help-23

[steep magnet]

• n = m

wtf formatting

thats supposed to be -1 and -n

Anyways

The equation of the line AC1:

y = mx + c

1 = (-n)0 + c

c = 1

y = -nx + 1

The equation of OD1:

y = mx + c

0 = (1/n)0 + c

c = 0

[cinder jasper]

What’s the question

[steep magnet]

This one

[steep magnet]

y = x/n + 0

[cinder jasper]

Yes what are you trying to find

[steep magnet]

Omg

I left it out of the screenshot

💀

[cinder jasper]

:joy

😂

[steep magnet]

Thank you hahaha

Fixed now

[cinder jasper]

Okay what is your plan?

[steep magnet]

First find the equation of AC1 using the points I have

[cinder jasper]

Ok lets do that

Good start

[steep magnet]

The slope of the line AC1:
0 - 1 = m(1/n - 0)
-1 = m/n
-n = m
The equation of the line AC1:
y = mx + c
1 = (-n)0 + c
c = 1
y = -nx + 1

[cinder jasper]

How are the coordinates defined?

[steep magnet]

Wym sry?

[cinder jasper]

Like what are the coordinates for point C

Is it n

[steep magnet]

C1 is x = 1/n, C2 is x = 2/n, etc

I think

[cinder jasper]

Okay

[steep magnet]

from how I understood it

[cinder jasper]

Then
A = (0, n)
C_1 = (1/n, 0)

[steep magnet]

Yeye

[cinder jasper]

Okay

The slope is
$\frac{0 - n}{\frac{1}{n} - 0} = \frac{-n}{\frac{1}{n}} = -n^2$

[flat frigate]

violet

[steep magnet]

Oh

[cinder jasper]

Agree?

Always check my maths

[steep magnet]

I used the slope formula (y2 - y1) = m(x2 - x1)

[cinder jasper]

Once you agree (or we find the correct slope) we proceed

[steep magnet]

with m being the slope

[cinder jasper]

What was the slope you found?

[steep magnet]

-n

0 - 1 = m(1/n - 0)
-1 = m/n
-n = m

[cinder jasper]

Ok let’s do it step by step. What is $y_2 - y_1$?

[flat frigate]

violet

[steep magnet]

0 - 1

Points are (0, 1) and (1/n, 0)

[cinder jasper]

The coordinate of A should have been 0, 1

My bad there, you should have pointed me out

[steep magnet]

Ah I missed it too haha sry

[cinder jasper]

Yes the slope is indeed -n

Now we find the equation

We have
y = -nx + c

Sub (0, 1)

Gives c = 1

[steep magnet]

Yep with you so far

[cinder jasper]

Consequently
y = -nx + 1

[steep magnet]

Yeye

[cinder jasper]

What is the plan next

[steep magnet]

Use the inverse slope of this and the coordinates of the origin to get the equation of the line OD1

[cinder jasper]

Sounds nice

[steep magnet]

so 1/n is the slope

[cinder jasper]

Agree

So y = x/n + c

For OD_1

[steep magnet]

0 = 1/n(0) + c

c = 0

[cinder jasper]

Yes

Y = x/n

[steep magnet]

Yeye

[cinder jasper]

What would you do next

[steep magnet]

Then set the 2 equations of the lines equal to find the coordinates of D1

[cinder jasper]

Okay

[steep magnet]

-nx + 1 = x/n

[cinder jasper]

-nx + 1 = x/n yes

Thats just a quadratic

Nx^2 - n + x = 0 yes?

[steep magnet]

Yep

[cinder jasper]

Now we solve it for x

[steep magnet]

Hmm ok

[cinder jasper]

Use the quadratic formula i guess

A = n, b = 1, c = -n

Take the positive answer

[steep magnet]

(-1 +- sqrt(1 - 4(n)(-n)))/2n

[cinder jasper]

$\frac{-1+/sqrt{1+4n^2}}{2n}$

[steep magnet]

(-1 +- sqrt(1 + 4n^2))/2n

[flat frigate]

violet

[steep magnet]

Yep

[cinder jasper]

So you have got the horizontal distance

How would you get the vertical

[steep magnet]

Of what sry?

[cinder jasper]

From O to D_1

Because O is 0, 0

[steep magnet]

Ah oke

So we sub in this into y = x/n

[cinder jasper]

Yes

[steep magnet]

Annoying numbers but

yeah

[cinder jasper]

Same but divided by 2n^2

Instead of 2n

[steep magnet]

wym sry?

[cinder jasper]

This

But with 2n^2 in the denominator

For the y

(Vertical distance)

[steep magnet]

Ah yeah

[cinder jasper]

I think the last thing now to do is just do x^2 + y^2

And then root

[steep magnet]

Like pythagoras?

[cinder jasper]

Thats the distance formula right?

