help-10

[queen panther]

I suspect that since I squared everything on line 4-5, maybe 2 of the solutions will not work

[thick chasm]

Sin2x+1=0
Sin2x=-1
x= (npi+(-1)^n(-pi/2))/2

3rd step is wrong

[queen panther]

what did I do wrong?

[thick chasm]

Cosx = sqrt(1-sin^2x) when 0<x<pi/2 or 3pi/2<x<2pi
Cosx =- sqrt(1-sin^2x) when pi/2<x<pi or pi<x<3pi/2

[queen panther]

does it make a difference since everything just gets squared immediately after?

[thick chasm]

Taking sinx into the root also varies

Sqrt(x^2)=|x|

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[hard fable]

Hi. Geometric sequence question here:

[hard fable]

How do I figure out the first element and the change value if I only have element 4 and 8?

In this case a4 = 108
and
a8 = 8748

[civic zealot]

if $a_n = a_0r^n$ then $\frac{a_8}{a_4} = \frac{a_0r^8}{a_0r^4} = r^4$\
so you can find r\
once you have r, you can find $a_0$

[warm shale]

Zybikron

[hard fable]

Thanks!!

This helped

This server is so good

.close

[obtuse pebble]

Channel closed

Closed by @hard fable

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[void elk]

Hello

[void elk]

I need help with this:

[jolly ginkgo]

What do you think

[obtuse pebble]

@void elk Has your question been resolved?

[silver oracle]

Thank u

[void elk]

I don’t know

[radiant surge]

hello

so

i assume yk the definitions of radius, circumference and diameter ?

@void elk

since the minute hand originated from the center to the circumference(perimeter) of the circle(clock), we know that the minute hand = radius

So radius = 5 inch

That is what goes in the box

the answer would be radius

now

we know circumference is 2r

so 5 × 2 = 10

so the circumference is 10 inch

and the circumference = 2πr

so it = 2 × 3.14 × 5

which = 10 × 3.14

= 31.4

So ur circumference would be 31.4 inches

hope that helps

.close

[obtuse pebble]

Channel closed

Closed by @radiant surge

Use .reopen if this was a mistake.

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[chilly crater]

I need help

[tired sparrow]

6x6 means a square with the lengths of 6 each side

when you add 6x6 you do not add the area outside

you just add 6x6 square

[chilly crater]

Oh

Thx

[tired sparrow]

to get the area of WXYZ try to calculate the length of |ZY| and the length of |XT|

[tired sparrow]

You're welcome

[chilly crater]

K

Bye

.close

[obtuse pebble]

Channel closed

Closed by @chilly crater

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[spark field]

how would we use limit comparison here

what would we choose as bn

[idle thunder]

turn it into p series

[spark field]

wym

sqrtk/k^9

[idle thunder]

$\frac{k^{\frac{1}{2}}}{k^9}$

[warm shale]

sills

[idle thunder]

@spark field

[spark field]

yea

so 1/k^8.5

[idle thunder]

yes

and p series for p>1 converges correct

[spark field]

then we plug that in for an/bn

[idle thunder]

yes

LCT

[spark field]

sqrtk/k^9+3/1/k^8.5

[spark field]

= 1

and 1/k^8.5 converges

so converges

[idle thunder]

,w sum k =1 to infinity of (sqrt(k))/(k^9+3) does converge or diverge

please

,w does \sum_{n=1}^{\infty}\frac{\sqrt{k}}{k^{9}+3} converge or diverge

im so sorry

,w \sum_{n=1}^{\infty}\frac{\sqrt{n}}{n^{9}+3}

[warm shale]

Results provided by WolframAlpha

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

Requested by sills#9713

[idle thunder]

there

@spark field

[spark field]

?

[idle thunder]

it converges

[spark field]

ik

[idle thunder]

you got the answer

[spark field]

i did limit comparison

lim of an/bn

[idle thunder]

yes

the answer is correct

[spark field]

ok wb this how is htis not convergent

by ast

1/n^3

n^3

that should covnerge

3>1

p series

.close

[obtuse pebble]

Channel closed

Closed by @spark field

Use .reopen if this was a mistake.

[idle thunder]

@spark field

no use ast

[spark field]

why

.reopen

[obtuse pebble]

✅

[idle thunder]

the series is alternating

[spark field]

yea so ast test

1/n^3 lim of it = 0

and decreasing

[idle thunder]

1. alternating

2. lim n -> inf = 0

3. decreasing

[spark field]

yes

[spark field]

it is all those things

alternates

decreases

[idle thunder]

ok so what can you conclude from the ast then

[spark field]

Converge

[idle thunder]

k

[spark field]

but why is it diverge

thats what im asking

[idle thunder]

it isnt

[spark field]

it is

[idle thunder]

how

[spark field]

by ratio test

[idle thunder]

,w does \sum_{n=1}^{\infty}\frac{\left(-7\right)^{n}}{n^{3}} converge or diverge

[warm shale]

Results provided by WolframAlpha

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

Requested by sills#9713

[idle thunder]

@spark field

ok

[ancient jacinth]

he said

byeee

[spark field]

what

[ancient jacinth]

that makes two of us

[obtuse pebble]

@spark field Has your question been resolved?

