help-38

[dull temple]

so the answer can't be 0

[marsh vessel]

what do you think it will be

@dull temple it is true for all 2m and n=m so what will be the answer

[dull temple]

i'm not just going to give you the answer, this is your problem to figure out. you asked if it was 0 and it looks like it isn't

[marsh vessel]

is it m

[marsh vessel]

is the answer m just one final help

<@&286206848099549185> is the answer M ways

[wraith hinge]

<@&268886789983436800>

[wraith hinge]

yes it is @

!noans

[trim jolt]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[wraith hinge]

!status

[trim jolt]

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

[wraith hinge]

first show your solution

[marsh vessel]

realllyyy?? thanks, im sending my solution can you check my work

[wraith hinge]

bruh wtf

i dont know

<@&268886789983436800>

[marsh vessel]

you just said this

[wraith hinge]

yes show your solution first

[dull temple]

what do you need

[wraith hinge]

this guy kept asking answer..

girl*

[marsh vessel]

i just wanted to confirm

my answer

[wraith hinge]

that's asking for answers

just recheck

[dull temple]

okay yes use your words first though

[wraith hinge]

if there's any error

then you will know

[dull temple]

we do check solutions for things here especially proofs, but you have to send it

[wraith hinge]

oh sorry.. aight bye

[marsh vessel]

is this good enough

[dull temple]

i don't think your answer makes sense for the question

if i gave you m = 2 and n = 3 it would be impossible right?

[marsh vessel]

no, ive mentioned where there are 2m people and n=m

[marsh vessel]

m=2 and n=1

[dull temple]

n can't be 1

[marsh vessel]

yea, just saw that

[dull temple]

anyway i think your answer should depend on m and n

[marsh vessel]

but in the question it's mentioned n is greater than 1

[dull temple]

and it's asking for the number of ways to seat those people

[marsh vessel]

so my solution still works

[dull temple]

no it.... doesn't? what are you even talking about

what solution

[marsh vessel]

this one

[marsh vessel]

so does it mean if m=6 and n=3 in how many distinct ways can I seat the 6 people?

[dull temple]

yes

[marsh vessel]

the answer will be 0 bcoz they have mention n<m

therefore 6 and 3 won't work out

[dull temple]

what

[marsh vessel]

For a given positive integer m, you have a round table of 2m seats, and m couples attending this party (all 2m people are distinct). Given an odd integer
1 < n < m, you want to seat everyone such that the two people in each couple
are exactly n seats apart (as in there are n−1 seats between them). How many
distinct ways are there to achieve this?

[dull temple]

yeah i know - it's pinned in the channel, you don't have to keep reposting it

[marsh vessel]

oh i didn't know that

[dull temple]

anyway what's the problem with 6 and 3

[marsh vessel]

3 is equal to m we need less than m

[dull temple]

oh right because there are 2m seats

[marsh vessel]

yea

so my initial answer surprisingly turned accurate

[dull temple]

you haven't really proven that

[marsh vessel]

catalan numbers

[dull temple]

what about catalan numberfs

"catalan numbers" is not a proof

[marsh vessel]

yea i read somewhere catalan number for odd number is 0

i need to restudy a bit tho

[dull temple]

great! why is that relevant to this problem?

[marsh vessel]

because n is odd

we will find c(n)

[trim jolt]

@marsh vessel Has your question been resolved?

[vivid glade]

are the people and/or seats considered distinct?

[marsh vessel]

i think so, but there are same number of people and seats

but there's no importance of seats

just the permutations of people

[marsh vessel]

<@&286206848099549185>

[marsh vessel]

.

[vivid glade]

so, question, is this meant to be a formal proof?

[vivid glade]

in response to this image

[marsh vessel]

I guess so but my work is informal

but is my work valid that's the question

[vivid glade]

the catalan numbers have so many plausible origin stories that it's difficult to accept even your first sentence on first blush, because it's stated so brazenly

[marsh vessel]

• non intersecting chords

[marsh vessel]

can you suggest a better way to frame

[vivid glade]

you can make your trailing parenthetical as a recollection of your definition for catalan numbers

make very clear the correlation between this counting problem and that which the catalan numbers count

[marsh vessel]

oh good suggestion but is my solution correct?

[marsh vessel]

yea that's why I added the circle point at the end to make some connections

[vivid glade]

the whole proof is pretty disorganized so I have to talk about the individual chunks. isn't n declared to be odd on the offset? why are we discussing if n is even?

[marsh vessel]

just stating some facts

[vivid glade]

the fact is that n is not declared as even

[marsh vessel]

yes that's why the answer is 0

[vivid glade]

so we don't care

[marsh vessel]

okay I'll note that

[vivid glade]

can you explain in your own words why it's infeasible to seat the couples in the desired way when n is odd?

the image is quite unclear about this and I'm more accustomed to a different environment for catalan numbers to thrive

[marsh vessel]

if you try to seat couples with an even gap between them(n-1) there would always be some seats left unoccupied

[marsh vessel]

.

[vivid glade]

how come?