You want the distance

[steep magnet]

ohhh

Yeye

[cinder jasper]

So you do \sqrt{x^2 + y^2}

I’m leaving soon can you do that your own

I’ll help while im here

[steep magnet]

Im just gonna put it into WRA

Cause I hate these numbers lol

[cinder jasper]

Okay

[steep magnet]

But wait

Its plus or minus because of the quadratic formula

but we only take the positive right?

Cause its in the 1st quadrant?

I think its wrong....

Cause this was my first answer

And the bits in red were the bits that were wrong... The WRA answer looks nothing like this

.close

[safe radish]

Channel closed

Closed by @steep magnet

Use .reopen if this was a mistake.

[safe radish]

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 dirge]

If a line segment goes from the origin to the point63, -6, then what angle does the line segment make with the x-axis?

[maiden dirge]

6sqrt3, -6

[icy lance]

what do you think

[maiden dirge]

i have the answer already, its a practice test. I just have no idea how to go about this.

[lime dust]

Have you drawn it?

[maiden dirge]

i thought the unit circle would be of some help, but no radian measure there comes close to 6sqrt3 :/

[icy lance]

wouldnt be 6sqrt(3)

ah i see what you mean

im backing samuel though

[maiden dirge]

draw the graph? im confused

[icy lance]

yeah

draw a little axis, plot the point, mark the angle

see if anything comes to mind

[maiden dirge]

looks like it goes through q4 at about 30 degrees?

[icy lance]

quite astute
but got any mathematical method?

[maiden dirge]

no thats full blown eyeballing unfortunately

[icy lance]

(make a triangle)

[lime dust]

📐

[maiden dirge]

i guess where im getting the most confusion is using the triangle to find the measurement of the angle without having anything but two points to go off

im very out of practice, its been probably 10 years since i've done geometry or trig

[icy lance]

do you remember soh cah toa or something like that?

[maiden dirge]

yes

[icy lance]

the point gives you the lengths of two sides of the triangle, you can use soh cah toa and the inverse trig functions to get the angle

[maiden dirge]

but there arent any lengths given. is there a way to find that based off the two points of the hypotenuse?

i see

i think most of my confusion is now coming from the answer key saying pi/6

which would be the measurement of 30 degrees in q1, no?

[icy lance]

its the angle it makes with the x axis, it doesnt speak as to which direction its going

[maiden dirge]

radian for 30 degrees rather

oh, i assumed it had to match the quadrant in the unit circle

[icy lance]

ah no not quite, here the angle would be 330 degrees if you were doing it like that

since it goes anticlockwise

[maiden dirge]

oh i see, that makes sense

so instead of the x axis being where i would "place" the unit circle id use the line segment i was given

[icy lance]

it would be easier imo since the points are unlikely to be ones you would find on the unit circle

though if you know youre looking for tan=1/sqrt(3) then you can maybe use it from there

but if you can use arctan, id just go with that

[maiden dirge]

how would one show their work for this if it had to be done by hand?

the worst part is this is just for a placement exam, i'm just using it as a study guide to see what i can pick back up

but the school was kind enough to give a mock exam with an answer key and a few problems worked out.

[icy lance]

id do my little diagram showing the triangle
id then say tan(x)=6/6sqrt(3)=1/sqrt(3)
then x=arctan(1/sqrt(3))=pi/6

id find thats generally sufficient

[maiden dirge]

thanks a ton for your help

[icy lance]

np

[maiden dirge]

.close

[safe radish]

Channel closed

Closed by @maiden dirge

Use .reopen if this was a mistake.

[safe radish]

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.

[tulip flower]

what happened to the four during integration? should it not be (8x^5/2)/5?

[fathom jewel]

looks like they forgot it

[tulip flower]

okay so it should be there

[fathom jewel]

Yes

[tulip flower]

okay thanks

[safe radish]

@tulip flower Has your question been resolved?

Channel closed

Closed by @tulip flower

Use .reopen if this was a mistake.

[safe radish]

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.

[fallen dragon]

how many significant figures are in (3.00 x10^4)

[indigo wave]

3

[safe radish]

@fallen dragon Has your question been resolved?

[fallen dragon]

how, isnt it 1?

3.00 x10^4 = 30000

[indigo wave]

But your specifying that the two digits after the decimal point are to be 0

3x10^4 is 1 significant figure

[fallen dragon]

oh okay okay thank you!

.close

[safe radish]

Channel closed

Closed by @fallen dragon

Use .reopen if this was a mistake.

[safe radish]

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.

[cunning pasture]

Help please.

[safe radish]

Please don't occupy multiple help channels.

[cunning pasture]

Another question lil bro

Another dimension actuallly

I am the only meolve

[wraith parcel]

no you dont

[cunning pasture]

I am an older member

[wraith parcel]

I am in discord since 2018

[cunning pasture]

So?

• your profile shows somethign else.