[trim portal]

7^n grows much faster than n^3

which means that whole fraction grows

since it's alternating (it's sign changes) it will be something like 1-2+3-4+5 etc, just alternating terms getting bigger forever

and since they are not getting smaller, it cant converge

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[orchid badger]

could someone double check this for me, and remind me how to find the equations for those planes(I have lost my notes over this)

[obtuse pebble]

@orchid badger Has your question been resolved?

[obtuse pebble]

@orchid badger Has your question been resolved?

[obtuse pebble]

@orchid badger Has your question been resolved?

[orchid badger]

<@&286206848099549185>

[orchid badger]

.close

[obtuse pebble]

Channel closed

Closed by @orchid badger

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[deep ravine]

How do i calculate the smallest interval for part c?

[obtuse pebble]

@deep ravine Has your question been resolved?

[deep ravine]

<@&286206848099549185>

[deep ravine]

<@&286206848099549185>

[obtuse pebble]

@deep ravine Has your question been resolved?

[deep ravine]

<@&286206848099549185>

[slow dome]

That would only give half of the curve try 2pi.

[deep ravine]

Wdym

By the way this is the answer key

[deep ravine]

<@&286206848099549185>

[slow dome]

My apologies I misread the question, from my understanding you would calculate the smallest interval for theta that traces the whole curve by checking how the equation graphs it. So it would be 0 < theta < pi/2 because that is the first section that is inclusive to the whole curve.

Because you only need one section to find the whole curve

[deep ravine]

Can you explain how this is the full curve?

Also why isn’t it -pi/2 < theta < 0?

[deep ravine]

.close

[obtuse pebble]

Channel closed

Closed by @deep ravine

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[wild pine]

<@&286206848099549185>

[viral blade]

indeed all three are incorrect, as well as the sum not being the actual sum of the 3 things you entered

Did you use Euler's formula?

actually, scratch the thing about the sum

I was probably wrong on that

[wild pine]

yea but i'm struggling with converting from polar exponential form to rectangular form

[viral blade]

can you show the work you did?

[wild pine]

uhh

its kinda a big mess

[viral blade]

I'll try my best

if I can't understand it I'll start from scratch

[wild pine]

a mess

basically i got the z^2 and z^3

but i dunno how to convert them to rectangular

so i tried some weird shit and it didn't work

[viral blade]

6pi/3 doesn't simplify to pi/2

[wild pine]

oh shit

[viral blade]

For the others, I'm guessing the mistake might have happened while evaluating the sines/cosines

[wild pine]

oh wait

i see what i'm doing wrong

thank you for your help

.close

[obtuse pebble]

Channel closed

Closed by @wild pine

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[opaque galleon]

what's the "trick" when doing derivatives of 1/something? besides low di high minus high d low

[opaque galleon]

there sems to be a pattern with the denominator

[latent walrus]

you can express 1/f(x) as [f(x)]^-1, then use the chain rule and power rule

[opaque galleon]

why did they get derivative here

[obtuse pebble]

@opaque galleon Has your question been resolved?

[opaque galleon]

.close

[obtuse pebble]

Channel closed

Closed by @opaque galleon

Use .reopen if this was a mistake.

[opaque galleon]

.reopen

[obtuse pebble]

✅

[opaque galleon]

where did they get C = ln3

ln(3) = right hand expression + C

how is that ln3 = C

[obtuse pebble]

@opaque galleon Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[timid silo]

Can this be solveable to applying limit laws then isolating f(x)?

[timid silo]

I did it and got the same answer as the answer key but they approached it in a different way

[pine sail]

You're asking if we can find f(x) based on given information?

[timid silo]

no no i just want someone to check if my way is fine

i just feel a lil bit skeptical let me send it rn

Sorry its a lil bit messy

[pine sail]

It's alright, and that's more or less the same.

It should work.

[timid silo]

ah ok ty

.close

[obtuse pebble]

Channel closed

Closed by @sturdy dragon

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[warm aurora]

how would i solve this question?

[warm aurora]

i just left b marked

[frigid prism]

the inverse of a function is just a reflection across the y = x line

[warm aurora]

so is it B?

[frigid prism]

no

[tacit gate]

kefir can i try and explain him

[frigid prism]

go ahead

[tacit gate]

@warm aurora do you logically understand what inverse function means?

if not then physically it's flipping the x and y axis

imagine grabbing the graph and rotating x to y and y to x

and that fact gives us a symmetry at y=x

why because inverse of y=x is y=x

[warm aurora]

so if i understood correctly it's C?

[frigid prism]

yes

[tacit gate]

no it's not c

the graphs in c are not symmetrical with line y=x

which option has symmetry along y=x @warm aurora

[warm aurora]

so A?

[tacit gate]

i mean there's nothing else left is there

[warm aurora]

yea true lol

[obtuse pebble]

@warm aurora Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[dapper gyro]

i have this hash function. 'h' equals the sum of squares of ascii values of the characters, h2 equals the sum of ascii values of the characters and 'len(key)' equals the number of characters in the key. the returned hash is: (h-len(key)) % h2. How can i prove/check if this function has any collisions or not.

[dapper gyro]

i dont wanna use the brute force method, is there a mathematical way?

[frigid prism]

collisions?

oh

this is hashing

ask in a cs server

[dapper gyro]

ig it can be solved through group theory or somethin

[frigid prism]

isnt really the place here

[dapper gyro]

ok...