[marsh vessel]

i deduced it from experimentation

[vivid glade]

counterpoint: A1 - B1 - C1 - A2 - B2 - C2 is a valid couple seating arrangement for m=3 couples with a gap of n-1=2

[marsh vessel]

e.g. A ,B, C, D are couples
gap is of 2
ABCABCDD

[marsh vessel]

n has to be less than m

stated in the question

[vivid glade]

word

A1 - B1 - C1 - A2 - B2 - C2 - D1 - E1 - F1 - D2 - E2 - F2

m = 6, n = 3

[marsh vessel]

oh yea this makes sense

[vivid glade]

they're not n seats apart in both directions

but at least one direction

[marsh vessel]

it's a round table so does that make any difference

[vivid glade]

that's up to the question asker to decide in my opinion

[marsh vessel]

now I'm confused as to what the answer should be

[vivid glade]

I never knew the answer either lol

[marsh vessel]

lol I'm cooked i need to do this question or I'm gone

[vivid glade]

such high stakes?

[marsh vessel]

yup

[vivid glade]

how come?

[marsh vessel]

it's required in my class

i don't how to calculate this what should I do😭

[vivid glade]

I don't think you traditionally get kicked out of an undergrad class for not answering one question

[marsh vessel]

yea but you're insulted

[vivid glade]

you can just ask someone who actually knows the answer for more insight

uhh by who?

[marsh vessel]

im asking on this group since morning no one's telling the answer😢

[vivid glade]

I really mean ask your professor

[marsh vessel]

can you help me with a geometry question

if I do that it will be fine

[marsh vessel]

i think there's some trick required which I'm not aware of

[vivid glade]

I'm confused by what you mean by this but sure

also I found a less trivial assortment of couples that isn't just two copies of the same permutation of couple-bound persons, if that makes sense

[marsh vessel]

okay

[vivid glade]

in A1 - D1 - C1 - F1 - E1 - A2 - B1 - C2 - D2 - E2 - F2 - B2

gaps of 5

[marsh vessel]

yes this makes sense

[marsh vessel]

is there some trick required to do this

[vivid glade]

any more context, such as course material?

[marsh vessel]

nope buddy this is random problem set but I think tangents

even I searched all circle theorems but I couldn't find something like this

i get the intuition that ab might be perpendicular to pq but idk if that's correct or not

[vivid glade]

that's definitely true

[marsh vessel]

how to prove it

[marsh vessel]

<@&286206848099549185>

[marsh vessel]

did you find some clue

[vivid glade]

this doesn't ask for a proof of anything, but I would argue by reflectional symmetry of the circles about the line containing their origins

the reflection action must fix the line segment defined by the intersection points of the circles, by virtue of fixing said points

this doesn't really need justification in my opinion because we already take this for granted in euclid-y (i.e. compass and straightedge) constructions of perpendicular lines in a standard geometry course

but it's still a good question

[marsh vessel]

and how would we proceed after that

i joined pq and ab and constructed triangle APO ( o is the point of intersection)

[marsh vessel]

.

[vivid glade]

also a good question, no good ideas yet

[marsh vessel]

@vivid glade that's okay we both can think some time

[marsh vessel]

does it need some circle theorem?

im trying to find one

[vivid glade]

alright sorry I was being dreadfully slow. I'm able to give hints now

in my defense it's been ages since I've done any geometry but still

the one additional point of intrigue is knowing angle APB

which is indeed in need of an application of some circle theorem

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[dawn tusk]

how would i do this?

[unique minnow]

There's three right triangles in there.

Write down their corresponding Pythagora's Theorem, and try to solve the system of equations for h

[dawn tusk]

oh okay ill try that

[jaunty scarab]

i would use similarity theorem, not pythagoras there.
Notice that all the triangles are similar, since they have the same angles

[unique minnow]

Yeah it would yield the same answer

I just think the system comes pretty nicely together 🙂

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[tiny valve]

Does anyone know a source that proves that k-linear applications are $C^{\infty}$?

[solid kiln]

tales

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[burnt fossil]

should I write all the cases

there must be another way right

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@burnt fossil Has your question been resolved?

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[earnest rune]

hello can someone explain this to me?

This is my answer

[twilit latch]

Your work is a bit unclear

This is supposed to be done using integration by parts

The final answer should not contain f'

Since you don't know much f'

[earnest rune]

yea thats where i was confused

and yes it is integration by paorts

sorry if its confusinfg

[prisma stone]

I found a number as result

[earnest rune]

i can clarify anythign

could u explain to me how u did it?

[prisma stone]

sure, wait a min pls

[earnest rune]

no worries

[prisma stone]

maybe this helps a bit

[earnest rune]

is this via integration by parts?

[prisma stone]

I've concated the two integrations

[earnest rune]

mmm

alr thank you

im js a little confused still

but the final answer is 5+a?

[prisma stone]

nope I just didn't want to send the answer

derivative will cancel the integration etc

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[spiral garnet]

f(x) = ab^t

a=185

b=(150/185)^(1/30)

im getting a negative number for t in part b

[wooden plover]

how did you end up with that expression ?

that log(105) sounds fishy

[spiral garnet]

105=(185*(105/185)^(1/30))^t

$log105=tlog(185*\frac{105}{185}^{1/30})$

[solid kiln]

MWB117

[spiral garnet]

$t=\frac{log\frac{105}{185}}{log(\frac{105}{185}^{1/30})}$

[wooden plover]

why is everything raised to the t here

[spiral garnet]

f(x)=ab^t

[wooden plover]

yeah

[spiral garnet]

shoot

ohhh

there?