• the real meolve has the studying role

[vapid anvil]

Are you talking to yourself

What's your question btw

[lime dust]

https://tenor.com/view/spider-man-we-one-gif-18212100

[cunning pasture]

Oh sorry.

A projectile is launched at an angle theta with speed u. After 2 seconds, the angle between the horizontal and the direction of velocity is 30 deg. It takes three seconds for it to reach its maximum height, from the start. Find theta and initial velocity u.

Can you help me in my other channel also?

I am getting theta as 45 deg

[safe radish]

@cunning pasture Has your question been resolved?

[cunning pasture]

<@&286206848099549185>

[vagrant jolt]

Does it say to assume g is something

If not I’m gonna use 9.8

And see what I can do

[cunning pasture]

yes.

g = 10 m/s^2

hey

<@&286206848099549185>

[vagrant jolt]

Hihi

Sorry

Okay

So have we drawn out the diagrams?

@cunning pasture

[cunning pasture]

yes

[vagrant jolt]

We know at max height

Vertical velocity is 0

[vagrant jolt]

Send diagram pics

[vagrant jolt]

Alrighty

[vagrant jolt]

We know this would happen here

That’s the max height

And so we can say V= u+at for the vertical component

Because we know V is 0

U is u sin 30

[cunning pasture]

what is U?

[vagrant jolt]

The initial speed

Unless you meant Mu

[winged flare]

definitely not

[cunning pasture]

mu?

what's m?
mass?

[winged flare]

you should be able to find the vertical component of velocity from the second equation

[cunning pasture]

u * sin theta?

[winged flare]

not relevant for now

[winged flare]

yep

[cunning pasture]

Okay?

[winged flare]

you know that $u_y = u \cdot sin(\theta)$ and $a_y = -g$

[cunning pasture]

yrs

why not just take -g?

[winged flare]

at maximum height do you know what $v_y$ will be?

[cunning pasture]

never mind

yes

0

[winged flare]

yep

we also know t

now which equation has all four of these?

[cunning pasture]

v = u+at?

[winged flare]

correct

[cunning pasture]

then

[winged flare]

you would get u sin theta as?

[cunning pasture]

30?

[winged flare]

30?

[cunning pasture]

yes

No?

[winged flare]

u = at

t is 2 and g is 10

[cunning pasture]

no.

[vagrant jolt]

-10

[cunning pasture]

for t = 3, v = 0

v_y

[vagrant jolt]

Usintheta is 30

[cunning pasture]

yes

Now what?

We gotta use the 30 deg thing.

[vagrant jolt]

Yh

We know that initial velocity is gonna be made up of vertical and horizontal components

[cunning pasture]

yesa

[vagrant jolt]

So we can divide them

[winged flare]

oh yeah my bad

[cunning pasture]

Yes?

np

[cunning pasture]

for t = 2?

at*

[vagrant jolt]

Mhm

[cunning pasture]

ok

[vagrant jolt]

So it’s usin30 / ucos30 = vertical component / horizontal component

[vagrant jolt]

Let’s work out the components

At t=2

Vertically what do we have

When t = 2

[cunning pasture]

we needa calculate the y-component to get the horizontal compoent

using v=u+at for t =2

let's take theta as A

so v_y_2 = u*sinA - 20

[vagrant jolt]

Lets try a different equation

[cunning pasture]

usinA - 20 = kcos 60

horizontal is constant

u*cos A

[vagrant jolt]

Moving on

So we have

[vagrant jolt]

This

[cunning pasture]

yes

[vagrant jolt]

We have vertical and horizontal

We can divide them to make our lives easier

[cunning pasture]

what are we calculating?

[vagrant jolt]

U

Initial

Speed

[cunning pasture]

Let's proceed.

[vagrant jolt]

If we divide them

We’ll get tan30

=

Usin30-20

/ ucos30

Is that all good?

[cunning pasture]

nope

[vagrant jolt]

Use trig

Tan30= vertical component

Over the horizontal

We have the opposite and adjacent

[cunning pasture]

oh

[vagrant jolt]

So we can use tan

[cunning pasture]

yes

got it

no

oh

yeah

[vagrant jolt]

😂😂

Be honest are you following?

If you don’t understand anything

We’re here to help you understand

And same for me if I don’t understand something someone else will hopefully

[cunning pasture]

Yes

[cunning pasture]

I am following

[vagrant jolt]

I’m using trig on only that bit

Because that’s what we’re working with when we say t= 2

[cunning pasture]

ok

tan 30 = 1/root3

[vagrant jolt]

👌👌👌

That equals

Vertical over horizontal

Vertical you’ve worked out

[cunning pasture]

horizontal remains the same

[vagrant jolt]

Usin30 - 20

[vagrant jolt]

This

We know theta is 30

In this case

So A is 30

[cunning pasture]

we need to do calculations

[vagrant jolt]

Rearrange a bit and lmk what you get idh my calc on me

[cunning pasture]

ok so 1/root3 = usinA-20)/(ucosA)

[vagrant jolt]

Yh

A being 30

[cunning pasture]

Ikr

Ok

,w 1/root3 = (usinA-20)/(ucosA)

[flat frigate]

Results provided by WolframAlpha

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

Requested by anshulyolo121

[cunning pasture]

this is an equation in two variables

[vagrant jolt]

Yh

We take

Positive

Because look at diagram

[cunning pasture]

how do we rearrange?