[frigid prism]

you can get a lot better assistance in a cs discord

[obtuse pebble]

@dapper gyro Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[obtuse pebble]

Channel closed

Closed due to the original message being deleted

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[mild flint]

I need to find sina and cosa, knowing that tga=-√3/3 and a€(90°:180°)

[stable rain]

a in (90°,180°)?

try drawing a triangle

[mild flint]

Triangle

Why?

[jolly ginkgo]

Hiii

[mild flint]

Yes a belongs to (π/2;π)

[stable rain]

on the unit circle

[mild flint]

Can't I just solve it with formulas?

3. or 5)

[obtuse pebble]

@mild flint Has your question been resolved?

[mild flint]

<@&286206848099549185> can u help with 3) or 5) ? I need to find sina and cosa

[mild flint]

.close

[obtuse pebble]

Channel closed

Closed by @mild flint

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[hot dawn]

anytips for this Q?

[hot dawn]

am stuck up to this part. Don't know how to finish this Q :/

[unreal musk]

Well seems like you wanted to write the (x,y) in terms of those two vectors v1 and v2

Oh I thought that said -32 and -43

Anyways, you can find the a and b in terms of x and y and then work from there?

[obtuse pebble]

@hot dawn Has your question been resolved?

[hot dawn]

I don't think that gets me anywhere though?

[unreal musk]

Well remember that T is said to be linear so replace the a and b that are in terms of x and y here, and do algebra

[hot dawn]

ohhhh

because we want [x; y] to be in terms of x's and y's too right

so like this?

[unreal musk]

Yep yep that’s the way you’d go about it

[hot dawn]

this ok too?

[unreal musk]

Looks good to me

[hot dawn]

wait, I don't know where I went wrong, but when I plug in v1 or v2, I don't get their given image

I'm so confused

[unreal musk]

What do you mean by plugging in v1 and v2, as in their values?

Well hmm

,calc -199(-3) + 9(-4)

[warm shale]

Result:

561

[unreal musk]

Maybe an algebra mistake somewhere I think

Oh yea also maybe here it should be multiplied by -1 as that’s the determinant of the matrix you’re inverting right?

[hot dawn]

oh yeah

because -9+8 = -1

oops

hmmm

[unreal musk]

It happens

[hot dawn]

does a single sign really make the difference here though/

[unreal musk]

Well yea I think it does

Oh and also again, even taking that into account…

So it should be a = -3x + 2y and b = -4x + 3y I think? (Watch me have made an oopsie there )

[hot dawn]

ahhh

[unreal musk]

At which point you get something I can’t be bothered to do the algebra for, but

x=-3 and y = -4

,calc -3(-3) + 2(-4)

[warm shale]

Result:

1

[unreal musk]

,calc -4(-3) + 3(-4)

[warm shale]

Result:

0

[unreal musk]

That gets you that you have (1,0) in that other basis as you should have

Similarly x=2 and y=3 should get you a=0 and b=1

,calc -3(2)+2(3)

[warm shale]

Result:

0

[unreal musk]

,calc -4(2) + 3(3)

[warm shale]

Result:

1

[unreal musk]

Which it does

[unreal musk]

So adjust all that algebra based on these, exercise left to reader

[obtuse pebble]

@hot dawn Has your question been resolved?

[hot dawn]

@unreal musk ok I don't thin kyour method works

I tried again with this similar Q

and it doesn't work with the vectors v1 v2

unless i did something wrong again

(I don't think so)

nvm I missed a sign again

[unreal musk]

https://tenor.com/view/ethannestor-unusannus-gif-22358917

[obtuse pebble]

@hot dawn Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[snow raptor]

Can someone please help me in this question? (the pic contains both the question as well as my approach)
Link: https://math.stackexchange.com/questions/4670117/to-find-the-sum-of-all-possible-perimeters-of-a-triangle

[obtuse pebble]

@snow raptor Has your question been resolved?

[snow raptor]

<@&286206848099549185>

[timid silo]

Ok so we can get a number theory question from the the given information

By using coordinate geometry

Let the point a be origin

So c will be 30,0 and b is 9,0

D will be a random point that lies on the perpendicular bisector of ac

Now the condition is that ad and bd are integers

So we get 2 equations like 225+k^2 and 36+k^2 must belong to integers

Where d is 15,k

So if we solve these we can get values of d probably the worst way to solve this but you can get an answer this way @snow raptor

[obtuse pebble]

@snow raptor Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[maiden cypress]

How would I compute the laplace of t * u(t-3)

[obtuse pebble]

@maiden cypress Has your question been resolved?

[dusk ruin]

Use the integral, shouldn’t be hard iirc for this

Instead of simply using the shortcuts to convert (which are to be fair a third of the reason for doing laplace)

To compute u(… you’ll need a second integral to subtract

Or wait think I misunderstood been a while since I did ODEs

You can use the shortcut/reference table directly, u(t-3) is e^-3s iirc multiplied by the laplace of whatever the u(…) is multiplied by

Or simply do the laplace integral by hand

Do from 0 to inf minus 0 to 3 and you’ll get the same thing iirc… I think

[obtuse pebble]

@maiden cypress Has your question been resolved?

