help-0

[glass lichen]

stop saying nonsense

it's asking for the rth, read the question

[ashen agate]

im bad with theoretical questions like this

[candid thistle]

This isnt theory

[glass lichen]

it's just a pattern, again.. that ive spelled out for you

[candid thistle]

It's just counting :/

[glass lichen]

.

[ashen agate]

what does it mean by rth tile

[glass lichen]

the rth choice.

[candid thistle]

If you have 10 items and you have picked out 6th items, how many are going to be remaining for you to choose for your 7th one

[glass lichen]

like how 1st means... first

rth means the rth one

[ashen agate]

does it start with r?

[candid thistle]

no, r is a variable

damn this geometry problem is hard :/

[ashen agate]

3-r?

[candid thistle]

Where did the 3 come from

Do you know how many tiles there are?

[ashen agate]

no

[candid thistle]

Then where did the 3 come from?

[ashen agate]

idek then should it be 2-r since u picked 2 tiles

[candid thistle]

(Please don't guess, think about that)

[candid thistle]

You havent picked out 2

If you are picking out your rth tile, how many have you already picked out?

That would help

[ashen agate]

3 tiles

[candid thistle]

What is r equal to, exactly?

[ashen agate]

4th tile?

[candid thistle]

No

Do you know what variables are?

It's a constant that you don't know the value to

Perhaps ask someone in person, itll be easier to explain than asking digitally.

Is it possible to find the area of a triangle from the semiperimeter and the inradius of the triangle??

Or am I just wasting my time by doing that? Perhaps I should try a different approach

[ashen agate]

@candid thistle n-r-1?

or n-(r-1)

[warped phoenix]

Hey guys do you think 3 days is enough time to review the entirety of the Algebra 2 course?

[candid thistle]

I can't simply say :P
Think about if and if you think you are sure then answer the question

[candid thistle]

wth I take 3 hrs to solve a problem and you're gonna go do alg 2 in 3 days

I don't think it is nearly enough t understand everything about that course but if you manage to pull it off then congrats you're a madman :P

[ionic jewel]

if you knew the content and are reviewing - maybe

[warped phoenix]

yeah

mb

[ionic jewel]

if you are trying to learn it all, no

[warped phoenix]

i should havbe calrified

[ionic jewel]

okay then its definitely possible

[warped phoenix]

i meant that

its review

ok, ty!!!!

[candid thistle]

Ahh if you werre learning from it, then I would think you are crazy
If it is review, go for it

(So you already have learnt most of the stuff in the course?)

[warped phoenix]

btw, do you know any good resources for review?? Right now I'm just using Khan Academy's mastery course and then reviewing what I get wrong off of that, but I'm not sure if there's something out there better

[warped phoenix]

hahahahah yeah i just took a summer course for it, i barely finished it in 2 months

2 months was the deadline

i was like 2 weeks behind at one point

[candid thistle]

Ahh KA's one is kinda doable, not that hard

[warped phoenix]

it was a miracle i cought up while keeping an A

[candid thistle]

(or not alg 2 but in general)

[candid thistle]

damn the procrastination got to you huh

I hate that :(

[harsh steeple]

how can i prove that △BED is congruent to △KEC, if i know that △KBD is congruent to △BKC, △KBE is an equilateral triangle and ∠BDK = ∠BCK? is there a way to write that you can just "subtract" off the shared △KEB?

[candid thistle]

Hmm, what parts of the circle are BED and KEC touching?

First off, what is one property that the two triangles have similar?

What stuff do you know are similar?

[harsh steeple]

ΔBED ~ ΔKEC, ΔKBD ~ ΔBKC

[candid thistle]

But you have to prove the first part

[harsh steeple]

no, i already know that ΔBED ~ ΔKEC

[candid thistle]

Oh ok

what are you trying to prove then?

[harsh steeple]

i need to prove that ΔBED is congruent to ΔKEC

[candid thistle]

Ahh

Well you could actually subtract out

That's way simpler than what I had thought

[harsh steeple]

my problem is i have no idea how to do write that

"formally"?

[candid thistle]

Actually I think you did prove it, subtracting out KEB would work right?

[harsh steeple]

it would but, how do u write it haha

plain subtraction?

[candid thistle]

Ahhh I dont know either

[candid thistle]

ig?

[harsh steeple]

😂 alright

just wanted to confirm

[candid thistle]

honestly I should not be the person to ocme to for help for how to write stuff

I end up dragging out my proofs to be longer than harry potter :/

[harsh steeple]

haha

[alpine sable]

super confused o this one

why Pt instead of Pr or just P

[red phoenix]

we want to mek to r = something

So we need to remove Pt from the r side

[candid thistle]

You are trying to isolate r

[alpine sable]

i looked at the answer key to this question but I still don't understand some steps

[celest anvil]

so basic exponent rules here. calculate the product inside the parentheses, divide by the denominator, then calculate for the exponent

[celest anvil]

which part is confusing?

[alpine sable]

this is the answer key

k so

let me write what is confusing

At the part where it shows the -1

under the 5^4

when it goes to the next step

how did they get rid of the -1

[celest anvil]

because taking a number to an even power makes it positive

so they did 5/-1 =-5 and -5^4 becomes positive then you take the power of 2

which is just 5^(4*2)=5^8

[alpine sable]

how did -5^4 become positive

[celest anvil]

let's do it this way

-5^2=-5*-5=25

-5^3=25*-5=-125

-5^4=-125*-5=625

you see a number to an even power always becomes positive?

so 625^2 is same as 5^8

[alpine sable]

OHHHHH

wait

yeahhhh

because like the power is completely separate from the number

????

i mean the negitave

not power

like its kind of like -(6)^4

you put in the neg after everything kind of

[celest anvil]

nope you keep the negative cause that's the sign

you know negative * negative becomes positive right?

