help-42

[amber bolt]

but you can put them in the other row

so that but 26, coud be right

[remote mural]

Wut? 😐

Sorry I’m a little bit confused

[amber bolt]

i probably guessed wrong

what did you mean by 6

[remote mural]

Is the number of places left for C and D

[amber bolt]

they don't have to sit beside each other

CABD#

would still be not allowed

[remote mural]

Oh jeez yes

Thanks for your help

I get it now

Thanks

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[icy mulch]

i have no idea how to start

i feel like i should get the first integral of the given f''(x) since thats prolly the slope?

-e^(1-x)+4x + C

idk tho

[dusty crescent]

Well you need f(x) so take the integral of f''(x) twice

then use the other information to determine constants c1 and c2

[icy mulch]

e^(1-x)+2x^2

[icy mulch]

how do i determine c1 and c2

nvm i think i know now

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[humble zealot]

can someone please help me understand eigenvalues and eigenvectors

[humble zealot]

my prof wrote that in the linear transformation T(x,y) = (-x, -y)

all vectors with x=0 or y= 0 and all vectors with x=y are eigenvectors

[remote mural]

@wintry carbon might be able to help

and i will try

[humble zealot]

but my guess is that in this linear transformation all vectors are eigenvectors

[remote mural]

so an eigenvector is a vector that gets mapped onto a multiple of itself by the transformation

the eigenvalues is the multiple

[humble zealot]

yes T(v) = lambda(v)

[remote mural]

yeah

[humble zealot]

v is an eigenvector, lambda is an eigenvalue

[remote mural]

yeah

[humble zealot]

and geometrically this means that the vector after the linear transformation stays on the same line

correct?

[remote mural]

yeah

it's just scaled

[humble zealot]

aight

in T(x, y) = (-x, -y), T(2,1) = (-2, -1) = -1 * (2, 1), so (2,1) is an eigenvector of T and -1 is an eigenvalue of (2,1)

correct?

my professor wrote that in T(x,y) = (-x, -y) all vectors with x=0 or y=0 and all vectors with x=y are eigenvectors

i think that in this linear transformation all vectors are eigenvectors, not only those vectors that he mentioned. am i right?

[calm coral]

@humble zealot Has your question been resolved?

[wintry carbon]

Yes, T≈-1, all vectors are eigenvectors with eigenvalue -1

[humble zealot]

ok thank you! i just wanted to get this clear

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[severe palm]

i got i) x<2.5 ii)0.5<x<5 which i marked but don't know how to do part b

[thin gulch]

the answer to part b will be the intersection of the answers in part a

so the intersection of x < 2.5 and 0.5 < x < 5

[severe palm]

thank you

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[proper echo]

is this correct?

[dusty crescent]

did you draw this in ms paint?

If you want to know if you did an integral right, just take the derivative of the solution

if you get the initial expression it's correct

[proper echo]

lol yeaa

[proper echo]

ngliwastoolazytodothatbutalr

[dusty crescent]

seems wrong

unless I made a mistake when taking the derivative

wait

nvm

it's correct

I dun goofd

[proper echo]

ah alrr, thankyou!

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[prime berry]

i need help with my homework

basically i dont understand shit and the teacher said if we do it all right we ll get a point on our next test

help would be much appriciated

[warped sky]

do you know what is a conjugate is?

[prime berry]

?

[prime berry]

no?

[warped sky]

ok think of complex numbers like 2d planes. X axis and Y axis.
You can write express complex numbers like so z = x + i y

i is just a imginary number. Just think of it like how far you go up on Y axis and you denote it with y times i to keep track of it.

[prime berry]

yea

[warped sky]

a conjugate of z is z bar (which is question 1a) z bar = x - i y

you flip i sign in simpler term

[prime berry]

trying to understand math in another language is proving to be way more difficult lol

[warped sky]

z = x + i y
comjugate of z = z bar = x + i y

[prime berry]

i want to understand what z1 with that line above it means

[warped sky]

the line above it is bar

[prime berry]

and the one with 2 bars next to it left and right

[warped sky]

so it is basically asking for the conjugate of z

[prime berry]

and re and im

[warped sky]

that is question b

it is called the magnitude.

Think about pythogerous

[prime berry]

a squared +b squared equals c squared

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[warped sky]

exactly

Re just means the real part of it. Which is x and Im is what? you guess it right

[prime berry]

you really are trying to help me

thanks man

[warped sky]

you think i was trolling 🤣

?

yw man happy to help

[prime berry]

idk man it s just that

[warped sky]

good luck

[prime berry]

thanks

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[proud kite]

how is this 1

denom is equivalent to x^3

i get inf as result

[mortal orbit]

why?