Channel closed

Closed by @maiden cypress

Use .reopen if this was a mistake.

[snow raptor]

ohh, well there was a better method though, but I did not know how to apply coordinate geometry here either, anyways, thanks for the answer 🙂

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[timid silo]

Can there exist a line such that it’s slope is 2 and it contains the point (-1,-6)?

[timid silo]

,tex .point slope

[warm shale]

Toby

[wanton hull]

yes

until only one point is there, there is a line for every value of m

[tacit gate]

dude said slope is 2

[wanton hull]

for which i replied yes just a message above

[obtuse pebble]

@timid silo Has your question been resolved?

[timid silo]

Okay

I have one more

What type of graph is appropriate to represent this data, bar graph or histogram?

I keep confusing them

[tame narwhal]

bar or dot plot would be appropriate

[timid silo]

Why though?

[tame narwhal]

because you have a single value for each group/area

[timid silo]

Why not historgram?

[tame narwhal]

because you have categorical data. see here: https://www.storytellingwithdata.com/blog/2021/1/28/histograms-and-bar-charts

[obtuse pebble]

@timid silo Has your question been resolved?

Channel closed

Closed by @eternal chasm

Use .reopen if this was a mistake.

[timid silo]

Thank you so much

Appreciate it

.close

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[stable iron]

in taylor series does it matter what point to expand at? in other words does the choice of a impact the estimation?

[stable iron]

when we use o(x^n) notation at the end

[fathom flicker]

impacts it yes, changes its validity? no

I mean expand at the point where you care about expanding at

[stable iron]

so technically any point can be used to estimate a function in integrals for example?

[fathom flicker]

not sure what you mean by in integrals, but any point where the function is continuous and differentiable yes

[stable iron]

$\int_a^b f(x) , dx = \int_a^b \sum_{i=0}^\infty f(y)^{(i)}\frac{(x-y)^i}{i!}$

[warm shale]

ta

[stable iron]

where y can be any point?

is that true for any y

[kind hawk]

well the radius of convergence might be different

and stuff like that

[stable iron]

but the equality holds?

[kind hawk]

for some y it probably wont converge

[stable iron]

is it safe to use y = 0

does convergence - choice of y - depend on a and b

[kind hawk]

of course

on a,b,f

[stable iron]

then using this in a proof is a bad idea if f can be any continuous function from R to R?

[kind hawk]

if f is only continuous then you cant even write down a taylor series

[stable iron]

its twice differentiable and I was thinking to use lagrange's remainder

this is the problem, but Id like to try to solve it myself

[kind hawk]

well dont write an infinite taylor series if you only want the first few terms

your approach is reasonable

(if lagranges remainder is the correct one, I forgot which one is which, there are a few)

[stable iron]

this is what we use in our college

c \in (x_0, x)

[kind hawk]

sounds reasonable, yeah

[obtuse pebble]

@stable iron Has your question been resolved?

Channel closed

Closed by @stable iron

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[proper forum]

I don't understand how the underlined = 6

There are 3 kinds of fruits so the way to select only one fruit should be 3. (any one among mangoes/apples/oranges).

[tame narwhal]

there are mangoes, apples, oranges, and three other fruits (each with n=1)

10 + 5 + 2 + 1 + 1 + 1 = 20

it's definitely easy to miss, so be sure to re-read the question carefully

[obtuse pebble]

@proper forum Has your question been resolved?

[proper forum]

Right, my bad. Thank you for your time and assistance.

[obtuse pebble]

Channel closed

Closed by @proper forum

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[solar wagon]

Using related rates how to solve this?

[solar wagon]

I'm having trouble forming diagrams and finding the required equations

[obtuse pebble]

@solar wagon Has your question been resolved?

[solar wagon]

<@&286206848099549185>

[unborn valley]

ok
Let Plane A have 200m/s speed
Let Plane B have 250 m/s speed

draw there routes of straight line and parallel.
The distance between routes is givien 12 km.

Now Plane A is ahead 5 km on Plane B

first, can you find the distance between two planes initially

[solar wagon]

how can I do that if their initial positions arent given

[unborn valley]

since Plane B is eventually gonna catch up with plane A, at what point of time will it be at exact parallel (i.e distance b/w them is 12km), you can calculate rate of change of distance then

[unborn valley]

assume Plane B on initial point, calculate w.r.t to it

[solar wagon]

I would have some sort of right angle triangle

[unborn valley]

yes

[solar wagon]

base 12

[unborn valley]

yup

[solar wagon]

and we want hypoteneuse

but im not sure what the height is

[unborn valley]

B is our initial point, now it is given that A is 5km ahead of it

[solar wagon]

still unsure

[unborn valley]

so height will 5

[solar wagon]

i thought 5 is hypoteneuse

[unborn valley]

well it is specified as 'ahead' and not 'distance between them'

so A is 5km ahead of B , try forming a right angle triangle using it

did you get it?

[solar wagon]

ah i see

so at that point distance/hypoteneuse would be 13 km

[unborn valley]

yup

[solar wagon]

so how do we formulate the related equations?

[unborn valley]

ok so how, distance between them initially is 13km
Now since B is faster, it will eventually catch up with A

when it 'catches up' with A, both A and B will be parallel , hence distance between them would be 12 km right?