[alpine sable]

yeah

wait so the rule is, any negitave number with a positive exponent is always positive?

wait so back to this

im confused because like when they got 5^8 from 5^4 from the exponent 2, dont you have to apply the exponent to the base (5) as well?

or just the exponent

[celest anvil]

so the reason why 5'4 went to 5'8 is because when you take an exponent of an exponent, it multiplies instead of adding

so 5^8=5^4*2

[celest anvil]

any number with a even exponent

[alpine sable]

i know i mean like, how come you didnt multiply 2 by 5

[celest anvil]

because 5 isn't an exponent

[alpine sable]

oh

ty for the photo btw<

and tysm for the help

i will try and do it now (:

[celest anvil]

[wintry vortex]

I did COS(25.29 Degrees)=H/7616 and got H=6886

Then Sin(25.29 degrees)=0/6686 and got O= 2916

What did I mess up on?

Ugh I dont see what I did wrong, i just did the rpoblem again and got the same answer

[strong falcon]

Sin is opposite over hypotenuse (SOHCAHTOA), so sin(25.29 degrees) should equal x/7616

[topaz wedge]

What’s the best way to minus 1 unvigintillion minus 1?

[limpid spade]

calculator

[wintry vortex]

what did I mess up on?

sorry if my handwritting is alittle bad haha

[gray isle]

you didn't interpret the angle of depression properly

actually

...

can you draw a better diagram

[wintry vortex]

i can try xD

omg i think i just found my mistake

nope

i did not

634.06 is also wrong

[gray isle]

why are you drawing your diagram rotated?

[wintry vortex]

idk haha, does the rotation of it matter? Is that whats messing me up?

if it is thats hilarious

[gray isle]

well an incorrect Orientation may end up confusing yourself

However the issue with calculations here is that aren't giving your answer to the nearest tenth

[wintry vortex]

ffs your right, where does it say nearest tenth? 0_0

oh it does

https://tenor.com/view/i-am-one-with-the-force-force-is-with-me-star-wars-gif-18534817

[gray isle]

unless you have a really good reason... the "horizontal" should be more or less horizontal in your diagram

[wintry vortex]

i didnt have a good reason, just kinda drew it lol

[candid thistle]

If all three lines are angle bisectors (lol bad drawing) would x = 2y

If so, how could I prove it

(perhaps with similar triangles?)

I know that the area of all 6 triangles are equal

[oak chasm]

What are x and y referring to? They're close to multiple sides and some angles.

[candid thistle]

oh one sec

red = y, blue = x

[oak chasm]

@candid thistle OK, looked into it. The point where the angle bisectors meet is called the incenter.

[oak chasm]

@amber spindle Sorry, channel is busy.

[amber spindle]

Okie , i send to another

[oak chasm]

The distance from the incenter to an angle is the length of the bisector (x + y) times the sum of the lengths of the two sides next to the bisected angle divided by the sum of the lengths of all three sides (https://mathvox.com/the-distance-from-the-vertex-to-the-incenter-formula-1/).

[candid thistle]

ok

[oak chasm]

So, (x = (x + y)(a + b)/(a + b + c)).

[ocean seal]

Chai T. Rex

[gaunt magnet]

hi

[candid thistle]

ok

[oak chasm]

x/(x + y) = (a + b)/(a + b + c)

[candid thistle]

okay

[oak chasm]

Now you think x/(x + y) = 2/3

[gaunt magnet]

$x/(x + y) = (a + b)/(a + b + c)$

[ocean seal]

Usman

[candid thistle]

so that means that x = 2, y = 1?

or a scaled up version of that

so yea

[oak chasm]

So, the triangle would probably have to be equilateral.

[candid thistle]

ah ok

[oak chasm]

Because the two triangle sides next to the angle have to be 2/3 of all three sides of the triangle.

[candid thistle]

ok

[oak chasm]

Hmm, not exactly.

Let's see.

The side length opposite the bisected angle has to be the average of the other two side lengths.

There.

[candid thistle]

ok

[oak chasm]

(a + b)/(a + b + (a + b)/2)
(a + b)/(3(a + b)/2)
2/3

Yeah, so that's the general solution if you want x to be twice as long as y.

[candid thistle]

okay thank you

[oak chasm]

No problem.

[tight locust]

how do you eat water?

[sudden crypt]

freeze it

[oak chasm]

You mix it with food powder.

[candid thistle]

about me ;)

[sudden crypt]

but idk about "eat"

[candid thistle]

(real)

[oak chasm]

Sometimes, I eat liquid food. I guess it's not pure water, but.

[tight locust]

yeah you don't really crunch down on an ice cube more just suckle on it until it melts

[candid thistle]

crunching it down is better

[tight locust]

i guess if you "eat" a popsicle though then you can eat ice

[wintry vortex]

Im alittle lost on this solution if anyone could help clear it up

This is the actual question

[tight locust]

given two points (a,b) and (c,d) the slope of the line between them is (d-b)/(c-a)

you can take that as axiom

i'm pretty sure this is one of euclid's postulates

you can't really prove the slope formula because it is the definition of slope itself

[wintry vortex]

well with their formula i got -0.8/0.5=0.8/-0.5

[tight locust]

for which one

[wintry vortex]

which idk how thats helpful lol. Is there another better to find the slope?

[oak chasm]

@tight locust The last image.

[tight locust]

it's just basic arithmetic man. find d-b, then find c-a. then divide

[oak chasm]

Now make the fraction have integers.

Or divide and use a decimal.