[proud kite]

cuz its x^3 not x

stronger x

[mortal orbit]

?

it's still 0/0

[proud kite]

ye but denom higher rank

[mortal orbit]

how do you know?

[proud kite]

^3

[mortal orbit]

and what tells you that sinhx - sinx is not smthg like x^4?

[proud kite]

or sin higher rank?

[mortal orbit]

it's not sin

it's sinh - sin

[proud kite]

oh

well what can i dO?

is equivalent to x-x

[proud kite]

i got 1/3 bro

but is wrong

[crude hinge]

I also got 1/3 on the back of an envelope
Currently checking for mistakes

[proud kite]

damn

[crude hinge]

Wolfram agreed with us

[proud kite]

oh

textbook wrong then ig

[crude hinge]

Ig

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[proud kite]

i made num become -x^2

then used hopital and got -2x/(2x/x^4+1)

it results -1 but is worng

<@&286206848099549185>

[untold summit]

i would keep the numerator the same and use lhoptial
also you can use, and seems like maybe you already did, pi/2 = arctan(x) + arctan(1/x)
so after lhopital we get -(sin(x) + sinh(x)) / (2x / (1 + x^4)) = -(sin(x) + sinh(x)) / (2x) - x^3(sin(x) + sinh(x)) / 2
the second term will go to 0 as x->0
and the first term we use lhopital again
-(cos(x) + cosh(x))/2 which tends to -1

so perhaps your book is wrong again? maybe check w wolfram alpha

[crude hinge]

I also got -1

[proud kite]

hey what i got is -1

bruh wtf???

this book making me waste so much time smh

getting things right and thinking they wrong bruh

[untold summit]

i would just start checking all your answers on wolfram if they dont agree with the book haha

[proud kite]

yeah typing em a bit boring but whatever

im just pissed i spent 20mins on this exercise i solved in 2

bruh

thx anyway

[untold summit]

thats how it goes sometimes unfortunately

try not to stress it

[proud kite]

thx

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[onyx quiver]

did i do this right so far and how do i solve/

[dusty crescent]

What did you do so far?

Oh you mean the sketch?

[onyx quiver]

yeses

[dusty crescent]

Hmmm... not sure if a sketch will help you a lot here, seems to be an analytical problem

[onyx quiver]

crap

[reef nimbus]

use the dot product

[onyx quiver]

i just did this

[onyx quiver]

how do you know when to use the dot product

[idle briar]

dont forget vector arrows

[onyx quiver]

oh yea

[idle briar]

can get a lot of deducted marks for that

[onyx quiver]

crap

[reef nimbus]

well it mentions the angle between two vectors, and that those other vectors are perpendicular (so their dot product is 0)

[onyx quiver]

ohhhhhhhhhhhhhhhhhhhhhhh

ohhhhhhhhhhhhhhhhhhhhhhhhhhhhhh

it all just clicked in my head

[idle briar]

💡

[onyx quiver]

🧠

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[onyx quiver]

how the hell did this happen

[dusty crescent]

uhhh.

they factored out a dot b

from the second and third term

[onyx quiver]

ohhhhhhh

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[late raptor]

how to solve recursive relations in easy way? for example

[solid steppe]

its kinda easy give a question

and i can show u

[late raptor]

find solution for recursive relation

that is question

[solid steppe]

uhhh okay i see mb lol

so how long have u come?

in the question

[late raptor]

i tried something like this

[solid steppe]

nah

the easy way first its to do this way so u get a grip of it

solve a_2

and a_3

a_4

just

and tell me what u got

[wanton spear]

Alternatively do you know the formula for the sum of the whole numbers up to and including some n?

[late raptor]

Okay, I know how to get a2,a3,…and then I should guess the formula, but I want a more general way.

[solid steppe]

its not rly a guess

if u see the pathern

early its hard thats why u need to do like that

when u have done a few u will see the pathern

[late raptor]

Sometimes it is harder to see patterns

[late raptor]

ok

[solid steppe]

but there is also a formula but i would advise u to do this so u just repeat and learn from it

like @wanton spear mentioned

[late raptor]

is formula usefull in general case

[solid steppe]

idk long time ago i did this lol

[late raptor]

like for all problems of this kind

[solid steppe]

but idk i had easy to see it

which year is this?

[late raptor]

ok i will try few examples

first

[solid steppe]

of uni?

[late raptor]

yea

[solid steppe]

rly?

[late raptor]

but easy example

[solid steppe]

do u guys read calculus?

or what?

[late raptor]

first in book

i just wanted general way for harder problems

[late raptor]

?