[vagrant jolt]

?

[cunning pasture]

WHAT

[vagrant jolt]

Do you have the answer alr?

Just so ik we didn’t go wrong somewhere

[cunning pasture]

ok

theta = 60

u = 20root3

yeah

[vagrant jolt]

We now

Want to get to that

[cunning pasture]

no way

[vagrant jolt]

Yh?

[cunning pasture]

how?

how can it solve a two variable equatopN?

[vagrant jolt]

God knows

😂😂😂

[cunning pasture]

LOL

[vagrant jolt]

Ok

So

[cunning pasture]

yes

[vagrant jolt]

Let’s go from here

I’ve just realised smth

So when t=3

It reaches its max

We can work stuff out

There

@cunning pasture

I g2g in like 5

Mins

[cunning pasture]

I said you.

[vagrant jolt]

We finish it asap 😭

[vagrant jolt]

This

[cunning pasture]

usinA - 20 = kcos 60

[vagrant jolt]

What

[cunning pasture]

where k is the arrow-head velocity at t = 2

[vagrant jolt]

This is the part we need now

From the diagram from before

We know

That at the max

T= 3

We good?

[cunning pasture]

Yes

We good

[vagrant jolt]

What else do we have

For the vertical component

Other than

V=0

and t= 3

[cunning pasture]

no

Nothign else

[vagrant jolt]

At the maximum point

[cunning pasture]

just v = 0

oh

[vagrant jolt]

We know

g is 10

And

U = usintheta

[cunning pasture]

huh

[vagrant jolt]

In this case -10

[cunning pasture]

oh

ok

[vagrant jolt]

Because we’re going up still

[cunning pasture]

I though A = -10 lol

[vagrant jolt]

g in this case is acceleration hence why I said a

[cunning pasture]

ok

[vagrant jolt]

Yh so

[cunning pasture]

then

[vagrant jolt]

We can use

Which equation

We have

v

u

a

t

Don’t have s

What equation do we use

[cunning pasture]

s = ut-1/2at^2?

wait nvm

v^2 = u^2 + 2as

[vagrant jolt]

We don’t have s

And don’t want it

Either

It stinks

We’re working with velocity

[cunning pasture]

so v = u+at?

[vagrant jolt]

From what we have previously

[cunning pasture]

0 = u*sinA - gt

[vagrant jolt]

The equation with wolfram

Yh

[cunning pasture]

t = u*sinA / 10

[vagrant jolt]

t is 3

[cunning pasture]

u*sinA = 30

[vagrant jolt]

Yh

Now

[vagrant jolt]

Remember this equation?

[cunning pasture]

yes

[vagrant jolt]

Sub

It

In

[cunning pasture]

sub?

oh substitute

[vagrant jolt]

Substitute

It in

[cunning pasture]

u * cosA = 10*root3

u* sinA = 30

tan A = 3*root3

,w arctan (3*root3)

[vagrant jolt]

Bing bong

[flat frigate]

Results provided by WolframAlpha

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

Requested by anshulyolo121

[winged flare]

🏓

[cunning pasture]

,w 1.38067*180/pi

[flat frigate]

Results provided by WolframAlpha

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

Requested by anshulyolo121

[cunning pasture]

wait

how is theta coming 79 deg?

[vagrant jolt]

It should be 60

I did it

On calc on internet

[winged flare]

hmm

somethings wrong

just wait a minute

[cunning pasture]

yeup

[winged flare]

ill make a diagram and come back

[cunning pasture]

diagram available

[vagrant jolt]

Should’ve got

Tan theta = 30/(10root3)

[cunning pasture]

yes

[vagrant jolt]

That equals

60

[cunning pasture]

oak

askd as

ajfsoajf

[vagrant jolt]

😭

[cunning pasture]

tan 60 = root3

I did root 3 in the denominator

THanks

for your help

[vagrant jolt]

Np

[cunning pasture]

🙂

GOod bye

[vagrant jolt]

And we can use that to solve for u glhf

[cunning pasture]

In the numerator.

Yes.

Easily.

20roo3

thanks

.close

[safe radish]

Channel closed

Closed by @cunning pasture

Use .reopen if this was a mistake.

[winged flare]

oh it's somced

nice

[safe radish]

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.