[wooden plover]

yeah

[solid kiln]

MWB117

[wooden plover]

wait I should have read the damn question

[spiral garnet]

?

[wooden plover]

ambient temperature is 75F

[spiral garnet]

ye

[wooden plover]

you didn't use that anywhere, did you ?

[spiral garnet]

its irrelevant if i already know the rate it decreases at right?

aka b

@wooden plover how do i use it

[wooden plover]

the problem is that form is slightly incorrect to begin with

it assumes your temperature goes to 0 when t goes to infinity

but the ambient temperature is 75F

so you'd expect the temp to look like f(t) = 75 + ab^t

@spiral garnet

you'll get different a and b from there

[spiral garnet]

mmm

oh i see

bro i cannot get this rgiht

a=110

$75+110b^{30}=150$

[solid kiln]

MWB117

[spiral garnet]

$110b^{30}=75$

[solid kiln]

MWB117

[spiral garnet]

$b^{30}=75/110$

[solid kiln]

MWB117

[spiral garnet]

$b=\frac{75}{170}^{(1/30)}$

[solid kiln]

MWB117

[spiral garnet]

is that right?

[wooden plover]

110 not 170 but yeah

@spiral garnet

[spiral garnet]

Oh

4088 F

[wooden plover]

75+ 110*...

[spiral garnet]

bruhhhhh

pl

[wooden plover]

not 75*110*...

[spiral garnet]

ok

thanks!

.close

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[eager lynx]

I'm having a hard time identifying which polynomials are prime, I don't know where to begin.

[eager lynx]

Isn't x^2-9 factorable?
(x-3)(x+3)?

oh

then wouldn't x^2+9 not be a prime either?
(x+3)(x+3)?

[solid kiln]

faiyrose

[eager lynx]

so it would be (x+3)^2

Then how would I factor x^2+9

Because I thought that was correct

so it's not possible?

you're right

diamond method aint working

Wow

How come that doesnt work but a^2-b^2 works

its cause of the difference of square rule rigt?

You're right again

so when doing the diamond method

and getting -3 on both sides

what does that mean exactly

I know that it means that its not a prime number now, but what does it mean besides that

Its like

its the thing you were talking about basically

but in a diamond

So if it's possible to get the left and right, its not a prime, but what does it mean actually?

I forgot

what

Yes

Wait does this mean a prime number is just not factorable

Okay

Back to the diamond method though, would -3 on both sides just mean what exactly in x^2+9

Cause I think I remember smt like doing x^2+3x-3x+9

to do smt

but I forgot, it's been a while

wait

I meant that one

+3 and -3

wait hold up let me restart

I might have messed up somewhere

[solid kiln]

faiyrose

[eager lynx]

Okay here is what I mean
in x^2-9
I get +3 and -3 on the sides
But I remember doing smt like x^2+3x-3x-9 and doing smt after, maybe factoring it again?

when you say first two terms are you saying x^2 and -9?

oh my fault

I misunderstood you

Okay

(x-3)(x+3)

but back to the -3 and +3 what are those called

from the diamond

okay but anyways anything that cant be put in the diamond is automatically a prime right?

alright thank you

also, are these able to be eyeballed?

or do I have to a diamond for each

a^3+b^3

or a^3-b^3

Wait

Is that not the sum of cubes

yessir

Alright

So

But none of those are among the rulle

ru;e

rule

because there is no b with ^3

oh wait

1 works

sorry

so (m+1)(m^2+x+1)

wait

I just gotta look at em right

So

it has to be one of the bottom 2

Now I use difference of squares?

so is it m^2+1

that does not factor

great

Thank god

Im ngl these polynomials are ruining me

alright have a nice day

thank you

.close

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[eager lynx]

Am I doing this correct?
5x^2(5x^2)
-4y(4y)
(5x^2-4y)(5x^2+4y)?

[eager lynx]

honestly the way I am doign it just makes it seem like I'm doing random stuff

[twilit latch]

Depends on how you went from line 1 to line 2

This is just a normal difference of squares

[eager lynx]

I just took them seperately tofactor them

then put them back together

[twilit latch]

Doesn't really make sense to me

[eager lynx]

Oh wait

was it supposed to be a^2-b^2= (a+b)(a-b)

But it has 25x^4, it aint squared

[vagrant marsh]

well x^4 is just (x^2)^2

[twilit latch]

(5x^2)^2

[twilit latch]

This is actually so funny to do it so wrong and still get the right answer lol

[eager lynx]

You're right

hold up let me try again

Oh I understand now

[eager lynx]

I dont know how this even happened

alright thank you guys

I dont know why but polynomials are a little bit confusing with all the terms/rules

[twilit latch]

Np

[eager lynx]

.close

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[queen hound]

You should always be prepared for possible problems. One risk in the firework show is that the fireworks might not shoot straight up. Make a list of the distances between the audience and each type of firework if it didn't shoot straight up and instead formed a 68° angle with the ground.

[queen hound]

PLSS

YALLLLLLLLL

[simple haven]

You're asking a problem that doesn't have nearly enough information to solve

! original

[trim jolt]

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.