[solid steppe]

i see idk bro i am right now preparing for my exam tomorrow xD and i haven't study a single minute before now so idk i have easy for math i guess lol

[solid steppe]

the math book is it called calculus or what?

[late raptor]

xD ok

[late raptor]

yea

[solid steppe]

weird lol its my first year also but we never study that or i missed that lol

anyways gl and practice it just

[late raptor]

ty braa

[solid steppe]

np

[late raptor]

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[severe granite]

If I have x^6-16 does it factor to (x^2+2)^3(x^2-(x^2)(2)+2^2)^3?

[quaint sphinx]

no

[severe granite]

😦

what did i do wrong

[humble oyster]

lets see your steps!

[severe granite]

all off the dome

what if i changed b to 2

[thin gulch]

we can't read mind, there was nothing in your question that mentioned what "b" is, so how are we supposed to know what you mean by "changing b to 2"

[severe granite]

isnt the formula (a-b)(a^2+ab+b^2)?

[thin gulch]

for a^3-b^3 sure

[fleet verge]

2^3 is not 16

[severe granite]

yeah

i realized that now

[fleet verge]

Ok first of all

[severe granite]

i also realized the answer is (x^3+4)(x^3-4)

[fleet verge]

Do you have to factor over integers, over reals… where?

Ok over integers

[severe granite]

I had a question earlier that i got side tracked on and never got the answer to

but is this right

is that what it is fully factored?

[fleet verge]

Yes the two together

(x-1)(x+1)(x^2-x+1)(x^2+x+1)

[severe granite]

i see

thank you

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[near lily]

there is an easier formula

[severe granite]

what is it

[near lily]

basically aⁿ -bⁿ=(a-b)(aⁿ-¹ + aⁿ-² b+aⁿ-³ b² +........+abⁿ-² +bⁿ)

basicqlly ou keep decreasing powers

idk if u see it or not

like if n=4 then a⁴-b⁴=(a-b)(a³ +a²b+ab²+b³)

[quaint sphinx]

in many cases (especially school settings) this formula is not "easier"

[quaint sphinx]

even in this example it's not a good idea to apply the formula because this can be factored further

and the a^3 + a^2b + ab^2 + b^3 doesn't make that obvious

[near lily]

ye u can factor the inside aswell

there is a³+b³

etc

[severe granite]

guys, with a cubic trinomial if lets say ax^3+bx^2+cx i can factor out an x right?

[quaint sphinx]

yes

[near lily]

why not

[severe granite]

what about if its just c

[quaint sphinx]

then you cannot

[severe granite]

ax^3+bx^2+c

how do i factor it then

[quaint sphinx]

in most cases you can't

[near lily]

nah unless u make it c/x

[severe granite]

oh so it just stays like that?

[near lily]

and x doesnt equal 0

[quaint sphinx]

if that's what you have, then yes

if a, b, and c have actual values, then you try to find a value of x that satisfies ax^3 + bx^2 + c = 0

[near lily]

isnt that hzrd

hard

[severe granite]

yeah solving for x then

without factoring

[near lily]

it depends on the equation

[quaint sphinx]

brother

[severe granite]

well thats good news

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[empty timber]

Let A, B, C and B be points such that:
|AB| = 2, |BC| = 2 and |BD|=1
the angle between AB and BC measures π/3 radians
AB and AC are both orthogonal to the vector (1, -1, 1) and
the vector (1, -1, 1) has a π/3 radians angle with BD.
Therefore, calculate the volume of the parallelepiped which has AB, AC and AD as edges

[empty timber]

I don't know where to start. I'm aware I must do the triple product between AB, AC and AD, but I don't know how to find those values

[calm coral]

@empty timber Has your question been resolved?

[empty timber]

<@&286206848099549185>

[empty timber]

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[drowsy ember]

How do I do f)?

[jovial narwhal]

they're asking for the vertical asymptotes (x) and horizontal (y)

[drowsy ember]

How do i get that?

[jovial narwhal]

do you know what asymptotes are?

[drowsy ember]

Is it x = -2, x = 1, y = -1, y = 2?

[jovial narwhal]

this point is the origin right?

[drowsy ember]

Yes

[jovial narwhal]

and these will be the vertical asymptotes

so they lie at x=-1 and x=2

x=a is a vertical line and y=a is a horizontal line

[drowsy ember]

I mixed up x and y. So is it x = -1, x = 2, y = -2, y = 1?