[final plinth]

Minima of (sin5x)/(sinx)^5

[compact wraith]

Have you done demoirves theorem?

[crystal palm]

is the ^5 on the whole fraction or only on the denominator?

[compact wraith]

You can expand sin5x in terms of sinx

Then set z=sinx, this will leave you with a rational expression that is easy to plot, then just remember than the range of sinx is [-1,1], so the domain of the rational function in z is [-1,1]

[pseudo scroll]

you could also logarithmically differentiate

[safe radish]

@final plinth Has your question been resolved?

[long oracle]

Some justification for why that works would be good

[safe radish]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[safe radish]

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.

[lunar prawn]

how do solve part a and b?

[daring crescent]

By looking at the graph how long does it take for the graph to "repeat itself, look where it first hits 0 by going down, then look at where the grapth crosses 0 by going down again

[lunar prawn]

i dont know tbh

im new to sin and cosine functions

just started it yesterday

[soft matrix]

Sine and cos are periodic functions and they repeat their graphs after a period leght of 2pi

[lunar prawn]

isee

[lunar prawn]

i understand this

[soft matrix]

Meaning sin(x) = sin(2pi + x)

[lunar prawn]

yes

[soft matrix]

On more thing is sin(x) = sin(pi-x) u can proove this using both the unit circle and sum formula

[lunar prawn]

how so?

[soft matrix]

Sin(a-b) = sinacosb - cosasinb

[lunar prawn]

i see

but how is this related to the question?

[soft matrix]

From here sin(pi-x) = sinpicosx - cospisinx here sinpi= 0 and cospi = -1 so your answer Simplifies to sinx

[lunar prawn]

hmmm

ok

[soft matrix]

The y coordinate will be same at sin(pi/4) sin(3pi/4) sin(9pi/4) sin

Sin(-pi/4)

[lunar prawn]

hmmm

but whered the sin(9pi/4) come from?

[soft matrix]

Add 2pi to pi/4

[lunar prawn]

one momenbt

ooh

i see

but it that case, where did the sin(3pi/4) come from?

[soft matrix]

Pi - pi/4

[lunar prawn]

.....

why do we add and subtract? does that mean 7pi/4 is also a valid anaswer?

i see

well thank you

[soft matrix]

A tip would be to go learn the unit circle and it's relationship with trigonometry

[safe radish]

@lunar prawn Has your question been resolved?

[safe radish]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[safe radish]

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 ledge]

Someone help

Why won’t my monitor connect to my pc

[ivory rampart]

i would recommend checking the cables

[hard ledge]

I have power to both as you can see

And I plugged that hdmi cord in

[ivory rampart]

did u try replugging all of them ?

[hard ledge]

It worked fine at my other house but then I moved and un packed and now it not working

[hard ledge]

Erm

I did

Just now

And nothing

[vast sentinel]

It could be the cable that isn't working

[hard ledge]

So over the 20min drive to this house the cable broke

[ivory rampart]

i usually just turn everything off and on until it works :)

[hard ledge]

😭💀

.close

[safe radish]

Channel closed

Closed by @hard ledge

Use .reopen if this was a mistake.

[safe radish]

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.

[celest tapir]

What is the syntax to get this function in latex?

[peak estuary]

well the letter is called \psi

but I dont know what font that is

[celest tapir]

Thanks that’s enough 👍

.close

[safe radish]

Channel closed

Closed by @celest tapir

Use .reopen if this was a mistake.

[sleek sentinel]

\Psi apparently yeah

[safe radish]

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.

[lunar tartan]

I find setting up constrained optimization problems quite intuitively difficult. I have an example question and would appreciate a demonstration of what my thought process should look like when setting up the objective and constraint equations

[lunar tartan]

<@&286206848099549185>

[indigo wave]

Have you tried drawing a diagram

[white umbra]

Please don't ping Helpers before 15 minutes have passed

[safe radish]

@lunar tartan Has your question been resolved?

[jolly shard]

!status

[safe radish]

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

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[safe radish]

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.

[rain dagger]

why is this <? it has to be =

[quiet plume]

You are right. It should be =.

[safe radish]

@rain dagger Has your question been resolved?

[safe radish]

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.

[tardy crescent]

idk how to account that the value of the dice cant be over 6 and more than 1

[empty gyro]

Maybe it means the four rolls total to 9?

[tardy crescent]

yes that what it means

[tardy crescent]

im supposed to use stars and bars right

[compact wraith]

Yea

[safe radish]

@tardy crescent Has your question been resolved?

Channel closed

Closed by @tardy crescent

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.

[magic flower]

I couldn't understand how to start

.close

[safe radish]

Channel closed

Closed by @magic flower

Use .reopen if this was a mistake.

[safe radish]

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.