[solar wagon]

yes

[unborn valley]

so you basically have to find out how much time it takes B to catch up with A

or at what point of time, A and B are parallel

[solar wagon]

ill try it out and get back to you

[unborn valley]

suree

[solar wagon]

So I need dD/dt

and that can be found by dD/dL * dL/dt

L is the height of triangle or vertical distance between the two planes

[unborn valley]

hmmm you can solve this by basic speed equations too

[solar wagon]

We find that dD/dL = x/sqrt(144+x^2)

and dL/dt is 50 (difference in speed)

multiplying these 2 together when L = 5, we get 19.2 m/s

which is the right answer

[unborn valley]

yup niceeee

great

[solar wagon]

thanks

[unborn valley]

welcome!

[obtuse pebble]

@solar wagon Has your question been resolved?

[obtuse pebble]

Channel closed

Closed by @solar wagon

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[high fiber]

i need help on this

[high fiber]

i need to find the absolute maximum and absolute minimum values of this function at the interval [0,2]

[thick field]

.

Find the first derivative

Then solve for x putting the equation equal to 0

Find the absolute lowest and greatest values

[fierce lagoon]

You need to test inclusive endpoints too

[thick field]

Test the endpoints as well

NGL

The server pfp caught me

[fierce lagoon]

Dang. We tried

[thick field]

Lul

[obtuse pebble]

@high fiber Has your question been resolved?

[thick field]

@high fiber How not

[high fiber]

i solved it and got 30 as the absolute maximum and -12 as the absolute minimum

[thick field]

Oh yeah

You have to substitute those x values back into the original equation

After solving for them in the first derivative

BUT

Since 30 reaches out 2

And -12 reaches past 0

We can forget about those

Test the endpoints

[high fiber]

lemme show you my work

[thick field]

2(0)^3 + 3(0)^2 - 12(0) + 4

And the same for 2

[high fiber]

<@&286206848099549185>

[high fiber]

i have all correct work up until the evaluating at the critical points. can someone help please

@fierce lagoon

[thick field]

Therefore, when x is 1 in the interval [0, 2], you get the absolute minimum value

And when x is 2

You get the maximum value

[high fiber]

ah i see so i just disregard x=-2

[thick field]

Nah, u need that one bc that gives u the maximum value in the interval [0, 2]

Disregard the other values

[high fiber]

so where did i make a mistake in my work?

[thick field]

You didn't

[high fiber]

wat

[thick field]

OHHH WAIT

U did

[high fiber]

yea lol

[thick field]

U put

-12

Wait

Yeah that's wrong bc -2 isn't in the interval

So put -3 since 1 IS actually in the interval

For the minimum

Minimim: X = 1; Y = -3

Maximum: X = 2; Y = 30

[high fiber]

ah I see

[thick field]

[high fiber]

let me redo it and ill show you

[thick field]

Alr

Ping me when u do

[thick field]

Nah

Remember, the numbers HAVE to fit in the interval

-2 reaches beyond [0, 2]

8 is the max

-3 is the min

@high fiber

[high fiber]

ahh

[high fiber]

its becaouse of the brackets right? it would be different if there were parentheses

[thick field]

Nah that's for domain and range

I thiiiiiiink

Intervals are [a, b]

[high fiber]

so its because the question states that it is a closed interval

[thick field]

That too

[high fiber]

yeah

[high fiber]

thanks for the help 😄

[thick field]

Npppp

[high fiber]

.close

[obtuse pebble]

Channel closed

Closed by @high fiber

Use .reopen if this was a mistake.

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[spark sigil]

i need help with a proof problem

[spark sigil]

And the thing to prove is:
The real part of every non-trivial zero of the function above is always 1/2

[mint tendon]

i hate this server

that false ping got me LOL

[spark sigil]

Lmao me too

[mint tendon]

easy

we will use the Kholonosky identity

[spark sigil]

:O

[mint tendon]

[spark sigil]

• multiplies everything by zero*

Proved

[mint tendon]

ezez

[spark sigil]

:O does that sum equal to -1/2?

[mint tendon]

yea grandi

[spark sigil]

I prefer killing infinity people

[mint tendon]

ur divergent huh

[spark sigil]

[spark sigil]

might be

[mint tendon]

why did the mathematician name his dog cauchy?

|| because it left a residue at every pole ||

[spark sigil]

why :O

[spark sigil]

hahahaha

marh jokes haha

well have a funny april fools day

.close

[obtuse pebble]

Channel closed

Closed by @spark sigil

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[timid silo]

How do I do iii?

[gloomy valve]

You already know FO = sqrt(6) and the radius of the circle is 1. Can you construct a right triangle which contains the angle XFY? (or rather, half of that angle)

[timid silo]

Are X and Y points on that circle?

[gloomy valve]

yes

[timid silo]

I got it

Thank you

.close

[obtuse pebble]

Channel closed

Closed by @pure pulsar

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[primal leaf]

One message removed from a suspended account.

[primal leaf]

One message removed from a suspended account.

One message removed from a suspended account.

One message removed from a suspended account.

One message removed from a suspended account.

One message removed from a suspended account.

One message removed from a suspended account.

One message removed from a suspended account.

[tardy torrent]

what is this

[primal leaf]

One message removed from a suspended account.

One message removed from a suspended account.

One message removed from a suspended account.