[jovial narwhal]

almost

it's y=2 not -2

this line

[drowsy ember]

Ok thank you very much

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[pure bolt]

hey can someone give me some starting points

im really stuck

and i have tried everything

but iwsnt parallele meaning mnp= 3,-4,1 or a multiple

however this means that there wont be any valuye of lambda that will allow for l1 to intersect with -1,3,0 in l2

<@&286206848099549185>

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[tame bramble]

How do I convert degrees to radians?

[remote mural]

Hey

[swift laurel]

how many degrees is a full circle, and how many radians?

[tame bramble]

for radians, it's 2pi isn't it

[lyric zephyr]

and how many degrees are there

[tame bramble]

360

[pearl skiff]

nice

[tame bramble]

oh so pi = 180 degrees

[lyric zephyr]

so.. 360 degrees = 1 full circle = 2 pi

[lyric zephyr]

yes

[tame bramble]

pi/2 = 90 degrees

[lyric zephyr]

mhm

[pearl skiff]

Correct!

[tame bramble]

pi/4 = 45 degrees

and so on

[lyric zephyr]

yep

[pearl skiff]

yep

[lyric zephyr]

so x degrees = x pi/180 radians

[tame bramble]

thanks guys

[remote mural]

I hy

Why

[pearl skiff]

you can close this by typing .close

[lyric zephyr]

follow same logic as bash

[tame bramble]

thanks guys

.close

[vernal crest]

pi = 180
pi/4 = 180/4 = 45

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[remote mural]

Ty

[calm coral]

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[cloud flume]

Hello again and again (sorry) I do not have idea does this makes sense. Thank you
The question SIMPLIFY

[tame quail]

start with combining the fractions

[inner delta]

That is tan right?

[cloud flume]

Yeah

[inner delta]

Alr

[cloud flume]

At the beginning?

[tame quail]

multiply right fraction by sin^2/sin^2

and multiply left by (sin + cos)/(sin + cos)

yeah

then we have the same denominator

wait

[cloud flume]

Kinda make no sense

Ehy sin²x

[tame quail]

multiply right fraction by cos^2/cos^2

not sin^2/sin^2

and I think we need to multiply by -1 as well

[inner delta]

Basically try to get a common denominator

[cloud flume]

Okay

[tame quail]

now we have a common denomiantor

the denominator is actually cos(2x), not sure if we want to make that substitution though

[cloud flume]

I did something... well i think it's not good lol

[cloud flume]

Makes more sense ye

[tame quail]

not sure if we can simplify more than this

[cloud flume]

What did hou do

[tame quail]

2sincos = sin(2x)

[cloud flume]

A

Look what i did

[tame quail]

which part?

[cloud flume]

Oh no i see my mistqke

[tame quail]

the sin^3 is subtracted

[cloud flume]

Wait no

[tame quail]

for cos^3 - sin^3 we do difference of two cubes

and for cos^2sin - sin^2cos we factor out sincos

and the denomiantor is difference of two squares

so we get a common factor of cos - sin that cancels

[cloud flume]

okay but did i did wrong

[tame quail]

yeah sin^3 should be negative

the whole fraction is subtracted

not just the first term

this should be negative

[cloud flume]

Yeah i see now

[tame quail]

then we just do this

and cos - sin cancels

also cos^2 + sin^2 = 1

hmmm, maybe we want the cos - sin, give me a moment

nah

I don't think we can simplify further

other than maybe substituting 2sinxcosx = sin2x

[cloud flume]

Look

I went on photomath

[tame quail]

it should be +cosxsinx

for the difference of cubes

to get the middle terms to cancel

[cloud flume]

They got thos

[tame quail]

a^3 - b^3 = (a - b)(a^2 + ab + b^2)

Hmmm

sin(x) + what?

[cloud flume]

Cos

[tame quail]

oh

I'm dumb

we don't want the sin^2 + cos^2 substitution

[cloud flume]

then what we need

Is it even correct on photomath

[tame quail]

yes

[cloud flume]

Aaaa

Okay that's understandable

Thank you @tame quail

. close

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[fallen lantern]

Can someone explain this to me?
I'm looking at a explanation of it online and im able to follow it so far but theres 1 part that I don't get.
How does x^2 -5x become x * (x-5)?

[verbal finch]

U take the x common from both terms

x*x -5*x
x(x-5)

[fallen lantern]

if u take away the x common doesnt it become
x * -5

[verbal finch]

Yes

Thats why u do x-5 instead of x+5

If u did it this way

x*x + (-5)*x

Ull get the same thing

[fallen lantern]

sorry i dont really understand, why would we do x+5?

[verbal finch]

We did (x-5)

U asked x^2-5x

[peak dune]

Guys I'm 7th grade its easy questio but pls dont make fun of me.