[agile wraith]

can someone please explain how they got from C to fcc

f by the way is A+AT

I am so confused

am i supposed to apply F(a) to c or take the inverse or something I am super confused

[dull sequoia]

What is the question

[agile wraith]

the question is how is Fcc derived

like how did they get that

like the blue matrix

from the first image i posted

[dull sequoia]

There’s no question in this picture

[agile wraith]

no

[dull sequoia]

That’s just the set up

What do we want to do

[agile wraith]

Ok hold on let me explain

this is work from my professor

i want an explanation on how he got from C to f cc

[dull sequoia]

Yeah but we can’t answer a question if there’s no question

[agile wraith]

that is my question

[dull sequoia]

Can you show the full question?

[agile wraith]

yes but essentially this is all the information you should need for my question

the other work is just how they got to C

if we assume C is true

how do you get to f cc

[dull sequoia]

I’m not gonna argue with you

[agile wraith]

im confused what is the arguement

this is the question from that part if this is nay help but im am super confused what is the arguement we are having right now lol

now with all this posted its like more confusing i feel

[dull sequoia]

This is what I’m looking for

[agile wraith]

ok

[dull sequoia]

The answer doesn’t make sense if I don’t know what the question is

[agile wraith]

ok

fair

[dull sequoia]

So if C is an eigenbasis of f

Let C = {c₁, …, c₄}

Then f(c₁) = λ₁c₁

Where λᵢ are the eigenvalues of cᵢ

[agile wraith]

mm ok

[dull sequoia]

If you take a look at how one constructs the matrix representation of a linear function in some bases

We notice that the first column is just [f(c₁)]_C

Which we know is just [λ₁c₁]_C

This is clearly just (λ₁, 0, 0, 0)^t

So that’s what’s in the first column

Repeat for every column and you get a diagonal matrix

[agile wraith]

mm ok wait so is c1 0 1 -1 0

[dull sequoia]

c₁ is a vector where if you apply f to it, you get λ₁c₁

[agile wraith]

so applying A+AT to c1?

[dull sequoia]

So this is f(c₁) = λ₁c₁ + 0c₂ + 0c₃ + 0c₄

Hence the coordinate vector of f(c₁) with respect to the basis C is (λ₁, 0, 0, 0)^t

[agile wraith]

I am so confused when doing stuff like this like how does C transform into that

like I feel like im missing a step

to understanding your result

im looking at C the image that isent

[dull sequoia]

What do you mean how does C transform into that

C is a basis it does not do anything

[agile wraith]

ok so you dont use C at all

[dull sequoia]

I don’t know what you mean

[agile wraith]

like ok

let me word it like this

[dull sequoia]

“How does C transform like that” is a nonsensical statement

[agile wraith]

this basis here

[dull sequoia]

the basis C

[agile wraith]

I am looking at the basis and trying to figure out how you got f(c₁) = λ₁c₁ + 0c₂ + 0c₃ + 0c₄

are you applying f to the basis?

[dull sequoia]

Since C is an eigenbasis

[agile wraith]

yes

[dull sequoia]

Then c₁ is an eigenvector of f

With corresponding eigenvalue λ₁

[dull sequoia]

Then this result is immediate by construction of C

[agile wraith]

ah ok ok i see

ok and f(c2) will be 0 + lamda2c2 right?

[dull sequoia]

Yes

[agile wraith]

and of course +0+0

mmmm ok

now it makes alot of sense

i see

[dull sequoia]

f(cᵢ) = 0c₁ + … + λᵢcᵢ + … + 0cₙ

And of course they are all 0 (except the λᵢ) because {c₁, …, cₙ} is a basis and therefore linearly independent

[agile wraith]

but I am confused shouldnt the 3rd one not b 2?

like shouldnt it be 4?

for the diag

[dull sequoia]

Where did b 2 come from

[agile wraith]

well so you are applying A+AT to them and placing the results in the slots correct?

because f is A+AT

but the 3rd lamda3c3 is 0 1 1 0

[dull sequoia]

That’s in the basis B

You’re saying that f(c₃) = 0b₁ + 1b₂ + 1b₃ + 0b₄

That’s f(c₃) written as a linear combination of the basis B

Not written as a linear combination of the basis C

[agile wraith]

mmm ok

I think i get it better now

I will ask my professor tommorow to iron out some details ig

[dull sequoia]

Vectors are not coordinate dependent

The components of a vector is coordinate dependent

And by coordinate dependent I mean dependent on the choice of basis

[agile wraith]

ok

[safe radish]

@agile wraith Has your question been resolved?

[safe radish]

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.

[twin solar]

How do I find the limit of this?

I started with

This but then I don't see using Hospital rule make sense

[drifting knot]

Yo

L hospital

[wet wigeon]

Denominator wrong

[twin solar]

So how should it be

?

Oh

Yeah

But it doesn't look any better now

[drifting knot]

You can write this as e^[(lnx)^2-x.lnx]

So u can write this as (e^lnx)^(lnx-x)

Yes

[twin solar]

Not

Exactly

As I think the denominator was wrong

Should it be like this

?