One message removed from a suspended account.

One message removed from a suspended account.

[timid silo]

Wdym the topic?

[tardy torrent]

yeah

I've never seen this before

[obtuse pebble]

@primal leaf Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[runic wraith]

Hi I was just wondering if I wrote the lower and upp bound correctly for the first integral

I converted to polar

I was thinking 4r^2 might actually be the upper bound and 4 the lower bound

[obtuse pebble]

@runic wraith Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[distant summit]

How do I find m<ABE (letter B), m<ADC (letter C) and AE (letter e)?

[timid silo]

For letter B, try to draw a triangle of that specific section including angle ABE, BAC, and AEB

It would become clearer from there

For letter C, try to review on rhombus properties regarding opposite angles and build on what you have done for letter B

[distant summit]

OHH RIGHT! I forgot about that, thanks

[timid silo]

For letter e, you can use some trigonometry

[distant summit]

how?

Oo wait nvm, I think how to do it

That will be all, thanks!

.close

[obtuse pebble]

Channel closed

Closed by @distant summit

Use .reopen if this was a mistake.

[timid silo]

Alright have a great day! Good luck with ur studies

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[slate elbow]

help

[slate elbow]

how do i find the SD and the t-value here?

[blazing lark]

Sd and t value of what?

[slate elbow]

of both post test and pre test

[blazing lark]

I don’t follow

[slate elbow]

you don’t know?

[blazing lark]

Is it like the combined mean of the three fields?

[slate elbow]

yes

[blazing lark]

The mean would just be add the three together and divide by 3

[slate elbow]

and what’s the standard deviation of it

[blazing lark]

You would have to use a calculator or the formula your teacher gave you

It will be more complex to calculate since it is dependent on sample size

[slate elbow]

and how do you find the standard deviation

[blazing lark]

Look up standard deviation formula

[slate elbow]

SD = sqrt( (sum(x - mu)^2) / N )

t = (mean - hypothesized mean) / (SD / sqrt(N))

correct?

[blazing lark]

Yea looks correct

You can calculate t values super easily if you have a Casio or ti 84 btw too

That’s what I did when I took stats

Makes t and z tests and intervals super easy to calculate as well

[obtuse pebble]

@slate elbow Has your question been resolved?

[slate elbow]

no

[slate elbow]

thanks

[obtuse pebble]

@slate elbow Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[slate elbow]

.reopen

[obtuse pebble]

✅

[slate elbow]

how do you find the SD from the mean value?

[obtuse pebble]

@slate elbow Has your question been resolved?

[slate elbow]

thanks

.close

[obtuse pebble]

Channel closed

Closed by @slate elbow

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[rapid spire]

Hello

[royal basin]

type your question here

[rapid spire]

okay, thanks

So my question is about the standard deviation being negative

I used the tabular form to complete the process of finding the mean and the variance, but the results when computing for the Standard deviation ended up being negative

hang on i'll send a pic of the table

[frosty spoke]

can you not type it out here or something

it's really tedious to transcribe it

[rapid spire]

okay

so the mean is 160.7 and the variance is 25194.3

I followed the guide / formula on how to compute the standard deviation and the result is -630.19

is there anyway i could fix it?

[frosty spoke]

huh? the standard deviation is the square root of the variance

[rapid spire]

wait

what came out from the calculator is 0+25.10358540129i

after i solved for the square root of -630.19

[frosty spoke]

yeah that's obvious

the variance cannot be negative

so you've goofed some calculation

[rapid spire]

can you help me figure out what part is it that had an error?

I would truly appreciate every ounce of help

[frosty spoke]

no, because I don't feel like transcribing the numbers into a computer to calculate it

as I said, it's really tedious to do it

now, if you typed them into a format I could copy-paste, maybe

[royal basin]

what guide did you follow and what exactly did you do?

if you found the variance then surely the stdev is just the square root of that?

unless you found something other than variance and misnamed it.

[frosty spoke]

,rotate cw

,rotate ccw

[rapid spire]

sorry its blurred

[frosty spoke]

well guess I can't do it to my own picture

looks like he calculated E[X^2] = 25194 or whatever

why don't you just put the numbers into a computer to check your answer

[rapid spire]

hang on, sorry

[quick mauve]

What’s the formula you’re using for variance

[rapid spire]

x * P(X)   x^2 
7.45       22201
15         22500
7.55       22801
31.4       24649
7.95       25281
16         25600
24.6       26896
8.35       27889
8.4        28224
16.9       28561
8.5        28900
8.6        29584

= 160.7 (mean)

x^2 * P(X)
1110.05
2250
1140.05
4249.05
1264.05
2560
4034.4
1394.45
1411.2
2856.1
1445
1479.2

= 25194.3 (VARIANCE)

[rapid spire]

σ² = ( (Σ x²) / N ) - μ²

as for the mean

[quick mauve]

I don’t normally use that formula but it doesn’t look wrong to me

And deviation is just square root of variance

So it should be positive

Which also makes sense with your numbers

[frosty spoke]

would've been great if you could

actually type out x

and P(x)

because you wasted a ton of time typing out stuff that's unusable

[rapid spire]

okay I'll type it

sorry

[frosty spoke]

the rest of that can easily be computed with a computer

so I don't need your handwritten values

[rapid spire]