[tight locust]

multiply by 10/10

10/10 = 1 so the equality will still hold

[wintry vortex]

ty 🙂

The way they worded that solution was just confusing the hell outa me

[cinder sundial]

Is it possible to get the N’s value

I tried it myself, it seems impossible

[vale wigeon]

8N = S, 32N = S+120?

how is it impossible? just subtract the two equations and you get 24N = 120

[cinder sundial]

let me try

N=5

S=40

[vale wigeon]

i think you lost sight of the fact that these are linear equations in N and S simply because the coefficients on N were written as powers

[cinder sundial]

what if i got equation(1): n * 2^13, equation(2): n * 2^15

can i divide them

i was tryin to divide them

[vale wigeon]

i mean, you could divide them, you'll get (S + 120)/S = 4

which you can solve for S and then use that to get the value of N

you can also subtract them instead and get (2^15 - 2^13)N = 120

or 3 * 2^13 * N = 120

[cinder sundial]

2^15-2^13

im not sure what it is

[vale wigeon]

2^15 - 2^13 is 2^15 - 2^13

if need be, you can write 2^15 as 4 * 2^13 to simplify it to 3 * 2^13

[cinder sundial]

got you

(S + 120)/S = 4 seems like those Ss will cancels each other out

if they cancels each other out, then i cant find S'svalue

[vale wigeon]

no they won't

you can't cancel out from a sum

[cinder sundial]

let me try

seems like i can

[vale wigeon]

no you cannot cancel like this

[willow wadi]

i take channel

Pikaboo

[vale wigeon]

@willow wadi this channel is busy

[willow wadi]

no please

ni

no

😭

[vale wigeon]

@cinder sundial well now that isn't some bullshit cancellation, thank god

[cinder sundial]

but it seems like i can

its legal to cancel them out

[vale wigeon]

no

[willow wadi]

Please watch the language

[vale wigeon]

it is not legal

[vale wigeon]

lmao who are you to tell me

[willow wadi]

good question

[vale wigeon]

i can swear like a sailor if i so desire

also you're being disruptive rn

[cinder sundial]

i remember i did sth familiar like this before

[willow wadi]

Im ur friend

[cinder sundial]

let me give you an example

[vale wigeon]

you must be confusing me for someone else. we aren't even acquaintances.

[cinder sundial]

yes its illegal

[willow wadi]

im ur classmate

we go to the same university

[cinder sundial]

it should be 4/3 instead

[willow wadi]

dont u know me

[vale wigeon]

is that so

[cinder sundial]

"you can't cancel out from a sum" its true

the question is solved now

[dreamy cedar]

@willow wadi please move out of this channel while people are trying to use it for help

[cinder sundial]

thank you @vale wigeon

[willow wadi]

same with u

move out

[sly mantle]

muted

[vale wigeon]

what an idiot

[gaunt magnet]

can i get help

[cinder sundial]

yes

this channel is free

[gaunt magnet]

good

who gonna carry me

@sly mantle hi i need active role

because im active mod

the blue role

[sly mantle]

active role is automatically given based on server activity

[vale wigeon]

you will get it in due time

[gaunt magnet]

ok

then

[wind bane]

what have u tried so far?

[gaunt magnet]

i know we will start off as

$y=f'(1)(x-1)+f(1)$

[ocean seal]

Usman

[wind bane]

great, so you just need to compute f'(1) and f(1)

[gaunt magnet]

yea then

$y = 5/6 (x - 1) - 1$

[ocean seal]

Usman

[wind bane]

if you havent made any computational errors, then you're done

[gaunt magnet]

no because

shouldnt

i simplify that

[wind bane]

uh, ig you could. as its written its perfectly fine

[gaunt magnet]

if i simplify i get 5x/6-11/6

[ornate wharf]

i have a quick question

for completing the square (quadratic equation) i identify b#, halve it and then square it

what if b# is negative, do i include the negative?

for example r^2-3r=1

(3/2)^2 or (-3/2)^2?

[oak chasm]

They're the same.

[sand jetty]

it does not matter

[oak chasm]

Both are 9/4.

[ornate wharf]

ok thanks

[final bane]

2+2

[covert berry]

a, b, c are positive real numbers. Prove:

I have tried using AMGM on the RHS and prove the new term is lesser or equal to LHS, but didn't work out.

[woeful pulsar]

looks like calculating differences, shouldn't be too hard

[hardy mirage]

Umm how can I solve this?

[oak chasm]

@hardy mirage Sorry, the last question hasn't finished yet. It looks like #help-8 is open.

[hardy mirage]

Ok, I will move to there

Sorry for interrupting

[ionic jewel]

why is it urgent

[warped phoenix]

how do i do this?

ive gotten the equation as D(t) = 0.2 x sin(b*t) + 1

now what?? how do i find b?

[fickle latch]

key word

maximum height

at t=0, it's at the middle of the oscillation

at t=pi/4, it's at the maximum height

what conclusions can we draw from this?

[warped phoenix]

1 sec

[fickle latch]

That's a pretty long second

[warped phoenix]

srry 😦

im back now

[fickle latch]

ok

[warped phoenix]

so at t = 0

its at the midline right

since its at the middle of the oscillation

and at t = pi/4, it's at the peak of 1.2

[fickle latch]

ye

so

[warped phoenix]

um

[fickle latch]

just as a hint

you should be able to get both frequency and period from this

[warped phoenix]

well i mean

[vale wigeon]

those last three terms should be subtracted rather than added

[gaunt magnet]

hi

[fickle latch]

hewwo uwu

[gaunt magnet]

hi

question

[fickle latch]

what's your question soldier

[fickle latch]

differentiate and plug in

there should be a formula in your textbook somewhere

[gaunt magnet]

yes got x-3 after doing that

[fickle latch]

yes and your question is?