[queen hound]

THATS THE ENTIRE QUESTION

​

[simple haven]

I guarantee that there's additional context, because it's referencing different types of fireworks

[queen hound]

Find the maximum heights of 5 distinct fireworks online and record them. You need to determine how far away the audience has to sit from the point where the fireworks will be lit. To help you do that, you will make a detailed list of the angles of elevation the audience will have to use to see each firework if they are sitting 50 feet away. Assume that the fireworks are shooting straight up so they form a 90° angle with the ground. If they need to look up at an angle that is more than 75°, increase the distance from the launching site to the audience until they can see the firework using a 75° angle or less. Record your list and the distance from the launching site to the audience in your plan. Remember that the audience should be sitting at the farthest distance you found while trying to get them to see the fireworks by looking up at a 75° angle or less.

[eager lynx]

bruh

[queen hound]

THAT WAS THE QUESTION BEFORE

You should always be prepared for possible problems. One risk in the firework show is that the fireworks might not shoot straight up. Make a list of the distances between the audience and each type of firework if it didn't shoot straight up and instead formed a 68° angle with the ground.

[simple haven]

Yeah, that's important context

[queen hound]

OK

[simple haven]

So did you find the information?

[hallow kite]

man what are schools having y'all do nowadays 😭

[simple haven]

@queen hound do you have the heights? If so, do you know how to find the location of a point that makes a 68° angle with the origin and has a displacement of the heights you obtained?

It should be a similar problem to the previous one.

[queen hound]

no i dont have the heights :(

[simple haven]

So you didn't do the previous problem?

[queen hound]

no

[simple haven]

Was it assigned?

[queen hound]

yes

[simple haven]

[queen hound]

its summer courses so it has a due date but i need it by like tmr

[simple haven]

Well, you need to solve the first problem before you can solve this one

[queen hound]

oh

can u help me tho :((

im really dumb

and

stoopid

[eager lynx]

You need the previous problem.

[queen hound]

lidk how to solve it

[simple haven]

Ok so, first

[simple haven]

No

Second

It's a trigonometry problem

[queen hound]

YEA I AMM

IDK HOW TO DO TRIGONOMETRY

BARLEY

[simple haven]

Have you been taught SOHCAHTOA?

[queen hound]

😭🙏

nozz

[simple haven]

Ok. Well, while you certainly are not stupid, it seems like you don't currently have the prerequisite understanding of trigonometry to tackle this problem.

May I recommend Khan Academy?

https://www.khanacademy.org/math/trigonometry

[queen hound]

😨

[simple haven]

I have confidence that you can learn the material needed.

[trim jolt]

@queen hound Has your question been resolved?

[queen hound]

nope

[queen hound]

thanks for the confidence i guess

[simple haven]

Well, because you need to learn your way around the basics of trigonometry, this thread isn't really something that can be addressed better, unless you can find someone willing to sit you down and show you the ropes. But that's kind of a big ask, and the results you'll get will probably not be significantly better than using Khan Academy, assuming that you're treating it like a school lecture.

[queen hound]

is this server not allowed answers pr smtg

[simple haven]

!noans

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The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

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[fallow plover]

I dont know what am i supposed to do

[twilit latch]

I would just draw this one

[dull thorn]

Multiply by cos x what do you get After simplification

[fallow plover]

sorry but i dont get it

[magic harbor]

tanx would equal to sinx/cosx

multiply the cosx by both sides to get rid of the fraction on the LHS

so sinx = 2sinxcosx

[twin kettle]

1/cosx=2

Cosx=1/2

[magic harbor]

get everything on one side

so 2sinxcosx -sinx = 0

factor sinx

so sinx(2cosx - 1) = 0

now u got two equations

sinx = 0

or 2cosx - 1 = 0

find their degrees but since x is equal to or between 0 and 360 degrees, there will be 2 or more degrees as an answer for each equation

based on how many degrees u found for both equations, those are the roots

for sinx, i got x = 0, 180 and 360

and cosx = 1/2, i got 60 and 300

so there's 5 roots

[fallow plover]

do i need to plot graphs to find the roots?

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[fallow plover]

nvm i get it

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[blazing geode]

I'm depressed

[blazing geode]

I need math question that can soothe me

a geometric one would be ideal.

I have been doing questions on khan for so long, that it creates some deja vu that I loath with.

I need new stuff.

[blazing geode]

thank you sir

I should go laid back and watch some novel

[vital nova]

goodluck with that

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[golden jay]

how do I solve this kind of questions?

[golden jay]

do I apply tan x = sin x/cos x?

[vital nova]

yup

[golden jay]

did I did something wrong here?

[vital nova]

it's not asking for the angle does it?

tan theta IS x?

[golden jay]

it is asking for the value x

[vital nova]

value x when x is tan theta

not the degree of tan theta

[golden jay]

uh, then what do I apply here ;-;

[vital nova]

you are done already

x = sqrt 3/3

• there is not a way to get the inverse tan anyway without some calculator as far as I know of?