X     P(X)
149   0.05
150   0.1
151   0.15
157   0.2
159   0.05
160   0.1
164   0.15
167   0.05
168   0.05
169   0.1
170   0.05
172   0.05

      = 1

[frosty spoke]

these are the values I get

check that yours are the same

do you see why using a computer is helpful lol

wait a minute

your probabilities sum to 1.1

[rapid spire]

wait no

it sums up to 1 for me

151   0.05 not 0.15

that's why it says 1.1 for you.

sorry

151's P(X) is 0.05

[rapid spire]

mine says 25194.3 for the X^2 P(X)

but it may be wrong

[frosty spoke]

then you added it up wrong

[rapid spire]

okay, it now says 49.81 in the standard deviation

wait

the square root is 7.05761999544

is this correct?

is the standard deviation correct?

[frosty spoke]

I believe that would be the standard deviation

[rapid spire]

omg omg thank you so much! I've been stressing over this problem for like 5 hours and its finally done

you are the best!

[frosty spoke]

you can always use an online calculator to figure this out to check your work

or use google sheets next time

doing it by hand and calculator is really inefficient

[rapid spire]

I'm still slowly familiarizing myself with excel, its a bit complicated, but you've proven it to be worth mastering

or learning

how to use it

I'm suppose to round it up right? cause I can't use the entire thing, so it would be 7.06?

[frosty spoke]

you can round it however you want

however the question asks you to round it

[rapid spire]

2 decimal places

'is it also allowed to round up the mean?

[frosty spoke]

depends on what you're asked

[obtuse pebble]

@rapid spire Has your question been resolved?

[rapid spire]

it has, thank you vrry much

[obtuse pebble]

Channel closed

Closed by @rapid spire

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[faint stag]

I need help drawing a diagram for this question, I don't even know where to begin.

[timid silo]

seems physics to me

not sure whether this is the right place to ask this question

[deft hazel]

Just read the mathematics bit and draw that

[faint stag]

from a maths exam

[timid silo]

ohh that's strange..I forgot how to do this things lol

[deft hazel]

What don't you understand

[faint stag]

literally nothing, ig i have a diagram drawn but im not sure if its correct

[deft hazel]

Before you send it

Do you have an isosceles triangle with vertices labelled ABC respectively and line segments AB and AC congruent

[faint stag]

yes, its more the fact that im not really sure how the forces are acting on it

[deft hazel]

and the angle at A double theta?

o

let me draw the diagram for myself

are we workin in radians or arcdegrees

or even gradians though extremely unlikely

[faint stag]

shouldnt matter, but im guessing degrees considering mechanics questions are usually degrees

i should add its a non calculator paper as well

[deft hazel]

i mean it wouldn't matter

but it'll just makes things more direct

[faint stag]

lets work in degrees then

[deft hazel]

okay

so this is my understanding

So the question is asking

[faint stag]

this is what i have as well

[deft hazel]

To show that the triangle ABC can rest in equilibrium with the peg in contact with any point on BC.

So just thinking about it and visualising it

It's true but we need to prove it mathematically/physically

So to know something is in equilibrium the net force and torque must be 0

[faint stag]

yeah so far so good

[deft hazel]

• principle of static equilibrium

one moment

So what two forces are acting on the triangle?

[faint stag]

well we have weight

so we can label that mg

[deft hazel]

ye

[faint stag]

and we have the force from the peg

which i labelled P

then we also have friction, but i dont know where it acts

[deft hazel]

we'll ignore that for now

the force of the peg be more specific

[faint stag]

the normal contact force

[deft hazel]

ye

Since the plane containing ABC is vertical, the weight of the triangle acts straight down and is balanced by the normal force from the peg acting straight up. Therefore, the net force is zero.

[faint stag]

yes, so i guess P = mg then

[deft hazel]

So knowing that we are in mechanical equilibrium

[faint stag]

if the peg is right in the middle

[deft hazel]

What else does the principle of static equilibrium say (which i've said before)

net force and what else must be zero

[faint stag]

moments

or torque not sure what you would call it

[deft hazel]

either

torque or moment of force abbr. moment

which is the rotational equivalent of linear force

[faint stag]

alright cool, so we need rotation equilibrium using moments, as well as vertical/horizontal equilibrium

[deft hazel]

ye

So principle of static equilibrium states that net force and net torque must be 0

we ascertained that net force is 0

[faint stag]

yes

[deft hazel]

so what are the torques acting on ABC

[faint stag]

the normal contact force

[deft hazel]

ye what else

[faint stag]

weight? but if it acts from the centre of the object then im not sure how we would incorporate that when we take moments

[deft hazel]

mb cuh someone just entered my dms

but ye the torque of the normal force and the torque of weight

let's choose A as the axis of rotation

[faint stag]

yeah

[deft hazel]

the torque due to the W of the triangle is zero, since W acts through point A. The torque due to the F_n from the peg can be calculated using ....

[faint stag]

perpendicular distance x force

[deft hazel]

ye tau=Fd

$\tau=F_nd_\perp$

ofg

bruh

[faint stag]

ahh april fools

[deft hazel]

We can denote torque by M too

but ye

[faint stag]

yeah so far it makes sense

[deft hazel]

Since the side BC is resting on the peg, the line of action of the normal force passes through point C. Let's call the distance from point A to point C x. Then, the perpendicular distance from point A to the line of action of the normal force is x sin θ. Therefore, the torque due to the normal force is ...