[graceful river]

dont quiet understand what the q is asking tbh

[fickle latch]

do you know how to find the distance between the curve and (4,1)?

[graceful river]

idk what that means

like between what point of the curve

[fickle latch]

okay rephrasing a bit

How far is the curve from touching the point?

[warped phoenix]

is this somewhat right?

[graceful river]

oh the horizontal distance?

[warped phoenix]

srry it took me a sec to draw it

i got confused lol

[fickle latch]

the distance distance

@warped phoenix It's a liitle bit off but I guess it captures the idea

[graceful river]

4 units to the right and 1 unit up

wait no

[fickle latch]

I guess I should draw it out

[graceful river]

oh

3 units to the right

?

[fickle latch]

Intuitively, this is how far the curve is from (4,1)

[graceful river]

oh

so the closest distance

[fickle latch]

Yeah

[graceful river]

between the curve and (4,1)

...

[fickle latch]

Now, what is the x coordinate of the point on that curve that is closest to (4,1)?

Is what the question is asking

[graceful river]

no clue

[fickle latch]

god dammit

[graceful river]

lol

[fickle latch]

Google it then

equation for closest distance

[graceful river]

https://www.youtube.com/watch?v=YbHOzJIHS1k

?

this?

[fickle latch]

https://math.stackexchange.com/questions/2264702/shortest-distance-from-point-to-curve

This should help

[graceful river]

oh

is it the point that makes a perpendicular line to the tangent of the poibnt on the curvbe?

[warped phoenix]

well

the frequency and period are there

right

i think

cuz frequency is just how many times it repeats right

from going from 0 to 2pi

or is that period

[fickle latch]

yeah probably

@warped phoenix Guess the period

[graceful river]

now the problem is i still don't know which x coord that gives the tangent which tne forms a perpendicular line with (4,1)

[fickle latch]

https://math.stackexchange.com/questions/2264702/shortest-distance-from-point-to-curve read solution 1

[graceful river]

oh

nvm

[fickle latch]

That should give you an idea

[graceful river]

i got it

wow its that straight forward lmao

[fickle latch]

Yes

yes it is

[graceful river]

so after symplifying the ans is

can u check for me pls?

[fickle latch]

uh

no

and besides

you're supposed to find a value for x

[graceful river]

yeah

i squared it

and diffed it

then set it equal 0

and x is 1.39

i followed the website guide u gave me

[fickle latch]

yeah that's about right

[warped phoenix]

im not sure....

its from that bottom peak

to the next bottom peak

right

[fickle latch]

Okay

okay

how many cycles does it take to go from peak to peak?

[graceful river]

ok cool

thank you

[vale wigeon]

have you made any progress on this so far?

dear god

that's just signing yourself up for a million arithmetic errors left and right

have you tried gaussian elimination?

$\left[\begin{array}{ccc|c} 1 & -2 & -1 & 2 \ 2 & 1 & -2 & 0 \ 3 & 4 & -3 & c \end{array}\right]$

[ocean seal]

Ann

[vale wigeon]

i have deliberately rearranged the equations somewhat to make the first elimination step easier

you mean -2R1 + R2 -> R2?

yes, sure, you can do that

doublecheck your right-hand side

you will get 5y = -4

would you like to take a convenient shortcut that just presented itself?

we basically just got the value of y for free.

y = -4/5

we can use that to rewrite the other two equations as:
x + 8/5 - z = 2
3x - 16/5 - 3z = c

simplifying, we get:
x - z = 2/5
3x - 3z = c + 16/5

thus for the system to be consistent we must have c + 16/5 = 3 * 2/5

well 3x - 3z = 3(x-z), no?

[warped phoenix]

1?

i mean cuz like 1 cycle gets it back to where it started

[fickle latch]

ye

how about valley to peak

@fringe robin I was working on that

[fickle latch]

good boy

[fringe robin]

[median osprey]

Hi

can someone please help me to revise log rules

i forgot them

for the question above do we do bring the powers down and then put ln to cancel e?

[fickle latch]

pi/2 - 2 via wolfram

must be black magic for pi to show up

[median osprey]

oh sorry i thought its free channel

[fickle latch]

$e^{a+b} = e^a \cdot e^b$

[ocean seal]

COVER Corporation

[fickle latch]

@median osprey

[median osprey]

where can i find these rules?

can you recommend me a website

[fickle latch]

Wikipedia

I dunno it's everywhere

[median osprey]

whats the keyword to find them

[fickle latch]

Google exponentiation rules

Or exponentiation properties

[median osprey]

thank you

found them

[fringe robin]

not anymore

[fringe robin]

is this your answer?

[fickle latch]

ye

[fringe robin]

ill check

oooo got it thanks

[surreal meadow]

[dire patrol]

help

<@&286206848099549185>

[fringe robin]

use the y=xtan theta formula

[dire patrol]

huh

whats the working out

i created two equations

y=10 and y dot = 0

and then i did simultaneous idk

im not geting the answer

[placid zinc]

Are those the equations you created?
Try creating one for height at time t, and another for horizontal distance at time t

[dire patrol]

ye

x=vt cos theta

and y=-5t^2+vtsin theta

and then i created two equations

0=-10t + v sin 36

and

10=-5t^2 +vtsin36

in the question is 10m not the max height?

[placid zinc]

No. Merely that the projectile passes through (20,10)

You don't benefit from taking a derivative

[dire patrol]

fgk

ok

i thought 10 was maxheight

hm

i found distance of the particle

i dont know how that helps though

how am i menat to use that

to find velocity

[placid zinc]

What is "distance of particle"?

