal wren]

Ok.

[mystic saffron]

log sections done

thank the lord

[regal wren]

Alrighttt

[mystic saffron]

cot is cos/sin right?

[regal wren]

Yes.

[mystic saffron]

perfect

big boy territory

[regal wren]

Pardon?

[mystic saffron]

nothing

just saying that the questions are gonna be tougher

thats what it says

[regal wren]

💀 💀 💀 💀 My humour is too bad.

[mystic saffron]

is this related to this

[mystic saffron]

lol ur good brother

ill send the question on its own too

lowkey dont know how to solve this question

idk what its asking

last 10 questions

wow amazing

[regal wren]

I am not quite sure of this question but i think you need to use the Binomial Series Expansion.

[mystic saffron]

yeah, thats the formula i sent right?

[regal wren]

Yes, the problem is 7/3 does not belong to N.

[mystic saffron]

what does that mean

[regal wren]

Since n is 7/3, which is not an integer nor a natural number.

[mystic saffron]

aha

so what should we do instead

[wet raven]

Instead, use the following:

$$(1+x)^n = 1 + nx + \frac{n(n-1)}{2!} x^2 + \frac{n(n-1)(n-2)}{3!} x^3 + ... $$

[clever fjord]

RadMeerkat62445

[mystic saffron]

taking n = 7/3

[wet raven]

Substitute -3x for x in the above equation and take n = 7/3

[mystic saffron]

right

and we do that only for the x^2 part since the rest is negligible

[wet raven]

yes

what do you get?

[mystic saffron]

let me do it rq

i got 14x^2

so 14

[regal wren]

But |-3x| has to be less than 1. @wet raven

[wet raven]

It doesn't matter because the question wants a series expansion, and in any case, taking an infinite number of terms will give you accurate values for all x

[mystic saffron]

(7/3(7/3-1))/2! * (-3)^2

which simplifies to

14/9 * 9

14

right?

[regal wren]

Yes.

[wet raven]

yes

[mystic saffron]

ok perfect

5 questions to go

30 mins left too so good pace

do we add or subtract the vectors here

im guessing add since its displacement

like i went 1 in the x direction then went 4 in the x direction which means i traversed a total of 5

last question btw

@regal wren @wet raven

[regal wren]

Do you know the Position Vector Formula?

[wet raven]

subtract

[mystic saffron]

oh

[mystic saffron]

probably but not by name

[wet raven]

how do i get from (1, 0, 4) to (4, 3, 5)

?

[mystic saffron]

oh right

i need to mvoe 3 to get to 4, 3 to get to 3 and 1 to go to 5

[wet raven]

I need to go x units in the x axis, y units in y-axis, and z units in z axis

exactly

[mystic saffron]

which means its none of the above

3,3,1

[regal wren]

It's like calculating a distance.

[mystic saffron]

yeah

i even said it

i said displacement

[wet raven]

sure about that?

[mystic saffron]

but i forgot displacement you subtract

[mystic saffron]

i realzied as soon as i sent my message ngl lol

aight well thats everything

ill take a quick scan before i submit

but thanks for the help guys

really appreciate it

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[mossy palm]

how do i solve this 😭

Formulate as many quadratic equations as you can using the floor plan you prepared. Solve the equations using the quadratic formula

[mossy palm]

like wt do i need to do it

its 72m^2

[brittle beacon]

Do you include the wall widths in that 72m^2?

Oh wait, they have measurements at the bottom and left

[mossy palm]

the whole floor area is 72m^2

[brittle beacon]

So that doesn't count the walls then do you have any more context for this question?

[mossy palm]

what kind of context

i have the lengths of the walls though

[dapper canyon]

if you sayso

[brittle beacon]

What are the wall lengths? (the measurements they give seem "interesting" )

[mossy palm]

bedroom/s 417cm x 12cm

like this

?

[brittle beacon]

12cm for a bedroom? Yeaaaa there's definitely something missing, if you want the floor area to be 72m^2

[mossy palm]

suggestions ? 😭

im cooked 😭

ty tho

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[undone crater]

yo guys i've been working on a problem about the inversibles of the group Z/nZ for the law .

[undone crater]

and i am trying to prove that if p is a prime odd number the Z/p(at the power a) is cyclic

i've found that p+1 is of the order p(power a-1)

but idk how this will help since the group of inversibles is of the cardinal (p-1)p(power a-1)

[low locust]

write ^ for power

p^a etc

[undone crater]

k lemme get my phone

[low locust]

iirc you have to treat a=2 and a>2 differently. for a>2 you can induction

[undone crater]

Alright i’ll try using induction

But before

Is the fact that p+1 is of the order p^(a-1) gonna help?