[faint stag]

Fxsintheta

[deft hazel]

ye

sorry cuh @timid silo stop do your circle trig 🤮

[faint stag]

wait so which force is acting opposite to Fxsintheta to keep it in equilibrium?

[deft hazel]

What can you express F_n as

[faint stag]

friction?

[deft hazel]

no F_n is the notation for normal force

read as "F sub (subscript also called suffix) n"

n for normal

[faint stag]

F_n = mg?

[deft hazel]

we denote COF as mu

yesn't

[faint stag]

i dont understand this; what is O and F?

[deft hazel]

acronym for coefficient of friction

[faint stag]

ohhhhh

[deft hazel]

F_n= Wcosθ/(1+μtgθ)

[faint stag]

tgtheta?

[deft hazel]

Where W denotes weight which is ma, but since we're on earth a=standard acceleration of free fall (denoted as g_0 or g_n)

tg is another notation for tan

[faint stag]

hold on, how come we've resolved weight using costheta

[deft hazel]

Because that's the perpendicular force

[deft hazel]

which i written over here

[faint stag]

right, but if we've taken moments about A, doesnt that mean we do not count weight?

[deft hazel]

no

hol up i lost track

wait so what are you confused about

[faint stag]

this

also, why is F_n passing through point C?

[deft hazel]

Because line segment BC is in contact with the peg

BC are clearly colinear and let's assume segment BC extends

and the peg is infinite

[faint stag]

wait.... the peg is infinite?

[deft hazel]

no

i said lets assume BC extends and the peg is infinite

[faint stag]

i just marked it as a dot under the segment BC

[deft hazel]

just to prove my point/help you understand

[faint stag]

ohh right okay

okay so if BC extends, and the peg is infinite

BC is now resting on this peg

[deft hazel]

yes

[faint stag]

wouldnt that mean that the force is point directly upwards?

not through C?

[deft hazel]

so that means all infinite points between BC including BC and above lie on/are contained within the peg

and the normal force acts on all points

wait

fuck

[faint stag]

yeah this part i understand as we assumed the peg is infinite

[deft hazel]

Definition. F_n
The normal force is the force that acts perpendicular to the surface of contact between two objects.

Since the wire is in equilibrium, the net force acting on it must be zero. This means that the vertical component of the tension force in the wire must balance the weight of the wire.

The weight of the wire acts downward and is distributed uniformly along the wire. Since the wire is symmetric, the weight is also symmetric and acts through the centroid of the triangle ABC.

Since the wire is in contact with the peg at point C, the normal force must act upward through point C to balance the weight of the wire. If the normal force were to act at any other point on BC, then there would be a net torque acting on the wire, which would cause it to rotate and not be in equilibrium. Therefore, the normal force must pass through point C.

[faint stag]

this part i dont, how can we model it as such?

why is the peg at point C?

it only says BC rests on the peg

so you could put the peg anywhere and it should be in equ right?

im guessing u just put it at C to make calculations easier?

[deft hazel]

fuck i'm getting confused now

well you could put the wire anywhere on the peg

and the peg is horizontal

[faint stag]

i didnt even realise it was horizontal....

i completely missed that part

i modelled it as a particle

[deft hazel]

bruh

i like that atom peg

[faint stag]

nah i mean just a dot

underneath the wire

didnt realise it was fully horizontal

alright that makes a bit more sense

but thwn why does the normal contact force act through C?

[deft hazel]

justified it here

[faint stag]

but if its weight is symmetric, surely the peg could act through B as well?

[deft hazel]

wait holy shit lemme just read the q again

i am confused at my confusion and your confusion

show me all the work you produced

[faint stag]

alright one second

this was my diagram originally

but thats literally all ive done

[deft hazel]

that is cold

test message

[faint stag]

whats cold 😭 😭

my diagrams?

[deft hazel]

ye

[faint stag]

thanks bro

its wrong anyways

do you know where to go from here?

[deft hazel]

ye hold on

okay i verified my answer

ye so it acts on all points in the line segment BC

[faint stag]

right

so like, its a bunch of arrows pointing upwards?

[deft hazel]

yes we call those vectors

normal vectors

to be precise

[faint stag]

now that i think about it, ive never though about how a normal contact force acts on two infinitely long surfaces

so how would we resolve it then if theres arrows everywhere?

[deft hazel]

errr

honestly lemme check if chatgpt can do this

honestly the first approach we were taking could've led to the same conclusion

[faint stag]

see this is what i dont get

why N = mgcostheta

[deft hazel]

Because it's perpendicular

[faint stag]

but if the normal contact foce was acting straight up

and the weight was acting straight down

they would just be equal

[deft hazel]

yes

that's why it's in mechanical equilibirum

but

let's look at

the weight in terms of it's vector components

And let the plane that contains ABC be expressed in the cartesian coordinate system

fuck my laptiop is so fucking slow i'm gonna break it

https://www.youtube.com/watch?v=caluozb2s1c me asf

[faint stag]

so the weight's componenets

are acting perpencidular to CA and parallel to CA

yes?

[deft hazel]

no

yes

lemme just write this down