[dire patrol]

idk

i used pythagorus

[placid zinc]

The projectile passes through (20,10). Plugging that point in, you have these two equations:
20 = vtcos(36)
10 = -5t² + vtsin(36)

That's two equations with two unknowns, it should be possible to get both v and t here

Of course you only want v

[waxen furnace]

anyone get the wording on D?

I graphed the first histogram but I have zero clue on what it's asking me

[surreal meadow]

@waxen furnace this channel is being used rn

[waxen furnace]

oh my fault

which one do I use

[dire patrol]

ye @placid zinc

i cant solve that

its impossible bro

[surreal meadow]

find one which isn't being used

[waxen furnace]

ight

thanks

[surreal meadow]

do you know how to solve a system of equations?

[placid zinc]

@dire patrol
Take the first equation:
vt = 20/cos(36)

Use that in the second:
10 = -5t² + (20/cos(36))sin(36)

And now it's easy

[dire patrol]

ye but sub it in

its so messy

i couldnt simplify to get v by itself

i got some random quadratic with sine and cos

[placid zinc]

Rewriting that last line:
t = √[2 - 4tan(36)]

Then sub that back into that first line I wrote:
v = 20/tcos(36)

[gaunt magnet]

intresting

<@&286206848099549185>

[gray isle]

what u try

[gaunt magnet]

oh no ur gonna ask how i did it

i got y=x-3

dont ask how

[sharp sigil]

Differentiate plug value get slope and put into y=mx+c and plug in point and get c done.

[gaunt magnet]

yes y=x-3
me right?????????????????????????????????????

[gray isle]

what's making you unsure of your answer?

[gaunt magnet]

nothing bcuz, my answers are mostly right

i will always double check

them

[gray isle]

so why the ping and do you actually need help with this?

[gaunt magnet]

the ping was to bring u to tell me if my answer was correct thats all

[alpine sable]

#❓how-to-get-help

[gray isle]

yes it seems to check out

[gaunt magnet]

yes i will check that

[alpine sable]

^ but please ping helpers after a while if no one answers

[gaunt magnet]

yes

[gray isle]

though you can check whether its correct using other resources

[gaunt magnet]

you could just say its correct by now

🥱

im waiting

[alpine sable]

[surreal meadow]

@gaunt magnet

[gaunt magnet]

ok thanks

i will read how to get help

very soon.

[rugged nexus]

How do you do this question

?

[placid zinc]

From the first line:
y = 9 - x

Sub that into the second line

You'll get a quadratic in x, solve as you would

[rugged nexus]

Yes I did that but

What’s the answer you’re getting tho

Because I’m getting an answer that has a simple i

What does that mean?

[gray isle]

can you show your work and solution

[sudden crypt]

always solving for one variable and plugging in smh, that's how you get complex solutions on accident. The way to solve these kinds of questions is to evaluate the expression without knowing what x and y are on their own

oh nvm I overlooked the = 0 in the second equation

[rugged nexus]

Is this correct ?

[ornate grove]

In terms of the
,
,
coordinates of a fixed space frame {s}, the frame {a} has its
-axis pointing in the direction and its
-axis pointing in the direction , and the frame {b} has its
-axis pointing in the direction and its
-axis pointing in the direction . Draw the {s}, {a}, and {b} frames, similar to examples in the book and videos (e.g., Figure 3.7 in the book), for easy reference in this question and later questions.

Write the rotation matrix . All elements of this matrix should be integers.

Could you please explain how problems solve 🥺

[alpine sable]

Anyone have time to explain a somewhat complex problem regarding possion distributions ?

[strong carbon]

Does (f - g)(3x) equal to 9x^2 - 3x if (f - g)(x) = x^2 - x ? Are there any tricks or can we just replace like that

[unreal valley]

15 cm and 4 mm in mm is 154 mm right?

PLEASE TELL I HAVE TO SUBMIT THIS IN 30 MINS

10 more left plssss tell

[gloomy lintel]

When it’s f(3x), it’s a stretch horizontally of scale factor 1/3

[unreal valley]

can u tell

[strong carbon]

Busy, quit spamming please

[unreal valley]

ohk

sorry

[strong carbon]

I don't get this part

[gloomy lintel]

Wait never mind I got confused lulll,

F(3x) means a stretch horizontally scale factor 1/3

Is what I was trying to say

But yes it’s still subbing in

3x

For x

[strong carbon]

So how do we find (f - g)(3x) if (f - g)(x) is given

[gloomy lintel]

Sub in 3x whenever you see an x

So (3x)^2 -3x

[strong carbon]

Oh so it 9x^2 -3x

Thank you

[alpine sable]

is it a test question?

[unreal valley]

no i need help with homework

[alpine sable]

why would it be 154?

[unreal valley]

idk

[alpine sable]

then how did you get this number

[unreal valley]

f i remember

its 1540

[alpine sable]

why would it be 1540?

[unreal valley]

idk

[alpine sable]

then how did you get this number

[unreal valley]

i multiplied it

[alpine sable]

why

[unreal valley]

....

[alpine sable]

just look up in your notes or book

what is cm

[unreal valley]

centimetre

[alpine sable]

yeah but how many milimeters is 1 centimeter?

check your notes

or book

[unreal valley]

10

[alpine sable]

yeah

so how many milimeters are in, for example, 5 centimeters?

[unreal valley]

50

[alpine sable]

yeah so how many milimeters in 15 cm and 4 milimeters?

[unreal valley]

154

[alpine sable]

why?