There is enough food for 24 people in a camp for 18 days. If 8 more people join the camp 2 days after it starts, for how many more days will the remaining food be sufficient for the rest of the people?

[verbal finch]

#❓how-to-get-help

[fallen lantern]

i still dont get why we keep 1 other x when we are suppoised to remove them on both sides

[verbal finch]

Dude look

U got x^2

Remove one x

What is left?

[peak dune]

@verbal finch what do you mean?

[verbal finch]

This channel is occupied by someone else

Go to #❓how-to-get-help

And read how to get help

[verbal finch]

@fallen lantern

[fallen lantern]

x?

[tacit linden]

x^2 - 5x
(x * x) - (5 * x)

same thing correct?

[fallen lantern]

yes

[tacit linden]

ok

[verbal finch]

Yes

[tacit linden]

do you know how to simplify

[verbal finch]

Now take out x from 5x

[tacit linden]

something like this

[verbal finch]

What is left

[fallen lantern]

5

[verbal finch]

Yes

What did he do

[fallen lantern]

so its x * -5

[verbal finch]

Add or subtract?

[verbal finch]

Ni just the 5x

Ignore the sign

[fallen lantern]

x * 5?

[verbal finch]

Yes

Now wht did he do

Add or subtract?

[fallen lantern]

subtract?

[verbal finch]

Yes

So what is there now?

x-5

And u took out x

So x(x-5)

[fallen lantern]

where did the first x come from though?

[verbal finch]

...

[fallen lantern]

x*x -5*x
remove the x from both sides =
x * 5
we subtracted so it turns into x -5

is this right so far

[verbal finch]

Yes

U got it

There u go

[fallen lantern]

but i thought we removed the x so why is it still there

[verbal finch]

U removed x from x*x

[tacit linden]

do you know how to factor out things like 7x + 14

[verbal finch]

So x left

[fallen lantern]

ohh

[fallen lantern]

like

u mean

[verbal finch]

See its simple

[tacit linden]

factor 7x + 14

[verbal finch]

U said 5x us 5*x

And 5 remains

Same thing

It is x*x

Instead if 5 there is x

[fallen lantern]

wdym

[verbal finch]

U remove x so x is left

Got it?

[fallen lantern]

yeah

thanks

[verbal finch]

Np

[tacit linden]

do you know how to factor by gcf

[fallen lantern]

greatest common factor of 7 and 14 is 7

right

[tacit linden]

good

[verbal finch]

Yes

[tacit linden]

now you can factor 7x+14

[fallen lantern]

so the answer is 7? or do we divide

[tacit linden]

divide

[fallen lantern]

so the answer is x + 2

[tacit linden]

yea

7(x+2)

very nice

[fallen lantern]

ohh so we times by the factor?

[tacit linden]

yes

you know the distributive property?

[fallen lantern]

whast that?

[tacit linden]

7(x+2)

= 7*x + 7*2

[fallen lantern]

oh yeah

i know that

[tacit linden]

ok

lets go back to the previous example

[fallen lantern]

yeah

[tacit linden]

do you know the gcf of x^2 - 5x

[verbal finch]

I just explained him

.....

[fallen lantern]

x?

[tacit linden]

yea

now divide the thing by the gcf

[fallen lantern]

so it turns into x(x-5)

alright

[tacit linden]

yea

[fallen lantern]

thanks

u guys helped me a lot

[tacit linden]

close the channel when youre done

[fallen lantern]

how?

[tacit linden]

.close

[fallen lantern]

.close

[calm coral]

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[calm coral]

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[remote mural]

I am trying to find the inverse Fourier transform of [
\6\FF\omega = 2\6\sin{\pi\omega}\9{\6\theta{\omega +1} - \6\theta{\omega -1}}
]
where $\theta$ is the heaviside function

[remote mural]

I am not sure how to do this

[tranquil tartan]

what subject is this🙆‍♂️

[calm coral]

@remote mural Has your question been resolved?

[remote mural]

this is for my circuit analysis class but this is about signal analysis

[lethal flame]

ask ai

to solve it for you

[remote mural]

chatgpt cant do math

[calm coral]

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[teal moss]

I'm a bit confused as to why the area formula of the cylinder is required for this question

[azure willow]

cuz the water tank is hollow inside

so only the area of the material required to build the curved sides of it+top and bottom is taken into consideration

[dusty crescent]

Basically, find the minimal amount of surface area for the given volume and shape

Since only the surface area will be made of metal and will affect the cost

(Although, as an engineer, I have to say that sometimes the minimal amount of surface area will not result in the lowest cost because using standardized dimensions is cheaper than cutting out custom part sizes so this question is really simplifying things)

[last light]

u dont wanna build a 1m2 suface and 200m height r u?