[low locust]

iirc, no

you need to start with a generator g of Z/pZ*

and then consider g+kp

[undone crater]

Alright , thank you

I’ll try that

Rn

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[mortal siren]

im completely lost on how to start question 3

[spark wolf]

do you know how to take a derivative?

[mortal siren]

a little, my teacher explained is briefly but i looked at some yt videos and they were using a different formula

[spark wolf]

what were they using?

[spark wolf]

ok, do you think you could find the derivative of 1/x?

If not then I can try and help you solve this a different way

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[onyx cloak]

,rotate

[onyx cloak]

hint: draw a line parallel to a going through the 75 degrees angle

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[steel haven]

Thank you sm

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[slow sandal]

what does this mean

[slow sandal]

context:

[odd edge]

@slow sandal Has your question been resolved?

[slow sandal]

<@&286206848099549185>

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[mortal dagger]

Im trying to get help with proving or disproving logical equivalence

im stuck on wethere my domains are right and what the next step is

2. Prove or disprove each of the following logical equivalences

I feel like im stuck at needing the correct domains to disprove that this is not logical equivallence

<@&286206848099549185>

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@mortal dagger Has your question been resolved?

[mortal dagger]

no

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[frank field]

yo idk why i got this wrong

[frank field]

#20

[frank field]

n that said 3/4 instead of 1/4 at first but i changed it but havent submitted it yet

oh i figured it out

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[static lance]

Are 1x1 Matrix scalars? I'm asking because in MATLAB if we had A=[2] C = [1 2 3; 4 5 6; 7 8 9] and made AXC. It treats it as a scalar. Can we do this in math too?

[vagrant hazel]

in mathematics yeah theyre pretty much considered scalars

when you multiply a 1x1 matrix (like A=[2]) with another matrix (like C), it's equivalent to multiplying each element of C by the scalar value in A

[static lance]

yeah in MATLAB they treat scalars as 1x1 vectors, but I guess it still behavies like a scalar.

Thank you.

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[static lance]

.reopen

[odd edge]

✅

[vagrant hazel]

still consistent with how we treat scalars in mathematical operations

[forest sky]

in matlab everything is a vector, this is unusual but due to its specialization in linear algebra

[vagrant hazel]

so its fine

[static lance]

yeah it took a bit to realize, but all good now

Thank you for the help

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[neon dune]

honestly lost

Lmk if anyone knows how to solvw

<@&286206848099549185>

@hushed bobcat

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[sterile blaze]

X/X is the trivial group?

[weary pelican]

yeah

[sterile blaze]

trivial

elementary

{e}

thanks

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[cursive hedge]

i know im wrong. is what im trying to express here correct? given that the response was negative, wouldnt this be the union of the two sets of A,B negative?

[cursive hedge]

oh, i assumed that A is independent, but this result doesnt feel right either.
im not sure if im modelling this correctly. im assuming im supposed to multiply the probability i got by the probability of the random person being in A too

[wicked kestrel]

Your bottom screenshot seems to apply the right logic

P(A|negative) = P(A and negative)/P(negative) and assuming I'm following your notation you expand the denominator correctly

[cursive hedge]

the union of A negative and B negative is disjoint is my assumption

[wicked kestrel]

Correct

[cursive hedge]

i dont think i factored in the fact of the probability of choosing someone from the A group. only the probability of the response being negative

or no.. i didnt say that right

[wicked kestrel]

Whatever you think you're missing, it looks fine to me

[cursive hedge]

wouldnt this have to factor in somehow?

[wicked kestrel]

What you have as $A_+^c$ reads to me as "negative response from group A"

[clever fjord]

Steakanator

[wicked kestrel]

My connection's about to get spotty so let's see if my messages come through

[cursive hedge]

dont worry im from the future

[graceful parrot]

whoa

[wicked kestrel]

Ah ok I didn't read your notation correctly, ok we can fix this

I think I'm just gonna let - represent the event of getting a negative response bc I'm on mobile and want to minimize characters

$P(A|-) = \frac{P(A \cap -)}{P(-)} = \frac{P(A)P(-|A)}{P(A)P(-|A) + P(B)P(-|B)}$

[clever fjord]

Steakanator

[wicked kestrel]

My P(-|A) is your P(A_+^c)

[cursive hedge]

Oh I'm so dumb. That makes more sense. I just took it as one piece instead of making it vondtional

Thank you 🥩

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[tulip dew]

could anyone help with b?

i believe that the correct answer for b is in the second picture but it says its incorrect?