[unreal valley]

15 cm = 150 mm + 4mm = 154 mm

[alpine sable]

yeah exactly

see, you can do it on your own

[unreal valley]

phew thanks

[alpine sable]

no need to spam

[unreal valley]

okk

thanks

[alpine sable]

next time I will ban you if you spam

[unreal valley]

ok sorry

[alpine sable]

all good

[sage bronze]

https://tenor.com/view/facitlities-f-or-that-big-man-big-shaq-interview-gif-17777771

but if u do im sorry dont ban me

[alpine sable]

You really think a 'Role that does nothing' really wouldn't do anything?

[sage bronze]

[strong carbon]

@gloomy lintel sorry for bothering again but can we find the value of f(6) by writing x = 2

if f(3x) = 9x² -x is given?

Does it work that way?

[alpine sable]

ye

[gloomy lintel]

Yes that’s fine

Wait

[alpine sable]

ye its fine

move forward sir

[gloomy lintel]

Ye Lol I was getting myself into a trap then lull

[alpine sable]

same

probably same trap

[tranquil yoke]

Hi I had a question like dis and it said find x it was on MN and it had radical numbers behind x or something idk how to really explain it :/

I'm trying to give an example but I don't really remember how it was written

[limpid spade]

Thales theoem?

[tranquil yoke]

This is the midpoint theorem

[limpid spade]

does this help

[tranquil yoke]

Yes kinda but the question had find x and x was on MN but there was a radical number behind √.. x something like this

If u can't help it's ok my friend can help but he is sleeping rn ;-;

[sterile beacon]

help please 😦

[cobalt coyote]

Could anybody please explain how the derivation of those christoffel symbols came I'm some confused while deriving those for polar coordinates

[cinder lily]

permutation cycles

[sterile beacon]

@cinder lily https://groupprops.subwiki.org/wiki/Cycle_decomposition_for_permutations

yes, I found it

[red phoenix]

Its just the levi-civita connection no?

Plug in the metric and you're good to go

[cinder lily]

awesome

[alpine sable]

When working with Rieman sum in Definite intergrals, is dx always dx = (b-a)/h or can the formula change?

[red phoenix]

the way things are specified, I cannot think of any other way to write dx.

[jagged raptor]

thats what Δx is

[alpine sable]

Okay

I got another question

Can you use the fundamental theorem of calculus to solve most intergral problems? Or does it only work on accumulation functions?

[quaint pond]

hey, could someone help me understand the solution to this problem:

[noble sinew]

what about it

[quaint pond]

i just dont know

how to solve it

i know the answer

[noble sinew]

start with figuring out what j's have a non zero probability

[quaint pond]

but i dont understand it

[noble sinew]

.

[quaint pond]

dont they all have non zero probability?

[noble sinew]

how would I get 1 correct?

is that possible

[quaint pond]

well

no'

yeah because

but

say i have cards abcd

and i guess a is green and b is green

if only 1 of my guesses is right

say a is green

then isnt it possible?

[noble sinew]

read the text again, you will then be saying c,d is not green

one of those will indeed not be not green

[quaint pond]

oh yes

so then yeah 1 is not possible

[noble sinew]

so what j's are possible

[quaint pond]

well 0

2

4

i guess if 1 is not possible

[noble sinew]

indeed

[quaint pond]

then 3 isnt too

okay so i know

there are

4! ways to arrange the cards, right?

@noble sinew

[noble sinew]

sure if you count the same coloured ones as distinct

but can just do, what is the probability of guessing 1st one correctly? That is 2/4. What is probability of guessing 2nd one correct. That is 1/3. So P(J=0)=P(J=4)=2/4 * 1/3=1/6

[quaint pond]

why is the second one 1/3?

[noble sinew]

Say you have two black cards and two red cards. If you guess 1st one correctly (black) there is only 1 black left and 3 cards in total

[quaint pond]

okay

i think i got it

for 0,4

but for 2

using the same logic

that would be: 2/4*2/3 ?

[noble sinew]

1 = P(J=0) + P(J=2) + P(J=4) is one way. Otherwise P(J=2)=2/4 * 2/3 * 2 (2 ways to arrange it)

[quaint pond]

wdym

2 ways

to arrange it

[noble sinew]

I can get either get 1st correct and 2nd wrong or 1st wrong and 2nd correct

But you also know sum of probability of all possible outcomes must be equal to 1, which is why you know 1 = P(J=0) + P(J=2) + P(J=4)

[quaint pond]

yeah makes sense now

thanks

[cobalt coyote]

Anybody please help me

I finally got this answer

How to find modulo of theta vector in polar coordinates

[alpine sable]

hi
I am working really hard to score well. I used to study from 5 pm to 1pm (recently learnt that its gonna have long term effects and stopped).Yet I am not able to always score well .My marks are very inconsistent and are unacceptable imo .Can anyone please suggest any strategies or habits that i shall develop in order to top or score extremely well (out of experience)?

would be really helpful and would make a world of difference

@alpine sable what are you trying to score on tho, plus I dont think this is the place for your question

probably #math-discussion

[alpine sable]

ohhk im sorry about that

I mean you can still ask tho @alpine sable

what book is this 👀

[keen jasper]

discrete mathematics

[alpine sable]

oh okay

I was trying to solve a relativeistic dynamic problem and I notice that something might be wrong with my conception of relativistic momentum
I have a particle with resting mass m that is moving at a certain speed u and bumping into antoher particle stationary and with the same mass. They are supposed to get together as a single body and I'm asked to find the final resting mass
now conservation of momentum gives me that the final momentum should be $m\gamma(u)u$ but how do I find the velocity the body is moving after the bump? Do i need to use conservation of energy too?