[dusty crescent]

Well, depends, if I'm feeling cute that day I might

[last light]

cute!!

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[limpid drum]

hi,i wanna do this fourier transfer function.im not sure if the t condition is unit step function, and which range for the differentiation i should use?

[limpid drum]

The formula im using

I suppose it 0->infinity for the range

[tidal grotto]

$f(t)=e^{-3t}u(t)$

[potent lotus]

🫎MooseyMooseMooser 🫎

[tidal grotto]

where u(t) is Heaviside/step function

technically it needs to be defined at 0, and in your example f(t) isn't defined at zero but eh

[limpid drum]

You mean=0?

[tidal grotto]

it was probably meant to have a leq one of the piecewise things

f(0) is not defined

[limpid drum]

Yeah

The example i have was >=

Can't find how to deal with the case only > 0,< 0

[calm coral]

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.close

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[merry crest]

what factors affect sound waves? and I don't really want to talk about humidity or other things like that. Im talking more about factors such as the loudness etc

[merry crest]

basically main focus is on graph and the function is self

what make like the sound wave's period smaller

or amplitude higher etc

[calm coral]

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[teal moss]

Is this a mistake in the solution or am I missing something here?

[teal moss]

(-3)^3 = -27

so that should conclude that the function is not continuous at x = -3 right?

[vital raven]

yes

since the limit doesnt exist

because there are different values when u approach it from different directions

[calm coral]

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[teal moss]

ah okay thanks

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[strange veldt]

is my formula right?

[mild wedge]

wat are u trying 2 do?

[strange veldt]

solving for A

or is it 175(A)+(1/2)(50)(A-50)+75(A-75)?

[void frost]

What's A?

[strange veldt]

A is like the height

Area

[void frost]

Is it now height or area?

[strange veldt]

its depth .. so height

[void frost]

If this is some exercise, it might be useful to include what it says here

[strange veldt]

or area .. now im confused

29568=175(A)+(1/2)(50)(A-50)+75(A-75)?

oh its.... depth

now im confused ...

I will close this now

.close

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[calm coral]

@idle fractal Has your question been resolved?

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[idle topaz]

Can you solve it like this?

I feel like I have the wrong answer

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@idle topaz Has your question been resolved?

[idle topaz]

<@&286206848099549185>

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[rain lark]

im not sure where to even start on this

[glacial nacelle]

what is given?

compare that with what is in the statement box

if its the same||, then you can just call it "Given"||

if its not||, then you did something wrong||

[rain lark]

I made a mistake in the title of it, i meant to say except A

[glacial nacelle]

oh lol

mbmb

um

if you weren't given this outline, think how you would prove it

or, if you aren't comfortable with that, think what you could prove with the reflexive propers

for b that is

[rain lark]

Wait i think i understand b and c now

b is the angle of cdb ≈ the angle of adb?

and c is the symmetric property

[glacial nacelle]

that won't be reflexive

reflexive is where you say that something is congruent to itself

[rain lark]

I think its the proof now

[glacial nacelle]

?

[rain lark]

I think the proof is what i thought b word

would B be ad ≈ dc? or do they have to be completely the same

I think its A: given B: AD ≈ DC C: Symmetric proof D: ∠ADB ≈ ∠CDB

would that be correct?

[calm coral]

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.close

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[flint mist]

So I was reading the solution for this and one thing confused me which is why did they say at the end that if e^t < 2

[flint mist]

shouldnt it have been if e^t neq 2?

oh wait its because if e^t > 2 thn it will result in a negative value? and we dont want that right

second question. they used the derivative of the MGF and set t = 0 to get the expected value

does this always work out? because I dont recall seeing this in my notes

ohhhh nvm I understand this aswell its because derivative of MGF and setting t = 0 results in E(X^k). if we take the first derivative then we get E(X^1) if we take the second we get E(X^2)

damn

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[mossy wigeon]

why is 3 and 5 wrong?

derivative of cos isnt it -sin

[median marsh]

can you post the question?

oh wait mb

[mossy wigeon]

taht is the question

ueah lol

i forgot n!

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[unique jackal]

[calm coral]

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[tough vector]

shipment of 29 flat screen televisions contains three defective units. In how many ways can a vending company purchase four of these units and receive the following?
(a) all good units ways
(b) two good units ways
(c) at least two good units ways

[tough vector]

is A just 29 C 4

using the nCr thing

and B) (29 C 2)*(3 C 2)

[white ridge]

no

a is 26C4

b is 26C2 x 3C1

[tough vector]

😭 bruh

i put 26 in my calc but wrote 29 here

[white ridge]

lol ok

[tough vector]

is c just ways of 2 + ways of 3 +ways of 4

[white ridge]

yeah

[tough vector]

alr ty

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[mossy wigeon]

how can i write factorial if they dont allow the use of !