[odd edge]

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

[tulip dew]

thought based off of this that sin of sec^1(x) would be (sqrt(x^2-1))x

[orchid torrent]

try $\frac{\sqrt{x^2-1}}{|x|}$

[clever fjord]

Civil Service Pigeon

[tulip dew]

thank you

why is it absolute value of x?

[orchid torrent]

Hint: Show that $\sin(\sec^{-1}(x)) \geq 0$

[clever fjord]

Civil Service Pigeon

[tulip dew]

so could you think of it like

the numerator obviously has to be greater than 0 because of the sqrt so if you want it greater than or equal to 0 the bottom also has to be positive therefore must be absolute value?

[orchid torrent]

basically

[tulip dew]

cool thank you

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[tulip dew]

.cose

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[vagrant hazel]

!status

[odd edge]

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

[crystal meteor]

i have 3 minutes lol

before the assignment closes

[verbal schooner]

It’s just asking for the equation at each interval

And u have the points

[vagrant hazel]

just fill it in

[crystal meteor]

ok

[bitter folio]

Fit the function to the interval

[crystal meteor]

thank you

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[scenic minnow]

how would i do part a?

[mystic saffron]

"number of heads on the first toss" ?
there is just 1 head right ?

[scenic minnow]

the wording confused me as well

[rigid dragon]

I assume these are both Bernoulli RVs

So they are binary

[mystic saffron]

they mean probability ?

[rigid dragon]

0 or 1

Number of heads on first toss is 0 or 1

W could be 0 1 or 2

So sorry W is not Bernoulli

But rather binomial

[scenic minnow]

is A like making a chart

i was late to lecture so i didnt learn this part

[rigid dragon]

Yeah I think a table is a good approach

Just compute the probability of each pair of outcomes

That is the joint distribution

Essentially

[scenic minnow]

so the possible outcomes could be (H,T) (T,H) (H,H) (T,T)

[rigid dragon]

Yeah I think so that’s the entire sample space

So you just need to determine the probability of each one of those outcomes

[scenic minnow]

would i just multiply the probability of each

like head head is .4*.4

[rigid dragon]

Yeah because they satisfy independence that is allowed

[scenic minnow]

so

for the table

if i have 2 as the number of heads on 2 tosses, and 0 as the number of heads on the first toss, how would that be possible?

do i put 0 because of that?

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[mystic saffron]

Can anyone check my answers

[wild hull]

?

[odd edge]

@mystic saffron Has your question been resolved?

[mystic saffron]

<@&286206848099549185>

Can anyone check my answers

[onyx cloak]

https://cdn.discordapp.com/attachments/903463355619110912/1286919277676466217/IMG_9362.png?ex=66efa879&is=66ee56f9&hm=1dd7117c787abb4bc3f46bd66101374ce2f9c7abb65a6295b812ebcb6155eed2&

,rotate

[mystic saffron]

like my answers a different from my other friends..

im not sure whos right or wrong so i asked here

[onyx cloak]

why are ur answers of the 4th question 14 and 2

a. 15 people liked both fish and chicken
b. 14 people liked only chicken

you made the venn diagram correctly

but final answers wrong

[odd edge]

@mystic saffron Has your question been resolved?

[mystic saffron]

Wb the notation?

<@&286206848099549185>

hello?

<@&286206848099549185>

please

how to do Notation for no. 4

[inland rover]

what exactly is the question?

[mystic saffron]

how do you do the correct notation for number 4

[mystic saffron]

<@&286206848099549185>

[odd edge]

@mystic saffron Has your question been resolved?

[mystic saffron]

<@&286206848099549185>

I waited 3 hrs

😭

How to do notation of no 4

[inland rover]

how did you get $n(F \cup C)=48$?

[clever fjord]

convergence

[inland rover]

your notation is alright although your answers are wrong..

[mystic saffron]

so what do i replace it with

[inland rover]

$n(A \cup B)=n(A)+n(B)-n(A \cap B)$ use this to find $n(F \cup C)$

[clever fjord]

convergence

[mystic saffron]

its 14 right

[inland rover]

no

[nocturne cargo]

can you send the question again

im unable to find it as the chat is clogged with TeXit

[odd edge]

@mystic saffron Has your question been resolved?

[odd edge]

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[odd edge]

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[haughty shell]

can someone help with part c

[brittle beacon]

You're given f is continuous - do you have any idea how to use the IVT to show what they want? (Do you know what the IVT states?)