But the exercise it is from is aboht hospital rule

So I shouod apply it

[safe radish]

@twin solar Has your question been resolved?

[wet wigeon]

Great, apply l'hopital on LHS

Nvm i dont think you get anything from that

[safe radish]

@twin solar Has your question been resolved?

[twin solar]

Yeah that s why I am stuck

I don't see purpouse doing that

[safe radish]

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.

[lean otter]

is there a way to rewrite in terms of a=b and ab?

[lean otter]

context is alpha and beta are the roots of that equation and i hhave to find the have of this

[hasty wagon]

did you try to find the common denominator?

[lean otter]

(ab)^5/8

[hasty wagon]

yea, and the numerators will become?

[lean otter]

oh man

a+b

.close

[safe radish]

Channel closed

Closed by @fair cypress

Use .reopen if this was a mistake.

[lean otter]

thanks

[safe radish]

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.

[lucid ibex]

(f(f(n))=f(n) while f(n) must be positive for all positive values of n and that f(n+1)>f(n). How many solutions for this?

[lucid ibex]

I have got to, almost nothing

<@&286206848099549185>

[cedar void]

by using my little piece of knowledge
all I can think of is identity function

but I'm still wondering how f(n+1)>f(n) will work

for n < 0, it will be false

[lucid ibex]

n must be a positive integer

[cedar void]

I thought that's only for first condition

my bad

[lucid ibex]

mb didn't say it clearly

It's for positive integers n, f(n) has following properties blah blah bla

[cedar void]

ah okok

[lucid ibex]

why not

[cedar void]

just ignore it

sorry

[lucid ibex]

ok thx

[safe radish]

@lucid ibex Has your question been resolved?

[lucid ibex]

.close

[safe radish]

Channel closed

Closed by @lucid ibex

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.

[cunning pasture]

Can displacement be negative in uniform circular motion

[cunning pasture]

?

Please tell.

[cedar void]

angular?

[cunning pasture]

circular

in a circle

[cedar void]

Such a stupid question I asked

[cunning pasture]

yeah

[cedar void]

Displacement of any kind could be negative

[cunning pasture]

no but in uniform circular motion can it be?

[cedar void]

like angular displacement is measured in radians

so it an angle and conventionally if it is measured in clockwise direction, it will be negative

[cunning pasture]

what would be the graph of it?

[cedar void]

like that

[cunning pasture]

The x-t graph

displacement-time graph

[cedar void]

generally we write theta instead of x

but anyways

[cunning pasture]

huh

No

I think you're not understanding.

I am not asking about the angular displacement graph

[cedar void]

oh okok

[cunning pasture]

The displacement-time graph

x = displacement

sorry

the s-t graph

x-t would be distance/position - time graph

[cedar void]

whatever

well if you're just talking about displacement in uniform circular motion then it will be simply a straight line graph as tangential velocity will be constant

and to account for the fact that it can be negative
you can think of it like, you decide a direction and the tangential velocity at an instant is opposite to that direction then the ds that particle will travel will be negative

there's not much practical application of this fact in uniform circular motion in general

got it?

[cunning pasture]

Oh.

Can you provide the graph of this 'displacement-time graph'

[cedar void]

simply that

[cunning pasture]

WAAAA

T

[cedar void]

but keep in mind this is valid only for "Uniform" circular motion

[cunning pasture]

Are you a phd in physics?

just asking

[cedar void]

bro wait

I think I just messed up

[steel agate]

bro

[cedar void]

oh nvm

[steel agate]

how is this d-t for UCM?

[cedar void]

I am just a fool

[cunning pasture]

I think your graph is not correct because the rate of change of displacement decreases as cos(x)

decreases

[cedar void]

it will be a sinusudial I meant

[steel agate]

the graph is wrong

this is graph of distance vs time for uniform circular motion

[cedar void]

yup @steel agate the graph is not correct

[steel agate]

mhm

[cunning pasture]

But my oversmart friends aren't accepting this fact.

Can you type some words to convince them

[steel agate]

they ain't so oversmart then, are they?

[cunning pasture]

wdym

[cedar void]

I meant sinosoidal graph bro

[cunning pasture]

oversmart doesn't mean very smart, does it?

[cedar void]

@cunning pasture definitely not

[steel agate]

still incorrect, displacement doesn't go negative

[cunning pasture]

@steel agate can you provide please

[cedar void]

at a particular instant it can

[steel agate]

are we considering directions too?

or just magnitude

[cunning pasture]

everything

[cedar void]

why don't we consider directions when talking about displacement

[steel agate]

yea then it could go in -ve

[cunning pasture]

and the graph would be cos(x) starting from (1,0)?

[steel agate]

Idk I just thought u guys weren't, mb

[cedar void]

bro nw

[cunning pasture]

north-west?