[golden jay]

the answer is on 1/ sqrt3 somehow

[golden jay]

o

[vital nova]

that's the unrationalized answer

[vital nova]

this is more right

[golden jay]

o alr

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[primal wraith]

uhm im tring to learn about markov chains... and im stuck on the highlighted line on the bottom

i get that they r trying to get the marginal distribution by summing over all the other rv's but i dont get why it gives (i) which i circled in red at the top

[marsh forum]

uh, I can't help, but just out of curisoity is your name supposed to be a reference to that problem in the foundation series ?

sorry

[primal wraith]

o no its not... its a refrence to a book by herman hesse called demian :3

out of curiosty what is thios problem??

[marsh forum]

thios ?

oh, this

just a fictional problem in a book afaik

[primal wraith]

ohh

well in my case it was a refrence to herman hesse but im pretty sure abraxas is the name of a deity in some belif system that i dont know about... so it makes sense for the name to crop up in multiple palces

<@&286206848099549185>

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[inner ember]

How many are Representatives chosen in each state? Based on what?

[marsh forum]

what's the context ?

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@inner ember Has your question been resolved?

[inner ember]

I wanna know how they calculated how many they should have representatives in each state

[marsh forum]

in the US?

[inner ember]

Yes.

[marsh forum]

I have no idea,sorry

[inner ember]

<@&286206848099549185>

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[inner ember]

<@&286206848099549185>

[brittle otter]

Number of representatives from each state is based on their individual populations

Larger population = more representatives

[inner ember]

ik, but is there a method? @brittle otter

[inner ember]

@pliant seal

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@inner ember Has your question been resolved?

[rotund grove]

In each state? You mean constituency?

https://www.visitthecapitol.gov/sites/default/files/documents/resources-and-activities/CVC_HS_ActivitySheets_CongApportionment.pdf

you may refer to this.

I have not the time to read that.

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@inner ember Has your question been resolved?

[tidal nebula]

See https://www.census.gov/newsroom/blogs/random-samplings/2021/04/how-apportionment-is-calculated.html
and https://en.wikipedia.org/wiki/Huntington–Hill_method

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[vague orbit]

I need some help! I'm supposed to prove that a given integral can equal either of two outcomes. I got through the first one without issue, but with the second one, I somehow ended up with one extra number in there that gums it all up. Can anyone help me figure out what I did wrong? The red marks the part I'm done with, so just ignore that. The yellow marks the answer I got for the second part, but as you can see, it's wrong, and I don't know why

[unique minnow]

First things first $\sqrt{-x^6} \ne -x^3$, it's actually undefined unless $x=0$.

[solid kiln]

Azyrashacorki

[unique minnow]

I think you meant that $$\frac{1}{\sqrt{1-(1-x^6)}} = \frac{1}{x^6}$$

[solid kiln]

Azyrashacorki

[vague orbit]

let me sheck again

trying to figure out the formatting here, hold on

so it's this $\frac{1}{\sqrt{1-\sqrt{1-x^6}^2}}$

wait no

[solid kiln]

PODEPOM

[vague orbit]

there we go

because the derivative of arccos is $-\frac{1}{\sqrt{1-x^2}}$

[solid kiln]

PODEPOM

[vague orbit]

and in this case x is actually $\sqrt{1-x^6}$

[solid kiln]

PODEPOM

[vague orbit]

that's how I made this

the square and the quare root cancel out, then the 1 and -1 cancel out

leaving $\frac{1}{-x^6}$

[solid kiln]

PODEPOM

[unique minnow]

No. $-(1-x^6) = -1 + x^6$

[solid kiln]

Azyrashacorki

[vague orbit]

oooohhhh I didn't distribute the negative sign correctly there

it's always those little tiny details that get me

I'll try ti run through the numbers with this and see if I get it right

might take a few minutes though

Alright, I got it!

Thank you so much for the help, I don't know if I'd ever have caught that little detail

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[vague orbit]

Here's a problem I still need help with. This is to do with error propagation, but I don't actually understand how to do what it's asking me, and I haven't been able to understand or apply whatever I've found online or in the textbook. I might just be dumb, but can anyone help me?

[vague orbit]

This is all I've got. I don't know what to do with it

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@vague orbit Has your question been resolved?

[vague orbit]

<@&286206848099549185> please help me

[vague lark]

wassup

[vague orbit]

hello

are you any good at calculus?

[vague lark]

which one

[vague orbit]

calculus 1

[vague lark]

sure

i took it last semester

ill try to help

[vague orbit]

that's really good to hear, thank you

[vague orbit]

so, I'm supposed to figure something out using differentials and propagated error

but I don't really understand it at all

[vague lark]

is it the problem above

[vague orbit]

yeah, the one abotu the measurement of the side of a square floor tile

[vague lark]

well lets the start with the obvious

area is x^2

[vague orbit]

right

[vague lark]

lets say like

A = x^2

[vague orbit]

so f(x)=x^2
f'(x)=2xdx

[vague lark]

The differential dA represents the propagated error in the area due to the small change dx in the side length.

yeye 2x

well then dA/dx is = 2x

then dA = 2x * dx

[vague orbit]

I'm trying to process this

ok, so when f'(x) would equal dA/dx, you now took the dx as an actual value and shifted it over to the other side of the formula

[vague lark]

yup

cuz differentials are like slope

[vague orbit]

and in this case, we have a value for dx

being +-(1/32)

[vague lark]

and x is 10

the side length

2x * dx

dx is 1/32

x is 10

substitute

sorry if im going a little fast

[vague orbit]

no it's ok

I think I got it!

so, the margin of error here is +-(5/8)in2

for my thing

[vague lark]

well possible error is more absolute

so just put 5/8

[vague orbit]

right, ok

so, that's part a finished!

now, part b is asking to approximate the percent error in computing the area of the square

which just

confuses me

[vague lark]

well percent error is given by the ratio of the absolute error to the actual value, multiplied by 100

if you want a definition for your notes id put like

Percent error: a measure of how significant the absolute error is compared to the actual value of the quantity being measured. It is calculated by dividing the absolute error by the actual value and then multiplying by 100 to convert it into a percentage.