[haughty shell]

yea, between a certain domain interval, there exists at least one root c e [a,b] such that f(c) = 0

[sonic nova]

It's moreso that there is some x value c so that all the values between f(a) and f(b) are achievable

In that interval

That's why they call it "intermediate value" all the values in between can be found for some f(c)

[haughty shell]

oh

[sonic nova]

You can use this to find zeros/roots

[haughty shell]

right got it

but idk how to find that interval

[sonic nova]

Because if one end of the interval has a positive value for f and the other a negative then you can say there's a zero in between

Part c i would play around with numbers to make different continuous intervals

You could graph it too to help pick

[haughty shell]

oh ya

these r easy functions to graph

but

okay, this was the solution posted

i js got no clue

[sonic nova]

There's definitely more than one possibility for interval

I'd be surprised otherwise

Just has to be one where one endpoint is higher than 27 and the other lower

Then because they want 2 such locations

You make sure to use two disjoint intervals

[haughty shell]

hmmmm

i get it

makes sense

but in the solution

whyd they choose both numbers above 27

[sonic nova]

Well

I would argue the solution is wrong

They only proved existence of one such location

Because the 2 intervals they chose overlap

The place where it hits 27 could be the same location

To really show there are 2 spots

You need 2 completely separate (disjoint) intervals

Because then you know it has to be 2 different x values achieving 27

Otherwise you can't be sure

As to the intervals themselves, they are each fine for one

You're better off using the 2nd part of the piecewise function for the other one

You can easily find negative values for x so that f(x) is above/below 27

[haughty shell]

thank you so much

ill check it out again n come back to it later

thank you

.close

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[versed siren]

i'm stuck. :T

[sterile blaze]

hi stuck. :T

[mental storm]

inclusion-exclusion principle

the slide they gave u is just generalised for 2 sets

[sterile blaze]

u can label each region

and write some equations

[fast sleet]

(ping me pls)

[mental storm]

no

[sterile blaze]

go to another channel

[mental storm]

!occupied

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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).

[versed siren]

@fast sleet #help-13 is available for you

[sterile blaze]

we knwo x+y+z+p+q+r+s=42

x+y+p+q=21

fill in more and u would be able to solve omehow

exactly 7 variables and 7 equations

[versed siren]

so these are my equations

[sterile blaze]

yea now

solve them

u can do it

[versed siren]

with what? there's basically nothing to go off from for SoE (not that i can even use a calculator)

[white tiger]

Put values you will get it

[sterile blaze]

u can do this

or just write a matrix and rref

[white tiger]

Yes this is right

[sterile blaze]

💪

[versed siren]

i don't know how to do this by hand

[sterile blaze]

havent heard of matrices?

[white tiger]

Last three is quite difficult to solve they are in functions

[versed siren]

here's what i've come up with

[sterile blaze]

honestly u can do it but its very painful

just cry

oh hey

isnt q meant to be an int

but u nearly got it

[versed siren]

i mean, Q is an integer

[white tiger]

This is easy put the value of Q in R and get answer

[versed siren]

okay but what is Q?

[white tiger]

It dosent matter

[sterile blaze]

triple int

people who eat every drug in the world

drug A B AND C

huge druggies

[versed siren]

no, i mean i can't find the numerical value of Q, because it's an int

and this SoE yields a fraction

[white tiger]

It is probability

[sterile blaze]

yea

u probably made a mistake

its ok

ull get it

[versed siren]

no shade, i don't think you're paying attention

[sterile blaze]

yea

ok dw

i just checked

ur equations r wrong

[versed siren]

nvm sec

[sterile blaze]

more like

at the first line

[white tiger]

It has to be a real number

[sterile blaze]

why do u think those double intersections added

[white tiger]

Where

[sterile blaze]

would give u Q

[versed siren]

i'm just gonna come back to this

.close

[sterile blaze]

wait nvm its correct

[odd edge]

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[sterile blaze]

idk

well its hard

[white tiger]

No intersection one maybe wrong

[sterile blaze]

nvm

maybe the question gave wrong numbers..

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[sterile blaze]

urs seems fine

[odd edge]

Please don't occupy multiple help channels.

[sterile blaze]

.close

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[swift canopy]

statics, blue is what im thinking that should be, why there is no division by singular vector of the string BG?

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@swift canopy Has your question been resolved?

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@swift canopy Has your question been resolved?

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@swift canopy Has your question been resolved?