[ocean seal]

Stephen

[alpine sable]

The physics discord is a better place to find an answer

[lusty hull]

Let there be a group of n men where every man has one hat. The hats are redistributed and every man gets a random hat back. What is the expected number of men that get their original hat back?

My approach is

E[n]= expected number of people that get their hats back out of n men 
E[n]=P(1st guy gets his hat back)(1+E[n-1]) + ((n-1)/n)(E[n-1])
E[n]=1/n+E[n-1]
But this gives wrong answer, where am I going wrong here in this recurrence?

[noble sinew]

should be very simple by just using that expectation is linear

[oak chasm]

@lusty hull Well, take n = 2.

E[1] = 1

[lusty hull]

yes

[oak chasm]

E[2] = 0.5(1 + E[1]) + (1/2)E[1] = 0.5(2) + (1/2)1 = 1 + 1/2 = 3/2.

But this isn't the expected number of people with 2 people.

Either both get their hats or none do.

So, the expected number of people is 1.

[lusty hull]

Yea makes sense, actually I know that my answer is wrong, but I am not sure what the correct recurrence would be

[lusty hull]

Yea it can, but I am thinking of a recurrence realtion

[oak chasm]

OK, so you have the last expected number.

You add one more person.

Let's see.

[noble sinew]

why tho - its legit just n * 1/n=1 using that fact

why make it more complicated

[oak chasm]

OK, let's try 3.

[lusty hull]

yea

[oak chasm]

(1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), (3, 2, 1)

(3 + 1 + 1 + 0 + 0 + 1)/6 = 1

[alpine sable]

hi

[lusty hull]

I think I found my mistake

I am unknowingly making the assumption that each person receives a random hat one by one

[alpine sable]

hi

[lusty hull]

So this would mean that the probability of each person getting the correct hat is no longer 1/n

But in reality it is

[lusty hull]

Thanks

So in my original solution if I just treat 1/n constant rather than a function of n, then I believe I would get the same answer

[dense blaze]

,tex $(p \ \vee \sim q) \wedge (p \vee q)$

[ocean seal]

sevenseas

[dense blaze]

can i ask if there's any way to simplify this, to eventually equate it to p?
this is under logic equivalence

,tex the original proving qn was
$\sim (\sim p \wedge q) \wedge (p \vee q) \equiv p$

[ocean seal]

sevenseas

[dense blaze]

but i simplified it using De Morgan's

[regal zinc]

pls help

[oak chasm]

@regal zinc Please don't post to multiple channels or when a question is still open. See the rules at #❓how-to-get-help.

[dense blaze]

umm i think u sent it in #help-2 already?

[regal zinc]

ok

sir

[regal zinc]

i am new in this server

sorry

[dense blaze]

its okay

[regal zinc]

so will u help me pls

[oak chasm]

@regal zinc You have to find a channel that's not busy. Check whether the last messages say they're done or whether the last timestamp next to chat was more than 30 minutes ago.

Looks like #help-9 is open.

@dense blaze

[ocean seal]

Chai T. Rex

[light magnet]

Hi im not sure if this is really related but lets say i have this uncompleted morse code sequence x.xx...x.xxx..-xx-.xxxx.-.-xxx.-.x..x.xxxx..x.xxx.-.-.xx-.-xxx..-.xx.x.x.--x.xxx. Im supposed to fill in the X's either a dot or a line, can anyone tell me how many possible combinations are there? and how exactly did they get to that number?

[oak chasm]

@light magnet Are there two possibilities for each x?

[light magnet]

yes

[oak chasm]

OK, so let's take two xs.

How many possibilities are there for that?

[light magnet]

4

[oak chasm]

List them off.

Right.

OK, let's take three xs.

How many possibilities are there for that?

[light magnet]

quite a lot lol

[oak chasm]

Well, list them off.