[vague orbit]

I see

hmmm

[vague lark]

do you want a formula instead

[vague orbit]

I love formulas, yes

[vague lark]

% error = (dA/A) * 100

[vague orbit]

I seeee

[vague lark]

dA was 5/8

[vague orbit]

and A is 100

[vague lark]

now do stuff

[vague orbit]

on it

I just need to make sure I write everything down

Alright, I think I finally got it!

[vague lark]

sick

was i helpful

[vague orbit]

you were so so SO helpful!

[vague lark]

lol

gl on your class

[vague orbit]

thank you so much, seriously, I've been stuck on this one problem for days, because what it was asking for just didn't make sense to me! You've been a humungous help to me tonight, and I seriously can't thank you enough for your help

[vague lark]

oh sick

i just joined this server today btw 😭

[vague orbit]

I joined yesterday, I'm right there with ya

[vague lark]

how old r u just wondering

[vague orbit]

23, though it's kind of embarrassing to admit. I feel I should be further along by now

[vague lark]

na college starts for everyone at different ages

my moms starting college at 43 lol

[vague orbit]

I think that's really inspiring

Thank you so much for your help, and for all of this. I'm gonna go now, because it's almost 3am and I'm turning this work in at 10:30

[vague lark]

lol

cya

[vague orbit]

.close

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[gentle sleet]

is there a typo here? shouldnt it have been 6^2/sqrt(50) ?

[gentle sleet]

oh shit im braindead

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[eager lynx]

Im thinking it's either the second or third one cause they're both correct

[eager lynx]

wait I think it's the 2nd

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[wild jewel]

2/x-1 - 3/1-x

how the do you even solve it? i got -1/ x-1 since i thought denominator the same vice versa but the numerator appearently isn't -1 for some reason and i don't understand why. like instead they plused the 2 and 3 instead of minusing when it literally says to minus

[warped plaza]

Hope you got it

[wild jewel]

i dont sorry wonderiing still how the answer of 2/x-1 - 3/1-x = 5/x-1

[wild jewel]

are you saying two negative make positive

wait no got it

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[woven geode]

Hi

[woven geode]

Was wrapping up hw n didn’t realise this was a question someone double check please

Very much appreciated 🙏🏽

Would this be right?

[trim jolt]

@woven geode Has your question been resolved?

[woven geode]

<@&286206848099549185>

[dark crag]

let me check

what does it mean by 5 second fuse ? it means all of them are going to explode after 5 second ?

@woven geode

[woven geode]

I believe so

[woven geode]

I’m not sure tho bc our teacher gave this for holiday hw and didn’t explain it much

[dark crag]

hmm

i think it means that they will take off after 5 second

so the function should give h=0 for 1<=t<=5

[woven geode]

Ohh alr

So mine wld be h(1)=

[dark crag]

i think you should introduce piecewise function for all of them

btw, as it says. first rocket has to have maximum value at t=10, and h=80. so -b/2a=10 and -delta/4a=80 having at^2+bt+c

[white iron]

I think the 5 second fuse means that the rockets will explode after 5 seconds of lifting off.

[dark crag]

so all of them should explode at time t=5. but the question is asking for a situation where second rocket would explode at 1 second interval after previous rocket

[woven geode]

So Like how do I write the 5 equations?

[dark crag]

assuming the situation is as i said, let me write the first one, and you would be able to write for others.

[woven geode]

Thank you so much

[white iron]

Yeah that's quite confusing. Maybe that's because the rockets are allowed to take off 1 second after the take off of the previous one?

[dark crag]

on the second line, it says they will all take off at the same time.

[woven geode]

From ground level therefore it’ll be a parabola because it’ll also land

Just Not know of the equations

[white iron]

Oh yeah true

[dark crag]

i think this is going to be first one's equation

[woven geode]

THAT IS WAY TOO CONFUSING FOR A DUMBASS LIKE ME

NO WAY U DID THAT

[dark crag]

😂 😂

we are still not sure if we got the question right

btw if by 5 second fuse, i means it would take off after 5 seconds, then this is the equation of that

[woven geode]

Yea na no way in hell I’m getting all this I’m js gonna go cry atp

But thank you so much!!