[cedar void]

huh?

[steel agate]

he thinks nw is north west

[cedar void]

no worries*

[cunning pasture]

oh

ok

[cedar void]

why did you asked this?

that's like so wrong

[cunning pasture]

yes sorry

sinusoidal graph then?

[cedar void]

yup

[cunning pasture]

ok thanks. How can I convice my friends about this?

[cedar void]

I am not literally sure

maybe you can try by giving some example

[cunning pasture]

yes i should know that bettwer.

thanks for help

.close

[safe radish]

Channel closed

Closed by @cunning pasture

Use .reopen if this was a mistake.

[safe radish]

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.

[torn iron]

Car X and Y are moving in the same straight lane on a highway. Car X is 30 m in front of car Y. Car X brakes suddenly and the driver of car Y applies the break as soon as he is able to react. Car Y takes 5 seconds to get to rest from 100kmh, the driver's reaction time is 0.4 seconds. Car X takes 3.4 second to go from 100kmh from rest. If car X just slows down to 12kmh instead of stopping.

What would be the shortest distance between cars

[torn iron]

.rotate

uh

,rotate

[torn iron]

there

[safe radish]

@torn iron Has your question been resolved?

[safe radish]

@torn iron Has your question been resolved?

[safe radish]

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.

[compact geyser]

For a short time, the motor drives gear A from rest with a constant angular acceleration of αA=4.5 rad/s2αA​=4.5rad/s2. Determine the speed of the cylinder and the distance it travels in three seconds. The rope is wound around pulley D, which is rigidly attached to gear B.

Given:

αA=4.5 rad/s2αA​=4.5rad/s2
Radius of gear A = 75 mm
Radius of gear B = 125 mm
Radius of pulley D = 225 mm

[compact geyser]

Could anyone please assist me with this excersise? I don't understand how to do it

[maiden marlin]

Ah, another Dutch exercise, nice

I would recommend calculating the angle (in radians) A has rotated first.

[compact geyser]

lol

[compact geyser]

Wait i'll show you the solution sheet

[maiden marlin]

Sure

[compact geyser]

we don't use angles do to this excersise

[maiden marlin]

Oh

[compact geyser]

So first of all for the external connections(? not sure if i translated that correctly) Va and Vd is 0, I can understand why since they aren't moving at all

but then Vb is also 0 and I don't understand why Vb = 0

[maiden marlin]

If A isn’t moving, B cannot be moving too, right?

[compact geyser]

Then for the gear connections

[compact geyser]

A and D are the central points in the two respective gears

[maiden marlin]

No gear A and gear B

[compact geyser]

but B, isn't B the outer point here?

[compact geyser]

oh

[maiden marlin]

I mean these

[compact geyser]

Oh is D its own seperate gear within gear B?

[compact geyser]

yes

[maiden marlin]

D is basically the same as B, but with a different radius

They turn at the the same velocity

[compact geyser]

I see

[compact geyser]

But why is the vector acceleration of A equal to the vector acceleration of B then?

[maiden marlin]

No?

The one of A is 4,5 rad/s^2 and the one of B is 1,5 rad/s^2

[compact geyser]

But that's just the acceleration, isn't it?

[compact geyser]

here look

oh wait nevermind I think I understand that part

[compact geyser]

Oh I get it now!

Thanks bro

.close

[safe radish]

Channel closed

Closed by @compact geyser

Use .reopen if this was a mistake.

[safe radish]

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 merlin]

I understand basically everything

I just don’t know why you have to multiply by n-1

[solar hazel]

we pick an arbitrary person A

there are n-1 other people

[spark merlin]

Yes

[solar hazel]

so n-1 cases for the thing described after introducing person A

it might help to look at it as f(n) = (n-1)*f(n-2) + (n-1)*f(n-1)

[spark merlin]

Is it becuz A could’ve chosen to take C’s hat instead of B’s

[solar hazel]

yea

[spark merlin]

Oh ok

[solar hazel]

there are n-1 choices for who person B is

[spark merlin]

Ok thank you

.close

[safe radish]

Channel closed

Closed by @spark merlin

Use .reopen if this was a mistake.

[safe radish]

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.

[obsidian oxide]

how do i find this?

i tried u-sub but i ended up getting 0 whereas the final answer is 8

the textbook doesnt show the work

[light shoal]

try using a trig identity involving x/2 (half angle)

[obsidian oxide]

im not very familiar with that, are you referring to this?

[light shoal]

yea

square that

in this case you'll want to use something of the form (x+c) instead of x

so that the -cos(x) will become sin(x) instead

[safe radish]

@obsidian oxide Has your question been resolved?

@obsidian oxide Has your question been resolved?

[cedar tide]

sup guys

an1 khnow how to solve this

I want to calculate the area of ​​the hemisphere