...
..-
.-.
.--
``` What else?

[light magnet]

---
--.
-..
-.-
...
..-
.--
.-.

[oak chasm]

OK, now there's a pattern here.

[light magnet]

yea i see

2^number of xs

[oak chasm]

Right.

[light magnet]

thanks

[oak chasm]

No problem.

[dense blaze]

@oak chasm i have issues with the sign
i only learn to use distributive law for p Λ (q V r) ≡ (p Λ q) V (pΛr). Hence, im confuse when theres conflicting sign for
(p Λ p) V (p Λ q) V (p Λ ~q) V (~q Λ q)

i have bolded the signs im confused with

[oak chasm]

You have (a S b) T (c S d)

Where S and T are both and or or.

[dense blaze]

yeah

[oak chasm]

(a T c) S (a T d) S (b T c) S (b T d)

See how the T was outside the parentheses to start with?

Now it's inside.

And the S was inside the parentheses to start with.

Now it's outside.

This is like basic algebra.

[dense blaze]

Yeahh

[oak chasm]

(a + b) · (c + d)
(a · b) + (a · d) + (b · c) + (b · d)

Do you still have a question?

[dense blaze]

yeap i finally understand this step thanks sm, but im unsure how the second step (p Λ q) V (p Λ ~q) is simplified to p?

[oak chasm]

Well, let's say q is true.

The first one is the only one that can be true.

It's true when p is also true.

Let's say q is false.

The second one is the only one that can be true.

It's true when p is also true.

So, in both cases for q, the part that can be true is true when p is true.

So, regardless of what q is, the whole thing is true when p is true.

So, it's equivalent to p.

[dense blaze]

Oh right yeahh I get what you mean

Thank you!

[oak chasm]

You're welcome.

@dense blaze Oh, wait.

Distributive property.

[ocean seal]

Chai T. Rex

[candid thistle]

Question: For a right triangle, the diameter of the circumcircle that is drawn around it is just the hypotenuse, right?

[oak chasm]

That's how to do the algebra.

[candid thistle]

What are those weird markings?

[oak chasm]

Those are boolean algebra for logic.

[candid thistle]

Ahh

If you go into light mode you can't even see TeXit's username

[dense blaze]

uh i dont get how this differs from what you said previously?

[oak chasm]

It doesn't, but this is how you show it algebraically.

[candid thistle]

Also using the formula where the radius of the incircle times the semiperimeter = area. We can find the radius of the incircle, right?

[oak chasm]

Like without my long explanation, you can just say distributive property.

@candid thistle Yes, the hypotenuse is the diameter.

[candid thistle]

Why does math have to have extremely confusing and difficult signs for basic elementary school stuff?

[candid thistle]

Thanks :)

[oak chasm]

No problem.

[dense blaze]

ahh okay, is the general approach of logic proving qn is to try to simplify as much as possible with the rules, and then try to deduce/simplify further like what you did here when it no longer fits any rule

sorry im q new to this topic, so quite noob

[oak chasm]

Yeah, it's easier to justify if you can point to a rule.

So that's usually the way to go.

For very complex stuff, you can use a truth table.

[dense blaze]

right thanks again!

[oak chasm]

You're welcome.

[oak chasm]

It's confusing at first, then you have a shorthand way to write about it that lots of people know.

[candid thistle]

Okay

[unique latch]

Man

U guys do hard stuff

I am starting geometry next year

Like when school starts

[glass lichen]

I mean.. it's a server for most branches

So it's expected there to be things above your level

[oak chasm]

@unique latch If you want a head start, Khan Academy is available: https://www.khanacademy.org/math/geometry.

Has video lectures and practice problems.

[dense blaze]

@oak chasm wait i got another qn does Λ or V take precedence, like for example the "operator" in each bracket may be different, and in algebra, - is above +, so like (a-b)(a+b) we take the minus

[oak chasm]

Well, with 1s and 0s for true and false, you have multiplication is and.

And addition is or.

So, and goes first.

And:
0 · 0 = 0
0 · 1 = 0
1 · 0 = 0
1 · 1 = 1

Or:
0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 1

I always put parentheses around the first thing I want to do, though.

To avoid confusion.

[dense blaze]

ohh that makes sense yeah i didnt think of it as this way, this is much clearer

icic yup 👍

[granite narwhal]

can anyone help: identify the equilibrium values. Which are stable and which are unstable? dy/dx=y^2-2y

[unique latch]

Wtf is a lecture

[oak chasm]

It's like where you're listening to your teacher teach.

[unique latch]

Oh

A lesson

Basically

[oak chasm]

Right.

@desert moon Sorry, channel is busy.

[oak chasm]

Open question

[meager leaf]

here

btw a question I made

i did it by this way

[vale wigeon]

@meager leaf wym by "circle size"?

[meager leaf]

idek, since i forgot how the question was back in 5 grade

[vale wigeon]

well then there is no properly stated question at all

do you mean the radius is 5, or that the diameter is 5, or that the area is 5?

[meager leaf]

the area is 5

[vale wigeon]

so... you have two pieces cut out of it, one whose area is 3/3 (aka 1) and another whose area is 12/8 (aka 3/2)

[meager leaf]

that be 5.5 then

[vale wigeon]

and you are asking for the area of what's left?

[meager leaf]

yes

!

[vale wigeon]

then it's neither 2 nor 5.5

it's 2.5

[granite narwhal]

ok nvm about taht one

but how to do this implicitly differentiate y^2-2y

so d/dx(y^2-2y)

[meager leaf]

@vale wigeon what question can it be

to make my method doing it right?

or u don't know that

[vale wigeon]

i have precious little idea what you're doing in the first place

you're doing some arithmetic, and it seems not only overcomplicated to hell and back, but also looks like it has nothing to do with anything

it... sounds like you wanted to calculate 12/8 - 3/3 but it didn't occur to you at any point to reduce either fraction before doing the subtraction

[dense blaze]

2y(dy/dx) - 2(dy/dx)

[bitter sage]

is this true?

[onyx pawn]

does it hold for f(x) = x^2 ?

[bitter sage]

x^2?

idk what they mean by x0

[onyx pawn]

It's just a variable, could be any value in the domain

[bitter sage]

but is it x times 0?

[onyx pawn]

no

it's just a symbol for a variable

[bitter sage]

ok

so x^2\

critical point is (0,0)

so its f''(0) = 0?

[onyx pawn]

Yeah but f''(0) = 2

[rugged tree]

False. The critical point is when f'(x0)=0 not f''(x0)

[bitter sage]

ok that makes sens

thanks

[onyx pawn]

you're welcome

[bitter sage]

for this question

shouldnt it be that f''(c) = 0?

[onyx pawn]

yeah that looks like an error to me 🙂

[meager leaf]

@vale wigeon i did a mistake

i should have add the 2 fractions and minues the 5

not minus the 2 fractions and minues the 5

my answer is now

-2.5

[rugged tree]

Why are you subtracting 5 from 60/24?

[meager leaf]

60/24 was the given number

[meager leaf]

.

5 is the total of the circle

[rugged tree]

I am asking why are you subtracting 5 when the result is going to be negative? The proper way is to subtract 60/24 from 5, since 5 is the area of the entire circle, right?

[meager leaf]

yes

[meager leaf]

so it is 2.5?

[rugged tree]

Then the proper way is to say the x = 5 - 60/24 = 2.5

[rugged tree]

It is

[meager leaf]

ok thx

u fixed a mistake of mine

[pearl solar]

Help