[ancient thistle]

it's not simplified

[mossy wigeon]

https://tenor.com/view/monkey-gif-18890916

ty

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[olive matrix]

hi

[olive matrix]

can someone explain to me the reasoning behind

why the resultant vector touches a point on the line

after the addition of a point vector and a vector parallel to the line

[potent igloo]

which resltant vector? Which line?

[olive matrix]

(x,y)

[potent igloo]

!original

[calm coral]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[olive matrix]

does the reasoning relate back to certain triangle theorems?

🤔

or is this it's own theorem

[potent igloo]

It's how vector addition is defined geometrically. Are you familiar with the geometric definition of vector addition?

[olive matrix]

not that I remember

[potent igloo]

look it up. Should hopefully answer your question in full

[olive matrix]

oh

I understand now

thank you

I wish teachers gave more specific insight into things like this

[potent igloo]

all good. Happy to help

[olive matrix]

it provides student with a greater comprehension of these subjects rather than blindly teaching

.close

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[flint wasp]

.close

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[unique jackal]

fastest doubt cleared in the west

[ancient helm]

🔡

⚔️

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[queen orchid]

how do i solve this plese help. idk hwo to graph

[queen orchid]

plz help 😭

<@&286206848099549185>

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[lament zephyr]

how have they diffrentiated

can someone please explain

[dull wagon]

power rule

(and power chain rule)

[lament zephyr]

whoops i see what i did wrong

thanks

.close

[calm coral]

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[calm coral]

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[lunar yacht]

help me pls

[stone flax]

Use properties of determinant

det(AB) = det(A)det(B)

and other such properties

[covert lark]

This specific question has been asked for like fifth time already lol.

det(A^(-1)) = 1/det(A)

[remote mural]

here x and t two are unknown and only 1 condition is given what about another?

[stone flax]

The funny thing is the question is asking you to find the det which is given as 5

So 5 is the answer

Bruh

t means transpose

[remote mural]

oh transpose we use T

[covert lark]

Some people even use ' for transpose lol

[remote mural]

damn first time im seeing like this i mean it can create confusion

[remote mural]

i think question is asking for x

[calm coral]

@lunar yacht Has your question been resolved?

[calm coral]

Channel closed

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[calm coral]

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[torn cloak]

how in the chicken nuggest frick can i do this

[torn cloak]

also i assume theres some way to do this with calculus, but unforunately i dont know calculus so there must be some other way

[stone flax]

How about you tell your approach

[torn cloak]

i have no idea

i know you can get the area of the quadrlateral

[stone flax]

Lets go step by step

[torn cloak]

ok so

[stone flax]

The two circles intersect at 2 points, say C and D

draw a line between C and D

[torn cloak]

mhm

[stone flax]

Now compute the area in two parts

Can you find the area of each of the parts independently?

[torn cloak]

?

yes?

[stone flax]

Then whats the issue

Once you find the area for both the parts, just sum them

That would be the answer

xD

[torn cloak]

how

what

i need the shaded region

[stone flax]

Forget the other circle

[torn cloak]

yes

[stone flax]

Can you find the area of a sector?

[torn cloak]

forgotten

[stone flax]

In a circle

[torn cloak]

yes ofc

[stone flax]

So whats the area of sector ACD?

[torn cloak]

gimme some time

[stone flax]

You need to find the angle CAD for that

[torn cloak]

yes

through trig i assume

[stone flax]

Any ideas for that?

[torn cloak]

no

sorry

[stone flax]

No need to be sorry

[torn cloak]

alg

[stone flax]

Yup, if you know trig

You can use that

[torn cloak]

where the rigt angle?

[torn cloak]

your profile pic is imtimitdating lmao

[stone flax]

ACB is a right angle

😂

Its meant to be

Since 6^2 + 8^2 = 10^2

[torn cloak]

ok well thankyou

ill get tha angle

[cerulean cradle]

Solved ?

[torn cloak]

no

[cerulean cradle]

Then what stage have you reached ?

!status

[calm coral]

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

[torn cloak]

i am currently using trigonometry to calculae the angle A, becuase this guy tole me to

so with angle A i can find the sector of the circle

[cerulean cradle]

Okay

[torn cloak]

however i dont know how that will help me find the shaded part (becuase i assumed this guy would tell me)

[deft dove]

Does anyone know how to solve this?