🙏🏽

[dark crag]

bro 😂 💔

you're welcome

[woven geode]

Ima try ChatGPT

For all 5 of them

[dark crag]

😂 😂 😂

[woven geode]

Let’s hope this works…

[dark crag]

let me know if chatgpt also gave the same equation for first rocket as i sent

[woven geode]

That’s what I got

[dark crag]

bro what is this. chatgpt is assuming that gravity's force makes rocket to move

someone: AI will replace humans.
also AI:

[woven geode]

HAHAHAHA

I can’t do this bro I’m gonna go depressed bc of maths in a second it’s js too much words for me

Fr

[dark crag]

dude its simple. we model the movement of the rocket by a piecewise function.
so for t<=5 its obviously zero.
and for t>=5 its going to be a parabola of equation at^2+bt+c
you have to form 3 equation to relate a and b and c. then find relative a and b and c

then you're done. equation of that rocket is found

so what three equation you should use ?

first: -b/2a = tmax ( for first rocket its 10, second 11 , third 12, .. )
second: -delta/4a = hmax ( for first rocket its 80, second 90, third 100, .. )
third: h(5) = 0 (the rocket should take off at second 5, so it should be at height 0 at second 5)

thats all

[woven geode]

And the equations part is what gets me

We haven’t learnt tmax ykwim

Haven’t learnt delta

[dark crag]

oh

what grade are you in ?

[woven geode]

10

🙏🏽

[dark crag]

then i think its natural

delta is b^2-4ac

[dark crag]

and that first and second equation i mentioned in there, is just something you should memorize

it has proof. but you dont need it. you should only memorize

[woven geode]

This is the first equation

If I’m not wrong

[dark crag]

no

let me

[woven geode]

Alright!

[dark crag]

this is the first equation

this is second equation. and the line after that tries to solve for c

this is the third equation, and in this equation we substituted 'b' and 'c' by some expression based on 'a'. so we can solve for a

then you basically substitute a in two equations you found before, to find b and c

then you're done

[woven geode]

Yk how you did that right one tho we haven’t learnt that method or anything

I feel like this work is way too advanced for me

[dark crag]

if you havent learnt basic things about parabolas. then it is!
because definition of delta and tmax and hmax are fundamental formulas for parabola

[woven geode]

Yea we definitely haven’t…

That alright thanks tho!

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[scarlet silo]

Hi, i know this is a math server but i need help with some physics questions

[trim jolt]

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[scarlet silo]

I have some questions from my review package if anyone could help me

<@&286206848099549185>

[crisp bronze]

Read this

[scarlet silo]

oh ok

[crisp bronze]

Also you gotta wait 15 min before helper ping

[scarlet silo]

one seconds, i i'll post the picture

[scarlet silo]

oh sorry

[crisp bronze]

What have you tried to do so far

[scarlet silo]

this is one of the questions i need help with

[scarlet silo]

I made a diagram

a triangle

[crisp bronze]

Nice, if you know an angle and a side of a right triangle do you remember how to solve for the other sides?

[scarlet silo]

oh wait actually i think i know what to do. Do i solve for the y cpmponent of the triangle?

[scarlet silo]

yah

[crisp bronze]

Yes

[scarlet silo]

wait I another question

[crisp bronze]

Okay

[scarlet silo]

I couldnt get the right answer for this

[jolly pebble]

Hi

[scarlet silo]

hey

[jolly pebble]

Where are you stuck?

[scarlet silo]

this question

im not really sure what to do

[jolly pebble]

What have you tried?

Oh

[scarlet silo]

its a physics question

[scarlet silo]

i made a diagram of the projectile and made a T table split into x and y component

[jolly pebble]

Ok

So we know the final velocity we want of the ball is 18

[scarlet silo]

yes

[jolly pebble]

It's horizontal velocity is already 16

Let horizontal velocity be v1 and vertical be v2

And final be v

What will be the formula connecting v v1 and v2?

[scarlet silo]

um, im not really sure. One sec ill send you my formula sheet

[jolly pebble]

Hmm you do know about vectors right?

[scarlet silo]

i think so

[jolly pebble]

Right so velocity is a vector quantity

How do you add 2 vectors?

[scarlet silo]

This is what I’ve done so far

[jolly pebble]

That's correct

[scarlet silo]

vf + vi?

[jolly pebble]

Sure and what about the magnitude?

v=(v1^2+v2^2)^0.5

Where v1 is horizontal and v2 is vertical

[scarlet silo]

oh ok

[scarlet silo]

is that formula on my sheet?

[jolly pebble]

No this is the basics of vector

[scarlet silo]

oh ok

[jolly pebble]

v= 18, v1 = 16

So calculate v2

And tell me

[scarlet silo]

i got -476

[jolly pebble]

How?

Show

[scarlet silo]

ok

wait i forgot to square root it

nvm i cant its undefined

its negative

[jolly pebble]

This is ^0.5

Not *0.5

[scarlet silo]

ohh sorry

[jolly pebble]

Pythagoras

At least it looks like that

What did you get?

[scarlet silo]

i got 2

[jolly pebble]

Show

[scarlet silo]

the 0.5 multiples into the bracket and makes it to the power of 1 right?

[jolly pebble]

No

Doesn't work like that

[scarlet silo]

oh, its been a while ive dont math lol

[jolly pebble]

Send the 0.5 to other side

Make it 18^2

[jolly pebble]

No worries

[scarlet silo]

You can do that?

[jolly pebble]

Yeah it's ^1/2 so it becomes ^2 when taken to the other side

[scarlet silo]

oh right

[jolly pebble]

It's basically squaring both sides

[scarlet silo]

ok i finally got the answer, 8.25

[jolly pebble]

Good

Now we have the final vertical velocity

[scarlet silo]

ok

[jolly pebble]

What will be the initial vertical velocity?

[scarlet silo]

its the same thing isnt it?

8.25

[jolly pebble]

No

[scarlet silo]

ohh its 0

[jolly pebble]

Yes

Now use the first equation of motion

v=u+at

[scarlet silo]

vf=vi+at?

[jolly pebble]

Yes

[scarlet silo]

and vf is 8.25?

[jolly pebble]

For vertical velocity

Yup

[scarlet silo]

ohh ok,

[jolly pebble]

What did you get for t?

[scarlet silo]

i got 0.84

[jolly pebble]

Correct

[scarlet silo]

thats the answer

[crisp bronze]

Good job

[scarlet silo]

i still dont get how you got 8.25 tho? Is there another way to get it using the formulas from my sheet?

[jolly pebble]

Hmmm no

[scarlet silo]

oh ok, i still have some more questions. Do you have time to help me with them?

[jolly pebble]

I am gonna leave but you can ask someone else perhaps?

[crisp bronze]

I can help now

For a little bit at least

[scarlet silo]

👍

[scarlet silo]

k

i didnt know what to do for this questeon

[crisp bronze]

So it is asking for the difference between the final and initial velocities

[scarlet silo]

i know that the change in velocity is equal to vf-vi

[scarlet silo]

yep

[crisp bronze]

Yep, so how do you subtract vectors through a diagram

[scarlet silo]

im not really sure

[crisp bronze]

That's fine

There's 2 ways

You can either:

• draw them tail to tail, then the resultant is from the tip of the 2nd to the tip of the 1st
• or you can add one vector to the negative of the other

[scarlet silo]

i think i like the first way better

ill try that one

[crisp bronze]

I'm gonna double check the first way

Idk if I said the correct resultant direction

[scarlet silo]

ok, because the first way is kind of what we have been doing in class.

[crisp bronze]

That's fair

[scarlet silo]

like this?

[crisp bronze]

Sort of

[scarlet silo]

the answer should be C tho?

[crisp bronze]

No

[scarlet silo]

thats what the answer key says

[crisp bronze]

I did a stupid

Yes it is C

[scarlet silo]

no problem haha

[scarlet silo]

so is this right?

it points towards the vf?

[crisp bronze]

Yes

[scarlet silo]

ok, i have a similar question

ill post it one second

[crisp bronze]

Okay

[scarlet silo]

ill try it first give me a second

I think I got it. Thank you so much.

[crisp bronze]

You did, good job

[scarlet silo]

how much more time do you have? Because i have a lot more questions

[crisp bronze]

I gotta go in like 5 minutes

[scarlet silo]

oh ok no problem, do i close this help channel and start a new one then?

[crisp bronze]

No just post your problem here and someone should come along to help

[scarlet silo]

ok 👍

[crisp bronze]

If they don't in 15 minutes then you can ping helpers

[scarlet silo]

ok, thank you so much for the help, im doing physics one year ahead in summer school and my test is today lol

[crisp bronze]

Good luck

[scarlet silo]

thank you!

Whats the difference between these two, why are the answers different?

<@&286206848099549185>

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[scarlet silo]

I think I got it. Thank you so much.

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[scarlet silo]

Oh sorry

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[wraith hinge]

F ( x ) = -√3 then what is maximum value of F ( - x ) ?

[frozen plover]

F(x) doesn't depend on x

[worldly wing]

!xy

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[frank merlin]

isnt it x/2 instead of x/4?

[kindred pier]

no. square

[frank merlin]

i dont get it

[kindred pier]

You are factoring out 2², not 2

[raw warren]

$(2-x)^2=(2(1-x/2))^2=4 \cdot (1-x/2)^2$

[solid kiln]

Calculustache

[frank merlin]

ah okay

thx

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[mighty canyon]

it is possible

Hint: think about (ax+b)(cx+d), why don't you let a to be negative number

are you sure?

you can have very large positive and small negative

to get to +30x

you don't need to get all positive to get to +30x. For example, +40x - 10x = 30x

ok... try (-2x + b)(4x + d) [since I let my first one to be -2, the c is automatically be 4 to get -8]

and solve for b, d

(ax+b)(cx+d), a = -2, c = 4

easier way is to think about the polynomial $8x^2 - 30x - 27$ and then redistribute the negative sign later

[solid kiln]

nobody

[mighty canyon]

that would be the answer

if I told you what is it

then that means I tell you the answer

I hint you that you can have large positive and small negative to get to 30 from the combinations

that means I tell you the answer. Things does not work like that here in this server.

I need to guide you, not just tell you the answer

And I am guiding you to stop and think about it. You can get to 30x in different way unlike what you are thinking

again... one way to get to 30x is to have 40x - 10x

I'm not telling you that is the right answer. I am telling you that is one way to get there

Think about the combination you have, you can reach there (differently) but using the same idea

your initial answer is, in fact, really close. You just have to do something different about it

Have you tried using what I suggest? (-2x+b)(4x+d)?

I am telling you that is not the right answer but that is the similar idea on how you can get 30 while having negative number