[torn cloak]

does anyone know how to be polite

get out of my ticket please

[cerulean cradle]

This page is taken

[torn cloak]

yes anyway

[cerulean cradle]

Yeah it will help surely

[torn cloak]

the angle of A = 2sin^-1(8/10)

[cerulean cradle]

We need angle MAO

[torn cloak]

oh

why>

[cerulean cradle]

Then we would be able to compute the value of MO

[stone flax]

Once you have A, then just calculate the sector area and subtract area of triangle ACD from it

To get the area of first part

[torn cloak]

what?

[cerulean cradle]

If you notice the required area is area of sector - area of triangle

[cerulean cradle]

For the individual circles

[torn cloak]

what

i am so confused

[cerulean cradle]

Understood ?

[torn cloak]

OHHHH

I GET IT

yes it is understood

you add the two segments of the two circles yes?

thanyou for your services

.close

[calm coral]

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[lunar yacht]

ye

[calm coral]

@lunar yacht Has your question been resolved?

[calm coral]

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[hearty peak]

How do I prove this

[hearty peak]

with math induction?

[desert nymph]

start with your base case

assume your n=k case

reduce your n=k+1 case to your n=k case + some extra stuff

[hearty peak]

Also I have to prove this later

for natural number >= 1

[desert nymph]

...wait, is this saying that 7n +1 is always divisible by 3?

because that's not true lol

[inner delta]

Yeah

[desert nymph]

I think this is the correct statement

[hearty peak]

yeah I guess

[desert nymph]

do you know how to induction

[hearty peak]

I only know n = k+1

[desert nymph]

okay, so first we need to prove the base case

(if you don't follow me, just say)

[hearty peak]

how?

[desert nymph]

so our base case is when n=1

can you prove that 2^n + 5^(n+1) is divisible by 3 when n=1?

[hearty peak]

yes

thats 27/3

[desert nymph]

yep, great

so now we assume it's true for n=k

that is, we can use "2^k + 5^(k+1) is divisible by 3" as a fact

if we can prove that, with this assumption, it's true for n=k+1, then we say when k=1 we've proven it's true for n=2, and if it's true forn=2 then it's true for n=3, and if it's true for n=3 it's true for n=4, etc etc etc for all naturals

so first we want to write out our equation with n=k+1

[hearty peak]

Wait so if I prove that its true for 1 then its proven?

[desert nymph]

if you prove it's true for n=1, and you prove "if n=k is true, then n=k+1 is true", then you have proven it's true for all n >= 1

because n=1, so n=1+1=2 is true
n=2 is true, so n=2+1=3 is true
...

so you need to write out what the equation with n=k+1 looks like

then you need to prove it's true; since we are assuming n=k is true (2^k + 5^(k+1) is divisible by 3) we just need to show that the n=k+1 case is the n=k case plus something else divisible by 3

[hearty peak]

Ok ok

I think I got it

If not I'll come back later 🙂

.close

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[native dragon]

S is a set, {1,2,3,4,5,6} and R is a relation, R:S --> S, where
|R| = 6
The number of ordered pairs (a,b) such that |a-b| >= 2 is mC6 ( m choose 26)
Find m

I dont remember the question correctly so if theres some ambiguity let me know

okay so what i did was that 1,1 2,2, 3,3 and so on...these wont be in the set cuz |a-b| >= 2
so 6 pairs
then there are 1,2 2,3 3,4 and so on and the vice versa cuz its an ordered pair so 5 x 2 = 10 pairs
so in total 16 pairs cannot be in the set

there are 36 elements in S x S
16 which cannot be
so 20 which can be
so shouldnt it be 20 C 6
the answer is 26
i dont understand how

[proper echo]

wait what does the |a-b| represent? Number of elements in the set or does it represent the modulus of the quantity?

[native dragon]

modulus of the quantity

like for example 1-1 is 0

it cant be

but 3-1 can be

cuz 2

[proper echo]

oh so basically what we have to do here is, take the numbers from the set (S) and have them such that |a-b|>=2?

ah alright

[native dragon]

yeah

[proper echo]

just a minute, am trying to solve it case wise

[native dragon]

another guy did it by like
he took every case of every number
1 has 4 options
2 has 3
3 has 2
4 has 1
so 4 + 3 + 2 + 1 = 10
and ordered pairs so vice versa is possible
so 10 x 2 = 20
but after that
i dont get how its 26

[native dragon]

mhm

[proper echo]

do we consider (a,b) as (6,4) and (4,6) different?

[native dragon]

yes

[proper echo]

oh well am also getting a total of 20 cases

[native dragon]

yeah

[proper echo]

are you sure that 26 is the correct answer?

[native dragon]

i am